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Optics and Lasers in Engineering 124 (2020) 105814

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Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng

Design and development of a ceiling-mounted workshop Measurement Positioning System for large-scale metrology Jiarui Lin a, Jiaqi Chen a, Linghui Yang a,∗, Yongjie Ren a, Zheng Wang b, Patrick Keogh b, Jigui Zhu a a b

State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, United Kingdom

a r t i c l e

i n f o

Keywords: Ceiling-mounted transmitter Coordinate control field Standard length constraints Layout optimization

a b s t r a c t This paper presents a new ceiling-mounted workshop Measurement Positioning System (C-wMPS) compensating for many deficiencies shown by conventional metrology systems, especially on the possibility of task-oriented designing for coverage ability, measurement accuracy and efficiency. A hybrid calibration system consisting of a high-precision coordinate control field and standard lengths is developed and implemented for the C-wMPS, which can be designed concretely to provide both traceability and the ability of local accuracy enhancement.

Layout optimization using a genetic algorithm based on grids is applied to design an appropriate layout of the system, therefore promotes the system’s performance and reduce cost. An experiment carried out at the Guidance, Navigation and Control laboratory (GNC Lab, 40 × 30 × 12 m) validates the prominent characteristic of C-wMPS and the fitness of the new calibration system and layout optimization method.

1. Introduction Large-scale collaborative digital manufacturing and assembly urgently requires precise, efficient and multi-tasking measurement technology in a unified coordinate system, which demands the measurement results be achieved in real-time [1,2]. The state-of-art measurement technology mostly focuses on centralized metrology systems (a typical representative is laser tracker), which partitioned working area into several sections to realize extra-large scale measurement, unavoidably bringing in accumulated error and inconsistent reference. Automation is also severely influenced by the transformations between stations [3,4]. Therefore, a representative distributed metrology system, indoorGPS (iGPS), which is based on a rotary-laser automatic theodolite, arose under such conditions [5–7]. iGPS handles the expanding working area and the growing complexity of the tasks much more effectively.

The “around-space” arrangement of iGPS determined by each transmitter’s measurement range shown in Fig. 1 provides relatively limited conditions to settle or adjust the whole metrology system. The ± 180∘ horizontal measurement range of each transmitter seems to be a fine ability but is largely wasted in engineering applications, therefore becomes much more costly to realize “full-coverage”. Additionally, the limited vertical measurement range (approximately ± 30∘ ) restricts the height to install the transmitters. Although several researches and experiments have been carried out to basically design a proper layout for

∗

current distributed metrology system [8,9], the transmitters and measured objects positioning at the same height left no much choice for layout design in engineering. For most industrial measurement tasks, the operating distance along the horizontal direction is much larger than in the vertical direction. The rather large measuring “depth of field” increases the variation of positioning error, which is almost impossible to overcome by adjusting the system’s arrangement. Also, light occlusion issues are very likely to happen, providing massive constraints for layout designing. Dynamic measurement is also difficult to realize [7,10].

In summary, these limitations lead to bad quality of iGPS that they usually lack the possibility of task-oriented designing.

This restricted quality not only affects the flexibility to design an outstanding layout for the transmitters but also confines the possibility to innovate the calibration method. Conventionally, scale bars are used as substantial constraints to adapt to the “around-space” arrangement as well as achieving calibration of the system. In the actual applications where measurement objects have already been arranged, the space to arrange the calibration system is usually confined. Intersection condition [11], as a major factor that affects accuracy, is mostly uncontrollable.

Lower-quality calibration results will inevitably damage the measurement accuracy.

Therefore, we developed a new ceiling-mounted workshop Measurement Positioning System (C-wMPS) mainly to construct an integral measurement field with a unified coordinate reference, improving the

Corresponding author.

E-mail address: icelinker@tju.edu.cn (L. Yang).

https://doi.org/10.1016/j.optlaseng.2019.105814 Received 29 May 2019; Received in revised form 2 July 2019; Accepted 24 July 2019 Available online xxx 0143-8166/© 2019 Published by Elsevier Ltd.

J. Lin, J. Chen and L. Yang et al.

Optics and Lasers in Engineering 124 (2020) 105814

Fig. 1. Effective vertical measuring range of a transmitter (the dark-red area represents the dead zone).

Fig. 2. Structure of a ceiling-mounted transmitter and its measuring range. The dark-red area represents the dead zone of a transmitter.

possibility of task-oriented designing. Ceiling-mounted transmitter, as the essential component of the system, emits two laser planes downward to cover a conical-shaped measurement area as shown in Fig. 2.

Arranging the transmitters appropriately on the ceiling can cover the dead zone of all transmitters by multi-station intersection. The working area, therefore, can be fully covered more easily. It can be seen that measuring “depth of field” is significantly reduced due to the different structure of transmitters because measuring directions are completely changed to adapt to common measurement tasks.

Improving the possibility of task-oriented designing primarily offers a sufficient condition to boost the performance of transmitters’ orientation and layout design, which are two key technologies for C-wMPS. A major superiority is that the installation structure of C-wMPS naturally extends the space for calibration systems to be designed, therefore offers the possibility for a better calibration method. Therefore, a new calibration method is proposed to make full use of the advantages as well as to overcome defects of the conventional calibration method.

A coordinates control field constructs high accuracy 3-dimensional constraints, which can be well designed to fuse with the working area and conditions. It can be established by a multi-station laser tracker system to optimize trackers’ angle measurement errors [12], providing high precision traceability. Characteristic points provided by the control field along with standard lengths as a local enhancement approach can be designed according to the specific demands of the task considerately, which will provide an optimal intersection condition [13] for the metrology system. The in-situ calibration system constructed before the measuring procedure also means that little human

interference is needed to implement measurement. Efficiency is largely promoted.

Due to the unrestricted installation space, being able to design a task-oriented layout of transmitters is another profitable outcome of the newly designed system. The novel construction and features of C-wMPS mean that the accumulated experience for layout design may have little value. To make the best of the new system, coverage ability, positioning accuracy and total cost are considered comprehensively according to specific requirements and a balance between these factors. Therefore, an accurate way with mathematical proof to optimize the layout aiming at the task is proposed. Genetic algorithm is applied to optimize the layout of the system. To promote efficiency and simplify calculations, the successive layout optimization problem is converted to a grid-based problem. Finite iterations are conducted to generate an optimized layout according to the target objective of the layout optimization procedure.

The remaining part of the paper is organized as follows: Section 2 introduces the measurement principle of the C-wMPS and the characteristics of a ceiling-mounted transmitter. Section 3 presents a novel calibration method mainly based on high precision coordinates control field with standard lengths as accuracy enhancement additionally. Section 4 proposes a genetic algorithm-based layout optimization method by dividing the available installation space into grids. In Section 5, experiments are presented to prove the validation for the above calibration and layout optimization methods. Finally, we present conclusions and potential future improvements for the system and technologies in Section 6.

J. Lin, J. Chen and L. Yang et al.

2. Measurement principle of C-wMPS Ceiling-mounted workshop Measurement Positioning System uses optoelectric processing to transform time information into 2dimensional angular information precisely. Transmitters working cooperatively can realize 3-dimensional coordinate measurement, and also, eectively extend the coverage ability of the system. Ceiling-mounted transmitters are the prime components of C-wMPS. A transmitter is mainly composed of a static base, laser modules and a precise rotating head. Tilted-angle and separation angle are two important parameters of a transmitter. The angles between two scanning laser planes and the rotary shaft are deďŹ ned as the tilted-angles. The intersection angle of two scanning laser planes on the horizontal plane (XY plane) is deďŹ ned to be the separation angle of a transmitter. Since the basic purpose to develop C-wMPS is to measure the downward space so that the working area is completely uninterrupted, two laser planes with a 90° separation angle between them are installed on a precise rotary shaft at a uniform speed. The planar laser beams emitted by the modules is tilted by a small angle so that rotating laser beams can form a conical-shaped measurement area with a small dead zone, as shown in Fig. 2. Mathematical analysis, simulation and experiments results show that 15–20° will be the appropriate range of the tilted-angle to balance between the size of measuring range and measurement accuracy. The typical ceiling-mounted transmitter has an operating distance of 3–25 m, and the measurement area is a 53° cone projection in which 15° is the dead zone. Screen printing is applied as an eective way to limit the inner boundaries of the laser beams by shading each transmitter housing appropriately, which can prevent the inner laser beams from intersection as shown in Fig. 2.

According to conventional wisdom, the “around-spaceâ€? conďŹ guration of a distributed metrology system is determined concerning the allocation of each transmitter’s measurement area, but inevitably a considerable percentage of them are wasted. Although it seems diďŹƒcult to ďŹ nd an approach to avoid the dead zone dealing with C-wMPS, the essence of distributed metrology systems is that multiple transmitters installed according to a proper conďŹ guration can form a system which possesses the ability to cover the full working area. A typical example is present in Fig. 3, where the dead zone of one transmitter can be covered by two other transmitters in the system. In addition, measurement area of each transmitter is fully utilized due to the installation feature.

To articulately explain the measurement principle of the system, deďŹ ne a local coordinate system (LCS) on a transmitter. The rotary axis is the Z-axis. The intersection point of the laser plane 1 and the Z-axis is the origin O. The X-axis is vertical to the Z-axis and on laser plane

Optics and Lasers in Engineering 124 (2020) 105814

1 at the initial time. Y-axis is deďŹ ned conforming to the right-hand rule.

A series of synchronization signals are emitted by laser modules on the static base is used to identify the period of the system. When synchronization signals are received by a transmitter, it marks the initial time as t0 . The two scanning signals as t1 and t2 . At the initial time, the ith laser plane of the kth transmitter can be described by plane parameters aki bki cki dki . The rotated angles of each laser plane are shown in Fig. 4.

When a receiver receives the scanning signal, the plane parameters of the relevant scanning laser plane are changed: ⎥đ?‘Žđ?‘˜đ?‘–đ?œƒ ⎤ ⎥cos đ?œƒđ?‘˜đ?‘– ⎢ ⎼ ⎢ ⎢ đ?‘?đ?‘˜đ?‘–đ?œƒ ⎼ = ⎢ sin đ?œƒđ?‘˜đ?‘– ⎢ đ?‘?đ?‘˜đ?‘–đ?œƒ ⎼ ⎢ 0 ⎢đ?‘‘ ⎼ ⎢ 0 ⎣ đ?‘˜đ?‘–đ?œƒ ⎌ ⎣

− sin đ?œƒđ?‘˜đ?‘– cos đ?œƒđ?‘˜đ?‘– 0 0

0 0 1 0

0⎤⎥đ?‘Žđ?‘˜đ?‘– ⎤ ⎼⎢ ⎼ 0⎼⎢ đ?‘?đ?‘˜đ?‘– ⎼ 0⎼⎢ đ?‘?đ?‘˜đ?‘– ⎼ 1⎼⎌⎢⎣đ?‘‘đ?‘˜đ?‘– ⎼⎌

(2.1)

Since the coordinates of the receiver in the LCS are (xl , yl , zl ), the equations of the two laser planes must be satisďŹ ed: { đ?‘Žđ?‘˜1đ?œƒ đ?‘Ľđ?‘™ + đ?‘?đ?‘˜1đ?œƒ đ?‘Śđ?‘™ + đ?‘?đ?‘˜1đ?œƒ đ?‘§đ?‘™ + đ?‘‘đ?‘˜1đ?œƒ = 0 (2.2) đ?‘Žđ?‘˜2đ?œƒ đ?‘Ľđ?‘™ + đ?‘?đ?‘˜2đ?œƒ đ?‘Śđ?‘™ + đ?‘?đ?‘˜2đ?œƒ đ?‘§đ?‘™ + đ?‘‘đ?‘˜2đ?œƒ = 0 The ultimate demand of the measurement task is to achieve the coordinates of all targets in a uniďŹ ed global coordinate system (GCS). This entails building or selecting an appropriate coordinate system as the GCS and determining the transformations of the GCS to each transmitter’s LCS. These transformations are represented by a rotation matrix Rk and a translation vector Tk . Summarizing the above statements, the coordinates of all targets can be calculated by implicit functions: (

)

F đ?œƒđ?‘˜đ?‘– , đ??ś =

[

đ?‘Žđ?‘˜đ?‘–

đ?‘?đ?‘˜đ?‘–

đ?‘?đ?‘˜đ?‘–

đ?‘‘đ?‘˜đ?‘–

[ ( ) ] đ?‘… đ?œƒđ?‘˜đ?‘– đ?‘‡ 0

][ 0 đ?‘…đ?‘˜ 0 1

⎥đ?‘ĽâŽ¤ ]⎢ ⎼ đ?‘‡đ?‘˜ ⎢ đ?‘Ś ⎼ =0 1 ⎢đ?‘§âŽĽ ⎢1⎼ ⎣ ⎌ (2.3)

Mounted on the ceiling, C-wMPS not only avoids interrupting the worksite but also retains enough room for the metrology system. The possibility of designing a proper distributed metrology system along with a calibration system is largely improved, which is rather diďŹƒcult to achieve for most other systems. Another signiďŹ cant advantage C-wMPS brings about is the decrease of measuring “depth of ďŹ eldâ€?, a deďŹ nition resembles depth of ďŹ eld (DOF) in photogrammetry. The intrinsic measurement principle of the system is mainly angle intersection, which means the positioning accuracy will be seriously aected by the

Fig. 3. A multi-station C-wMPS, dead zone of each transmitter can be covered by other transmitters in the system.

J. Lin, J. Chen and L. Yang et al.

Optics and Lasers in Engineering 124 (2020) 105814

Fig. 4. Measurement principle of C-wMPS transforming time information to angular information.

Fig. 5. Hybrid calibration system for C-wMPS.

distance between targets and transmitters. C-wMPS considerably control the measurement accuracy by decreasing the measuring “depth of field”, that is, the practical operating distance. In other words, C-wMPS has changed the direction of the measuring “depth of field”, in order to adapt to most measurement tasks.

3. Orientation parameter calibration 3.1. Calibration method based on a precise coordinate control field with local accuracy enhancement Performance of a distributed metrology system mainly depends on two elements: performance of a single measurement unit, and the accuracy of the orientation and position parameters of all the measurement units in the system [14]. For the latter, promoting the accuracy of the system’s calibration procedure will effectively make the system perform better.

The prevailing method for iGPS is to arrange scale bars vertically in front of the transmitters to construct some length constraints all over the working volume. The expectations are that there is enough clear space for scale bars to be arranged at many positions, and intersection angles between the transmitters and scale bars are acceptable. For common industrial application, these expectations are usually too rare to be

achieved at the same time, resulting in a poor quality of the calibration procedure.

With the worksite largely emptied, it seems that the traditional method remains applicable for C-wMPS. However, the advantages of C-wMPS is not utilized. Thus, we deployed a hybrid calibration system for C-wMPS shown in Fig. 5.

Firstly, a coordinate control field consisting of a number of characteristic points can be well arranged in the working area according to worksite conditions. It can construct 3-dimensional coordinate constraints with high accuracy. Being designable according to the task requirements and traceable to the precise coordinates are two best features of a control field. Characteristic points providing geometrical constraints can be designed according to the specific requirements and the condition of the worksite. Once produced and fixed in-situ before measurement, the control field guarantees the traceability of accuracy during the whole measurement procedure. Also, it makes recalibration more convenient for the metrology system.

Additionally, placing several standard lengths in the measurement space as constraints can significantly improve local measurement accuracy. According to the experience for most measurement tasks, the accuracy requirements are rarely uniform but usually varies in different locations. Hence local accuracy enhancement is meaningful and necessary.

J. Lin, J. Chen and L. Yang et al.

Optics and Lasers in Engineering 124 (2020) 105814

These two kinds of constraints constitute a hybrid calibration system. In Fig. 5, a series of characteristic points are installed, forming a control ďŹ eld. Relocating a laser tracker to several positions to form a measurement network can optimize the angle measurement accuracy by redundantly combining the high-accuracy Laser Interferometer Measurement (IFM), therefore improve the accuracy of the control ďŹ eld. In this way, the control ďŹ eld can have measurement uncertainty typically better than 0.02 mm in 15 m measurement range [15-17], which is far more accurate than measured by a single laser tracker. Because C-wMPS receivers and laser tracker reectors share the same size, improving the accuracy of the control ďŹ eld can eectively improve the calibration accuracy.

There is hardly a strict demand for how to arrange such a control ďŹ eld. Basically, characteristic points surrounded the working area can noticeably improve the calibration accuracy. If the worksite condition sometimes cannot provide such good conditions, placing the characteristic points alongside the measurement targets is a ďŹ ne alterable choice. It is also required that the control ďŹ eld should be ďŹ xed on stable positions such as on the load-bearing walls or on the oor. The stability of the control ďŹ eld can guarantee the correctness of the calibration procedure.

Standard length constraints are also shown in Fig. 5 as a local accuracy enhancement approach. A most common way to bring in standard length constraints is to use scale bars. Besides costly and cumbersome, traceability is also diďŹƒcult to ensure since the scale bars are usually removed once the calibration procedure is ďŹ nished. To abandon substantial scale bars, we propose a more eective solution to construct some “virtualâ€? standard lengths the same time the laser tracker forming a measurement network for the control ďŹ eld. Theoretically, two target reectors ďŹ xed steadily in the measurement space can constitute a standard length similar to a scale bar. When measured roughly along the distance measurement direction of a laser tracker (IFM can be reďŹ ned to micron level precision) [17], the angle measurement error will rarely aect the result. In this way, the distance between the two target reectors can be precisely determined. It makes it possible and convenient to construct standard lengths almost everywhere in the worksite with accuracy traceable to laser wavelength of IFM. It can be inferred by mathematical demonstration and proved by experiments that area near those standard lengths has relatively higher accuracy than the rest of the worksite. To make full use of the enhancement property, the speciďŹ c locations to allocate standard lengths are determined according to the measurement task. This enhancement can be very useful, especially in the binding area for some assembly tasks.

