Future Metrology Hub Academic Publications covering Work Package 8

euspen’s 20th International Conference & Exhibition, CERN, Geneva, CH 2020 www.euspen.eu

Degradation monitoring of machine tool ballscrew using deep convolution neural network Nurudeen Alegeh 1, Abubakar Shagluf 1, Andrew Longstaff 1, Simon Fletcher 1 1Centre

for precision Technologies, University of Huddersfield

Nurudeen.Alegeh@hud.ac.uk

Abstract High-value manufacturing often requires a high level of accuracy. While this may be an achievable aim, the demands of consumers and end-users are also for the often competing targets of lower cost, greater efficiency and resource-lean products. Notwithstanding the ambition for higher accuracy, increased availability of production machines is a fundamental requirement to maintain competitiveness in the manufacturing industry. Ballscrews are a fundamental part of the transmission system for most high-value machine tools. They are therefore integral to the positional accuracy and performance of the machine and also represent a weaklink in terms availability. Hence, the state of the ballscrew is essential in determining machine accuracy and availability.

This work proposes a deep learning approach for ballscrew performance monitoring. The technique works such that remedial activities can be scheduled and carried out when degradation is detected before breakdown occurs. The deep learning algorithm uses convolution to distinguish between a worn and good ballscrew in a machine tool. The technique was tested on a five-axis gantrytype machine tool with two parallel axis ballscrew. The results from the test carried out indicates that an overall accuracy of 94 % can be achieved with this technique.

Ballscrew, condition monitoring, machine learning, deep learning.

1. Introduction Computer Numerical Control (CNC) machine tools used for production are required to operate within certain acceptable limits of tolerance, which become ever tighter with the availability of new enabling technology and greater customer drive. As industrial competition grows, more emphasis is increasingly being placed on both diagnosis and failure prevention, whilst predicting reliability and availability for manufacturing machines [1, 2]. This is due to an ever-growing need for tighter tolerances on manufactured components and on machine tools that can more reliably produce them [3].

No part is ever made perfectly and no measurement is exactly correct. Therefore, achieving tolerances on manufactured components is only assured if the sum of all sources of inaccuracies does not exceed the total tolerance. This in itself contributes to the discussion of machine accuracy, since it represents only one component of the total error budget for a manufactured product and solutions are often found by making compensating adjustments in other areas [4]. Herein lies the main argument against regular maintenance of the machine to preserve accuracy; a machine can continue to produce parts by adapting the process to suit changing conditions [5].

There is therefore often a reluctance to spend time understanding the error budget at a granular level if the overall statistical process control (SPC) results show good consistency [5]. However, such an approach is only viable where the same product is produced in sufficient quantity on a given machine to allow the process to be modified, based upon errors found on previous parts. Machines producing small numbers of differing

product down to “batch size one” require right-first-time-everytime.

This paper does not seek to provide a universal answer to the question of “the best” strategy but rather proposes a predictive method to detect ballscrews unforeseen failures. It exploits the already established framework of the bottom-up modelling solution for data-driven machine health monitoring systems [6].

The majority of machine tools are comprised of a number of linear axes, sometimes with the addition of rotary axes to increase flexibility and functionality. This paper focuses on the motion of linear axes, though the principles developed could easily be extended to other motion systems.

The translational motion for a machine tool linear axis can be achieved in several ways such as ballscrew and ballnut, rack and pinion, leadscrew, belt drive etc. However, ballscrews are most widely used in high-precision machines because of their high accuracy in converting rotary to linear motion [7] and low friction, leading to better dynamic performance and reduced backlash. They are also well suited to other precise position control and levelling systems, such as aircraft wings [8].

Ballscrews found in high-speed drive systems such as machine tools suffer from wear in the raceway and the ball-bearings and can generate excessive heat due to friction, thereby causing geometric and thermal deformation. These deformations adversely affect the machine tool accuracy [9]. Typically, ballscrew deterioration occurs due to wear under unbalanced operation, improper lubrication, or installation errors. At present, major ballscrew deterioration detection systems are either based on vibration or Acoustic Emission (AE) signatures as there is a direct link between vibration and noise levels associated with increased bearing deterioration [10].

The rest of this paper is arranged as follows; section 2 machine learning and its application to ballscrew monitoring. Section 3 discusses convolution neural network as it is applied in deep learning. Section 4 and section 5 deals with the experiment set up and results obtained respectively. And finally, the conclusion is outlined in section 6.

2. Machine learning applied to ballscrew monitoring The functional complexity of the ballscrew system makes machine learning algorithms a viable candidate to accurately model the non-linear characteristics of the ball screw degradation [11]. Machine learning is a data-driven method of modelling non-linear systems and it involves feature extraction and pattern recognition [12]. One of the most commonly used machine learning algorithms for monitoring the health condition of a ballscrew is the artificial neural network (ANN) [11].

Although, many researchers have used ANNs for condition monitoring and fault diagnosis with good results [13], their accuracy is greatly dependant on the feature extraction method employed. Hence, in order to effectively use neural network or more generally machine learning for that matter, good knowledge of signal processing techniques and fault diagnosis is mandatory. Applying good domain knowledge requires expertise that can deterministically identify and monitor every failure mode for every component on a machine tool, thus creating a potential source of error in the model.

This research seeks to establish methods that can be applied more efficiently to keep pace with rapid developments in mechanical, sensor and control technology. As such, a concept of deep learning first proposed in 2006 by Hinton and Salakhutdinov [13] has been investigated to overcome this deficiency. Many researchers have used deep learning for various diverse studies [14, 15]. Showing how effective and accurate deep learning can be in a wide variety of complex applications. This has led to the adoption of these techniques for fault diagnosis and condition monitoring [16]. In the field of predictive maintenance, deep learning has been used in several ways; scalable and unsupervised feature engineering method that uses vibration imaging and deep learning [16], a multiobjective deep belief networks ensemble for remaining useful life estimation in prognostics [17] and a deep learning approach for fault diagnosis of induction motors in manufacturing [18]. All of these research focus on induction motors, probably due to their prevalence in many sectors. However, very little research exists on the use of deep learning for the condition monitoring of ballscrew/ballnut assemblies [11].

A major advantage that deep learning offers over traditional machine learning, is the ability to perform feature extraction directly from the input data within the model. Hence, prior domain knowledge or expertise on the side of the algorithm designer is not required. A similar approach to the one proposed in this research has been used in the field of remote sensing [15], however, this implementation remains limited as only a single layer of feature extraction is used. Similar methods have also been used to develop a deep learning strategy for earth observation classification [19] (improving overall prediction accuracy from 83.1 % to 92.4 %) and for object classification [20]. Even with the success of such methods, there are very few relevant studies found addressing the CNC machine tool domain.

3. Deep Convolution neural (DCNN) The advent of DCNN and the emergence of large natural image database for vision-related classifications such as ImageNet [21] sets the stage for efficient image-based classifications. ImageNet

is a pre-trained convolution neural network originally designed by training about 15 million labelled images divided into about 22 thousand classes, which allows the DCNN to offer a rich and varied feature description from broad-spectrum images [21].

The condensed descriptions contained within these feature description works well for a set of diverse image classification tasks and performs better than typical classification methods.

These outcomes give sustenance to the idea that the descriptions from the DCNN are universal and aids transfer learning between different domains, especially where the amount of available data is limited [19].

In this paper, the DCNN used is derived from the ImageNet pre-trained networks. It is a deep learning neural network with ten layers; the first layer is the input layer, the last layer forms the output layer and the rest forms the hidden layers. Table 1 shows the DCNN architecture.

Table 1. The DCNN architecture

Layer

Description

Neurons

Dimension

1

Input

2

227X227X3

2

Convolution 1

96

11x11x3

3

Convolution 2

256

5x5x48

4

Convolution 3

384

3x3x256

5

Convolution 4

384

3x3x192

6

Convolution 5

256

3x3x192

7

Fully connected 1

4096

-

8

Fully connected 2

4096

-

9

Fully connected 3

2

-

10

Output

2

In the DCNN algorithm, the feature extraction is done internally within the algorithm by the convolution and the fully connected layers. It is initiated in layer 2, which corresponds to the convolution layer, with edge and colour detection at different angles.

The following is a description of the different layers of the model: The input layer – the input to the network is a coloured image file of size 227x227x3 with zero-centre normalization. The number of input neurons is determined by the number of classes to predict, in this case – there are two classes, which are the “good� and “worn� states of the ballscrew/ballnut. The network is presented with raw data files of acoustic emission obtained from ballscrews during operation (one worn and the other in good condition).

The hidden layer – the hidden layer performs the feature extraction and classification activities. The feature extraction is done by five convolution layers, while the classification is achieved by three fully connected layers.

Each of the hidden layers has a Rectified Linear Unit (ReLU), except for layer 9. The ReLU is a non-saturating non linearity function f(x) [20]. đ?‘“(đ?‘Ľ) = {

đ?‘Ľ, 0,

đ?&#x2018;Ľâ&#x2030;Ľ0 đ?&#x2018;Ľ<0

1

The ReLU performs a threshold operation to each element of the input such that any value less than zero is set to zero. DCNNs with ReLU trains six times faster than their equivalents without ReLU [20]. In layer 2 and layer 3, local response normalization is performed on the data via channel-wise normalization. This is

typically required before ReLU nonlinearity to aid data generalization.

Data down-sampling is achieved in layer 2, layer 3 and layer 6 by dividing the input into rectangular pooling regions and calculating the maximum of each region. This process is known as maximum pooling and it is observed that overlapping pooling helps reduce overfitting in models [22].

The fully connected layer performs the supervised learning on the extracted features received from the convolution layer based on the known classes. The first two layers have 4096 neurons each and perform random dropouts by setting to zero any input elements with a probability of less than half. The technique of performing dropouts reduces overfitting of data thereby improving the neural network [22]. This is done by randomly breaking up the co-adaptations that would normally develop in standard backpropagation supervised learning.

However, the use of dropout will lead to an increase in training time as the model without dropouts takes a longer time to converge.