In summary, since C-wMPS greatly improves the possibility of taskoriented designing, a hybrid calibration system is designed to promote the performance of the metrology system. The calibration system is mainly composed of a high-precision coordinate control ďŹ eld together with several standard lengths. While many of the advantages of the new calibration system have already been explained, it is necessary to mention that a slight adjustment to the measurement system will not invalidate the calibration procedure. Scalability and exibility are both improved by the new method.

3.2. Detailed calibration procedure and optimization algorithm When a receiver receives the scanning signal from a transmitter, the relevant laser plane rotates and the parameters of the laser plane transfer according to (2.2). Transforming the plane parameters from LCS to GCS:

[ đ?‘Žđ?‘”đ?‘˜đ?‘–đ?œƒ

đ?‘?đ?‘”đ?‘˜đ?‘–đ?œƒ

đ?‘?đ?‘”đ?‘˜đ?‘–đ?œƒ

] [ đ?‘‘đ?‘”đ?‘˜đ?‘–đ?œƒ = đ?‘Žđ?‘”đ?‘˜đ?‘–

đ?‘?đ?‘”đ?‘˜đ?‘–

đ?‘?đ?‘”đ?‘˜đ?‘–

đ?‘‘đ?‘”đ?‘˜đ?‘–

[ ] đ?‘…−1 đ?‘˜ 0

đ?‘‡đ?‘˜âˆ’1 1

]

(3.1) Suppose that a control point P(xm , ym , zm ) in the control ďŹ eld is being scanned. The distance between the control point and the current laser

plane can be determined as:

đ?‘‘đ?‘šđ?‘˜đ?‘–

‖ ‖ ‖ ‖[ =‖ ‖ đ?‘Žđ?‘”đ?‘˜đ?‘–đ?œƒ ‖ ‖ ‖ ‖

đ?‘?đ?‘”đ?‘˜đ?‘–đ?œƒ

đ?‘?đ?‘”đ?‘˜đ?‘–đ?œƒ

đ?‘‘đ?‘”đ?‘˜đ?‘–đ?œƒ

[

]

đ?‘…đ?‘˜ 0

đ?‘‡đ?‘˜ 1

]

⎥�� ⎤ ⎢ ⎼ ⎢ �� ⎼ ⎢ �� ⎼ ⎢1⎼ ⎣ ⎌

‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖2 (3.2)

The above equation can be described as a laser plane constraint equation [16]. Rk and Tk represent the rotation matrix and translation vector, respectively, from the GCS to the kth transmitter’s LCS. Dealing with standard lengths in the system, target balls on both ends of a standard length will receive signals from transmitters. On one hand, these endpoints are measured by multi-station laser trackers before the calibration process, thus they can be treated as common control points in the ďŹ eld so that laser plane constraint equations as (3.1) can still be constructed. On the other hand, a standard length will bring in a length constraint to the calibration process. To calculate the length according to the measurement of the wMPS, assume that the coordinates of the endpoints are unknown. If the measured coordinates of the endpoints are Pr1 (xr1 , yr1 , zr1 ) and Pr2 (xr2 , yr2 , zr2 ), laser plane constraint equations can be constructed: ‖ ‖ ‖[ đ?‘‘đ?‘&#x;đ?‘—đ?‘˜đ?‘– = ‖ ‖ đ?‘Žđ?‘”đ?‘˜đ?‘–đ?œƒ ‖ ‖ ‖

đ?‘?đ?‘”đ?‘˜đ?‘–đ?œƒ

đ?‘?đ?‘”đ?‘˜đ?‘–đ?œƒ

đ?‘‘đ?‘”đ?‘˜đ?‘–đ?œƒ

]

[ đ?‘…đ?‘˜ 0

đ?‘‡đ?‘˜ 1

]

⎥đ?‘Ľđ?‘&#x;đ?‘— ⎤ ⎢đ?‘Śđ?‘&#x;đ?‘— ⎼ ⎢đ?‘§ ⎼ ⎢ đ?‘&#x;đ?‘— ⎼ ⎣1⎌

‖ ‖ ‖ ‖ (� = 1, 2) ‖ ‖ ‖ ‖2

(3.3) The above constraint equations show a similar format as (3.2), except that (xrj , yrj , zrj ) is an unknown coordinate set. Dierences between the length calculated from the measurement result of the wMPS and the calibrated length can be used to construct a length constraint: √ ( )2 ( )2 ( )2 Δđ?‘™đ?‘— = (3.4) đ?‘Ľđ?‘˜1 − đ?‘Ľđ?‘˜2 + đ?‘Śđ?‘˜1 − đ?‘Śđ?‘˜2 + đ?‘§đ?‘˜1 − đ?‘§đ?‘˜2 − đ??żđ?‘?đ?‘˜ With these constraints constructed as above, Rk and Tk can be determined. Furthermore, when using Euler angles (đ?œƒ, đ?œ“, đ?›ž) to express the rotation matrix as shown in (3.5), the orthogonality of the matrix indicates that constraint equations as in (3.6) must be satisďŹ ed: ⎥đ?‘&#x;11 R = ⎢đ?‘&#x;21 ⎢ ⎣đ?‘&#x;31

đ?‘&#x;12 đ?‘&#x;22 đ?‘&#x;32

⎥cos đ?›ž cos đ?œ“ = ⎢ cos đ?›ž sin đ?œ“ ⎢ ⎣ − sin đ?›ž

đ?‘&#x;13 ⎤ đ?‘&#x;23 ⎼ ⎼ đ?‘&#x;33 ⎌ cos đ?œ“ sin đ?œƒ sin đ?›ž − cos đ?œƒ cos đ?œ“ cos đ?œƒ cos đ?œ“ + sin đ?œƒ sin đ?›ž sin đ?œ“ cos đ?›ž sin đ?œƒ

đ?‘“đ?‘— = đ?‘&#x;đ?‘?1 đ?‘&#x;đ?‘ž1 + đ?‘&#x;đ?‘?2 đ?‘&#x;đ?‘ž2 + đ?‘&#x;đ?‘?3 đ?‘&#x;đ?‘ž3

{ 0đ?‘?≠đ?‘ž = 1đ?‘?=đ?‘ž

sin đ?œƒ sin đ?œ“ + cos đ?œƒ cos đ?œ“ sin đ?›ž ⎤ cos đ?œƒ sin đ?›ž sin đ?œ“ − cos đ?œ“ sin đ?œƒâŽĽ ⎼ cos đ?œƒ cos đ?›ž ⎌

(3.5) (3.6)

The number of constraint equations as well as unknown parameters can be decided based on the numbers of control points, reference bars, and transmitters. When the number of constraint equations is not less than the number of unknown parameters, the objective function can be formulated: { đ?‘€ ∑ đ?‘ ∑ 2 đ?‘‡ 6 ∑ ∑ ∑ ( )2 đ?‘“đ?‘—2 đ?‘? ≠đ?‘ž 2 F= đ?‘‘đ?‘šđ?‘˜đ?‘– + đ?œ†1 (3.7) Δđ?‘™đ?‘— + đ?œ†2 ( )2 đ?‘“đ?‘— − 1 đ?‘? = đ?‘ž đ?‘š=1 đ?‘˜=1 đ?‘–=1 đ?‘—=1 đ?‘›=1 đ?œ†1 , đ?œ†2 are weight parameters of a dierent part of the objective function. đ?œ†1 is usually greater than 1 since the standard length is a more accurate constraint than control point coordinates. đ?œ†2 is a much greater to make sure that the rotation matrix is orthogonal.

It is necessary to ensure that each receiver can receive scanning signals from at least two dierent transmitters. The Levenberg–Marquardt algorithm [18] is chosen to be the optimization algorithm for Eq. (3.7).

The optimization problem can be solved and the orientation for each transmitter is then determined. In this way, the orientation parameter calibration of the system is completed.

J. Lin, J. Chen and L. Yang et al.

Optics and Lasers in Engineering 124 (2020) 105814

4. Layout optimization using grid-based genetic algorithm

4.2. Detailed principles for layout optimization

4.1. Mathematical model of the optimization problem in C-wMPS

Before we describe the principles in detail, it should be noticed that these principles is not entirely independent. Coverage ability and positioning accuracy are in close connection with the system cost. One obvious example is that a better performance in coverage ability and positioning accuracy can make it possible to decrease the number of transmitters to control the total cost of the system. In turn, assessing the system’s total cost will expose those transmitters with a relatively lower utilization ratio. These transmitters have a modest eect on the system’s function, so they are more likely to be removed.

C-wMPS oers a better opportunity to design a proper layout, especially for complicated measurement tasks. Typical conďŹ gurations of some common distributed metrology systems have been discussed and veriďŹ ed by experiments [11–13,19]. The dominant contradiction of layout optimization is between the high expectations of the tasks and the conďŹ ned space to arrange the distributed metrology system. Also, conventional systems such as iGPS are easily aected by perturbations insitu. Changes in the task or the condition often mean that an entirely different layout needs to be designed because of additional light occlusion issues and the accuracy variations. C-wMPS breaks the contradiction by changing its installation mode so that the worksite and the metrology system installation area are separated and “non-interferenceâ€?. As for the perturbation problem, C-wMPS with a smaller measurement “depth of ďŹ eldâ€? will remain workable when slight regulations occur. The layout is quite stable once designed, and only need adjustment when dramatic changes are happening.

Yet another factor which cannot be ignored is that installation mode of C-wMPS is much more inconvenient than most other systems. Installation locations for ceiling-mounted transmitters need to be produced in advanced. Once determined, it would be extremely troublesome to exploit new locations. For the matter of that, designing a layout for C-wMPS is more complicated and challengeable. Available installation locations also need to be considered carefully. We proposed a mathematical model for the layout optimization problem. Instead of merely concerning about the system’s accuracy in early study, our model proposed three principles to be considered when evaluating the system’s performance.

Coverage ability of a metrology system is essential to ensure the task is performable. Besides the measurement range of the each transmitter combined together, light occlusion issues caused by the measured object and other equipment in the worksite will inuence the measuring range.

Positioning accuracy is the key approach to promote the performance of the system. Total cost is a rather speciďŹ c problem, which roughly demands the system to be under budget and each transmitter to have an acceptable utilization ratio. A mathematical model is built considering the principles mentioned above in (4.1): đ??šđ?‘œđ?‘?đ?‘— (đ?‘Ľ) = đ??ž1 đ?‘‚1 + đ??ž2 đ?‘‚2 + đ??ž3 đ?‘‚3

(4.1)

K1 , K2 , K3 in the function are the weights and should satisfy: 3 ∑ đ?‘–=1

đ??žđ?‘– = 1

(4.2)

O1 , O2 and O3 are parts of the objective function describing the coverage ability, positioning accuracy and total cost of the system respectively. These parts will be speciďŹ ed later.

The optimization goal is to minimize the function Fobj (x). x contains every essential parameter, including the transmitters’ position and orientation. The empirical way to assign the weights is that measuring range usually shares a high-priority because it directly aect the feasibility of the task, so that K1 is usually much bigger than K2 , K3 . It should be noted that there is no rigid conventions for how to assign the weights. Weights can change according to the concrete requirements of the task. It can also be allocated dynamically when it behaves worse than expected [20]. There is no clear evidence that the objective function must be declared in such a way. On the contrary, with full consideration of the principles of optimization, objective function can be constructed under the speciďŹ c requirements of the task or be regulated in the circumstances.

4.2.1. Coverage ability Coverage ability is the key request of a measurement task. Approximately 80–90% of the demanded measurement space should be covered by the system, given that the fringe area of the region is likely to be meaningless for the task. Since light occlusion issues have been weakened by the feature of C-wMPS to some extent, they have to be considered more concretely.

Dealing with light occlusion issues, we quantify the geometry information of the equipment referring to the concept of stereolithography (stl) ďŹ le format [21], which uses a set of spatial triangles to mesh an entity. The light occlusion issues hence become a judging problem of whether the measuring vector will collide the mesh representing the equipment. Moller and Trumbore [22] presented a quick approach to determine whether a ray intersects a triangle. Compared to the old model using several cuboids to represent the equipment approximately, the vector-mesh collision model for light occlusion sacriďŹ ces eďŹƒciency to promote the operability and exactitude of the optimization process.

The objective function of measuring range can be deďŹ ned: đ?‘› đ?‘‚1 = 1 − đ?‘š (4.1) đ?‘› In this function, đ?‘› is the total number of targets sampled from the measured space, and nm is the number of targets that can be measured by the current layout of transmitters. In general, the value of the objective function is expected to be no more than 0.2, or the layout may be invalid.

4.2.2. Positioning accuracy In most cases, a measurement task requires that positioning accuracy is constrained in a certain range. Improve positioning accuracy is a signiďŹ cant way to optimize the metrology system. When designing a layout, only angle measurement errors are taken into consideration, while coordinate transformation errors [14] and other systematic errors are ignored.

The evaluation of the positioning accuracy is treated as a simulation process. When the target coordinates P(xi , yi , zi ) and orientation information Rk , Tk of all transmitters are given. A virtual measurement process can generate the measurement results as well as the positioning uncertainty for each target. The measurement model in a virtual measurement process is similar to an actual measurement system as shown in (2.3). The relationship between the angle measurement uncertainty and coordinate uncertainty can be established according to the measurement principle: ( ) đ?‘‘đ?‘ƒ đ?‘‘đ?‘ƒ đ?‘‡ đ?‘˘đ?‘? = đ?‘˘ (4.2) đ?‘‘đ??ś đ?‘? đ?‘‘đ??ś where uc represents the covariance matrix of angle measurement and dP/dC is the sensitivity matrix that can be calculated by the implicit differentiation method. up represents the covariance matrix of coordinates, which can be expressed by: ⎥ đ?‘˘ 2 (đ?‘Ľ ) đ?‘˘đ?‘? = ⎢đ?‘˘(đ?‘Ś, đ?‘Ľ) ⎢ ⎣đ?‘˘(đ?‘§, đ?‘Ľ)

�(�, �) � 2 (� ) �(�, �)

�(�, �)⎤ �(�, �)⎼ ⎼ � 2 (� ) ⎌

(4.3)

The covariance matrix clearly represents the uncertainty distribution information, which involves both magnitude and direction. The deďŹ ciency is that the covariance matrix is diďŹƒcult to compare with the

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Optics and Lasers in Engineering 124 (2020) 105814

requirements of the task. An intuitive term named GDOP (Geometric dilution of precision) introduced in the area of GPS is used to evaluate distributed metrology system’s precision property [23]. The function O2 is constructed as follows, where GDOPm is the maximum permissible GDOP of the task and nm is the number of targets that are able to be measured: { đ?‘›đ?‘š 1, GDOPđ?‘– ≤ GDOPđ?‘š 1 ∑ đ?‘‚2 = 1 − (4.4) GDOPđ?‘š , GDOPđ?‘– > GDOPđ?‘š đ?‘›đ?‘š GDOP đ?‘–=1

đ?‘–

When each of the targets’ positioning accuracy satisďŹ es the task’s demand, the value of the objective function will be 0. Conversely, if the value of the function approaches 1, it is very likely that the present layout is not suitable for the task.

4.2.3. Total cost DeďŹ ne the utilization ratio of a transmitter: đ?‘› đ?‘“đ?‘&#x; = đ?‘š (4.5) đ?‘› In this function, nm is the number of targets that the transmitter can scan, and đ?‘› is the number of all targets in the working area. In this way, a transmitter with a bigger fr in the system is deďŹ ned more “usefulâ€?.

Therefore, the objective function of total cost of the system can be deďŹ ned as: ⎧ 1, đ?‘š > đ?‘šđ?‘šđ?‘Žđ?‘Ľ ⎪ đ?‘š đ?‘‚3 = ⎨ 1 ∑ ⎪1 − đ?‘š đ?‘–=1 đ?‘“đ?‘&#x;đ?‘– , đ?‘š ≤ đ?‘šđ?‘šđ?‘Žđ?‘Ľ ⎊

(4.6)

where fri represents the ith transmitter’s utilization ration and mmax is the maximum number of transmitters the task can permit.

Once the total cost of the system is under budget, the utilization ratio should be considered. A smaller function value means the satisfaction of the task requirements and the high utilization ratio of the present layout.

4.3. Optimization method based on genetic algorithm The mathematical model for layout optimization for a C-wMPS we proposed is aimed to optimize a rather complex discrete objective function. Algorithms based on dierential of the function is no longer workable. Meta-heuristic algorithms are powerful methods for solving optimization problems [24]. The genetic algorithm is a typical metaheuristic algorithm introduced by Holland in 1975 [25]. The optimization process based on this algorithm is produced by a owchart in Fig. 6.

Table 1 Representation of an individual.

1 0

2 1

3 0

‌ ‌

24 0

đ?œƒ1 0∘

đ?›ž1 0∘

đ?œƒ2 0∘

đ?›ž2 0∘

đ?œƒ3 0∘

đ?›ž3 0∘

‌ ‌

Encoding is a fundamental procedure in genetic algorithm. Crossover and mutation are conducted on the basis of the encoding options. One important thing to consider is the discrete encoding model of C-wMPS. The installation locations for ceiling-mounted transmitters need to be produced on the ceiling in advance and will be diďŹƒcult to regulate thereafter. Therefore, the available locations are discrete. After a thorough consideration of the task, an interval was determined to divide the entire ceiling into a uniform grid for convenience of producing the installation locations in advance. Numbers are given to the grid nodes to represent the installation locations simply.

We also pay attention to the alterable orientation of ceiling-mounted transmitters before determining the encoding model. Being dierent from the position, the orientation of a ceiling-mounted transmitter can change in a predeďŹ ned range. This is one of the main dierences between ceiling-mounted transmitter and wMPS transmitter. The latter one is mostly installed on a tripod and perpendicular to the oor.

For the discrete encoding model, choose a simple encoding options which set the value corresponding to a grid node to 1 if there’s a transmitter installed; otherwise the value remains 0. Dealing with the alterable orientation model, the continuous Euler angle expressing the orientation are reasonably discretized to reduce the computing time but can still provide enough available solutions for the problem.

Take an example that initially the ceiling was divided into 4 Ă— 6 uniform grids and 3 transmitters are installed, an individual can be expressed as (Table 1): Length of an individual is 24 + 2 Ă— 24. Because there are only 3 transmitters installed, values corresponding to the last 2 Ă— (24 − 3) bits of the individual are set to NULL. The number of the transmitters installed is not explicitly involved in the encoding result, but can easily be calculated. As a result, all input parameters are covered by the encoding model and the objective function value can be calculate. Possibilities are generated to guide the crossover, mutation and selection procedure: ( ) đ??šđ?‘œđ?‘?đ?‘— đ?‘Ľđ?‘– đ?‘ƒđ?‘– = ∑đ?‘Ą ( ) đ?‘–=1 đ??šđ?‘œđ?‘?đ?‘— đ?‘Ľđ?‘– Fig. 6. Flowchart for genetic algorithm.

(4.9)

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where đ?‘Ą represents the population of a generation and Pi represents the possibility for the ith individual. Choosing a reasonable đ?‘Ą is quite an inconclusive question that should be implement based on the complexity of the task and accumulated experience.

After several iterations, the latest generation is expected to satisfy the demand of the optimization problem. Then the individual with the best ďŹ tness, in other words, the minimized function value, will be selected as the optimal individual of the problem. Decoding the individual to obtain the optimized layout for the transmitters.

5. Experiments in GNC Lab An experiment was carried out to prove the feasibility of the new calibration method and layout optimization for C-wMPS. The GNC Full Physical Simulation Laboratory (GNC Lab) in the National Aerospace Test Base (Tianjin) demands to realize real-time measurement of a simulated spacecraft moving in the entire space. The C-wMPS was applied to the GNC Lab because of its parallel measurement ability, large measuring range, and high precision. Most importantly, the installation feature of ceiling-mounted transmitters ensures that the working area is not disturbed by transmitters or any related equipment, which is almost impossible be achieved by other metrology systems.

To satisfy the requirements of the measurement task, designing a good layout of C-wMPS is of great importance.

5.1. Designing a layout for C-wMPS in GNC Lab The Simulation Experiment Platform in the GNC Lab has a size of 42 m Ă— 32 m. In an experiment, it was required that the 3-dimensional coordinates of any target on the platform or within 3 m above the platform can be measured with a demanded accuracy tolerance. The speciďŹ c requirements of the measurement task are listed in Table 2.

On the ceiling 12 m above the platform in the laboratory, we designed a 6m-interval grid which has 20 installation locations. The interval is mainly determined by the height of the ceiling and the measuring

Table 3 Orientation for 10 transmitters represented by Euler angles.

Transmitters

Horizontal angle/°

Vertical angle/°

1 2 3 4 5 6 7 8 9 10

225 135 225 180 0 45 0 45 0 45

170 175 170 175 175 175 175 170 170 175

range of the ceiling-mounted transmitter. The grid and grid nodes are shown in Fig. 7. With the aim of covering the whole measuring space of the task required, 3 planes parallel to the platform were selected to perform the simulation, which were respectively 0 m, 1 m and 3 m above the platform. 3813 targets were sampled in each plane at 1 m intervals to check the performance of the system. Since the available positions for transmitters are determined, the ďŹ xtures on each location allow the horizontal angle to be adjusted within 0–360° and the vertical angle 165–180°.

In practical, the optimization procedure started with an initial generation of 10 individuals and took 53 iterations to generate the ďŹ nal layout with 10 transmitters installed. After the optimization, the position arrangement is shown as red circles in Fig. 7 and the orientation angles describing the horizontal and vertical angle of the rotary axis are shown in Table 3. Simulations results shown in Fig. 8 veriďŹ ed the performance of the system is able to satisfy the task’s requirements. Although some marginal area remains unmeasurable (represented by white color in Fig. 8), the following experiments carried out in the GNC Lab have proved them insigniďŹ cant. The measurement uncertainty is less than

Table 2 SpeciďŹ c requirements of the task.

Requirements of the system

Parameter

Measurement space Measurement accuracy The total cost Installation positions

40 Ă— 30 Ă— 3 m above the experiment platform MPE: Âą 0.5 mm No more than 10 transmitters The ceiling of GNC Lab is 12 m away from the experiment platform(working area 40 Ă— 30 Ă— 12 m)

Fig. 7. Optimized layout of C-wMPS in GNC Laboratory.

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Optics and Lasers in Engineering 124 (2020) 105814

Fig. 8. Simulation results for C-wMPS of the optimized layout.

Fig. 9. Metrology system and working area in GNC Laboratory.

0.5 mm, which is significantly decreased compared to the initialized layout before optimization and satisfies the requirements of the task.

5.2. Verification GNC Lab put forward a rather challenging measurement task since the work site is extremely larger than usual. Meanwhile, the upper limit of measurement accuracy is very strict considering such a large scale and low budget. C-wMPS with the optimized layout shown in Fig. 7 and Table 3 has been applied in the GNC Full Physical Simulation Laboratory. Acceptance test was conducted using the system. Also, we proposed an experiment to verify the property of the new calibration method mentioned in Section 3.

After installing all the transmitters and the relevant equipment correctly, we have fixed 50 points on the floor roughly uniform to construct a control field. A multi-station laser tracker system was used to measure the coordinates of these control points. At the same time, 10 of these control points in the middle area where simulated spacecraft usually go past were chosen together with several scale bars to form 8 standard lengths measured by the method proposed in Section 3. The standard lengths were used to verify the local enhancement ability of the calibration method. The control field together with the standard lengths forms the calibration system of the experiment (Fig. 9).

With a reasonable calibration result, the measurement system satisfied all of the preparatory work. To verify the performance of the system,

a scale bar with target reflectors fixed on both ends was brought into the working area. The calibrated length of the scale bar was 1652.11 mm.

It was moved to 84 different positions approximately 1.4–2.0 m above the platform in the working area, and the lengths of the scale bar were measured by the metrology system. Part of the deviations between the measured lengths and the calibrated length are shown in Fig. 10. The maximum deviation is 0.21 mm. It can be seen from the figure that positions near the standard lengths constructed in the calibration system (marked area in Fig. 10) actually have a relatively higher measurement accuracy, which shows the capability of the calibration method.

To further prove that the system can satisfy the requirements of the measurement task, more than 400 target points were distributed in the worksite with heights from 0.5 m to 2.0 m in a series of experiments. A multi-station laser tracker was used to measure these target points as to provide the reference coordinates. Then the target points were measured

by C-wMPS. Part of the deviation results is shown in Fig. 11. The local accuracy enhancement verification resembles the previous one. The first 15 test points (marked area in Fig. 11) clearly have relatively lower deviations because these targets are located in the middle area where measurement accuracy is enhanced by standard lengths.

The complete verification experiment results show some testing targets present lower-than-expected deviations, causing the maximum deviation reach −0.72 mm. But more than 91% of the testing targets have satisfied the task requirements, which is a privilege for such an extralarge scale task. More to the point, almost all the bad-performing targets

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Optics and Lasers in Engineering 124 (2020) 105814

Fig. 10. Part of the acceptance test results using scale bars.

Fig. 11. Part of the acceptance test results for target coordinates.

are located at the marginal area, where for most measurement tasks has little significance. Besides, the system’s layout and calibration system can be easily regulated when the marginal area is used to satisfy the adjustment of the measurement tasks.

6. Conclusion A ceiling-mounted transmitter workshop Measurement Positioning System (C-wMPS) has been designed to improve the performance of current distributed metrology system. Possibility of task-oriented designing is largely improved for the metrology system as well as the whole measurement process. We then present calibration and layout optimization methods to make the best of the highly designable feature of the system. The calibration system is composed of a high precision coordinate control field and several virtual standard lengths. The control field is highly designable according to the task requirements and ensures the accuracy traceability of the calibration procedure. Standard lengths were brought into the system to enhance the accuracy in a local area. Furthermore, the novel calibration method reduces the level of manual input and therefore promotes efficiency and automation of the measurement process. The flexibility to design a better layout is another key advan-

tage of C-wMPS. A layout optimization method that considers coverage ability, positioning accuracy and the system cost is proposed based on genetic algorithm to make it possible to design a suitable layout for a specific measurement task, which needs few accumulated experience.

Experiments in GNC Laboratory have provided evidence that C-wMPS has specific advantages for some tasks compared to the conventional systems and that the calibration and layout optimization methods are not only available but also have the ability to improve the performance of the system.

Funding This work was supported by the National Natural Science Foundation of China (51775380, 51835007, 51721003), the EPSRC through the Light Controlled Factory under EP/K018124/1 and the EPSRC through the Future Advanced Metrology Hub under EP/P006930/1.

Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.optlaseng.2019.105814.

J. Lin, J. Chen and L. Yang et al.

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Measurement 135 (2019) 260–277

Contents lists available at ScienceDirect

Measurement journal homepage: www.elsevier.com/locate/measurement

Reducing the latency between machining and measurement using FEA to predict thermal transient effects on CMM measurement Naeem S. Mian ⇑, S. Fletcher, A P. Longstaff University of Huddersfield, Queensgate, Huddersfield HD1 3DH, UK

a r t i c l e

i n f o

Article history: Received 15 January 2018 Received in revised form 8 November 2018 Accepted 12 November 2018 Available online 14 November 2018 Keywords: Thermal error CMM CNC Soaking times Temperature measurement Thermal contact conductance

a b s t r a c t Coordinate Measuring Machines (CMM) are widely used to validate the dimensional conformance of machined components. Since time frames are critical in ensuring cost effective production, it is important to know when a machined component is ready for dimensional inspection. A common approach is to delay the inspection until the component has reached thermal stabilization such as 20 °C as standard, however, this latency incurs an uncertainty of getting either under or overestimated which can result in a considerable waste of time and resources lowering cost effectiveness. Conversely, premature measurement could also increase the measurement uncertainty if significant temperature gradients exist.

This paper presents an approach to predict the required latency at which the machined component is within critical thermal boundary conditions and ready for dimensional checks. The approach is comprised of experimental tests required to obtain key boundary conditions including convective and Thermal Contact Conductance (TCC) values. FEA was then used to simulate and validate the latency based on anticipated workpiece conditions. The method was validated on an industrial part, namely a Venturi vessel, in two typical scenarios i.e. placed on the (1) Chuck and (2) CMM to predict the latency required for thermal stabilization using a pre-selected part tolerance level of 1.5 mm. The validation revealed 8.3 min for (1) and 7.6 min for (2) which is a considerable reduction of latency in comparison to waiting for longer periods. This technique was also compared with a typical CMM measurement regime of using a single temperature sensor for compensation. A simple comparison yielded an over or under compensation of 7 mm depending on the position of temperature sensor on the vessel surface. The validations have allowed the formation of a platform for the FEA software to be effectively used to predict the required latency to improve the management of CMM machine usage while ensuring low uncertainty and a cost effective solution. Ó 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

1. Introduction In a typical manufacturing process, a machined component goes through several stages before it reaches the final state of shipping or assembling. Out of the several stages, one of the most important is the dimensional measurement and validation stage which is often performed on a Coordinate Measuring Machine (CMM) or other dedicated metrology system. CMMs are designed to deliver accuracy for which they are specially designed with chosen high strength and low conductivity material. Most CMMs are thermally sensitive and are typically housed in a temperature controlled environment nominally set to 20 °C as standard, yet components that need to be measured on such machines are most often produced in non-temperature controlled environments or they undergo processes that significantly increase or decrease their ⇑ Corresponding author.

temperature. This means that temperature soaking of the machined component prior to the measurement is a crucial step to avoid erroneous measurements due to differentials in temperature and thermal expansion coefficients. Temperature soaking is a method adopted to ensure that the machine component has reached a suitable temperature stability or equilibrium i.e. it is at a temperature similar to the CMM temperature. Kruth et al. [1] have mentioned the effects of temperature variations during the measurement process on the CMMs and highlighted the usefulness of acquiring soaking procedures to avoid errors in CMM measurements. In addition to this, there are reviews [2] and ‘Guide to dimensional measurement equipment’ [3] available which also highlights the importance of temperature soaking prior to dimensional inspections. However, a major concern within engineering industries is the lack of understanding of the required time frames (latency) for temperature soaking prior to the commencement of dimensional measurements on CMMs.

https://doi.org/10.1016/j.measurement.2018.11.034 0263-2241/Ó 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

N.S. Mian et al. / Measurement 135 (2019) 260–277

Following production, uncertainty in the temperature and stabilisation (cooling or heating) behaviour can cause the engineer to under or overestimate the latency for temperature soaking prior to dimensional checks on the CMM. A few of the research work has dealt with simple gage blocks and digital calipers where soaking times has been a major concern to ensure confidence in measurement results. For example, considering the calibration of simple gage blocks, the proposed recommendations has been that they should be laid flat and side by side on a metal plate for a minimum of 30 min soaking time. Recommendations have also been proposed for larger items as to be left overnight [4]. In another research, a fan was used to supply air in order to cool down a 20 in. gage block which was heated up to 30 °C. They investigated the effect of different air flow speeds and recommended that 1 m/s of air flow could reduce the soaking times to less than 1 h as compared to 3 h in still air [5]. The importance of temperature soaking is not restricted to CMMs only, it expands to other measurement devices also such as calipers. In one of the example, digital calipers were used as a measurement device to measure a 1 in. (25.4 mm) aluminium component. The component was manufactured and measured in a machine shop which had 25 °C of ambient temperature however the rod was then taken to a quality inspection lab which was at 22 °C. They applied a one-hour soak time to the component to avoid the influences that environmental temperature had on the component to avoid invalidation of calibration results if the errors have deviated beyond acceptable limits [6].

Although the aforementioned research work were able to predict soaking times however the target has been on the smaller components whereas the soaking times for larger components has not been addressed properly apart from the recommendation of leaving them overnight. This suggests that the engineers would generally acquire a play-safe approach which is to leave the components for periods as long as 24 h which could be an excessive over-estimation. The knowledge of time frames are of importance as the underestimation may deteriorate the CMM thermally, and over-estimation may contribute towards the unnecessary machine downtime incurring an inevitable effect on the costs associated with the management of CMMs availability. When dealing with large batches of components, the machine downtime further contributes and can prove itself expensive on a large scale. Significant research [7–10] has been conducted towards the cost effective management of CMM utilization and provides good solutions such as creating intelligent inspection plans and routines, implementing automated software capture and development of intelligent measurement sequences which can essentially reduce the machine downtime. However, none of the measurement guides have mentioned about the required time frames for temperature soaking; and none of the research activities included the aspect of machine downtime associated with the temperature soaking stage and its relationship to particular accuracy requirements or impact on the conformance zone.

This paper provides a methodology for calculating the mandatory latency required for component soaking prior to dimensional checks using the FEA (Finite Element Analysis) method using two conditions; (a) the part reaches the temperature equilibrium and (b) the part has not reached the temperature equilibrium but is within the accepted rate of change of dimensional tolerance. The offline FEA simulations enable the estimation of the required soaking latency for the component post machining provided that there is knowledge of the component temperature after the process has finished. Hence the methodology used will ensure the availability of set latency prior to the commencement of measurements on CMMs which eventually will reduce the associated machine downtime for both one offs and large batches of components, provide efficient utilization of the CMM and ensure effective management

261

of CMM resources. The approach is comprised of several stages including (1) Experimental tests conducted in order to obtain key boundary conditions such as the convective heat transfer coefficients and Thermal Contact Conductance (TCC) values. The TCC tests were conducted using a simple aluminium plate and a simple granite block to imitate a scenario of dimensional measurement on CMM machines which typically has beds made of granite material. The obtained TCC values were intended to be used in the FEA simulations to obtain the thermal behaviour of a warm part being placed on a CMM bed which is relatively cooler. The convective heat transfer coefficient was obtained during further validations conducted on a Venturi vessel mentioned in point 4.

(2) The TCC values were further optimised using FEA design study feature since practical limitations such as sensor location and accuracy result in errors in these parameter.

(3) FEA was used to simulate the thermal behaviour of the aluminium plate and granite block. The results were then validated with the experimental results (4) Once the FEA methodology was established, the method was validated on an industrial part, namely a Venturi vessel from the Oil industry. Two typical scenarios were used in which the Venturi was placed on the (a) Chuck and (b) CMM to predict the latency required to reach thermal stabilization using a pre-selected part tolerance level of 1.5 mm. The validation revealed 8.3 min for (1) and 7.6 min for (2) which is a considerable reduction of latency in comparison to the common approach of waiting for longer periods.