The output layer â&#x20AC;&#x201C; the output presents the final classification according to the accuracy of the developed model. The number of neurons in the output will typically be equal to the number of classes required. This layer assigns each input to each of the two neurons (one for each class). The error function E(θ) used is the cross-entropy function for a 1-of-2 coding scheme [23], given by đ?&#x2018;&#x203A;

1 000, 2 500, 3 000, 5 000, 7 500, 9 000 and 10 000. Thirty data set was collected for each of the seven different speeds for both ballscrew. Figure 2 shows the Fast Fourier Transform (FFT) of the signal captured at 1 000 mm min-1 for the good and worn ballscrew. The good ballscrew shows more prominent frequency content at a higher amplitude compared to the worn one.

Figure 1. AE sensor on the healthy ballscrew nut

2

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2

đ?&#x2018;&#x2013;=1 đ?&#x2018;&#x2014;=1

Where tij indicates that the ith sample belongs to the jth class, yj(xi,θ) is the output for sample i, n the number of observations and θ is the parameter vector. The output yj(xi,θ) is the probability that the network associates the ith input with jth class, which is interpreted as P(tj = 1|xi). Also, the output unit activation function is given by a softmax function which satisfies the conditions 0 â&#x2030;¤ yj â&#x2030;¤ 1 and â&#x2C6;&#x2018;jyj = 1.

đ?&#x2018;Śđ?&#x2018;&#x2014; (đ?&#x2018;Ľ, đ?&#x153;&#x192;) =

đ?&#x2018;&#x2019;đ?&#x2018;Ľđ?&#x2018;? (đ?&#x2018;&#x17D;đ?&#x2018;&#x2014; (đ?&#x2018;Ľ, đ?&#x153;&#x192;)) â&#x2C6;&#x2018;đ?&#x2018;? đ?&#x2018;&#x2019;đ?&#x2018;Ľđ?&#x2018;? (đ?&#x2018;&#x17D;đ?&#x2018;? (đ?&#x2018;Ľ, đ?&#x153;&#x192;))

3

Figure 2. FFT of captured AE data for good and worn ballscrew

5. Results Note that the yj(x,θ) will remain unchanged with the addition of a constant term to all value of aj(x,θ), hence the error is the same in some directions in weight space [23].

4. Experiment set-up The experiments were conducted in a workshop environment on a five-axis CNC milling machine. The machine was chosen because the gantry is comprised of two ballscrews, one of which is in a good state of health and the other is worn. The AE sensor setup on the (good/worn) ballscrew of the CNC machine is shown in figure 1. The AE sensor used is a piezoelectric type with an integrated amplifier. The frequency response range is 100 000 Hz to 450 000 Hz and the normal operating temperature is between - 40 °C and 85 °C. The AE sensor was positioned as close as physically possible to the ballscrew nut. The experiment was designed such that the AE sensor continuously acquires data from the ballnut as the ballscrew axis moves. Testing was under a controlled motion from one end of the axis to the other, a distance of 2 200 mm.

Figure 1 shows the diagram of the machine tool with the AE sensor attached. Data were collected while this movement is repeated at different speeds, from low through moderate to high speed, within the normal operating speed in manufacturing. The speed/mm min-1 of movement included

The input to the DCNN is an image file, so in order to perform the DCNN analysis on the AE data obtained from the experiment, the input data is organised as a two-dimensional array of pixel values. The first convolution layer initialises the process of feature extraction by applying sliding filters to the input image such that it can learn from various features of the input data irrespective of their absolute location on the image. This is done by moving the filter along the vertical and horizontal coordinate of the input and performing the dot product of the learned weight and input and then adding a bias term [23]. Subsequent convolution layers and the fully connected layers perform highlevel combinations of the features learned in the previous layers.

The third fully connected layer is the final feature extraction stage that is used for classification.

The goal of the experiment is to show the effectiveness of DCNN to accurately predict the state of a ballscrew. For this purpose, the collected data was analysed using DCNN method and compared to Long Short Term Memory (LSTM) and various other machine learning algorithms namely: decision tree, support vector machine (SVM), K-nearest neighbour (KNN) and artificial neural network (ANN).

For the machine learning algorithms, feature extraction was performed before classification is done based on the extracted features. The extracted features are the mean value, root mean

square (RMS), skewness, kurtosis, single value decomposition (svd), and standard deviation (std). The extracted features consist of 420 observations. Using 80 % of the data for training and 20 % for validation to reduce the risk of overfitting. The result is shown in table 2, and It can be observed that the decision tree algorithm is the best performer at 87 %.

Table 2. Validation results

Model type

Accuracy/%

Decision tree

87

SVM

84

KNN

77

Neural network

75

LSTM

51

DCNN 94 At the classification stage, the DCNN is able to achieve an accuracy of 94 % from 420 observations and 20 % hold out validation.

6. Conclusion In this research paper, we have applied the deep convolution neural network (DCNN) for monitoring and detecting ballscrew degradation. The motivation for this work is to reduce the burden of explicit domain knowledge required to implement machine learning techniques. Such knowledge is difficult and expensive to apply and oversights can lead to errors in the model, missing potential sources of degradation. We showed that by formatting the input data as images, we are able to use DCNN to analyse and classify ballscrew health state. We were able to achieve a high rate of classification accuracy of 94 %. The main characteristic of this method is that it requires minimal data processing and still achieves a high rate of accuracy. We then compared the proposed algorithm with five other machine learning algorithms: decision tree, SVM, KNN, feed-forward neural network and LSTM recurrent neural network. The results obtained showed that the DCNN was able to improve the accuracy of the next best classifier (decision tree) by 7 %.

This work is focussed on the degradation of ballscrews in CNC machines for high-value manufacturing, where their condition can fundamentally affect the availability, performance and quality of the machine. Precision ballscrews are prevalent in many different applications, such as in aircraft, automotive brakes, robotics, etc. The proposed methodology is extensible to these applications.

The presented technique has shown the applicability of the method for the chosen problem domain. Future work will increase the granularity of classification to take into account the progressive stages of degradation which would make predictive maintenance more effective.

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) and the partners on the Innovate UK project “Metrology and Digital Manufacturing for Servitisation of Manufacturing Machine” (Grant Ref: 102787).

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Journal of Materials Processing Tech. 271 (2019) 584–598

Contents lists available at ScienceDirect

Journal of Materials Processing Tech. journal homepage: www.elsevier.com/locate/jmatprotec

Quantitative analysis of cooling and lubricating effects of graphene oxide nanofluids in machining titanium alloy Ti6Al4V Guangxian Lia, Shuang Yia, Nan Lia, Wencheng Panb, Cuie Wena, Songlin Dinga, a b

T

⁎

School of Engineering, RMIT University, Mill Park, 3082, Victoria, Australia Centre for Precise Technology, University of Huddersfield, Huddersfield, HD1 3DH, United Kingdom

A R T I C LE I N FO

A B S T R A C T

Associate Editor: E Budak

Ti6Al4V is widely used in industry due to its outstanding mechanical properties. However, the severe abrasion and high temperature at tool/chip and tool/workpiece interfaces cause various types of tool wear in machining Ti6Al4V. To ensure high machining efficiency and high quality of machined surface, cooling fluid is often used to reduce the cutting temperature and friction. In this paper, the cooling and lubricating effects of coolant with graphene oxide nanosheet suspension were investigated experimentally and theoretically. Cutting experiments were conducted to compare the performance of conventional coolant with that of the coolant with graphene oxide nanosheets of different weight percentages (0.1% and 0.5%). Cutting force and temperature on the rake face were measured in each cutting pass. A theoretical model based on computational fluid dynamics (CFD) was developed to investigate the temperature distribution and cooling efficiency quantitatively. Friction force and coefficient of friction at tool/chip interface and tool/workpiece interface were calculated to analyse the lubrication effects of different types of coolant. The results showed that the performance of cooling and lubrication of the coolant became better with the addition of graphene oxide nanosheets. Results from the analysis of flank wear and crater wear and the morphological characteristics proved that there was a significant further reduction in cutting temperature and friction force when coolant with graphene oxide nanosheets was used.

Keywords: Coolant Graphene oxide nanosheets Cooling Lubrication Cutting temperature Friction force Tool wear

1. Introduction Ti6Al4V is the most widely-used titanium alloy in industry due to its outstanding properties including low density, high strength and exceptional corrosion resistance (Oosthuizen et al., 2010). However, in machining Ti6Al4V, the harsh cutting conditions at the tool/chip and tool/workpiece interfaces result in various types of severe tool wear, which significantly reduce tool life and eventually cause the failure of the cutting tool. Furthermore, due to the low thermal conductivity (6.7 Wm−1K−1) and high strain rate, a huge amount of heat is generated in cutting Ti6Al4V (Amin et al., 2007); the high cutting temperature at tool/chip interface and tool/workpiece interface leads to thermal-induced damages on the cutting tool and machined surfaces. To increase the machining efficiency and ensure the quality of machined surface, coolant or metalworking fluid with excellent cooling and lubricating properties has to be used to reduce the cutting temperature as well as the friction at tool/chip and tool/workpiece interfaces.

Researches on developing new approaches to improve cooling and lubrication effects have been conducted for many years in both

academia and industry. Oil was the most widely-used cutting fluid in metal cutting processes decades ago (El Baradie, 1996a). Owing to their better performance in high-speed cutting, water-based cutting fluids replaced cutting oil later on (El Baradie, 1996b). Nowadays, various cooling methods including cryogenic cooling, minimum quantity lubrication (MQL) and coolant with nanoparticle suspension have been developed to achieve better cooling and lubrication effects (Debnath et al., 2014).

Cryogenic cooling uses liquid gas (generally liquid nitrogen LN2 ) to create an extremely-low-temperature environment (−150 ℃ to −180 ℃) to reduce the temperature in metal cutting processes (Yildiz and Nalbant, 2008). Dhananchezian and Kumar (2011) found, by comparing with that of using conventional coolant, the surface roughness was reduced by 35% and the tool life became 39% longer with the application of cryogenic cooling in turning Ti6Al4V. With the application of cryogenic cooling, Ahmed and Kumar (2016) found that surface roughness, cutting force and cutting temperature were reduced by 52%, 10% and 61% respectively in drilling Ti6Al4V. However, the complicated cooling devices and the strict safety requirement on storing

⁎

Corresponding author.

E-mail addresses: guangxian.li@rmit.edu.au (G. Li), s3516088@student.rmit.edu.au (S. Yi), s3468780@student.rmit.edu.au (N. Li), w.pan@hud.ac.uk (W. Pan), cuie.wen@rmit.edu.au (C. Wen), songlin.ding@rmit.edu.au (S. Ding). https://doi.org/10.1016/j.jmatprotec.2019.04.035 Received 8 October 2018; Received in revised form 14 April 2019; Accepted 24 April 2019 Available online 25 April 2019 0924-0136/ © 2019 Elsevier B.V. All rights reserved.

Journal of Materials Processing Tech. 271 (2019) 584–598

G. Li, et al.

5000 W⋅m−1⋅K−1 (Zhu et al., 2010). Both reasons made graphene oxide a type of promising material as added suspension in cutting fluid in metal-cutting processes. In the experimental research of Smith et al.

(2015), the temperature could be reduced by 50% by using the coolant with graphene oxide nanosheet suspension. Singh et al. (2018) investigated the influences of water-based graphene nanofluids with different mass concentration on the cutting temperature and surface roughness (Ra) in milling processes, and it was found that the Ra and temperature were significantly reduced with the increase in the mass concentration of graphene. In the cutting experiment conducted by Li et al. (2019), the nanofluid consisting of graphene and vegetable oil was applied in combination with MQL. They used Taguchi Method to investigate the influence of the hybrid coolant on surface roughness, hardness, cutting temperature and cutting force, and found that the improvement rates were 24.82%, 8.36% 13.59% and 18.13% respectively.

However, although the addition of nanoparticles in cutting fluids can improve the overall thermal properties of the coolant, the application of fluid with metallic nanoparticles could cause scratches on the machined surface due to the agglomeration of the hard nanoparticles.

Zhang et al. applied MoSe2 nanoparticles in MQL when grinding Nibased alloys (Zhang et al., 2016), and found that the roughness of machined surface increased when the cutting fluid with larger concentration of nanoparticles was applied. They concluded that the agglomeration of the hard nanoparticles could deteriorate the quality of machined surface. Similarly, in the experiment conducted by Nam et al.

(2011), the nanofluid consisting of 30 nm nanodiamond particles and oil were used in drilling Al6061. Scratches were found on the hole surface although the torque and thrust force were reduced when using diamond nanofluids.

Nanofluids can reduce both cutting temperature and cutting force; the types, sizes and concentration of the nanoparticles influence the performance of nanofluids in the cutting process. However, current research is limited to experimental investigations, most of the results on the performance of nanofluids are obtained via experimental results, there is a lack of in-depth theoretical analysis of the cooling and lubrication mechanisms of nanofluids. In this paper, the performance and mechanism of cooling and lubrication of coolants with graphene oxide nanosheet suspension were investigated quantitatively. A new hybrid FEM-analytical model was developed to describe the heat convection among the cutting tool, workpiece and nanofluids. The lubricant mechanism at two different tribo-systems, tool/chip interface and tool/ workpiece interface, were analysed and discussed. Additional turning experiments using conventional cutting fluids and graphene oxide suspended fluid were conducted. Titanium alloy Ti6Al4V was machined with PCBN inserts with both conventional coolant and cutting fluids with graphene oxide nanosheet suspension. The results of this research will provide useful information to the industry and pave the way for further research in this area.

a huge amount of liquid LN2 are the obstacles hindering the wide application of cryogenic machining in industry (Jayal et al., 2010). To meet the requirement of cleaner production, MQL was developed to avert the environment problem caused by the massive use of oil-based metalwork fluids. Compared with conventional coolant, the amount of cooling liquid used in MQL was significantly reduced but the ability of lubrication was increased. This made MQL a promising and eco-friendly cooling method in metal-cutting works (Sharma et al., 2016). However, it was also found by some researchers that the performance of MQL in cutting hard-to-machine materials was not as good as expected. For example, Su et al. reported that the cooling efficiency of MQL was limited in machining superalloys due to its low cooling capacity (Su et al., 2007); whereas in the turning experiment conducted by Leppert et al., it was found that the reduction of cutting force when using MQL was not obvious, compared with that of using conventional cutting fluids (Leppert and Peng, 2012).

Since the pioneering work made by Choi et al in 1995 (Choi, 2009), extensive research has been conducted on applying nanofluids as a new heat transfer fluid (Taylor et al., 2013). Commercial products of nanofluids for machining including turning, milling and drilling have already been available in the global market. These products have been applied by various companies in manufacturing industry and resulted in significant reductions of manufacturing costs (Derek, 2014). Nanofluids are applied in metal cutting works because of their better capability on enhancing the performance of heat transfer (Sidik et al., 2017). The thermal properties of the nanofluids are influenced by the types of nanoparticles and the volume or mass fraction (Phuoc et al., 2011).

Among different metallic oxides, Al2O3 nanoparticles were the widelyused compound in making nanofluids (Chandrasekar et al., 2012). It was found that Al2O3 of 13 nm with the volume fraction of 13% increased the thermal conductivity of water by 30% (Sharma et al., 2015). By adding nanoparticles of CuO, Al2O3 and ZnO2 with the weight fraction 40% (Vajjha and Das, 2009), Vajjha and Das found that the thermal conductivities of the nanofluids were increased by 60%, 69% and 48.5% respectively. In addition to metallic oxides, nanoparticles of other compounds have been attempted as well to make nanofluids with better physical and mechanical properties. For example, Li et al. (Li et al., 2014) added MoSe2 powders into oil-based coolant liquid to make mixed nanofluids in friction tests and found that the new nanofluids showed better friction-and-wear properties because of the formation of a tribofilm at the sliding interface. Gajrani et al. (2019) investigated the nanofluids consisting of commercial mineral oil and 0.3% nanoparticles (MoS2 and CaF2 ), and an average increase of 15% in the overall thermoconductivity of the cutting fluid was achieved. Sridharan and Malkin (Sridharan and Malkin, 2009) compared the performance of nanofluids which consisted of oil and two kinds of nanoparticles, carbon nanotubes (CNT) and MoS2 respectively, and found CNT nanofluids had better performance on lubrication compared with that of MoS2 nanofluids.

CNT nanofluids were often applied combinedly with MQL to improve the cooling and lubrication effects. In the experiment conducted by Prabhu and Vinayagam (2011), better surface finishing was obtained with the hybrid strategy (CNT nanofluids + MQL) in comparison with that of single MQL. The nanosheets of graphite have a unique lattice structure. This structure increases the contact area between the nanosheets and the friction pair, and provides better lubrication effect in metal-cutting processes (Lv et al., 2018). Huang et al. (2006) pointed out that adding graphite into oil and using it as cutting fluids could reduce cutting force and tool wear. The reduction in cutting temperature was 58% in the study conducted by Samuel et al. (2011), and the improvement of lubrication and the reduction of cutting force were 59% and 26% respectively. Similar to graphite nanosheets, graphene oxide is a kind of nano-material consisting of two-dimensional sheets. This material is hydrophilic and can be dispersed in water to form stable colloidal suspensions (Stankovich et al., 2007). Also, the graphene oxide nanosheets has a relative high thermal conductivity ranging from 600 to

2. Experiment 2.1. Experimental setup The experiment was conducted to investigate the cooling and lubrication effects of coolant with graphene nanosheet suspension in cutting processes. Three types of coolant were used in the experiment: conventional coolant (Con_Cool), coolant mixed with 0.1% weight percentage (w.t.) nanosheets (GraO_0.1%) and coolant mixed with 0.5% weight percentage nanosheets (GraO_0.5%). The base liquid for the nanofluids was industrial metalwork coolant (ROCOL Ultracut Clear) and the addition was graphene oxide nanosheets made by Sigma Aldrich. The properties of the metalwork coolant and added nanosheets were listed in Tables 1 and 2 respectively. Fig. 1(a) shows the morphology of graphene oxide nanosheets under transmission electron microscopy (TEM). To prepare the new coolant mixed with graphene 585

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2.2. Experimental results

Table 1 Property and composition of ROCOL Ultracut Clear.

Density (g/cm3)

Mineral oil

Natural oil

Water

Others

0.95

20%

20%

60%

< 1%

Fig. 3 presents the average cutting temperature measured at the position 1 mm away from the cutting edge. It was found that the temperature decreased with the application of GraO_0.1% and GraO_0.5, which proved the better cooling effect of graphene oxide nanofluids.

Specifically, under 1 bar pressure, the temperature reductions at different cutting speeds were averagely 15 ℃ and 35 ℃ when GraO_0.1 and GraO_0.5 were used. The larger reduction of temperature when using GraO_0.5 indicates that the better heat transferring capability of the nanofluid with high-concentration nanoparticles, which was in accordance with the result of Singh et al. (2018). Under the pressure of 10 bar, the cutting temperatures were lower with the application of low coolant pressure because more amount of heat was transferred away by the coolant with larger flow velocity. The pressure did not cause significant influence on the temperature reduction of GraO_0.1%. In contrast, the average temperature reduction under high pressure was 25 ℃ when using GraO_0.5%, which was smaller than that of under the pressure of 1 bar. Furthermore, the influence of the concentration of graphene oxide nanosheets on temperature was less obvious under 10 bar pressure, compared with the temperature reduction under 1 bar pressure. The reduction of temperature was within 10 ℃ when increasing the concentration of graphene oxide nanosheets at the cutting speeds of 80 m/min and 160 m/min. This phenomenon is consistent with the findings made by Smith et al. (2015) because the cooling ability of the nanofluids reached the threshold value when 0.5% graphene oxide nanosheets was added.