(5) This technique was also compared with typical CMM measurement regimes where a single temperature sensor is used for workpiece compensation. A simple comparison on the Venturi yielded an over or under compensation of 7 mm depending on the position of temperature sensor on the vessel surface.

2. Thermal contact conductance (TCC) In order to achieve reliability in the results of heat transfer simulation, it is important to obtain the thermal contact conductance parameter that acts between the interface of the component and the bed of the CMM machine or fixture. Although fixtures are often used which may differ in material, the scope of the contact conductance research is on measurements performed with the workpiece placed directly on a CMM bed and where surface contact area is substantial. The general simulation technique is however validated for a situation involving a fixture in Section 7. Thermal Contact Conductance (TCC) (hc W/m2/°C) is an interfacial parameter which controls the heat transfer between two components. This will be used in the FEA software to simulate the rate of heat transfer from the component into the CMM bed and predict the deformation rate of the component to achieve confidence in the results. The TCC values will be beneficial to simulate those particular cases in which a component that has met the condition (b) i.e. it is within the accepted dimensional tolerance but is still warmer or cooler relative to the CMM. A series of experiments, the setup of which is shown in Fig. 2, were conducted to obtain the TCC parameters. The setup included a heater, an aluminium plate of dimensions 0.11 m 0.13 m 0.03 m and a granite block of dimensions 0.256 m 0.256 m 0.078 m that had two circular voids of 46.5 mm diameter as a design feature in the middle of the block separated by 82 mm distance. Granite was selected since the majority of CMM machine beds are constructed using this material

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due to properties enabling good dimensional stability including high damping, low conductivity and high specific heat capacity.

The true area where the interface between the plate and the block takes place was measured as 0.0143 m2. The averaged surface finish of the aluminium plate at that area was Ra = 0.2 mm and of the granite block was Ra = 0.5 mm. The granite block enabled sensors to be embedded close to the conducting interface which could not be achieved with experiments on the CMM bed. Due to the low conductivity of the granite, it was considered acceptable to use a much smaller size of the block when compared to a normal CMM bed.

This is because the thermal gradient at the block surfaces over the duration of the test which was 200 s, showed temperature differences of less than 0.1 °C compared to the initial temperature (the same as the ambient temperature) resulting in negligible heat transfer through convection.

It should be noted that these tests were conducted to obtain a range of TCC values to understand the rate at which the heat transfer is taking place. The range will then be used to carry out design studies in the SolidWorks FEA software to further optimise them to increase the level of confidence in predictions of temperature distribution and magnitudes in the FEA. This methodology was chosen because of the uncertainties associated with the experiments, mainly around the variable rates of convection and the measurement of the internal temperature gradients.

Fig. 1. (a) Granite block with two circular voids (b) Bespoke part placed inside the void.

To position the mass, a bespoke three point stand was created which had the overall mass of 400 g exerting a force of 3.9 N. The stand consisted of three small pointed nylon pillars, the design of which prevented heat transfer from the aluminium plate into the stand by reducing surface area and low thermal conductivity of the Nylon of 0.25 W/m2 °C. The placement position of the pointed pillars on top of the aluminium plate were determined by using the Airy points to distribute the load as evenly as possible. Fig. 3 shows the bespoke stand with three pointed nylon pillars and also shows a demonstration of mass added on top of the bespoke stand.

The heat energy flowing from the aluminium plate to the granite block was calculated transiently using the energy balance heat transfer Eq. (1).

3. Test setup and experiments for the TCC values Two sets of experimental tests were conducted and in both sets, the aluminium plate was heated to a temperature of approximately 50 °C and then immediately placed onto the granite block.

The first set of tests were performed using the dry aluminium plate whereas the second set used the oil on the plate to imitate a real industrial process in which the coolant which is used during machining is generally wiped off but not thoroughly cleaned before commencing measurements on CMMs. Each set of tests further contained a series of tests adding mass. Starting with the aluminium plate on its own subsequent tests had the addition of 1000 g mass placed on top of the aluminium plate, and reaching a final mass tested of 7400 g.

The material properties used for the two components are shown in Table 1. Four temperature sensors were embedded inside the aluminium plate so that they were located close to the centre of the plate. A total of nine sensors, in three strips with three sensors in each, were placed inside the voids in the granite block. Fig. 1(a) shows the granite block with two circular voids. A bespoke part was designed and 3D printed for placing it inside the void, as shown in Fig. 1(b), which located directly under the plate to insulate the temperature sensors and reduce the effect of natural convection. The designed part was made of PTFE material which has a very low thermal conductivity of 0.25 W/m°C.

Q 0 ¼ mCpDT=t þ hA T surf T air

ð1Þ

where Q is the heat energy input in Watts, m is the mass, Cp is the specific heat capacity of the granite (receiving end). Tsurf is the temperature from the aluminium plate. For ambient temperature Tair, a separate temperature sensor was placed close to the aluminium plate. The convective heat transfer (h) of 6 W/m2/°C was used which was taken from the previous research conducted by Mian et al. [11].

All the sensors were Dallas DS18B20 direct to digital temperature sensors calibrated to provide an accuracy of ±0.2 °C over the temperature range of the tests using a dry block calibrator.

After determining the heat energy transfer from the aluminium plate to the granite block, the TCC through the joint was calculated using Eq. (2), which is an approach to calculate one dimensional steady heat conduction in a composite wall with contact resistance at the interface [12]

hc ¼

QK 1 K 2 ADTK 1 K 2 Q ðDx1 K 2 þ Dx2 K 1 Þ

ð2Þ

where Q’ is the energy in Watts, Dx1 and Dx2 are the length (mm) of wall 1 and wall 2 respectively. k1 and k2 are the conductivities (W/ m/°C) of the aluminium plate and granite block respectively and hc is the thermal conductance (W/m2/°C) through the interface of the joint. DT is the temperatures difference between the sensors placed in the aluminium plate and the granite block. For calculations, the average of the four sensors in the aluminium plate; and only one sensor in the strip 2 (S2 sensor 1) was considered as it was in the

3.1. Aluminium plate and granite block Fig. 2 shows the test setup where the aluminium plate is placed over the granite block. It further shows the illustration of the test setup with the position of temperature sensors.

Table 1 Properties of the materials used. The same properties were used during the simulations.

Conductivity (k) Density Specific heat capacity (Cp) Modulus of elasticity Coefficient of linear expansion Poisson’s ratio

Plate (Aluminium Alloy 5083-0-H111)

Granite

Venturi (Cast stainless steel)

Chuck (Gray cast iron)

Units

121 2650 900 72 109 25 10 6 0.394

3 2900 850 20 109 3 10 6 0.39

37 7700 520 190 109 15 10 6 0.26

45 7200 510 66 109 12 10 6 0.27

W/m/°C Kg/m3 J/Kg/°C N/m2 m/m/°C

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Fig. 2. Granite block and aluminium plate with the illustration of test setup showing the placement of temperature sensors.

Bespoke stand to support additional

Additional mass

Aluminium plate sensors S2 Sensor 1 is the most sensitive and considered for the calculations of TCC

Pointed nylon pillars positioned at the Airy points Fig. 3. Bespoke three point stand with pointed nylon pillars holding the additional mass.

best location (in the middle) and also the most sensitive at the receiving end (closest to the heat transfer). Fig. 4 illustrates the sensor positions inside the plate and also shows the distances of the walls considered for calculations. Fig. 5 shows temperature profiles from a test to justify the selection of the temperature sensor (S2 sensor 1) for calculations (only a few profiles were added with line markers to distinguish). Fig. 6 shows an average of the four temperature profiles from the plate sensors (Plate avg) and the temperature profile from the strip sensor (S2 sensor 1). The calculations were performed transiently at 10 s intervals for the total time span of 200 s. This time span was selected on the assumption that immediate heat transfer at the highest flow rate from the plate into the granite block had taken place before the state of the temperature equilibrium emerges between them. The equilibrium state could also be visualised in the Fig. 6 where the TCC values being observed fluctuating significantly due to the fact that temperature flow from the aluminium plate to the granite block has reduced to almost negligible. It also highlights the initial time period where the sensitivity of the temperature sensor was high and hysteresis was low.

A similar methodology was used for the second set with oil as the interfacial fluid. The plate was heated to approximately 50 °C and a fine layer of machine oil was applied on the interfacial surface and wiped off immediately using a cloth before being placed on the granite block. This method was adopted to imitate the realistic shop floor procedure used to wipe off the coolant from

Wall 2 ( Wall 1 (

2) 1)

Fig. 5. Temperature measured from the aluminium plate and the granite block (from a test).

machined parts before they head towards dimensional checks on a CMM. It is acknowledged that the wiping off action would have uncertainties with the force and cloth type applied and with the levels of remaining layer of oil, therefore, it was assumed that the remaining fine layer of oil would be consistent during all tests.

Table 2 shows the calculated TCC values between the aluminium plate and the granite block in both dry and oiled conditions for a range of masses. Equivalent forces exerted by those masses are also shown. It also shows the results from SolidWorks design studies which are also discussed in Section 5.

It can be observed in Fig. 7 that the progression of TCC values with the increase of mass had a complex non-linear behaviour especially when the plate was dry. The fluctuations in the data including the decay in the values after 5400 g is suspected to be due the deformations/bending in the plate caused by the three pillars from which the concentrated force is being exerted. The tests with oil at the interface, however, have revealed a reduction of these fluctuations in data and showed an expected linear increase which is highly likely to be the case of oil filling the interfacial voids holding the conductivity constant throughout the interface.

It was mentioned previously that there was some uncertainty in changing the interfacial fluid and the application of heavy loads on

Aluminium

15 mm 5 mm

Granite block Sensor for calculations (S2 sensor 1) Fig. 4. Illustration of the wall thickness considered for the calculations.

Sensors

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Time period of high sensitivity of temperature sensors and low hysteresis

Test span considered for calculations

Assumed thermal equilibrium area

Fig. 6. Temperature profiles from the plate (averaged) and S2 Sensor 1 (From 6400 g TCC-Oil test).

Table 2 Experimental TCC values between the aluminium plate and granite block in dry and oiled conditions (Headers: Exp-Experimental, SW-SolidWorks, Diff-Difference).

Mass (grams)

Equivalent force (N)

Exp TCC-Dry (hc W/m2/°C)

SW TCC-Dry (hc W/m2/°C)

Exp TCC-Oil (hc W/m2/°C)

SW TCC-Oil (hc W/m2/°C)

0 400 1400 2400 3400 4400 5400 6400 7400

0 3.9 13.7 23.6 33.3 43.1 53 62.8 72.6

269 291 292 289 286 295 312 305 261

258 274 265 270 261 265 281 270 243

307 306 318 327 336 340 343 350 363

292 284 277 309 323 317 325 310 316

simulations to validate the results and obtain optimised TCC values respectively.

4. SolidWorks simulations and design studies The purpose of this work is to reduce the uncertainties associated with the experimental procedures as discussed in the earlier section by using SolidWorks design studies to optimise the experimentally obtained TCC values. Furthermore, this section would discuss the possibilities of using the FEA to predict the TCC values based on the temperatures which could be obtained once the production process has been completed.

Fig. 7. Profiles of the TCC values between the aluminium plate and the granite block in dry and oiled conditions.

the distribution of that force across the boundary. In addition to this, there is some uncertainty due to the practical placement of the temperature sensors and their inherent accuracy. Finally, there is also the assumption in Eq. (2) that the temperature gradient in the materials is linear. However, because the conductivity of Granite is very low, the reality is that a significant exponential gradient forms even close to the interfacing surface, adding error to the temperature measurement and which adds a significant uncertainty in the calculation. In order to reduce all the aforementioned uncertainties, it was decided that an optimisation, based around SolidWorks design studies and Finite Element Analysis, would improve the TCC prediction since this would take account of the internal temperature gradients. The following section will detail work on the CAD modelling, FEA simulations and design study

4.1. Modelling and simulation settings CAD (Computer Aided Design) models of the aluminium plate and the granite block were created to conduct the FEA simulation and compare the simulated and experimentally obtained results.

The model had a symmetrical geometrical shape and features due to which only half of the model was used in the simulations.

Fig. 8 shows the CAD model of the granite block and aluminium plate assembly with symmetry. It shows the interface section which was sectioned to apply the TCC values. The contact was modelled as a local ‘contact set’. A 10 mm gap between the plate and block was used to ease the selection of surfaces for the application of TCC values. This gap is only a software feature and did not affect the simulation results.

Thermal simulations were set in SolidWorks using the standard ‘Thermal’ study. Material properties shown in Table 1 were applied to the respective components. Similar to the experiments, the plate was applied with an initial temperature and allowed to cool on the

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The overall simulation time including the design study for each experiment took approximately 4 h on the PC (AMD FX-8350 Octa core processor, 16 Gb Ram, AMD Radeon 2 GB graphics and Windows 7 64bit). Table 2 in Section 4.1 shows the predicted TCC values by the SolidWorks design study for both dry and oiled conditions. Simulation results are shown and discussed in Section 5.3. Fig. 10 shows a preliminary simulation result with the heat flow from the aluminium plate to the granite along with the conduction through the granite block.

4.2. Design study setup

Fig. 8. CAD model of the Granite block-Aluminium plate assembly.

granite block for a total simulation time of 200 s. The initial temperatures magnitudes noted from each experimental test (both dry and oiled) were applied exactly the same to the aluminium plate and the granite block in their respective simulations. They were applied as ‘Thermal loads’ and further on by selecting ‘Initial temperature’ option. One such example is 50.81 °C applied to the plate and 22.5 °C applied to the granite. To imitate the effect of experimental mechanical loading in simulations, the experimental TCC values obtained for each load (see Table 2) were applied at the interface of the aluminium plate and granite block to simulate the temperature flow for all dry and oiled tests. No other software based mechanical loading features were applied and the surfaces were assumed to flat in simulations.

The aforementioned convection coefficient of 6 W/m2/°C was applied to the exterior faces of the model and on the surface of the exposed hole. The remaining surfaces under the plate were considered as areas of negligible convection. Since the SolidWorks software do not accept a zero value for the convection coefficient, a selection of values ranging from 1 W/m2/°C to 1.e 10 W/m2/°C were tested. It was found that the convection value of 1. e 10 W/m2/°C did not have any effect on the overall simulation results therefore it was chosen.

As the size of the model was large and the tests were conducted within a localized area, the meshing size for the elements was selectively chosen to reduce simulation times. A high density tetrahedral mesh of 2 mm element size was used at the concerned areas of heat transfer leaving the other tetrahedral elements meshed at a lower density of 35 mm element size giving a total of 150,258 tetrahedral elements and 221,217 nodes. This meshing method was kept consistent for both dry and oiled plate simulations.

Fig. 9 shows the meshed model of the aluminium and granite block assembly.

The SolidWorks software offers the feature of design studies which can effectively be used for optimising parameters based on their referenced parameters. Due to the uncertainties reported earlier, this feature was used for predicting optimised TCC values based on the temperature values read from the sensors.

For the design study, ‘Thermal sensors’ (terminology used in SolidWorks for an area representing reference temperature) were created for both the plate and the block to represent areas in the model similar to where the real temperature sensors were placed physically in both components. The ‘Thermal sensor’ for the plate represented all four sensors where the average of all four experimental temperatures was applied and the ‘Thermal sensor’ for the block represented the area where the S2 Sensor 1 was placed and applied with its temperature. The applied reference temperatures were noted from the experiments at 100 s and 200 s to allow the design study to predict TCCs based on two referenced temperatures at those times. This should enable simulation to optimise the transient behaviour as well as the steady state solution. The design study was set with the prediction range of ±1.5 °C because any lower range was failing the design study optimisation i.e. a solution was not being found.

It should be noted that the TCC values are defined in terms of Thermal Contact Resistance (TCR) in SolidWorks and that all the results obtained were later inversed to obtain the equivalent TCC values.

The solutions were found based on the given range of the TCC given in terms of resistance from 0.00172 m2 °C/W to 0.00515 m2 °C/W. This was the default range available to run the design study in SolidWorks and it was found to be sufficient. This resistance range relates to the interface of the aluminium plate and the granite block which, as mentioned before, modelled as a local ‘contact set’ however the overall optimised solution for the TCC values will be global since it takes into account the boundary conditions applied to both components.

In addition, the design study default step size of 0.00003 m2 °C/ W was used for predictions, resulting in a total of 114 iterations being performed by the simulation to predict the solution. The discussion on the optimised TCC values from the design studies is presented in the next section, followed by the results.

4.3. Comparison of experimental and SolidWorks optimised TCC results

Fig. 9. Meshed model of the aluminium plate and granite block assembly.

A three stage sequence was followed for the thermal simulations. Firstly, normal transient thermal simulations were conducted using the experimental TCCs obtained from both dry and oil tests reported in Section 4.1. This was followed by the design study simulation for each test. Thirdly, normal simulations were conducted again using the optimised TCCs obtained from the design studies to validate the results.