Fig. 4 shows the measured values of main cutting force and feed force in each cutting pass. From Fig. 4(a) and (b), it is found that the main cutting force decreased with the increase of the concentration of graphene oxide nanosheets in the cooling fluid, which agrees with the findings about nanofluids in cutting processes made by Zhang et al.

(2016). The force reduction was around 30 N and 40 N when the concentration of the coolant was 0.1% w.t. and 0.5% w.t (1 bar pressure).

The maximum reduction was found when the cutting speed was 80 m/ min, specifically, the main cutting force was reduced by 56 N and 87 N respectively when coolants of GraO_0.1% and GraO_0.5% were adopted. The main cutting force was smaller under the higher coolant pressure compared with that under the normal pressure. The average force reduction when using GraO_0.1% and GraO_0.5% were 20 N to 40 N. The reduction of main cutting force could be ascribed to the lubrication effect of nanofluids at the tool/workpiece interface. Based on the lubrication mechanism of Gajrani et al. (2019), the nanofluids could reach the friction interface due to the vibration of the tool and workpiece system. A tribo-film consisting of liquid and nanoparticles reduced the abrasion between the cutting tool and workpiece, which caused the reduction of main cutting force. In comparison, the influences of the type and the pressure of coolant on feed force were insignificant. The change of feed force did not present an obvious trend with the increase of the concentration of graphene oxide nanosheets.

Table 2 Properties of Sigma Aldrich graphene oxide nanosheets.

Purity

Thickness (nm)

Diameter (nm)

Layers

Specific surface area

99%

1-1.77

0.5-5

1-5

300-450

oxide nanosheets, the powder of nanosheets was weighed and added into 1 kg conventional coolant. Firstly, the graphene oxide nanosheets of different weights were mixed with 100 mL conventional coolant, and the 100 mL nanofluid was processed via ultrasonic vibration at the frequency of 25 kHz in order to break large blocks of nanosheets in the liquid. The 100 mL nanofluid was poured into the 1 kg Con_Cool afterwards and the mixed liquid was pumped for 30 min to make the nanosheets dispersed thoroughly in the liquid. The whole mixing process was repeated before every cutting test to ensure the uniform distribution of the nanosheets in the coolant. The samples of the three kinds of coolant used in the cutting experiment are shown in Fig. 1(b).

Ti6Al4V rods of the diameter of 20 mm were used as the workpiece, and CBN tools (SECO) with the 6° rake angle and 10° clearance angle were used in the experiments. Fig. 2(a) presents the experimental setup for the cutting test. The experiment was to turn the titanium alloy on a CNC vertical machining centre (HAAS VF1R160). To test the performance of the coolants at different cutting speeds and under different pressures, cutting speeds of 80 m/min, 160 m/min and 240 m/min were selected as the low, normal and high cutting speeds; whereas pressures of 1 bar and 10 bar were adopted as the low and high coolant pressures to test the performance of the nanofluids under two extreme pressures.

The cutting depth and feed rate were 0.1 mm and 0.05 mm/rev and they were fixed throughout the experiments.

In each cutting pass, the signals of main cutting force (Y direction/ tangential direction), feed force (Z direction/axial direction) and back force (X direction/radial direction) were obtained by the force measurement system including a 3-axis dynamometer (Kistler 9257B), an amplifier (Kistler 5070 A), a DAQ card (National Instrument 6036E) and the software program SignalExpress. Also, a K-type thermocouple (OMEGA 5TC-TT-K-40-36) was used to measure the average temperature in each cutting pass. A slot was machined near the tool tip via wire electrical discharge machining to fix the temperature sensor on the rake face. The thermocouple was then calibrated by using a thermocouple calibrator (MS7220) to ensure the accuracy and reliability of the measurements. The forces and temperatures when they became steady during the cutting process (Fig. 2(b) and (c)) were recorded as cutting force and cutting temperature for analysis in Section 2.2.

Fig. 1. (a) Morphology of graphene oxide nanosheet under transmission electron microscopy (b) three kinds of coolant.

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Fig. 2. (a) Experimental setup of the cutting test (b) measured cutting force (c) measured temperature.

Fig. 3. Measured cutting temperature under different cutting conditions (a) temperatures under1 bar coolant pressure (b) temperatures under 10 bar coolant pressure.

The forces under different cooling conditions fluctuated around 63 N when cutting speeds were 80 m/min and 160 m/min. Minor increments on feed forces could be found at the cutting speed of 240 m/min.

the heat transfer during the cutting processes. It is known that the status of liquid flow including temperature T and pressure p is governed by the continuity equation, the momentum equation and energy equation (Tu et al., 2018). In this study, the cooling process in cutting was solved as a two-dimensional problem; therefore, the governing equations of the dynamic coolant are simplified as follows:

3. Analysis of cooling effects 3.1. Modelling of the cooling process

Continuous equation: To further investigate the cooling effects of three kinds of coolant theoretically, a hybrid CFD-analytical model was developed to describe 587

∂u ∂v + =0 ∂x ∂y

(1)

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Fig. 4. Cutting forces under different cutting conditions (a) main cutting forces under 1-bar coolant pressure (b) main cutting forces under 10-bar coolant pressure (c) feed forces under 1-bar coolant pressure (d) feed forces under10-bar coolant pressure.

proportion of the heat is transferred to the cutting tool via the tool/chip interface. The modelling of heat source was based on the theory proposed by Komanduri and Hou (2001). Specifically, the temperature rise on the tool side was caused by the heat transfer from stationary rectangular heat source to the tool rake face via the tool/chip contact region, and the boundary on the tool side (OD) is adiabatic (Fig. 5(b)). As a result, a line heat source with the length of tool/chip contact should be modelled at the tool/chip interface. To ensure the availability of the calculation in ANSYS, the heat source was modelled as a narrow groove (1 μm) and the gap between the heat source and the tool rake face was controlled to be close enough (Fig. 5(c)). The heat was transferred by convection processes at the interfaces of coolant fluid and tool faces, and the boundary conditions on the faces of the tools (DA, AB, BC and CO) can be presented by Eqs. (5)–(7).

Momentum equation ⎧ ρ ⎛u ∂u + v ∂u ⎞ = − ∂p + μ ⎛ ∂2u + ∂2u ⎞ 2 ⎪ ∂x ∂y 2 ⎠ ∂y ⎠ ⎪ ⎝ ∂x ⎝ ∂x : ⎨ ∂p ∂ 2v ∂ 2v ⎪ ρ ⎛u ∂v + v ∂v ⎞ = − + μ⎛ 2 + 2 ⎞ ⎪ ⎝ ∂x ∂ ∂y ⎠ y ∂ y x ∂ ⎝ ⎠ ⎩ ⎜

⎜

⎟

⎜

⎟

⎜

⎟

⎟

(2)

∂T ∂T ∂ 2T ∂ 2T ⎞ Energy equation: ρc ⎛u + v ⎞ = K⎛ 2 + x y x ∂ ∂ ∂ ∂y 2 ⎠ ⎝ ⎠ ⎝ ⎜

⎟

⎜

⎟

2

2

∂v ⎞ ⎫ ⎧ ⎛ ∂u ⎞2 ⎛ ∂v ⎞ ⎤ ⎛ ∂u + + μ 2⎡ ⎥ + ∂x + ∂y ⎬ ⎨ ⎢ ⎝ ∂x ⎠ ∂ y ⎝ ⎠⎦ ⎝ ⎠⎭ ⎩ ⎣ (3) ⎜

⎟

⎜

⎟

where u and v are the two orthogonal directions in Cartesian coordinate system.

The simulation of the cooling process was conducted in ANSYS Fluent, the sketch of workpiece, chip flow, cutting tool and coolant fluid were modelled in SOLIDWORKS 2017, and then imported and meshed in ANSYS Meshing. When developing the CFD model, the status of coolant fluid follows the following assumption:

OD : Qtool − chip = Ktool

∂ 2T ∂v

DA: Qcoolant _ 1 = Hcoolant1

AB: Qcoolant _ 2 = Hcoolant2

1 the liquid of coolant is incompressible and viscous; 2 the change in density, viscosity, and thermal conductivity of the coolant liquids are negligible; 3 the heat exchanges at the interfaces are stable.

BC: Qcoolant _ 3 = Hcoolant3

In a metal cutting process, heat is generated by the shear deformation of workpiece material in primary deformation zone and by the tool/chip friction in the secondary deformation zone, and a

CO: Qcoolant _ 4 = Hcoolant4

588

u = 0, 0 ≤ v ≤ vD

∂ 2T ∂v

u = 0, vD ≤ v ≤ vA

(4)

(5)

∂T ∂u∂v

0 ≤ u ≤ uB, v = vA

(6)

∂T ∂u∂v

u = uB, 0 ≤ v ≤ vB

(7)

∂ 2T ∂u

v = 0,0 ≤ u ≤ uC

(8)

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Fig. 5. (a) the CFD model of the cooling process in ANSYS R16.0 (b) boundary conditions at the faces of the cutting tool (c) stationary plane heat source on the side of the chip.

Table 3 Physical and thermal properties of different kinds of coolant.

Coolant

Density

Con_Cool GraO_0.1% GraO_0.5%

0.94 0.94 0.94

q=

Thermal conductivity

Specific heat

(W.m−1 K−1)

(J. g−1℃−1)

0.249 0.253 0.267

3.24 3.24 3.24

(K ):

KGraO − KCon

(ρ):

Qprimary = Fs Vs = (Fz cosθ − Fx sinθ)

(13)

Qsecondary = Ff Vc = (Fx cosα − Fz sinα )

(14)

K GraO _ Cool

Cool ⎡ 3 + 2φ K ConCool = K ConCool ⎢ ⎢ 3 − φ KGraO − KConCool KGraO ⎣

Density

(12)

where Ltool − chip is the tool/chip contact length.

As introduced in the aforementioned section, the rise of tool temperature was caused by the heat transferred from the stationary heat source via the tool/chip interface. Fig. 6(a) shows the heat transfer to the cutting to via the tool/chip interface. The total amount of heat transferred to the cutting tool (Q) was influenced by both the heat generated in primary deformation zone Qprimary and in secondary deformation zone Qsecondary (Yan et al., 2014). Qprimary and Qsecondary can be calculated as follows:

Density, thermal conductivity and specific heat of the coolant changed with the concentration of graphene oxide nanosheets, which can be calculated with the following equations (Behroyan et al., 2016; Hadadian et al., 2014; Zhou and Ni, 2008), and the results are listed in Table 3.

Thermal conductivity

Q Ltool − chip

⎤ ⎥ ⎥ ⎦

(9)

ρGraO _ Cool = (1 − φ) ρCon _ Cool + φρGraO

(10)

Specific heat (C ): CGraO _ Cool φ (ρGraO •CGraO ) + (1 − φ)(CCon _ Cool•ρCon _ Cool ) = ρGraO _ Cool

where, Fs , Ff , Vs , Vc stand for shear force in primary shear zone, friction force at tool/chip interface, the shear velocity and the velocity of chip flow on rake face respectively (Fig. 6(b)). R chip is the partition of the heat to chip flow, and the value was set as 0.82 based on the empirical results of relevant experiments (Egana et al., 2012). Qprimary and Qsecondary were calculated by adopting the measured cutting forces, geometric parameters and the cutting speeds, and the results are listed in Table 4 The flow chart in Fig. 7 shows the processes of calculation and validation. The heat flux q, which is the main input for CFD analysis, was calculated based on the analytical model with MatLab2016R by adopting the cutting parameters and cutting forces measured in the experiments. Combining the pre-calculated properties of three kinds of coolant, the heat transfer model could be solved to obtain the temperature distribution on the tool rake face. The calculated results were

(11)

where φ is the weight percentage of the graphene oxide nanopowder.

Heat flux to the cutting tool via the tool/chip interface was calculated by the established analytical model. The heat flux q in the 2-D heat transfer problem is calculated with the following equation: 589

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Fig. 6. (a) Heat generation and transfer in cutting processes (b) forces, velocities and geometric parameters in orthogonal cutting.

compared with the averages of measured temperature to validate the hybrid analytical-CFD model.

3.2. Calculated results Fig. 8 presents the temperature distribution on tool/chip interface within the range of 0–2 mm along the direction which is vertical to the cutting edge. To validate the model, the temperature at the position of the thermal couple was extracted to compare with the measured data (Table 5). The error was within 20%, which means that the calculated results of temperature are acceptable. From the distribution of temperature, it was found that the temperature on tool rake faces reduced significantly at the position away from the cutting edge, and the addition of graphene oxide nanosheets did not affect the trend of temperature change. Furthermore, it can be found that the highest temperature at the tool/chip interface decreased significantly with the addition of graphene oxide nanosheets. Specifically, the maximum reduction in temperature at tool/interface can reach 100 ℃ when 0.5% w.t. graphene oxide was added into the coolant under the 1 bar coolant pressure although the temperature reduction at the measured position was only 30 ℃. Under the higher pressure, the largest temperature reduction was nearly 60 ℃ when the cutting speed was 240 m/min.

To comprehensively investigate the cooling effect of different types of coolant, the ratio between the heat transferred to the cutting tool (Q ) and the heat transferred away by the coolant (Qc ) within the range of 0–2 mm was calculated. In the following equation, Qc and Q are the integration of the heat flux qint2 and qint1 within their corresponding regions, L1 is the tool/chip contact length and L2 is the length of the

Fig. 7. Calculation and validation processes.

tool/coolant interface which equals to (2- L1) mm.

L

R=

∫ 2 qint 2 (l) dl Qc = 0L Q ∫0 1 qint1 (l) dl

(15)

The calculation was conducted via the post processor of ANSYS R16.0, and the results are presented in Fig. 9. Different from the temperature which was influenced by the concentration of graphene oxide nanosheets, the ratios are all around 7% without any obvious distinction. This means that the addition of graphene oxide nanosheets does not increase the proportion of the heat transferred away by the cutting fluids.

Table 4 Qprimary and Qsecondary (W) under different cooling conditions.

Qprimary Coolant pressure

1 bar

10 bar

Cutting speed

80 m/min

160 m/min

240 m/min

80 m/min

160 m/min

240 m/min

Con_Cool GraO_0.1% GraO_0.5%

233.53 163.35 133.1

330.17 248.23 180.75

388.41 290.4 228.69

134.31 114.95 98.01

231.36 163.88 139.78

268.62 203.28 145.2

Qsecondary Coolant pressure

1 bar

10 bar

Cutting speed

80 m/min

160 m/min

240 m/min

80 m/min

160 m/min

240 m/min

Con_Cool GraO_0.1% GraO_0.5%

51.87 61.18 49.21

130.34 143.64 114.38

200 200 192

67.83 73.15 58.52

140.98 146.3 127.68

212 220 204

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Fig. 8. Distribution of temperature on tool rake face at different cutting speeds and coolant pressure.

3.3. Cooling mechanism

Table 5 Calculated temperature and experimental data.

Pressure

1 bar

It is believed that the cooling is the combined effects of different heat exchange processes including conduction, convection, evaporation and very little radiation (Yan et al., 2015). Among these types of heat transfer, the forced convection between the cutting tool and coolant is the dominant process that transfers the heat away (Daniel et al., 1996).

The heat transfer coefficient describing the heat convection is the function of Nusselt number, Reynolds number and Prandtl number, which is presented in the following form when machining cylindrical workpieces (Holman, 1989),

10 bar

Coolant

V (m/ min)

Exp (℃)

Cal (℃)

Err (%)

Exp (℃)

Cal (℃)

Err (%)

Con_Cool

80 160 240

113 140 165

96 128 153

15 8.6 7.3

86 112 143

69 99 126

19.8 11.6 11.9

GraO_0.1%

80 160 240

91 125 156

79 109 133

13.2 12.8 14.7

73 99 129

60 87 113

17.8 12.1 12.4

GraO_0.5%

80 160 240

75 107 131

64 89 113

14.7 16.8 13.7

66 93 109

54 79 96

18.2 15 11.9

h = f (Nu, Re , Pr ) =

Nu (Re , Pr ) K D

(16)

In this study, the fluid flow of coolant was considered as coolant jet ejected to the cutting tool and workpiece surface. With this flowing status, the Nusselt number Nu could be determined with the values of Reynolds number, Prandtl number and the geometric parameter G 591

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Fig. 9. The ratio of heat transferred away by the coolant at different cutting speeds (a) under 1 bar coolant pressure (b) under 10 bar coolant pressure.

cutting edge, and l axis is parallel to the cutting edge. Mathematically, the transformation of cutting forces from the global coordinate system to the oblique coordinate system was conducted by using the rotating matrix [TM], as presented in the following equations:

which is determined by the size of workpiece and the position of jet stagnation point (Martin, 1977):

Nu = 2GRe 0.5Pr 0.42 (1 + 0.005Re 0.55)0.5

(17)

For cylindrical workpieces, the Reynolds and Prandtl numbers are determined by the properties of the coolant liquid (thermal conductivity K, density ρ , specific heat cp and the dynamic viscosity μ ) and the size of workpiece material (D), which are presented in the following equations (Holman, 1989):

Reynolds number

Prandtl number

(Re ):

(Pr ):

ρVD Re = μ Pr =

⎡ Fx ⎤ ⎡ Fl ⎤ ⎢ Fm ⎥ = [TM ] ⎢ Fy ⎥ ⎢F ⎥ ⎢ Fn ⎥ ⎣ ⎦ ⎣ z⎦

(20)

(18)

cosθn 0 − sinθn ⎤ ⎡ [TM ] = ⎢− sinθs sinθn cosθs − sinθs cosθn ⎥ ⎢ cosθ sinθ sinθs cosθs cosθn ⎥ s 0 ⎦ ⎣

(21)

(19)

Therefore, the three force components in the new coordinate system are calculated as follows:

μcp K

⎧ Fl = −Fx sinθs sinθn + Fy cosθs − Fz sinθs cosθn Fm = Fx cosθs sinθ0 + Fy sinθs + Fz cosθs cosθn ⎨ Fn = Fx cosθn − Fz sinθn ⎩

Based on Eqs. (16)–(19), it is found that the addition of graphene oxide nanosheets in coolant can hardly cause obvious changes to the status of heat convection (h) as the difference in the properties of the three types of coolant is insignificant, and this is in consistence with the results presented in Fig. 9. As a result, the heat transferred away by the coolant was not the only reason contributing to the reduction of cutting temperature. It is well known that the heat in metal cutting processes is generated by the chip formation (shear deformation of workpiece in material primary deformation zone) and the tool/chip abrasion in the secondary deformation zone (Abukhshim et al., 2006). According to the calculated results in Table 5(a), obvious reduction in the amount of heat generated in the primary deformation zone was found with the increase of the concentration of graphene oxide nanosheets, leading to the decrease of temperature at tool/chip interface. The energy of shear deformation was strongly influenced by the shear force which is a component of the main cutting force. For this reason, it can be concluded that the reduction in cutting temperature was caused by the decrease of main cutting force due to the better lubrication of coolant with graphene oxide nanosheets, which will be introduced and discussed further in the following section.