The simulated temperature profiles from the sensor locations (Plate avg and S2 Senor 1) in the model were plotted and compared against the experimental temperature profiles from the temperature sensors. It can be observed that the predicted optimised values for the plate sensors are very similar (around 0.1 °C),

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Fig. 10. Simulation results for preliminary design study configuration.

however the granite block sensor is inconsistent, with readings that are lower than the experimental values for both dry and oil tests. This is suspected to be due to the design studies attempting to balance the TCC values based on the reference temperatures and the given material property values. This is evident from the obtained results shown in Figs. 11–14 where the correlation and error ranges for the plate have reduced slightly whilst the same have increased for the granite block. Due to a number of tests (a total of 18) and simulations performed, one result from the dry tests and one result from the oil tests are shown as charts. The overall correlation and residual error ranges obtained from the total number of tests are shown in Table 3. The following section will detail about the tests conducted to check the repeatability of the TCC values and to validate the displacements (thermal expansion) using the experimentally obtained TCC and optimised TCC values.

firm the testing method (2) to validate the simulated displacements by comparing them with experimentally obtained displacements (3) compare the displacements obtained from using the optimised TCCs with the experimentally obtained displacements.

5. Tests for the TCC repeatability and displacement validation The purpose of the work is to improve dimensional measurement accuracy therefore following the heat transfer simulations, separate tests were performed to monitor the displacement (thermal distortion) whilst the TCCs were monitored. These tests were aimed to check; (1) the repeatability of obtained TCC values to con-

Fig. 11. Plot of the experimental and simulated temperature profiles (Experimental TCC – Dry – 0 grm – 269 W/m2°/C) Correlation: Plate 93% – Granite 83% Error range: Plate 0.59 °C – Granite 1.67 °C.

Fig. 12. Plot of the experimental and simulated temperature profiles (Optimised TCC – Dry – 0 grm – 258 W/m2°/C) Correlation: Plate 92% – Granite 85% Error range: Plate 0.66 °C – Granite 1.52 °C.

Fig. 13. Plot of the experimental and simulated temperature profiles (Experimental TCC – Oil – 7400 grm – 363 W/m2°/C) Correlation: Plate 92% – Granite 80% Error range: Plate 0.69 °C – Granite 2.0 °C.

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Fig. 14. Plot of the experimental and simulated temperature profiles (Optimised TCC – Oil – 7400 grm – 316 W/m2°/C) Correlation: Plate 91% – Granite 83% Error range: Plate 0.86 °C – Granite 1.74 °C.

To imitate the real process for inspecting the aluminium plate, it was decided to use the oiled interface on the plate with no extra mass added. The plate was heated to approximately 50 °C and then a layer of oil was applied and wiped off immediately, representing a simple cleaned component, before placing it over the granite block. The displacement was monitored using an automated measurement routine on a Zeiss CMM for the duration of the tests which was similar to the simulation of 200 s. The measurement cycle took 22 s and involved four touch trigger measurements to obtain the size of the plate from the larger dimension only. The absolute size of the part is not relevant since we are only interested in the relative changes in the dimension of the plate as it cools, therefore the results are presented as values relative to a nominal size. The plate measurement showed an error of 103 mm at the beginning of the test when the plate is warm, which then contracted to 74.5 mm during the cooling down period of 200 s.

Fig. 15 shows the temperature and the displacement of the plate during the measurement period. It must be noted that, for the presentation purposes, the experimental displacement data in Fig. 15 has been interpolated to match with the temperature points at every 10 s. The rate of change between measured points is smooth and the difference in data capture rate is relatively small therefore a simple 2nd order polynomial fit was used.

The above mentioned experiment was then repeated a further four times. The calculated values (using Eq. (2)) can be seen in Table 4, with variation of less than 2%.

5.1. Uncertainty ‘Type A’ evaluation of repeatability data gives uncertainty of ±5 W/m2/°C at a 95% confidence level (±2r) for the experiments.

A ‘Type B’ evaluation was not performed due to the difficulties in obtaining uncertainty data for factors such as the granite material, aluminium plate, flatness measurement capability and real error in the temperature sensors. For the results in Table 3, this equates to an uncertainty in the temperature comparison with the experiments of 0.02 °C based on the modelled relationship between the

Fig. 15. Plate temperature and displacement.

Table 4 Repeatability tests for the TCC values.

Test #

TCC-Oil (hc W/m2/°C) – Repeatability

1 2 3 4 5

307 311 313 310 313

TCC and the plate average temperature; and 0.12 °C between the TCC and the granite sensor. In addition to this, it was recognised that some of the test parameter changes such as oil and mass variation could change the uncertainty therefore the variability in the comparisons for all the tests was calculated using the standard deviation of the error ranges between the experiment and simulated temperatures. A greater variability in the results would indicate a greater uncertainty in the experiments. The largest standard deviation was found to be 0.18 °C for the comparisons, the reasons for which were discussed in Section 5.3, however the effect on the evaluation of the thermal expansion is still relatively small such as for the 130 mm aluminium plate, it equates to an error of 0.58 mm using the standard thermal expansion coefficient Eq. (3).

DL ¼ 1 DT L

ð3Þ

25 lm=m C2 0:18 C 0:13 m ¼ 0:58 lm where DL is the change in length of the material, 1 is the thermal expansion coefficient and DT is the change in temperature.

Fig. 16 shows the repeatability of displacements in the plate monitored in all five tests (including the first test whose TCC is reported in the Table 2) where the error difference between the results remained less than 1.25 mm suggesting good process repeatability. The TCC values will be used in the FEA software to simulate the effect of temperature and the displacements will be validated.

Design study simulations were first run to obtain the optimised TCC values for the repeated four tests, the values from which were found to be the same 292 W/m2°C as per the first test reported in

Table 3 Comparison of temperature correlation and error ranges between experimental and optimised TCC results (Headers Exp = Experimental, Std Dev = Standard Deviation).

Tests

Exp TCC correlations range (%)

Error range (°C)

Exp Error range Std Dev (°C)

Optimised TCC correlations range (%)

Error range (°C)

Optimised Error range Std Dev (°C)

Dry

Plate Granite

91–93 81–86

0.59–0.79 1.49–1.92

0.07 0.14

90–93 84–88

0.66–0.91 1.21–1.67

0.08 0.15

Oil

Plate Granite

91–93 77–83

0.64–0.80 1.66–2.18

0.05 0.18

90–92 78–85

0.71–0.88 1.53–2.08

0.07 0.17

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bottom corners of the plate were constrained using spring connectors and were allowed to move only in the axial direction. The plate was constrained in all six degrees of freedom from one side allowing free expansion on the other side while the spring connectors were used as constraints at the interface of the plate and the granite allowing only the axial movement. Fig. 17(a) shows the location of constraints applied to the assembly.

The simulations were run for a time span similar to the experiment which was 200 s. Fig. 17(b) shows the displacement distribution/gradients in the plate and also shows the measurement point. Due to the similar nature of data, results from only the first two tests are shown in Figs. 18–19 which shows the plots of simulated displacements using the experimentally obtained TCC values and the optimised TCC values; plotted against the experimentally obtained displacement results. The legends ‘Sim – Exp TCC’ stands for Simulated – Experimental TCC and ‘Sim – Optimised TCC’ stands for Simulated – Optimised TCC. Table 5 summarizes the information about the obtained results for displacement using the experimentally obtained TCC values and the optimised TCC values.

It can be observed in Table 5 that the residual displacement errors from all five experiments were reduced after using the optimised TCC value of 292 W/m2/°C. The Table 5 also shows the averaged percentage improvement of 19% from all five tests in addition to the percentage improvements from individual tests.

It is evident from the validated results that the optimised TCC values obtained using the design study feature in SolidWorks have optimised the displacement prediction. Provided with the flexibility of placing temperature sensors on the components to be measured and the CMM bed, the design studies can be run offline to

Fig. 16. Displacement monitored on plate during the repeatability tests.

Table 2. This further confirms the repeatability of the experimental method and the simulation such as the application of thermal boundary conditions and fixture constraints. This validation may also encourage to consider that the optimised TCC values obtained in Table 2 for all loading conditions; from 0 g to 7400 g; in both dry and oiled conditions would also be repeatable and therefore may be used to simulate for the respective conditions and loadings.

The next step was to run the displacement simulations using both the experimental TCCs (from Table 4) and optimised TCC value of 292 W/m2°C and compare their results.

The transient displacement simulations were conducted using the ‘Non-Linear’ study in SolidWorks in order to pass the relevant temperature field at different stages of the simulation. The four

Y X

Displacement measurement point

Z Spring connector

Spring connectors

(a)

Fixed constraints

(b)

Fig. 17. (a) Location of the fixtures constraints applied to the assembly (b) Displacement in the plate.

Fig. 18. Displacement results for Test 1 using (a) Experimental TCC values (b) Optimised TCC values.

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Fig. 19. Displacement results for Test 2 using (a) Experimental TCC values (b) Optimised TCC values.

Table 5 Correlations and error ranges for the displacement using the experimentally obtained TCC values and optimised TCC values for the repeatability tests.

Test #

Displacement correlation (Exp TCC value) (%)

Residual error (mm)

Displacement correlation (Optimised TCC value) (%)

Residual error (mm)

Residual error percentage improvement (%)

Averaged Percentage improvement (%)

Test Test Test Test Test

94 96 95 93 95

1.48 1.05 1.12 1.6 1.23

95 97 97 94 97

1.33 0.93 0.93 1.3 0.78

10 11 17 19 37

19

1 2 3 4 5

Fig. 20. Location of the temperature sensors (a) surface temperature sensors (b) illustration of ambient temperature sensor locations.

estimate the TCC values which can be further used to predict the necessary time frames required for future parts to be measured.

This may be based on the part reaching thermal equilibrium or is within an acceptable tolerance range.

To further test the validity of the obtained TCC values, the following section details the tests conducted on a Venturi from the Oil and Gas industry. This is a cylindrical component, shown in Fig. 20 that is used to control the flow of oil. The aim was to imitate the real industrial process where a part has been machined and now requires dimensional confirmation using a CMM. 6. Validation of TCC values and displacement using an industrial part

Three temperature sensors were placed on the surface at different heights over the full height of the Venturi and the fourth temperature sensor was placed on the bottom flange. In addition to the surface sensors, three temperature sensor were used to measure the ambient temperatures with two sensors placed around the Venturi (one placed at the top and the other at the side). The third sensor was placed inside the Venturi to measure the air temperature of the air pocket that exists due to the hollow geometry [13]. Fig. 20 shows the location of the temperature sensors where (a) is the picture of the Venturi showing the location of surface sensors and (b) is the CAD illustration showing the location of ambient sensors.

6.1. Case study 1 (Venturi-Chuck test)

Here two case studies have been presented, (1) the Venturi was placed on top of a jig (chuck) already fixed to the CMM (2) the Venturi was placed directly on the CMM granite bed. The Venturi was made of cast stainless steel and the chuck was made of grey cast iron. The material properties are shown in the Table 1.

The Venturi was placed on the heater in the up-right direction and heated from the bottom flange until the Venturi Bottom sensor reached 31.5 °C and then immediately placed on the chuck already present on the CMM for dimensional measurements. The temper-

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ature data was measured every 10 s and the displacement data was measured at both bottom and top flanges every 48 s (limited by the speed of the CMM routine) for the total test span of 1300 s (22 min). Figs. 21 and 22 shows the experimental temperature and displacement data respectively. These results will be discussed later in this section.

The CAD model of the Venturi and the chuck were created in SolidWorks. The measured temperature information from the Bottom Flange sensor was used to obtain the heat power parameter using the energy balance method [11,14] for the heat source which, in this case, was considered to be the bottom flange of the Venturi; and which revealed a heat power of 75.4 W. Due to the larger size and shape of the Venturi, it was not sufficient to have a global initial temperature because the heating process using the hot plate produced a significant gradient. This was replicated by applying the heat power until the initial conditions of the model matched the initial conditions of the real part. In addition, the structure of the Venturi is such that most of the surfaces from which convection will occur are vertical therefore the previous convection parameter, obtained and used for components with a mixture of surfaces, was deemed to be inadequate. A separate test was therefore conducted to obtain a new convection coefficient for the Venturi, using the same principal of natural convective (the structure was isolated as before to remove conduction) cooling [11], which revealed the convection coefficient of 10 W/m2/°C. This was applied and assumed to be consistent over the whole Venturi structure. The interfacing sections were applied with the 1. e 10 W/m2/°C to consider a negligible convection. For the outside structure of the Venturi, the bulk ambient temperature was set to an average temperature magnitude of 22.5 °C noted from the Ambient Side and Ambient Top sensors during the experiments; and for the inside of structure, 30 °C from the Ambient Air pocket sensor was used.

At this point, it was important to obtain the TCC value for the Venturi-chuck interface for which the same method discussed earlier was used. The Venturi was heated up to approximately 42 °C and was placed immediately on the chuck. A sensor was placed on the Venturi bottom flange to obtain the temperature of the Venturi and thermal imaging was used to obtain the temperature information from one of the jaws of the chuck which revealed a

Fig. 22. Displacement data measured at the bottom and top flange (Venturi Chuck test).

TCC of 963 W/m2°C. Fig. 23(a) and (b) illustrates the test and the thermal image respectively.

Fig. 24(a)–(d) show the CAD models of the Venturi and chuck and their assembly respectively; (c) shows the sections where the values of the TCC were applied. Similar to the plate displacement tests, Fig. 24(d) shows the location of the spring connectors which were used to allow free expansion of the base. Temperature measurement points are also shown along with the displacement measurement points for the diameter selected. Similar to the plate tests, the concerned areas of heat transfer were meshed with the higher density tetrahedral elements. The Venturi and the jaws of chuck were meshed with an element size of 5 mm and the chuck was meshed with an element size of 30 mm resulting in a total of 86,592 tetrahedral elements and 149,151 nodes. The gap between the Venturi and chuck was intentionally chosen for the ease of selection of the surfaces. This is a software feature and has no effect on simulation results. Again the mechanical loads and load variations were not applied in the simulations for both case studies.

6.1.1. Venturi-Chuck results and validations The simulation results are shown in comparison with the experimental results in Figs. 25 and 26. It can be observed that the simulated temperature profiles have matched well with the

Fig. 21. Measured temperature data (Venturi-Chuck test).

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Venturi bottom flange Chuck

(b)

(a)

Fig. 23. Test for obtaining the TCC between the Venturi and the chuck.

(a)

(b)

Sections for the TCC values

(c)

Z X

Y Temperature measurement points

Fixed constraints

Displacement measurement points

Spring constraints (d)

(e)

Fig. 24. CAD models (a) Venturi (b) Chuck (c) sections where TCC values were applied (d) Venturi-chuck assembly with measurement and constraint locations (e) Applied mesh.

Fig. 25. Comparison of experimental and simulated Venturi Bottom temperatures (Venturi-Chuck test).

Fig. 26. Comparison of experimental and simulated Venturi Middle temperatures (Venturi-Chuck test).

experimental temperature profiles. The temperature differences were 2.5 °C and 0.9 °C for the Venturi Bottom and Venturi Middle sensors respectively. Negligible change occurred at the top. The difference between the Venturi Bottom temperature profiles is probably due to the assumed constant convection coefficient

parameter applied to the whole model; and due to the assumption of a constant temperature inside the air pocket area. It is known that the air inside this pocket will change but its incorporation as an active thermal mass/sink was outside of the scope of this research.

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During the experiment, the displacement ranges were measured as 40 mm contraction at the bottom flange and 5 mm expansion at the top flange during the test span of 1300 s. The top flange expanded as the heat contained at the bottom section of the Venturi flowed in the vertical direction even after it was removed from the heater due to the fact that the top flange was cooler relative to the bottom flange. Both ranges have been referenced to zero i.e. relative to the start of the test. Figs. 27 and 28 show the comparison between the experimental and simulated displacement profiles for both bottom flange and top flange respectively. The correlation between the experimental and simulated displacements for the bottom flange remained within 91% with the error difference of 3.8 mm and remained within 77% for the top flange with an error difference of 1.2 mm. Fig. 29 shows the simulated temperature and displacement distribution/gradients in the Venturi-Chuck assembly.

6.2. Case study 2 (Venturi-CMM) Similar to case study 1, the Venturi was heated until the Bottom temperature sensor reached 31.5 °C. The Venturi was then imme-

diately placed directly on the CMM machine bed and allowed to cool down for 1300 s. The temperature data was measured every 10 s and the displacement data was measured at both bottom and top flanges every 50 s (due to the measurement routine of the CMM). The displacement ranges were measured to be 36.7 mm contraction at the bottom flange and 1.6 mm expansion at the top flange. The charts for the experiment are shown with the simulation results in the following section.

For the simulation, the CAD model of the Venturi was placed on the CMM as shown in Fig. 30(a). The smaller round section on the CMM bed was meshed with the same element size of 5 mm as the Venturi for the heat transfer and where the TCC values would be applied. The rest of the CMM bed was meshed using an element size of 250 mm which revealed a total of 96,273 elements and 161,880 nodes. Fig. 30(b) shows the mesh applied to the whole bed and to the smaller round section. Fig. 30(c) shows the applied constraints to the model. Since the temperature at the Venturi Bottom sensor revealed a similar temperature, the same heat power of 75.4 W previously calculated was used for the simulations. Both the model of the Venturi and the CMM bed were applied with a convection boundary condition of 10 W/m2/°C. The bulk ambient

Fig. 27. Comparison of the experimentally obtained and the simulated displacement – Bottom flange.

Fig. 28. Comparison of the experimentally obtained and the simulated displacement – Top flange (Venturi-Chuck test).

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Z X Y

(b)

(a)

Fig. 29. Simulated results (a) Thermal simulation showing the temperature distribution (b) Simulated displacement of the Venturi-Chuck assembly (Venturi-Chuck test).