(22)

As shown in Fig. 10(b), on the rake face, the friction force and the force normal to the rake face are equal to Fn and Fm respectively; as a result, the friction coefficient μrake is presented as follows:

μrake =

frake Nrake

=

Fx cosθn − Fz sinθn Fn = Fm Fx cosθs sinθ0 + Fy sinθs + Fz cosθs cosθn

(23)

Similarly, the friction coefficient on flank face μflank can be calculated using the following equation:

μflank =

f flank Nflank

=

Fz cosαn − Fx sinαn Fz sinαn + Fx cosαn

(24)

Fig. 11 shows the calculated friction forces and friction coefficients on flank faces under different cutting conditions. A reduction in friction force on flank face in the range of 25%–50% could be found when the coolant with graphene nanosheet was applied. Specifically, the friction forces in using GraO_0.1% were reduced by 56 N, 32 N and 35 N compared with that of using conventional coolant when the pressure was 1 bar. The friction force was reduced by over 40% with the application of coolant GraO_0.5% indicating better lubrication effect of the coolant with larger concentration of graphene oxide nanosheets. Under higher coolant pressure, the reduction in friction forces was significant as the application of high pressure coolant increased the amount of lubricating liquid at the friction area (da Silva et al., 2013). Also, friction force decreased with the increase of the concentration of graphene nanosheets in the coolant, and the percentage of reduction was around 35%–50% at different cutting speeds and coolant pressures when GraO_0.5% was applied. Similar to the change of friction force, friction coefficient decreased with the application of graphene nanosheets as well in the coolant under different cutting conditions (Fig. 11(c) and (d)). However, the concentration of graphene nanosheet did not cause

4. Analysis of lubrication effect 4.1. Calculation of friction force and friction coefficient In a cutting process, friction happens on the rake face and flank face due to the tool/chip and tool/workpiece abrasion. To investigate the lubrication effects on tool surfaces, the friction forces and friction coefficients on flank face and rake face were calculated when using different types of coolant. As presented in Fig. 10(a), to calculate the friction coefficients on different faces, the three components of the resultant cutting force F in the global coordinate system (XYZ) were firstly transferred into the oblique cutting system. In the new coordinate system, the m axis and n axis form the plane which is vertical to the 592

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Fig. 10. (a) The global coordinate system and oblique cutting coordinate system (b) Forces in oblique plane.

10 bar, and it was around 45 N when using GraN-0.1 under both 1 bar and 10 bar pressures. The difference in friction forces caused by using three types of coolant was insignificant. As for the coefficient of friction on the rake face, the concentration of graphene oxide nanosheets did not cause too much difference at the low and normal cutting speeds.

Smaller friction coefficients were found when conventional coolant was applied, and the reduction was 0.34 (240 m/min, 10 bar).

significant difference in friction coefficient; the reduction was basically within 0.1 when the concentration of graphene oxide nanosheets was increased from 0.1% to 0.5%.

The change of friction force and friction coefficient on rake face was different from that on flank face (Fig. 12). Generally, both friction force and friction coefficient on flank face were relatively larger when the coolant with graphene oxide nanosheets was used. Under the 1 bar coolant pressure, the friction force increased with the increase of the concentration of graphene oxide nanosheets, however, the increment was within 10 N. Also, the effect of coolant pressure on the friction forces of rake face was insignificant. The friction forces fluctuated around 50 N when using conventional coolant under the pressure of

4.2. Lubrication mechanism Based on the calculated results, it is obvious that the lubrication effects were not the same at the two interfaces (the tool/chip interface

Fig. 11. Calculated frictional forces and friction coefficients on flank faces: (a) friction force at 1 bar coolant pressure (b) friction force at 10 bar coolant pressure (c) friction coefficient at 1 bar coolant pressure (d) friction coefficient at 10 bar coolant pressure.

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Fig. 12. Calculated frictional forces and friction coefficients on rake faces: (a) friction force under 1 bar coolant pressure (b) friction force under 10 bar coolant pressure (c) friction coefficient under 1 bar coolant pressure (d) friction coefficient under 10 bar coolant pressure.

Fig. 13. Lubrication mechanism (a) the proposed lubrication mechanism (Sharma et al., 2018) (b) the lubrication mechanism in this study.

and the tool/workpiece interface). On the flank face, the significant reduction in friction forces when GraO_0.1% and GraO_0.5 were used reflects that the addition of graphene improved the lubricating effects of coolant. However, on the rake face, the minor difference of friction force indicates that the addition of graphene oxide nanosheets did not reduce the tool/chip friction. To explain the difference of lubricating performance, the mechanism of lubrication on the two faces has to be analysed. Sharma et al. studied the lubrication mechanism of graphene nanosheets (Fig. 13) and concluded that graphene oxide nanosheets penetrated into the interfaces with the coolant liquid, and the laminate structure of graphene oxide was easily exfoliated by the shear forces forming a tribo-film at the sliding interfaces (Sharma et al., 2018). This conclusion was proved by the reduction on the development of flank

wear with the application of coolant with graphene nanosheets when cutting speed was low (around 70 m/min). However, considering the characteristic of different sliding interfaces as well as the ability of penetration of the cooling fluid, according to the findings made by Childs (2006), the liquid films cannot be formed along the tool/chip interface when cutting speed is high due to the intensive tool/chip contact and high cutting speeds. Moreover, the stress distribution on the rake face and flank face are different. As shown in Fig. 13(b), the normal stress on rake face σrake was larger than the normal stress on flank face σflank (Grzesik et al., 2014), which made the coolant jet hardly penetrate into the tool/chip interface. Therefore, the coolant can only reach to the end of tool/chip contact area due to the intensive interaction between tool rake face and chip back surface. This explained 594

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Fig. 14. Flank wear of the cutting tools under different coolant conditions (a) Con_Cool (b) GraO_0.1% (c) GraO_0.5%.

Fig. 15. Flank wear of the cutting tools under different coolant conditions (a) Con_Cool (b) GraO_0.1% (c) GraO_0.5%.

Fig. 16. Roughness of machined surface under different cutting conditions (a) 1-bar coolant pressure (b) 10-bar coolant pressure.

was significantly improved because both higher coolant pressure and larger concentration increased the amount of nanosheets in the lubricating process.

why the coolant pressure and concentration had minor influence on the friction force on rake faces. In comparison, the coolant can reach the tip position and results in better lubrication effects on flank face, which is reflected by the significant reduction in friction forces. When coolant pressure was increased or the coolant with higher concentration of graphene nanosheet was applied, the lubrication effect on flank face 595

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Fig. 17. Crater wear of the cutting tools under different coolant conditions.

Fig. 18. Worn areas of tools under different types of coolant: (a) Con_Cool (b) GraO_0.1% (c) GraO_0.5.

investigated by analysing the width of flank wear (VB) and the roughness of machined surface (Ra), both of which were measured by the Alicona microscope (Measurement Suite). The VBs of the three tools were 96 μm, 81 μm and 78 μm respectively when conventional coolant and coolants with graphene nanosheets of different concentrations were applied (Fig. 15). The reduction of 15% and 20% in VB proved the better lubrication ability of coolants with graphene oxide nanosheet suspension, which is in consistence with the reduction of friction force and friction coefficient in Section 4.1. Also, the lubrication condition when using different types of coolant was reflected by the roughness of machined surface (Ra). As shown in Fig. 16, values of Ra were smaller

5. Tool wear analysis Tool wear can directly reflect the effects of cooling and lubrication as the adhesive-abrasive process is strongly influenced by the cutting temperature and chip-tool-workpiece friction (Li et al., 2017). As presented in Fig. 14, tool wear caused by abrasion and adhesion was found on the rake face and major flank face, the conditions of the flank wear and crater wear of the tools with different kinds of coolant were different.

Flank wear is the material loss on the flank face mainly caused by the tool/workpiece abrasion. The condition of flank wear was 596

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influence of the addition of graphene oxide nanosheets on heat convection process was limited.

Both friction force and friction coefficient on flank face were reduced significantly with the addition of graphene oxide nanosheets because the smaller normal pressure made the nanosheets easier to penetrate into the tool/workpiece interface reducing the tool/workpiece abrasion. On tool rake face, the change of friction force under different types of cooling conditions were insignificant as the coolant can hardly reach the tool/chip interface due to the intensive tool/chip interaction.

Morphological characters on the worn areas reflect the cooling and lubrication effects of the three coolants. The improved lubrication ability and cooling effect of coolant when using the graphene oxide nanosheets were shown by the reduced VB and K c respectively.

However, similar values of Ltc proved the minor influence of graphene oxide nanosheet on abrasion at tool/chip interface.

with the using of GraO_0.1% and GraO_0.5%, this was in consistent with the experimental results on nanofluids of graphite-based nanoparticles (e.g. (Li et al., 2019)). The values of the surface roughness with Con_Cool were generally over 120 nm under different pressures. In contrast, the surface roughness of GraO_0.1% and GraO_0.5% were below 120 nm under different cutting conditions and this that the tool/ workpiece abrasion was reduced with the addition of graphene nanosheet. Especially, when using GraO_0.5%, the largest roughness was merely higher than 100 nm, and the reduction on Ra was 30–60 nm (over 30%) compared with that of Con_Cool. This is similar to the findings made by Singh et al. (2018) because more lattice structured graphene were conveyed to the interface between flank face and workpiece surface, lubricating the tool/workpiece abrasion during the cutting processes.

Crater wear is stimulated by the high stress and temperature at tool/ chip interface resulting in the loss of tool material and the adhesion of workpiece material on the rake face (Li et al., 2018). The worn areas on rake faces were examined by Alicona (Measurement Suite), as shown in Fig. 17, it was found that the size of the worn area was reduced with the increase of the concentration of graphene oxide nanosheets. The depth of the crater (K c ) and the tool/chip contact length (Ltc ) were two factors describing the condition of tool wear on rake face. Based on established models, K c was the function of temperature (Huang and Dawson, 2005) and Ltc mainly reflected the status of tool/chip abrasion (Bahi et al., 2012). In our experiments, it was found that K c decreased with the addition of graphene oxide nanosheet in coolants, which indicated the reduction of the temperature at tool/chip interface. The tool/chip contact lengths (Ltc ) of the three tools are similar (around 180 μm). This indicates that the influence of graphene oxide nanosheet on abrasion at tool/chip interface was insignificant because the graphene oxide nanosheets could hardly penetrate into the interface due to the intensive tool/chip contact.

Fig. 18 shows the morphological characters of worn area when using different types of coolant; defects caused by the adhesive-abrasive process were found on rake faces of tools. BUE were found on all three tools because of the blunt cutting edges. The abrasive areas within the worn areas show that the tool/chip abrasion on the three faces was severe. Surface near the tool/chip contact area was burned, which means the temperature of chip flow when using conventional coolant was much higher than that of using the coolant with graphene oxide nanosheets. Also, the adhesion layer was found near the cutting edge of the tool with the coolant GraO_0.5%. In contrast, the adhesion layer on the other tools was not obvious. Because of the higher temperature at the tool/chip interface, the removal of the adhesion layer as well as the part of adhered material by the chip flow became easier.

Acknowledgements The paper is partially supported by the Australian Research Council (DP180100762). The authors acknowledge the facilities, and the scientific and technical assistance of the RMIT Microscopy & Microanalysis Facility (RMMF), a linked laboratory of Microscopy Australia.

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The International Journal of Advanced Manufacturing Technology (2020) 107:4645â&#x20AC;&#x201C;4659 https://doi.org/10.1007/s00170-020-05346-2

ORIGINAL ARTICLE

A prediction model for the milling of thin-wall parts considering thermal-mechanical coupling and tool wear Ge Wu 1 & Guangxian Li 1 & Wencheng Pan 2 & Xu Wang 1 & Songlin Ding 1 Received: 17 February 2020 / Accepted: 16 April 2020 / Published online: 1 May 2020 # Springer-Verlag London Ltd., part of Springer Nature 2020

Abstract In thin-wall milling processes, the interactions between cutting loads and the displacement of the thin-wall part lead to varying tool-workpiece engagement boundaries and undesired surface form errors. This unavoidable issue becomes more severe in the machining of titanium alloys due to their poor machinability caused by the low thermal conductivity, high strength and high chemical reactivity. This paper presents a new predictive model to calculate the cutting-induced thermal-mechanical loads and workpiece deflection in milling Ti-6Al-4V thin-wall components. The cutting heat sources and the development of tool flank wear were considered in the modelling process to improve the prediction accuracy. The cutting loads were modelled analytically and calculated using an efficient iterative algorithm, and the deformation of the thin-wall part was simulated through a finite element model. A series of cutting experiments were conducted under various cutting conditions to validate the predicted results.

Both the cutting forces and thin-wall displacement were recorded to examine prediction accuracy, and good agreements have been achieved between the measured results and simulated outcomes. The predicted cutting forces in the radial, feed and axial directions are within errors of 14%, 10% and 5%, respectively, concerning the experimental values. Meanwhile, the maximum predicted deformation errors at the initial, middle and end portions of the workpiece are less than 20%.

Keywords Thin-wall milling . Deformation prediction . Finite elementâ&#x20AC;&#x201C;analytical model . Tool flank wear . Thermal-mechanical coupling

1 Introduction Thin-wall components made of titanium alloys are widely used in the automotive, aeronautical and aerospace industries. In the milling process, the low rigidity of thin-wall components and cutting-induced loads may cause deformation of the thin walls, which result in the deviation of tool-part engagement boundaries from the nominal positions and lead to unavoidable surface form errors. Ti-6Al4V is one typical kind of difficult-to-machine materials due

* Ge Wu s3636981@student.rmit.edu.au Wencheng Pan W.Pan@hud.ac.uk 1

School of Engineering, RMIT University, Melbourne, Victoria 3082, Australia

2

Centre for Precision Technologies, School of Computing and Engineering, University of Huddersfield, Huddersfield, UK

to its poor thermo-mechanical properties. The low thermal conductivity causes the accumulation of large amounts of cutting heat in the cutting region, which results in high cutting temperature [1], whereas the high chemical activity leads to severe adhesion and diffusion wear of the cutting tool. Therefore, the prediction of the cutting loads and deformation of the workpiece in the milling of titanium thinwall components is of significant importance.

In the last decades, many efforts have been made to solve the deformation, or geometrical deviation, problem in milling thin-wall components. In these studies, the cutting force model is an essential tool for both deformation prediction and process optimization, and the outcomes of the force model can be used as a fundamental database for prediction of tool/workpiece deflection, machining stability, stress distribution and surface integrity. According to published literature, many force models have been proposed for helix end mill [2â&#x20AC;&#x201C;6]. Usually, these models were established by mechanical and analytical methods. In most mechanical models, the cutting edges of the tool were discretized into a finite number of elements along the axis direction and the cutting action of each

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slice was modelled as the oblique cutting process. The cutting force components of each slice were calculated from specific cutting coefficients obtained from experimental results [7].

Thus, the accuracy of the model depended on the calibration and fitting of the specific cutting coefficients obtained from a large number of experiments with various cutting conditions.

Meanwhile, this method is only valid for a given toolworkpiece pair. Therefore, many studies devoted to developing analytical models in which the orthogonal cutting theory was extended to oblique cutting through equivalent plane approach, and mathematical relations between force components, tool geometry, material behaviour and cutting conditions were established [4, 8â&#x20AC;&#x201C;10]. Similarly, each cutting tooth was discretized into a series of infinitesimal slices in these models, and the cutting action of each slice was equivalent to the classical oblique cutting process. Compared with mechanical models, analytical models were more efficient, and these models can be applied to various cutting conditions.

Apart from the calculation of cutting forces, tool wear is another critical issue that needs to be considered, especially in machining of titanium alloys. The poor machinability of titanium alloys usually leads to severe tool damage. Previous studies have shown that under the condition of tool wear, additional cutting loads have a significant influence on the interaction of tool and workpiece [11, 12]. In order to develop worn tool force models that can provide accurate prediction, detailed discussion about the nature of tool flank wear was proposed by Usui et al. [13] and Smithey et al. [14]. In these studies, the linear relation between the width of the plastic flow region and total wear land was studied, and the worn tool force models for both turning and milling process were established. Sun et al. [15] developed a 3D milling force model under the effects of tool flank wear. Hou et al. [16] proposed a wear recognition method of flat end mill for milling of difficult-to-cut materials. Liang and Liu [17] and Liang et al.

[18] investigated the effects of tool wear on the plastic deformation; prediction models of the plastic deformation depth induced by additional thermo-mechanical stress considering tool flank wear were proposed. Li et al. [19] investigated the mechanism of flank wear of PCD tools and developed an analytical model by considering the combined effects of tool/workpiece dynamic characteristics and properties.

Concerning cutting loads, cutting heat has also been taken into account in the milling process. During the milling process, cutting heat is generated due to plastic deformation of workpiece material and frictional effect between tool and workpiece. The cutting heat could not be ignored in metal cutting since it seriously affects the integrity of the finished surface, material properties and tool wear conditions. In metal cutting, heat partition ratios and temperature rise on chip and tool were determined analytically through functional analysis, and several analytical cutting temperature modelling approaches have been proposed [20â&#x20AC;&#x201C;23]. Yan et al. [24]

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presented an analytical model of the effect of tool flank wear on thermal stresses and residual stress. Further, better prediction results of the workpiece temperature distribution were achieved for end mill by the study of Lin et al. [25]. In a more recent study, the temperature predictive model in intermittent milling process with continuously varying chip thickness was proposed by Sun et al. [26].

However, above studies were carried out for normal turning or milling process and they were under the assumption of rigid workpiece without considering workpiece deformation. To solve the issues in thin-wall milling process, Budak and Altintas [27] analysed the variations of workpiece structure and the disengagement of tool-workpiece when predicting the peripheral milling process of flexible structures. Ratchev et al. [28] presented an integrated method for prediction of workpiece deflection during milling of low-rigidity parts. Based on the previous work, it was recognised that the flexible force model and iterative algorithm have a direct impact on the accuracy of prediction results. Thus, several algorithms associated with the flexible model in the peripheral milling of the thin-wall component have been presented. Wan and Zhang [29] developed a general model that considers the contact conditions of tool-workpiece and iterative corrections of radial cutting depths as well as the rigidity of workpiece. Kang and Wang [30] established two new efficient iterative algorithms including the flexible iterative algorithm and a double iterative algorithm. Inspired by these algorithms, an improved flexible iteration strategy was presented by Sun and Jiang [31] to predict the force-induced deformation and varying engagement boundaries.

It can be seen that the majority of previous studies on the thin-wall milling process focused on the force-induced errors, chip temperature rise and 3D-FEA analysis, while few literatures regarding tool wear and multiple cutting loads exist. Therefore, this paper presents a more accurate machining error prediction model that focused on cutting loads induced deformation in milling of thin-wall components. In the proposed model, a theoretical cutting force model of helical milling tool was developed based on the oblique cutting analysis. The influence of tool flank wear was considered to meet the actual cutting conditions, so the basic cutting force model was extended to include the effects of tool flank wear. This model also considered the combined impact of both the primary and tertiary heat sources and predicts the thermal deformation of the workpiece based on the FEA method. The workpiece deflection was predicted using a flexible iterative algorithm considering the feedback effect of deformation and tool-workpiece engagement variation. The calculation of cutting loads and simulation of part deformation were implemented in MATLAB and ABAQUS software. The accuracy of the model was demonstrated by force and displacement

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measurements in real time during milling of Ti-6Al-4V thin-wall workpiece under various machining conditions.

2 Dynamical cutting loads in thin-wall milling process In this study, the thin-wall milling process was modelled with the consideration of the dynamic cutting forces, the development of tool wear, the thermal-mechanical coupling effect and the real-time deformation of the thin-wall part.

2.1 Forces in oblique cutting processes In order to simplify the complex tool geometry and toolworkpiece engagement, the cutting teeth of the helical tool were discretised into a finite number (n) of axial elements with equal thickness along the tool axis and each axial segment has a length of dz = ap/n, as shown in Fig. 1. For an infinitesimal element {i, j} of the cutting tooth, the cutting action can be represented with the oblique cutting mechanism, and {i, j} presents the cutter node which is the intersection of ith cutting tooth and jth horizontal mesh line. The index of the tooth i = 1, 2, …Nf, where Nf is the total number of cutter tooth. The index of the axial elements j = 1, 2, …n, where n is the number of axial elements.