X

Fixed constraint

Section for the TCC values

Z

Y

CMM bed (granite)

(a)

Spring connectors

(b)

(c)

Fig. 30. (a) Venturi placed on the CMM (b) Applied mesh (c) Location of constraints.

temperatures at the outside of the Venturi and in the Air pocket were 22.5 °C and 32 °C respectively. Again, the gap between the Venturi and CMM bed was intentionally chosen for the selection of the surfaces. This is a software feature and has no effect on simulation results.

6.2.1. Venturi-CMM results and validations To represent a typical industrial scenario, the Venturi was assumed to have the residues of coolant/oil. The mass of the Venturi was approximately 7000 g which allowed the use of the TCC values discussed in Table 2. Since the mass lies between the range of 6400 g and 7400 g, an averaged value of 313 W/m2°C was used.

The simulation results showed a very similar behaviour to case study 1, with the differences between the experimental and simulated temperature profiles of just 2.2 °C, 0.9 °C and 0.7 °C for the Venturi Bottom, Venturi Middle and Venturi Top sensors respectively. The larger difference between the Venturi Bottom temperature profiles is again suspected to be due to the assumed constant convection coefficient parameter applied to the whole model; and due to the assumption of a constant temperature inside the air pocket area discussed previously.

Fig. 31 shows the measured temperatures while Figs. 32 and 33 show the comparison between the experimental and simulated

displacement profiles for both bottom flange and top flange respectively for the Venturi-CMM test. The correlation between the experimental and simulated displacements for the bottom flange remained 90% with the error difference of 3.6 mm, however, the results from the top flange did match well for the time span of 600 s (10 min) and the error difference remained within 0.2 mm, which then started to deteriorate up to approx. 1.3 mm which is suspected to be due to the assumed constant convection coefficient. Although the measured displacement in the top flange has been very low (1.6 mm), the matching level of the simulated results within the time span of 600 s may be considered useful for a variety of CMM measurements regimes requiring less than 10 min time span for a complete measurement. It is however acknowledged that larger complex parts with complex thermal behaviour would require latency time greater than 600 s to commence measurements which would also ensure the error deterioration (that started after 600 s) to decrease as temperature stabilizes with time, for which, longer time simulations would be needed. Fig. 34 shows the simulated temperature distribution and displacement in the Venturi-CMM assembly.

This case study has proven the utilization of the obtained TCC values and has shown a potential of being used for a variety of other components with masses ranging from 1 g to 7400 g. A

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Fig. 31. Measured temperature data (Venturi-CMM test).

Fig. 32. Comparison of the experimentally obtained and the simulated displacement – Bottom flange (Venturi-CMM test).

Fig. 33. Comparison of the experimentally obtained and the simulated displacement – Top flange (Venturi-CMM test).

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Fig. 34. Simulated results (a) Thermal simulation showing the temperature distribution (b) Simulated displacement of the Venturi-CMM assembly (Venturi-CMM test).

potential exists to extrapolate the ranges for the components with heavier masses. It should also be noted that the condition of the surface finish on components would influence the TCC values therefore additional experiments may be needed to extrapolate for significant differences in the surface finish.

7. Predicting soaking times Considering all displacement validation tests, it can be observed that the first validation test for the aluminium plate and granite block (Test 1 in Table 5) revealed up to 10% improvement for the displacement results by using the optimised TCC values. Further on the displacement residual errors from all repeatability tests revealed an averaged percentage improvement of 19% with the maximum of 37% improvement. These results prove that FEA can effectively be used to predict optimised TCC values using the design study feature in SolidWorks.

In addition to the above, the results obtained from the case studies for the Venturi-Chuck and Venturi-CMM are summarised in the Table 6.

These results have also shown the potential of using the FEA method to simulate the thermal behaviour for any component using the obtained optimised TCC values.

Since the simulated data from both case studies have revealed a lower residual error in comparison to the experimental data, the simulated data can now be used to estimate the soaking times, for which, ‘gradient plots’ are plotted which shows the rate of change of the error over time. For better representation, only the data from the bottom flange was used and a tolerance limit of 1.5 mm was selected, this would represent 10% uncertainty contribution limit for a typical tolerance value of 15 mm considered within precision machining applications such as milling and turning. Figs. 35 and 36 show the gradient plots for the Venturi-Chuck and Venturi-CMM tests respectively. The plots effectively show the time estimation for both tests when the dimensional measure-

Fig. 35. Gradient plots showing the estimation of temperature soaking times – Venturi-Chuck test.

ments on the CMM may be commenced based on the selected limit of 1.5 mm.

It can be observed that the obtained soaking times were different for both tests, suggesting that the measurements using the Venturi and chuck arrangement may be commenced after the 500 s (8.3 min) of delay. This is a 99.4% improvement considering a typical 24 h delay for the part to stabilize and a 98.3% improvement if only an 8 h shift pattern is considered. This delay time also ensures the temperature equilibrium where the temperature difference remained within 0.8 °C. Similarly for the arrangement when the Venturi is directly placed on the CMM bed, the measurements may be commenced after 460 s (7.6 min) of delay, at which point the temperature difference is 0.6 °C. This again is a 99.5% improvement considering a typical 24 h delay and a 98.4% improvement for an 8 h shift pattern. Clearly the charts can be used easily for different levels of dimensional effect. Once set up,

Table 6 Simulated results for the Venturi-Chuck and Venturi-CMM case studies.

Venturi-Chuck test Venturi-CMM test

Bottom flange error (mm)

Bottom flange residual error (mm)

Top flange error (mm)

Top flange residual error (mm)

40 36.7

3.8 3.6

5 1.6

1.2 0.2 (up to 600 s)

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Fig. 36. Gradient plots showing the estimation of temperature soaking times – Venturi-CMM test.

the simulation can be easily adjusted for speculative situations such as increased convection achieved by artificially cooling using fans etc. Such time savings will have an increasingly important role to play as inspection moves from dedicated facilities and closer to, or even onto, the machine.

The experimental gradient profiles for both case studies are also plotted on the same graphs (Figs. 35 and 36 respectively) for the purpose of comparisons. Considering the selected 1.5 mm tolerance, the comparison reveals a 0.1 mm error difference at 500 s (8.3 min) for the Venturi-Chuck test (Fig. 35) and 0.2 mm error difference at 460 s (7.6 min) for the Venturi-CMM test (Fig. 36). It can also be observed that both data profiles in both figures have got different time constants causing them to have different slopes. This is suspected to be due to the assumed constant convection coefficient used for the Venturi during simulations which do not take into account the effect of change of convection rates compared to, for example, the experimental heating process, where the inner side of the Venturi had a higher air temperature due to the warm air being trapped which may cause the convection rate to alter.

Although it is acknowledged that the transition period during which the Venturi was being placed on the Chuck/CMM had lost some of the trapped air, however, after being placed on the chuck/CMM, the Venturi still had the effect of the trapped air during the cooling period in terms of higher temperature. This is evident from the temperature profile of ‘Ambient Air pocket sensor’ in Fig. 21 for the Venturi-Chuck case study and Fig. 31 for the VenturiCMM case study.

This technique is very productive for typical CMM measurement regimes where a single temperature sensor is used for the temperature measurement and thermal compensation. The placement of the temperature sensor is typically chosen for convenience where a suitable flat surface is available, but this may have a significant impact on the compensation routines of the CMM especially in the cases of workpieces having significant temperature gradients such as the Venturi. Since this was warmer around the bottom flange area than the top flange area, if the CMM temperature sensor was placed near the bottom flange, then the thermal compensation in the CMM may over compensate the error for the areas near the top flange. In this example, the temperature of the venturi was 30 °C near the bottom flange and 23 °C near the top flange. The difference in diameter between the locations of the Venturi Bottom sensor (90.5 mm) and the Venturi Top sensor (178 mm) is approximately double in size, the expansion near the lower flange area was calculated as 14 mm based on 30 °C and near the top flange as 8 mm based on 23 °C using the Eq. (3).

Clearly the CMM thermal compensation model, depending on the location of the single temperature sensor, would either under

or over compensate the thermal error. The FEA simulations would therefore also contribute towards the estimation of the time to reach the uniformity of temperature such that the remaining gradients are sufficiently small in the whole structure for which, a single temperature sensor may be adequate.

From an absolute dimension perspective rather than the gradient effects shown in, for example Fig. 36, and sensor placement; the thermal behaviour of the Venturi was observed during another test with an extended cooling period, for which, the Venturi was heated up to similar temperatures and then placed on the CMM to cooling down for an extended period. The absolute size measured on the CMM at 22.5 °C was 199.565 mm for the bottom flange (it should be noted that although, the temperature in the CMM room was maintained at 20 °C ± 3 °C, it was found that the ambient temperature was approximately 22.5 °C on average for the duration of the test). When the Venturi was measured after 460 s (7.6 min) with CMM temperature compensation active, it revealed 199.602 mm of compensation. The calculations are as follows, - Experimental temperature change after 460 s (measured at the Bottom Flange sensor at 7.6 min) was 12.2 °C (34.7 °C – 22.5 °C = 12.2 °C), therefore using the absolute dimension of 199.565 mm and the expansion coefficient of 15 mm/m°C, Eq. (3) gives 36.5 mm of displacement after 7.6 min until it reaches 22.5 °C. - During the cooling period, the absolute experimental displacement measured at 460 s (7.6 min) was 199.602 mm which revealed 199.566 mm of displacement (199.602 mm – 0.0365 mm = 199.566 mm).

The obtained value of 199.566 mm was then used to obtain the change in displacement from 7.6 min to when it reaches 22.5 °C. This took approximately 1.46 h and revealed 37 mm change (199.602 mm – 199.565 mm = 0.037 mm). For comparison, the same process, using an extended simulation cooling to 22.5 °C, showed 31.2 mm change for this same period revealing a 5.8 mm difference between the experimental results and simulated predictions. This difference is again suspected to be due to the assumed constant convection coefficient used during simulations which may be reduced by using the experimentally obtained convection coefficients.

8. Conclusions CMM machine availability for dimensional measurement and its management have been a significant challenge, especially with industries where larger production rates are frequent. As soon as a component is manufactured, a general approach is to wait for long time periods for temperature soaking before commencing dimensional checks on the CMM. This engages the machine for long durations without effective production and therefore counts towards the non-productive downtime, or uses valuable floor space. This paper presents a method based on Conduction boundary condition optimisation and FEA simulations which is able to predict the measurement latency accurately i.e. the time spans required by the component to reach either thermal equilibrium or reach a state at which uncertainty due to temperature is within allowed acceptable dimensional tolerance range or contribution to the conformance zone.

To predict these time frames, the first step was to obtain the Thermal Contact Conductance (TCC) values associated with a component being placed on a CMM for measurement. These were calculated experimentally by heating a simple aluminium plate and placing it on a granite block and allowing it to cool down while

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detailed temperature measurements were performed. The TCC values were then further optimised using a FEA design study feature.

Both experimental and simulated data for the temperature and displacements were then compared which revealed that the use of optimised TCC values had improved the results by an average of 10%.

Further validations for the optimised TCC values were conducted on a real industrial part, a cylindrical vessel for controlling flow called a Venturi. Two case studies were conducted to demonstrate two scenarios of a hot Venturi (1) placed on a chuck and (2) placed directly on a CMM bed and allowed to cool down. Both case studies revealed low residual errors which allowed the estimation of the temperature soaking times for the Venturi which were estimated to be 500 s (8.3 min) for the Venturi-Chuck and 460 s (7.6 min) for the Venturi-CMM case studies respectively based on a selected 1.5 mm tolerance limit. These estimated time frames are very short i.e. the latency has been reduced, in comparison to the general approach of longer waiting times of many hours; and have effectively suggested the commencement of measurement on a CMM. For typical CMM measurement regime, a single temperature sensor is often used for the temperature measurement and thermal compensation. A simple comparison on the Venturi yielded an over or under compensation of 7 mm depending on the position of the temperature sensor on the Venturi vessel surface. The FEA simulations would therefore also contribute towards the estimation of the time to reach the uniformity of temperature where a single temperature sensor may be adequate.

Temperature information from the part can be acquired as soon as it has finished machining. In order to set reasonable initial conditions in the simulation, a number of temperature readings (horizontal, vertical or combined direction) may be required to account for significant thermal gradients. It is acknowledged that a typical CMM may only have one or two sensors therefore low cost sensors or low cost thermal imaging could be applied for this purpose. As a practical guideline, it is recommended to use at least one sensor for every 3 °C of gradient (the Venturi had 3 sensors in the vertical direction) to ensure useful temperature information is obtained such as the gradients and rapid changes of temperatures to model them effectively in the FEA. The simulations are then conducted using the TCC values found in this paper to estimate the latency the part would take to reach either the temperature equilibrium or to obtain the displacement information to confirm the dimensional tolerance prior to the commencement of measurement. This will have a significant effect on the management of the CMM resources and would greatly reduce the machine downtime by efficiently managing the machine availability. Although the case studies presented in this paper used the Venturi vessel from the Oil and

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Gas industry however, it is anticipated that this technique has a great potential to target industries such as Automotive, Aeronautical, Marine, Precision Engineering and other industries where manufacturing and measurement in bulk takes place.

Future work will investigate more precise locations for the placement of temperature sensors on machined parts and any fixtures to be used to measure the temperature distribution more accurately. Further, Computational Fluid Dynamics (CFD) analyses will be incorporated to model more complex industrial parts containing complex geometries and air pockets to ensure more accurate latency can be predicted since it is known that the existing average convective coefficient can introduce uncertainty in such cases.

Acknowledgement The authors gratefully acknowledge the UK’s Engineering and Physical Sciences Research Council (EPSRC) funding of the Future Metrology Hub (Grant Ref: EP/P006930/1).

References [1] J.-P. Kruth et al., Interaction between workpiece and CMM during geometrical quality control in non-standard thermal conditions, Precis. Eng. 26 (1) (2002) 93–98.

[2] J.D. Claverley, R.K. Leach, A review of the existing performance verification infrastructure for micro-CMMs, Precis. Eng. 39 (2015) 1–15.

[3] R. Royce, Guide to Dimensional Measurement Equipment, Rolls-Royce plc, 2015.

[4] J.L. Bucher, Q. American Society for, and D. Measurement Quality, The metrology handbook. 2012, Milwauke, Wis.: ASQ Quality Press.

[5] T.M.D. Doiron, A. Schneider. Use of air showers to reduce soaking time for high precision dimensional measurements. in Proceedings of the Measurement Science Conference. 2007. Long Beach, CA. 2007.

[6] C.L. Grachanen, Know your surroundings: Environmental influences impact tests and calibration, Qual. Prog. Qual. Progr. 46 (6) (2013) 50–51.

[7] D. Anagnostakis et al., Knowledge capture in CMM inspection planning: barriers and challenges, Proc. CIRP 52 (2016) 216–221.

[8] R. Salman et al., An industrially validated CMM inspection process with sequence constraints, Proc. CIRP 44 (2016) 138–143.

[9] M. Siemiatkowski, W. Przybylski, Simulation studies of process flow with inline part inspection in machining cells, J. Mater. Process. Technol. 171 (1) (2006) 27–34.

[10] S.M. Stojadinovic et al., Towards an intelligent approach for CMM inspection planning of prismatic parts, Measurement 92 (2016) 326–339.

[11] N.S. Mian et al., Efficient thermal error prediction in a machine tool using finite element analysis, Meas. Sci. Technol. 22 (8) (2011) 085107.

[12] K.D. Hagen, Heat Transfer with Applications, Prentice Hall, Upper Saddle River, N.J, 1999.

[13] N.S. Mian et al., The significance of air pockets for modelling thermal errors of machine tools, in Laser Metrology and Machine Performance X, L. Blunt and W. Knapp, Editors. 2013, EUSPEN: Bedfordshire, UK. p. 189–198.

[14] A. Abuaniza et al., Thermal error modelling of a CNC machine tool feed drive system using FEA Method, Int. J. Eng. Res. Technol. 5 (3) (2016) 118–126.

Journal of

Manufacturing and Materials Processing

Article

Precision Core Temperature Measurement of Metals Using an Ultrasonic Phase-Shift Method Olaide F. Olabode * , Simon Fletcher, Andrew P. Longstaff

and Naeem S. Mian

Center for Precision Technologies, University of Huddersfield, Huddersfield HD1 3DH, UK * Correspondence: olaide.olabode@hud.ac.uk Received: 29 June 2019; Accepted: 2 September 2019; Published: 4 September 2019

Abstract: Temperature measurement is one of the most important aspects of manufacturing. There have been many temperature measuring techniques applied for obtaining workpiece temperature in different types of manufacturing processes. The main limitations of conventional sensors have been the inability to indicate the core temperature of workpieces and the low accuracy that may result due to the harsh nature of some manufacturing environments. The speed of sound is dependent on the temperature of the material through which it passes. This relationship can be used to obtain the temperature of the material provided that the speed of sound can be reliably obtained. This paper investigates the feasibility of creating a cost-effective solution suitable for precision applications that require the ability to resolve a better than 0.5 ◦ C change in temperature with ±1 ◦ C accuracy.

To achieve these, simulations were performed in MATLAB using the k-wave toolbox to determine the most effective method. Based upon the simulation results, experiments were conducted using ultrasonic phase-shift method on a steel sample (type EN24T). The results show that the method gives reliable and repeatable readings. Based on the results from this paper, the same setup will be used in future work in the machining environment to determine the effect of the harsh environment on the phase-shift ultrasonic thermometry, in order to create a novel technique for in-process temperature measurement in subtractive manufacturing processes.

Keywords: core temperature measurement; phase-shift method; manufacturing; ultrasonic thermometry

1. Introduction Dimensional accuracy and the surface integrity of manufactured products are key specifications that determine conformance to the design intent. The adherence to these specifications is an indication of the quality of the product and that it will meet the needs of customers. Temperature variation during manufacturing can influence both the dimensional accuracy and the surface integrity of the product.

Therefore, temperature control or compensation of the thermal effects is essential in order to produce high quality components.

Exact temperature variation values are not given in the literature, as it is difficult to get a generic value due to different manufacturing processes. However, temperature variation in a workpiece during machining can reach 10 ◦ C. A 10 ◦ C variation will result in a differing expansion in different materials.

In precision manufacturing, workpieces often need to be machined with a dimensional error of less than 5 µm. The accuracy and resolution with which workpiece temperature needs to be measured for different materials is given in Table 1.

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Table 1. Required accuracy and resolution for the precision manufacturing of different materials.

Material

Coefficient of Thermal Expansion (×10−6 /◦ C) [1]

Expansion of 200 mm Part at 10 ◦ C Change in Temperature (µm)

Required Temperature Accuracy (◦ C)

Required Temperature Resolution (◦ C)

Structural Steel Aluminum Cast Brass Tungsten Copper alloys

12 24 21 4.6 18

24 48 42 9.2 36

±2 ±1 ±1.2 ±5.4 ±1.4

1 0.5 0.6 2.7 0.7

The core temperature variation of metals affects their dimensional accuracy. The existing temperature measurement methods in manufacturing are limited in that they only represent the surface temperature of the workpiece. This paper investigates the possibility of creating a novel system for the precision core temperature measurement of metals which can be adapted for use in different manufacturing processes. One such manufacturing process is the machining process. Metal cutting is arguably the most important aspect of manufacturing and there have been advancements in optimizing the rate of metal cutting. New technologies have helped to increase the cutting speed, depth of cut and feed rate. However, with these increments also comes the increase in heat generation originating near the tool–workpiece interface [2]. Combined with effects from change in ambient temperature, heat sinking to fixtures and non-deterministic heat transfer between the component and cutting fluids, indirect monitoring of the temperature of the workpiece is a very challenging problem. Most of the temperature measurement techniques for manufacturing described in literature only deal with the machine [3] or cutting tool temperature [2].

One of the temperature measurement methods for workpieces reported in literature is the tool/workpiece thermocouple [4–6]. The main difficulties reported concerning the use of this method are the parasitic electromotive force (EMF) from secondary joints, the necessity for the accurate calibration of the tool and workpiece as a thermocouple pair, the need to isolate the thermocouple from the environment and the lack of clarity on what the EMF represents [5,6]. Also, this method does not indicate the core temperature of the workpiece. Infrared thermometry is another method that has been used in both dry conditions and with the presence of coolant [7]. However, the measurement only represents the surface temperature, and the accuracy that can be achieved with this method is less than the required accuracy for the precision machining of some materials, as infrared cameras’ stated accuracy is typically ±2 ◦ C [8]. Moreover, this value is only valid in ideal conditions, as the accuracy will greatly reduce in harsh machining environments. Infrared cameras also require a good line of sight to work. Of all the methods previously used, none gives a direct indication of the core temperature of the workpiece, which is the parameter that affects the dimensional expansion.

The speed of sound in any material is dependent on the temperature of the medium of propagation.

This dependence has been used in a variety of ways to measure the temperatures of different media.

The pulse-echo technique uses the time-of-flight method to measure ultrasonic velocity which can then be related to the temperature of the medium [9]. The pulse-echo method is relatively simple, but the resolution of measurement may reduce with distance due to attenuation of the echo signal [10].

Another main technique is the continuous wave method which evaluates the distance of ultrasonic travel by computing the phase-shift between transmitted and received signals [11]. Some modifications and combinations of the two techniques have also been used, such as the two-frequency continuous wave method [11,12] and multiple frequency continuous wave method [13,14]. These techniques make use of two or more ultrasonic frequencies to increase the range of measurement and improve resolution.

Hu et al., using the temperature range of 25 to 200 ◦ C, modified the ultrasonic velocity equation based on the effects thermal expansion has on the travel path of ultrasonic waves. They reported an increase in accuracy based on the compensations made for expansion [15]. Another recent work by Ihara et al. is the use of laser ultrasonic thermometry to measure the internal temperature of heated

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cylindrical rods. The authors reported that the results almost agree with those measured using a thermocouple, however the accuracy of the method is not sufficiently described [16]. Different methods of ultrasonic measurement have been used and modified for use in different fields of measurement, however, their use in precision manufacturing is not sufficiently described in the literature.

This paper explores the use of ultrasonic waves for the precision core temperature measurement of a steel workpiece. The results from simulation using the two main techniques are evaluated to find the best option for core temperature measurement in metals. The initial work consists of simulations in the k-Wave MATLAB toolbox—an open source toolbox for time domain acoustic and ultrasound simulations [17]. This was used to study the two main ultrasonic thermometry methods—the ultrasonic pulse-echo and phase-shift methods. k-Wave was chosen for simulation because of its flexibility for defining different parameters and media of interest—it also gives a real-time A-scan of the propagation medium during simulation, as well as its propagation plot. In an A-scan, the amplitude of an ultrasonic pulse is represented as displacement in y-axis and the corresponding travel time is represented on the x-axis. Based on the simulation results, ultrasonic phase-shift experiments were conducted in a metrology laboratory and the results of these experiments will serve as input to a future experiment which involves the use of the developed techniques in subtractive manufacturing processes.

2. Materials and Methods The Pulse-echo method is the traditional means of ultrasonic measurement. It uses the principle of time-of-flight (tof ), where an ultrasonic pulse is propagated through a medium and the pulse is reflected when it encounters a medium of different physical property [18]. The tof from the ultrasonic transmitter to the receiver and the length of the travel path is used to compute the ultrasonic velocity [19]. This relationship is given as: d c= (1) to f where c is the ultrasonic velocity, d is the distance travelled and tof is the time of flight [20].

The phase-shift method, on the other hand, uses the difference in the phase of steady state frequency ultrasonic wave between transmitted and received signals [13]. For an ultrasonic wave of known frequency travelling through a known distance, the phase difference between the transmitted and received signals can be used to compute the ultrasonic velocity through the medium. The relationship between the ultrasonic velocity and phase-shift is given in the equation below:

ϕ c L = n+ 2π f

(2)

where L is the distance between the transmitter and receiver, n is the integer number of wave periods, φ is the phase-shift, f is the ultrasonic frequency and c is the ultrasonic velocity through the medium [19].

A modification of the phase-shift method which considerably improves both the range and resolution of measurement is the two-frequency continuous wave method (TFcw). It uses two frequencies for ultrasonic velocity computation. The TFcw equation is given as: c=

2πL∆ f ∆ϕ

(3)

where c is the ultrasonic velocity, L is the length of travel, ∆f is the difference between the two frequencies (f 1 –f 2 ) and ∆φ is the difference between the phase-shifts given as [13]: ∆ϕ = ϕ1 − ϕ2 , i f ϕ1 > ϕ2 , ∆ϕ = ϕ1 + 2π − ϕ2 , i f ϕ1 < ϕ2

(4)

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â&#x2C6;&#x2020;đ?&#x153;&#x2018; = đ?&#x153;&#x2018; đ?&#x153;&#x2018; , đ?&#x2018;&#x2013;đ?&#x2018;&#x201C; đ?&#x153;&#x2018; đ?&#x153;&#x2018; , (4) â&#x2C6;&#x2020;đ?&#x153;&#x2018; = đ?&#x153;&#x2018; + 2đ?&#x153;&#x2039; đ?&#x153;&#x2018; , đ?&#x2018;&#x2013;đ?&#x2018;&#x201C; đ?&#x153;&#x2018; đ?&#x153;&#x2018; 4 of 12 By adding a third frequency, the range and the resolution can both be further improved. This technique is known as the multiple frequency continuous wave method (MFcw) and the MFcw By adding third frequency, the range and the resolution can both be further improved. This equation is givena as [21]: technique is known as the multiple frequency continuous wave method (MFcw) and the MFcw equation đ??ż is given as [21]: đ?&#x2018;?= (5) Î&#x201D;đ?&#x153;&#x2018; Î&#x201D;đ?&#x2018;&#x201C; đ?&#x2018;?

L Î&#x201D;đ?&#x153;&#x2018; đ?&#x2018;&#x201C; đ?&#x2018;? đ?&#x153;&#x2018; đ?&#x2018;? c =đ??źđ?&#x2018;&#x203A;đ?&#x2018;Ą 2đ?&#x153;&#x2039; Î&#x201D;đ?&#x2018;&#x201C; Î&#x201D;đ?&#x2018;&#x201C; + đ??źđ?&#x2018;&#x203A;đ?&#x2018;Ą 2đ?&#x153;&#x2039; Î&#x201D;đ?&#x2018;&#x201C; đ?&#x2018;&#x201C; + 2đ?&#x153;&#x2039; đ?&#x2018;&#x201C; (5) â&#x2C6;&#x2020;Ď&#x2022; â&#x2C6;&#x2020; f Ď&#x2022; â&#x2C6;&#x2020;Ď&#x2022; f Int 2Ď&#x20AC;1 â&#x2C6;&#x2020; f2 â&#x2C6;&#x2020;cf + Int 2Ď&#x20AC;2 â&#x2C6;&#x2020; 1f fc + 2Ď&#x20AC;1 fc J. Manuf. Mater. Process. 2019, 3, 80

1

2

2

1

1

2.1. Simulations 2.1. Simulations Three simulations were performed in MATLAB R2017b using the k-Wave toolbox. The first Three simulations were performed in MATLAB R2017b using the k-Wave toolbox. The first simulation was set up to resolve 0.1 â&#x2014;ŚÂ°C change in temperature with tof of ultrasonic wave. Steel was simulation was set up to resolve 0.1 C change in temperature with tof of ultrasonic wave. Steel was chosen as the medium of propagation with a nominal length of 200 mm. The k-Wave grid (Nx) was chosen as the medium of propagation with a nominal length of 200 mm. The k-Wave grid (Nx) was â&#x2C6;&#x2019;4. The defined as 6.561 Ă&#x2014; 1033 grids, the spacing (dx) was defined as 1.2 Ă&#x2014; 10â&#x2C6;&#x2019;4 ultrasonic wave parameters defined as 6.561 Ă&#x2014; 10 grids, the spacing (dx) was defined as 1.2 Ă&#x2014; 10 . The ultrasonic wave parameters were set up to achieve sensitivity of 0.1 °C. The sensor position for the simulation is given in were set up to achieve sensitivity of 0.1 â&#x2014;Ś C. The sensor position for the simulation is given in Figure 1.

Figure 1.

Figure 1. A-scan image of simulation.

Figure 1.

The ultrasonic velocity used is based on the temperatureâ&#x20AC;&#x201C;velocity relationship given by This is given as: Ihara et al. [22]. This v(T ) = â&#x2C6;&#x2019;0.636T + 5917.6 (6) (6) đ?&#x2018;Ł đ?&#x2018;&#x2021; = 0.636đ?&#x2018;&#x2021; + 5917.6 where v(T) is the temperature-dependent ultrasonic velocity and T is the temperature. where v(T) is the temperature-dependent ultrasonic velocity and T is the temperature.

The simulation was run over the range of 25 to 25.5 â&#x2014;Ś C to observe if the corresponding change in The simulation was run over the range of 25 to 25.5 °C to observe if the corresponding change time of flight can be reliably measured. Equation (6), which was used for the simulation, is almost in time of flight can be reliably measured.

Equation (6), which was used for the simulation, is almost linear for a temperature range of 0â&#x20AC;&#x201C;200 â&#x2014;Ś C [22]â&#x20AC;&#x201D;hence, in this simulation, the sensitivity is prioritized linear for a temperature range of 0â&#x20AC;&#x201C;200 °C [22]â&#x20AC;&#x201D;hence, in this simulation, the sensitivity is prioritized over range. The peak detection technique was used to record the time the ultrasonic pulse strikes the over range. The peak detection technique was used to record the time the ultrasonic pulse strikes the sensor at both the transmitting and receiving positions [20]. sensor at both the transmitting and receiving positions [20].

The second simulation was carried out to observe the individual effect of change in ultrasonic The second simulation was carried out to observe the individual effect of change in ultrasonic velocity and change in material dimension (expansion) on tof. This was performed in order to verify if velocity and change in material dimension (expansion) on tof. This was performed in order to verify the tof can be reliably estimated from the change in velocity alone, expansion alone or by combining if the tof can be reliably estimated from the change in velocity alone, expansion alone or by combining both. The ultrasonic velocity was varied using Equation (6), while material expansion was varied both. The ultrasonic velocity was varied using Equation (6), while material expansion was varied using Equation (7) given below: using Equation (7) given below: â&#x2C6;&#x2020;L = ÎąL â&#x2C6;&#x2020;TL (7) (7) Î&#x201D;đ??ż = đ?&#x203A;ź đ?&#x203A;Ľđ?&#x2018;&#x2021;đ??ż where â&#x2C6;&#x2020;L is the change in length, ÎąL is the linear coefficient of thermal expansion, â&#x2C6;&#x2020;T is the change in where Î&#x201D;L is the length, material ÎąL is the linear temperature andchange L is theinoriginal length.coefficient of thermal expansion, Î&#x201D;T is the change in temperature and L is the original materialusing length.

The third simulation was performed the phase-shift method, with the aim of obtaining the frequency pair which can consistently sense a 0.1 â&#x2014;Ś C change in temperature. This same simulation was modified for the MFcw method and, for this simulation, the length of material was scaled down by

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The third simulation was performed using the phase-shift method, with the aim of obtaining the 5 of 12 frequency pair which can consistently sense a 0.1 °C change in temperature. This same simulation was modified for the MFcw method and, for this simulation, the length of material was scaled down a of ten to to reduce computational load. byfactor a factor of ten reduce computational load.Also Alsousing usingthe thephase-shift phase-shiftmethod, method, aa simulation simulation was performed for a 15 mm piece of steel—this was performed to predict the possibility of using 5 MHz performed for a 15 mm piece of steel—this was performed to predict the possibility of the using the ◦ ◦ transducer to obtain 10 C arange 0.1 and C resolution.

5 MHz transducer toaobtain 10 °Cand range 0.1 °C resolution.

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Simulation Results Results 2.2. Simulation ◦ C, a tone burst of 1.2 MHz and sampling In In order order to to achieve achieve aa measurement measurement resolution resolution of of 0.1 0.1 °C, a tone burst of 1.2 MHz and sampling ◦ C and the tof for the whole range of frequency of 10 GHz were used.

The recorded tone burst at 25 frequency of 10 GHz were used. The recorded tone burst at 25 °C and the tof for the whole range of simulations simulations are are given given in in Figure Figure 22 and and Table Table 22 respectively. respectively.

Figure 2.

2. Recorded Figure Recorded tone tone burst. burst.

Table 2.

Table 2. Time of flight variation with temperature. temperature.

Temperature (◦(°C) C) Temperature

Velocity(m/s) (m/s) Velocity

Tof(µs) (µs) Tof

25.0 25.0 25.1 25.1 25.2 25.3 25.2 25.4 25.3 25.5

5901.70 5901.70

33.4372 33.4372

5901.63 5901.63 5901.57 5901.51 5901.57 5901.45 5901.51 5901.38

25.4

5901.45

33.4376

33.4376 33.4380 33.4384 33.4380 33.4388

33.4384 33.4392 33.4388

◦C

With 10 GHz sampling frequency, change in temperature will cause a change in time 25.5 a 0.1 5901.38 33.4392 of flight that can be resolved at the fourth decimal place of tof in microseconds. The costs of pulsers/receivers samplefrequency, at 10 GHzafrequency are considerably high.

With 10 GHzthat sampling 0.1 °C change in temperature will cause a change in time of of Ihara al., fourth the relationship between velocity andThe temperature flightFrom that the canfindings be resolved atetthe decimal place of ultrasonic tof in microseconds. costs of ◦ C [22], as is the effect from the change in distance from is almost linear within the range of 0 to 200 pulsers/receivers that sample at 10 GHz frequency are considerably high. thermal expansion.

The for relationship expansion and ultrasonic speedvelocity were performed over this From the findings ofsimulations Ihara et al., the between ultrasonic and temperature is linear result this simulation shown in Figure 3. almostrange. linear The within theofrange of 0 to 200is°C [22], as is the effect from the change in distance from

thermal expansion. The simulations for expansion and ultrasonic speed were performed over this linear range. The result of this simulation is shown in Figure 3.

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Figure 3. Effect of change in speed and expansion on tof.

Figure Figure 3.

3. Effect Effect of of change change in in speed speed and and expansion expansion on on tof. tof.

Figure 3 shows that the time of flight varied largely due to changes in velocity, while the Figure 33shows showsthat that time of flight varied largely to changes in velocity, the thethe time of flight varied largely due todue changes in velocity, while thewhile variation variation due to expansion is relatively smaller. Expansion across the range ◦of 0 to 200 °C is 480 µm variation due to expansion is smaller. relativelyExpansion smaller. Expansion the0 range 200µm °Cin is total 480 µm due to expansion is relatively across the across range of to 200 ofC0isto480 for in total for 200 mm steel. The tof can be reliably estimated by considering ultrasonic velocity while in total for 200 mm steel.

The tof can be reliably estimated by considering ultrasonic velocity while 200 mm steel. The tof can be reliably estimated by considering ultrasonic velocity while compensating compensating for expansion. compensating for expansion. for expansion.

The MFcw technique was used in the third simulation for the estimation of ultrasonic velocity.

The MFcw technique technique was was used used in in the the third third simulation simulation for for the the estimation estimation of of ultrasonic ultrasonicvelocity. velocity.

First, relatively low frequencies of 0.6 and 0.5 MHz were used to estimate ultrasonic velocity through First, relatively low frequencies of 0.6 and 0.5 MHz were used to estimate ultrasonic velocity through phase-shift—this is the TFcw technique. Thereafter, based on Equation (3), 0.5, 0.51 and 10 MHz were phase-shift—this isisthe Thereafter, based on Equation (3), 0.5, MHz were phase-shift—this theTFcw TFcwtechnique. technique.

Thereafter, based on Equation (3), 0.51 0.5, and 0.51 10 and 10 MHz used to improve the sensitivity of the simulation for a 0.1 °C change in temperature (MFcw). The ◦ C change used to improve the sensitivity of theofsimulation for a for 0.1 a°C0.1change in temperature (MFcw).

The were used to improve the sensitivity the simulation in temperature (MFcw). results for the simulations are given in the Figure 4a,b and Table 3 respectively. results for the are given in the 4a,b4a,b and and Table 3 respectively.

The results forsimulations the simulations are given in Figure the Figure Table 3 respectively.

(a) (a)

(b) (b)

Figure 4.

4. Two-frequency continuous wave method (TFcw) technique (a) 11.6 phase-shift at 0.6 MHz; Figure 4. Two-frequency continuous wave method (TFcw) technique (a) 11.6 phase-shift at 0.6 MHz; (b) (b) −110.3 −110.3 phase-shift at 0.5 MHz. (b) −110.3 phase-shift at 0.5 MHz.

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Table Simulation results using multiple frequency continuous wave method (MFcw) technique. 7 of 12 J. Manuf.

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PhasePhaseUsed Calculated PhaseTemperature Shiftfrequency continuous wave method (MFcw) technique.

Table 3. Simulation results using multiple Shift (10 Ultrasonic Ultrasonic Shift (0.5 (°C) (0.51 MHz) (°) Speed (m/s) Speed (m/s) MHz) (°) Calculated Used MHz) (°) Temperature Phase-Shift Phase-Shift Phase-Shift (10 Ultrasonic Ultrasonic ◦ ◦ ◦ ◦ ( C) ( ) (0.5198.54 MHz) ( ) −106.95 MHz) ( ) 5904.88 20 (0.5 MHz) −23.33 Speed (m/s) Speed (m/s) 5904.86 20.1 −23.261 98.61 −105.64 5904.825904.88 5904.8 5904.86 20 −23.33 98.54 −106.95 20.2 −23.2 98.67 −104.32 5904.75 5904.73 20.1 −23.261 98.61 −105.64 5904.82 5904.8 20.2 20.3 −23.2 98.67 −104.32 5904.695904.75 5904.675904.73 −23.13 98.74 −103.01 20.3 20.4 −23.13 98.74 −103.01 5904.635904.69 5904.615904.67 −23.06 98.81 −101.7 20.4 −23.06 98.81 −101.7 5904.63 5904.61 20.5 −23 98.88 −100.38 5904.56 5904.54 20.5 −23 98.88 −100.38 5904.56 5904.54 −22.93 98.94 −99.07 5904.5 5904.5 5904.485904.48 20.6 20.6 −22.93 98.94 −99.07 −22.87 99.01 −97.76 5904.445904.44 5904.415904.41 20.7 20.7 −22.87 99.01 −97.76 20.8 20.8 −22.8−22.8 99.08 −96.44 99.08 −96.44 5904.375904.37 5904.355904.35 20.9 20.9 −22.74 99.14 −95.13 −22.74 99.14 −95.13 5904.315904.31 5904.295904.29 21 −22.67 99.21 −93.82 5904.24 5904.22 21 −22.67 99.21 −93.82 5904.24 5904.22 The result result of The of the the simulation simulation with with 55 MHz MHz transducer transducer and and 15 15 mm mm steel steel plate plate is is given given in in Figure Figure 5.

5.

Figure 5. Phase-shift vs. temperature temperature for for 15mm 15mm steel.

From the results of the simulations, both the pulse-echo method and the phase-shift method were able to resolve 0.1 ◦°C C change in temperature. However, a pulser/receiver is needed to use the ◦ C change detection, the pulser/receiver needs samples at up to 10 GHz pulse-echo method. For a 0.1 °C change detection, the pulser/receiver €20,000 mark. However, However, for the phase-shift method, the cost and the cost of such device can reach the €20,000 detector is under under €400. €400. The Thephase-shift phase-shiftmethod method was waschosen chosenbecause because of ofits itscost costeffectiveness, effectiveness, of a phase detector therefore, the experiments described in Section 3 are all based on the phase-shift method. are all based on the phase-shift method.

3. Experiments Experiments 3.

3.1. Experimental Setup 3.1. Experimental Setup Based on results from the k-Wave simulations, a phase-shift experiment was set up as shown in Based on results from the k-Wave simulations, a phase-shift experiment was set up as shown in Figure 6.

Figure 6.

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Figure 6. Ultrasonic phase-shift experimental setup.

A A sinusoidal sinusoidal waveform waveform was was generated generated using using aa Spectrum Spectrum M2i.6022-exp M2i.6022-exp arbitrary arbitrary waveform waveform generator (Spectrum Instrumentation, Ahrensfelder, Grosshansdorf, Germany) .

The waveform generator (Spectrum Instrumentation, Ahrensfelder, Grosshansdorf, Germany) . The waveform was was then Devices, Norwood, Norwood, MA, MA, USA) USA) then sent sent to to the the input input A A port port of of the the Analog Analog Devices Devices AD8302 AD8302 (Analog (Analog Devices, phase phase detection detection board board and and the the transmitter transmitter probe probe of of aa 55 MHz MHz ultrasonic ultrasonic transducer. transducer. Using Using steel steel (type (type EN24T) as the medium of propagation, the received signal from the receiver probe of the transducer was then detector calculates thethe difference in then sent sent to to the theinput inputBBport portofofthe thephase phasedetector. detector.The Thephase phase detector calculates difference phase between the transmitted and the received signal and sends the voltage equivalent as the phase in phase between the transmitted and the received signal and sends the voltage equivalent as the difference value through the phase-out port of theofphase detector board.

To reduce noise fromfrom the phase difference value through the phase-out port the phase detector board.

To reduce noise ‘phase’ value, a low filterfilter was used to cuttooff high signals.

A 3.4 A Hz3.4 filter the ‘phase’ value, a pass low pass was used cut off frequency high frequency signals.

Hz was filterused, was however, a cut off frequency of similar value will give results.results.

An NI-9239 analogue input used, however, a cut off frequency of similar value willsatisfactory give satisfactory An NI-9239 analogue card Instruments, Austin, TX, USA) used data which was then stored input(National card (National Instruments, Austin, TX, was USA) wasfor used foracquisition data acquisition which was then using NI LabVIEW. A calibrated Maxim DS18B20 digital temperature sensor was used as reference stored using NI LabVIEW. A calibrated Maxim DS18B20 digital temperature sensor was usedand as the measured recorded using WinTCalusing software, whichsoftware, is proprietary research reference and temperature the measuredwas temperature was recorded WinTCal whichto is the proprietary group.

A PT100group. temperature sensor was usedsensor for monitoring resolution finer changes of 0.1 ◦ C. Using to the research A PT100 temperature was used finer for monitoring resolution changes aofthermostatic temperature controller, a ceramic heater was used to gradually change the temperature 0.1 °C. Using a thermostatic temperature controller, a ceramic heater was used to gradually change of steel workpiece predefined steps. ultrasonicsteps. transducer with a center frequency MHz thethe temperature of theinsteel workpiece in An predefined An ultrasonic transducer withofa 5center and approximate bandwidth of 3 MHz was used. The of the temperature on change the phase frequency of 5 MHz and approximate bandwidth ofeffect 3 MHz waschange used. in The effect of the in of the ultrasonic wave was recorded and will be discussed in the results section. temperature on the phase of the ultrasonic wave was recorded and will be discussed in the results

section.

3.2. Experimental Results 3.2. Experimental Results Using the setup described in Section 3.1, the AD8302 board was used to obtain the voltage equivalent values of phase-shift.

A typical showing theboard relationship between the phase output Using the setup described in Sectioncurve 3.1, the AD8302 was used to obtain the voltage (V) and thevalues equivalent phase difference (Degrees) is given in 7 and between 8, respectively.

Figure 7 is equivalent of phase-shift.

A typical curve showing theFigures relationship the phase output the response specified in the datasheet while Figure 8 was obtained experimentally using the same (V) and the equivalent phase difference (Degrees) is given in Figures 7 and 8, respectively. Figure 7 parameters as those used in forthe thedatasheet phase-shift experiments input, 40experimentally mV received signal and MHz is the response specified while Figure 8 −2 wasVobtained using the5 same ultrasonic frequency. parameters as those used for the phase-shift experiments −2 V input, 40 mV received signal and 5 MHz ultrasonic frequency.

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Figure 7.

7. Phase Phase Output vs.

Input Phase Difference [23].

Phase Output Output vs. vs. Input Input Phase Phase Difference Difference [23].

Figure

8. Phase InputPhase Phase Difference Difference using the experiment. experiment.

Figure 8.

Phase Output Output vs. vs. Input Input Phase Difference using the the same same parameters parameters for for the Figure

Based on on the the phase-shift phase-shift simulation, simulation, aa steel steel sample sample of of 15 15 mm mm (type (type EN24T) EN24T) was was used used for for the the Based ultrasonic experiment. experiment. With With aa 55 MHz MHz transducer transducer signal, signal, measurements measurements were were made made for for aa temperature temperature ultrasonic ◦ C. range of 20 to 30 °C. The choice of this temperature range is based on a typical temperature variation range of 20 to 30 °C. The choice of this temperature range is based on a typical temperature variation during manufacturing processes.

For the first experiment, temperature was varied in of manufacturing processes. processes. For For the the first first experiment, experiment, temperature temperature was was varied varied in in steps steps of ofsteps °C— during manufacturing 11 °C— ◦ ◦ ◦ 1thereafter, C—thereafter, another experiment was carried out the from the range ofto 21.5 to°C 23.5 C in°C C steps. another experiment was carried carried out from from the range of 21.5 21.5 to 23.5 °C in 0.1 0.1 °C0.1 steps.

The thereafter, another experiment was out range of 23.5 in steps.

The The ‘Phase Out’ values are the output from AD8032 phase detection board, which represents the ‘Phase Out’ Out’ values values are are the the output output from from AD8032 AD8032 phase phase detection detection board, board, which which represents represents the the phasephase‘Phase phase-shift between the transmitted the received ultrasonic signals.

The recordedphase phaseout out vs. vs. shift between between the transmitted transmitted and and the received received ultrasonic signals.

The recorded phase out vs. shift the and the ultrasonic signals.

The recorded temperatures for both experiments are given in Figures 9 and 10. are given in Figures 9 and 10. temperatures for both experiments are given in Figures 9 and 10.

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Figure 9. Results of 20 to 30 °C range in 1 °C steps (a) Phase output vs. temperature; (b) Residual plot. ◦C ◦ C steps (a) Phase Figure 9. Results of 20 to 30 °C temperature; (b) Residual plot. range in 1 °C steps (a) Phase output vs. temperature;

(a) (b) (a) ◦ C range in 0.1 ◦ C steps (a) Phase output(b) Figure10.

10.Results Resultsof of21.5 21.5to to23.5 23.5°C vs.temp; temp;(b) (b)Residual Residualplot. plot.

Figure range in 0.1 °C steps (a) Phase output vs.

Figure 10. Results of 21.5 to 23.5 °C range in 0.1 °C steps (a) Phase output vs. temp; (b) Residual plot.

Discussion 4.4.Discussion 4. Discussion The simulation, simulation, as as well well as as experimental experimental results, results, confirm confirm that that with with the the phase-shift phase-shift technique, technique, The temperature change in a material can be measured, these results agree with the reviewed literature and temperature change inasa material can be measured, these resultsthat agree with reviewed technique, literature The simulation, well as experimental results, confirm with thethe phase-shift otherother existing studies based based on the on dependence of ultrasonic velocity on temperature.

The achievable and existing the dependence of ultrasonic velocity on reviewed temperature.

The temperature changestudies in a material can be measured, these results agree with the literature measurement resolution as well as the range of measurement depend on the choice of frequency. achievable resolution as the welldependence as the rangeofofultrasonic measurement depend on the choiceThe of and other measurement existing studies based on velocity on temperature.

Ultrasonic frequencies for phase-shift measurement need to be chosen to suit the expected range of frequency. frequencies for phase-shift measurement need to be chosen to suit achievableUltrasonic measurement resolution as well as the range of measurement depend on the the expected choice of measurement and the useand of wideband transducers covering the expected range measurement can range of measurement the use of wideband transducers covering the of expected of frequency.

Ultrasonic frequencies for phase-shift measurement need to be chosen to suit therange expected reduce the cost of the test set up.

For this experiment, where a 15 mm steel plate was used,steel the range measurement can reduce and the cost theoftest set up. For this experiment, where 15 mm plate range of measurement the of use wideband transducers covering thea expected range of can be increased with the selection of suitable frequencies based on Equations (3) and (5).

Lower was used, thecan range canthebecost increased with the For selection of suitable frequencies on measurement reduce of the test set up. this experiment, where a 15 mm based steel plate frequencies will in a higher range, butresult within lower resolution.

It iswith possible use the TFcw Equations andresult (5). Lower will aselection higher range, but lowerto resolution. is was used,(3)the range can frequencies be increased with the of suitable frequencies basedIt on method with high frequency will improve both the resolution and the range. possible to (3) uselow theand TFcw method withtransducers—this lowwill andresult highin frequency will resolution. improve both Equations and (5).

Lower frequencies a higher transducers—this range, but with lower It is Two major limitations of theTwo AD8302 board are the of lack clarity on the are signthe oflack the phase difference the resolution and range. limitations theofAD8302 board of clarity onboth the possible to use thethe TFcw method major with low and high frequency transducers—this will improve based on the reading obtained from the phase output in voltage and the non-linearity experienced at sign of the phase difference based the limitations reading obtained from theboard phaseare output in voltage and the resolution and the range.

Two on major of the AD8302 the lack of clarity onthe the the extremes as shown in Figures 7 and 8.

It is possible to avoid the non-linear regions by carefully non-linearity experienced at the extremes shownobtained in Figures 7 and It is possible to voltage avoid the nonsign of the phase difference based on the as reading from the8.phase output in and the selecting the transducer frequency forthe thetransducer length of the material for to be measured. linear regions by carefully selecting frequency the length of theisto material whose non-linearity experienced at the extremes as shown in Figures 7whose and 8. temperature It is possible avoid the nonChanges in temperature can be measured over the linear region, even the sign of the temperature is by to be measured.

Changes inreliably temperature can beformeasured reliably the linear linear regions carefully selecting the transducer frequency the length ofwhen the over material whose phase is not known. region, even when sign of the Changes phase is not known. temperature is to the be measured. in temperature can be measured reliably over the linear

region, even when the sign of the phase is not known.

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5. Conclusions This study showed that an ultrasonic measurement of the speed of sound in a metal based on the phase-shift method can be used to obtain the core temperature of the metal with a resolution of up to 0.1 ◦ C. Based on simulation results of the two main ultrasonic measurement techniques—the pulse-echo and the phase-shift techniques—phase-shift is the less expensive technique for high resolution ultrasonic thermometry in metals. The two-frequency continuous wave method (TFcw) and multiple frequency continuous wave method (MFcw) are two improvements on the general phase-shift method for longer range and finer resolution measurements. A simulation was performed to observe the individual effects of expansion and change in ultrasonic velocity on time-of-flight. Based on the simulation, ultrasonic velocity can be relied upon for measuring time of flight and, where necessary, compensations can be made for the material expansion. Using a 5 MHz transducer, 15 mm steel plate and varying the temperature from 20 to 30 ◦ C, a voltage equivalent of phase difference was obtained. Overall, the results demonstrate that phase-shift ultrasonic thermometry can be used for core temperature measurement with a resolution of 0.1 ◦ C. A possible application of this study would be for temperature monitoring during co-ordinate metrology, such as on a co-ordinate measuring machine. As part of future work to deploy this setup in subtractive manufacturing, more experiments will be undertaken to understand the effects of swarf and coolant on ultrasonic thermometry. Future experiments will also be carried out to understand the effect of temperatures above 200 ◦ C on ultrasonic velocity. Also, as different materials have different physical properties, ultrasonic thermometry must be calibrated for the material of which the measurement is to be made. Future work will also address the possibility of using ultrasonic thermometry to measure the temperature of a region or a point within different materials. The use of switching algorithms to different frequencies for different materials and material sizes will also be researched.

Author Contributions: Formal analysis, O.F.O.; Funding acquisition, S.F.; Methodology, O.F.O. and S.F.; Software, O.F.O.; Supervision, S.F., A.P.L. and N.S.M.; Writing–original draft, O.F.O.; Writing–review and editing, O.F.O., S.F., A.P.L. and N.S.M. Funding: This research was funded by the UK’s Engineering and Physical Sciences Research Council (EPSRC), grant number EP/P006930/1.

Conflicts of Interest: The authors declare no conflicts of interest.

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