Fig. 1 Material removal process in thin-wall milling

In this model, the cutting planes and parameters are defined in the local coordinate of cutting tool. The instantaneous tangential, Ft(ϕi, j), radial, Fr(ϕi, j) and axial Fa(ϕi, j) cutting forces acting on element {i, j} can be presented as functions of cutting edge oblique angle λs, shear strength τs, uncut chip thickness h(ϕi, j), oblique shear angles (ϕn, ϕe), oblique rake angles (γn, γe), oblique friction angles (βn, βa) and resultant force direction (θn, θe) [3]:

τs bh ϕi; j cosðβn −γn Þ þ tanηc sinβn tanλs qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F t ϕi; j ¼ sinðϕn Þ cos2 ðϕn þ βn −γn Þ þ tan2 ηc sin2 βn

τs bh ϕi; j sinðβn −γn Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

F r ϕi; j ¼ sinðϕn Þ cosλs cos2 ðϕn þ βn −γn Þ þ tan2 ηc sin2 βn

τs bh ϕi; j cosðβn −γn Þtanλs −tanηc sinβn qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F a ϕi; j ¼ sinðϕn Þ cos2 ðϕn þ βn −γn Þ þ tan2 ηc sin2 βn

ð1Þ where b is the width of cut and h(ϕi, j) is the varying chip thickness determined by the immersion angle ϕi, j.

Apart from the calculation of shearing forces, the effect of tool wear has also been taking into account. Tool wear occurs due to the continuous rubbing contact and plough effect between the tool flank surface and workpiece surface, resulting in additional friction force generated in the contact area. Only Rotation

Deformed workpiece Undeformed workpiece

Feed Deflected contact line

(i,j+1)

Initial contact line

(i,j) dz

z x o

y

X Y

Z

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tool flank wear was considered and discussed in this model because it contributes most significantly to the temperature rise of the workpiece. The contact area of flank wear land and workpiece is shown in Fig. 2.

Taking into account the effects of tool flank wear, the cutting forces can be expressed as the superposition of the cutting forces attributed to the shear effect and those attributed to the effect of rubbing contact. The forces under the effect of tool flank wear are analysed in cutting direction and thrust direction. As a result, the instantaneous cutting forces can be modified as: 8 0

> < F t ϕi; j ¼ F t ϕi; j þ F tw 0 ð2Þ F ϕ ¼F ϕ þF > r 0i; j r i; j rw : F a ϕi; j ¼ Fa ϕi; j where Ftw and Frw are the feed component force and rubbing force respectively, which can be calculated by integrating the flow stress along the length of wear land [18]:

F rw ¼

F tw

8 0 0 > VB −x2 0 VB > > ∫ σ dx b 0 > 0 < 0 VB

0

VB < L*VB

0 2 2 > 0 0 > VB −x 0 VB −L* 0 VB 0 > VB > σ0 dx þ b ∫VB0 −L* σ0 dx VB ≥ L*VB : b ∫0 0 VB VB pffiffiffiffi 8 0 τ 0 0 > VB 1− σ0 > VB −x2 0 VB 0 0 > b0 ∫ > ffi μσ0 τ 0 dx þ b ∫ 0 pffiffiffi dx VB < L*VB < 0 0 τ0 VB 1− σ VB 0 ¼ ffi 0 2 2 > τ0 0 > 0 VB0 −L*VB pffiffiffi > VB −x 0 VB 0 σ0 > p ffiffiffi ffi : b ∫0 τ 0 dx þ b ∫VB0 −L* τ 0 μσ0 dx VB ≥ L*VB 0 VB σ0 VB

ð3Þ where b′ and VB′ are the effective contact width and the effective wear band width on the contact area in oblique cutting. σ0 and τ0 are the normal and tangential stresses that can be obtained from the modified Oxley’s force model. μ is the friction coefficient at the tool-workpiece contact area. L*VB is the critical length of flank wear land, and this value for a fixed toolworkpiece material pair can be obtained by experimental observations [14].

Fig. 2 Tool flank wear land in oblique cutting

0 0 With the determination of elemental forces F t ϕi; j , F r

0 ϕi; j and F a ϕi; j , the component forces within the reference Cartesian-Coordinate can be calculated by the following transformation: 8 0 9 8 9 > = < F t ϕi; j > < F x ϕi; j = 0 F y ϕi; j ð4Þ ¼ T F ϕ i; j r > : ; ; : 0 > F z ϕi; j F a ϕi; j where Fx(ϕi, j), Fy(ϕi, j), Fz(ϕi, j) are forces in the feed, normal and axial directions. T is the transformation matrix defined as: 2

−cosϕi; j T ¼ 4 sinϕi; j 0

−sinϕi; j −cosϕi; j 0

3 0 05 1

ð5Þ

On any infinitesimal segment of the cutting tooth, the differential forces acting on this segment can be expressed as:

d F d ðϕ; zÞ ¼ F d ϕi; j ðzÞ dz ðd ¼ x; y; zÞ ð6Þ In order to calculate the total cutting forces on each tooth, the differential cutting forces on the jth segment of ith tooth are integrated along the axial direction as following:

zu ð7Þ F d ði; jÞ ¼ ∫zl F d ϕi; j ðzÞ dz ðd ¼ x; y; zÞ where zu and zl are the upper and lower limits of z-axis boundaries for element {i, j}.

In the cutting force model of helix end mill cutter, the immersion-dependent upper and lower axial limits of z-axis boundaries can be defined as [27]:

1 2πði−1Þ ϕ1;0 − −ϕen ψi; j Nf

1 2πði−1Þ zl ¼ ϕ − −ϕex ψi; j 1;0 Nf

zu ¼

ð8Þ

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Overall, the instantaneous cutting forces acting on multiple cutting edges can be obtained by integrating the total differential forces along each tooth:

n n f f F x ϕi; j ¼ ∑N Fy ϕi; j ¼ ∑N i¼1 ∑ j¼1 Fx ði; jÞ; i¼1 ∑ j¼1 Fy ði; jÞ;

n f Fz ϕi; j ¼ ∑N i¼1 ∑ j¼1 Fz ði; jÞ

ð9Þ

2.2 Modelling of thermal loads A huge amount of cutting heat is generated due to the plastic deformation of workpiece material, tool/chip and tool/workpiece friction during the cutting process of metallic materials. Since the cutting heat affects material properties and thermal stress which are crucial to the prediction of thin-wall deflection, the dynamic thermal load has to be calculated in the model.

As shown in Fig. 3, there are three heat sources in the milling process: the primary deformation zone, the secondary deformation zone at the tool/chip interface and the tertiary deformation zone at the tool/workpiece interface. The total heat generated can be expressed as the sum of heat generated in the three deformation zones: Qgen ¼ Qs þ Q f þ Qr

ð10Þ

where Qs is the amount of heat generated in the primary deformation zone, Qf is the amount of heat generated in the secondary deformation zone due to the friction effect and Qr is the amount of heat generated in the tertiary deformation zone due to the rubbing effect.

However, not all the heat is consumed in the raising of the workpiece temperature. In the milling processes, a proportion of heat generated in the primary deformation zone and tertiary deformation zone is transferred to the chips and cutting tool. And most of the heat generated in the second deformation zone is moved away by the cutter and continuous chip flow due to the extrusion and friction on the tool-chip interface, which has little influence on the

V Chip

Tool

Secondary heat source Tertiary heat source Coolant applied here

Primary heat source

VB

Workpiece

Fig. 3 Heat generation in the cutting process

Heat loss

temperature rise of workpiece. Therefore, the total thermal energy flows into workpiece during the milling process can be expressed as follows: Qgen ¼ ð1−R1 ÞQs þ ð1−R3 ÞQr

ð11Þ

where R1 and R3 is the partition coefficient of heat energy conducted into chips and tool in the primary deformation and tertiary zones, respectively.

The heat flux in the primary deformation zone and tertiary deformation zone is expressed with the following equations: 8 Q Fs Vs Fs Vs > > qs ¼ s ¼ ¼ > > b h J As J As > > J < cosλs sinϕn ð12Þ Qr Fr Vr Ftw V > > q ¼ ¼ ¼ 0 > 0 r > J Ar J Ar > VB b > : J cosλs cosλs where Fs, Fr, V, VS and Vr are the shear force, the frictional force, the cutting velocity, the component of cutting velocity along the shear plane and the component of cutting velocity along the flank face, respectively. As and Ar are the contact area in the shear plane and tool flank surface and J is the heat equivalent work.

The shear force Fs and shear velocity VS are calculated with the following equations [25]: h i 12 F s ¼ ð Fa cosλs −Ft sinλs Þ2 þ ð Fa cosλs cosϕn −Fr sinϕn þ Ft cosλs cosϕn Þ2 cosλs cosγe V Vs ¼ cosηc cosðϕe −γe Þ

ð13Þ The heat partition coefficients R1 and R3 can be estimated using oblique moving rectangular heat source method and stationary plane heat source model [20], and also Blok’s and Venuvino’s approach [32].

2.3 Modelling of flexible cutting forces In thin-wall milling, the cutting forces are continually influenced by the deflection of workpiece and variation of workpiece rigidity because the geometry of the tool/workpiece engagement is constantly changed. As presented in Fig. 4, cutting parameters of each element such as the instantaneous chip thickness and radial cutting depth deviate from the nominal values and need to be modified with regard to the deformation of thin wall. Therefore, the flexible model was developed with the consideration of workpiece deflection, which could increase the accuracy of the predictive results.

Based on the results of previous studies, only the correction of the radial cutting depth is considered in this work, namely, the variations of the immersion boundary [33]. At each en0 gaged cutting element, the actual immersion starting angle ϕen

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Fig. 4 Illustration of thin-wall deflection behaviour

in down milling after deflection can be determined by solving the following equation:

0 2aem 0 −1 ϕen ¼ π−cos 1− ð14Þ R 0

and actual radial cutting depth 2aem can be calculated as: 0

2aem ¼ ae −δw

ð15Þ

where δw is the normal workpiece deviation due to the action of cutting loads, and ae is the desired radial cutting width. δw can be obtained using thermo-mechanical finite element analysis. The immersion starting angle ϕen is then submitted into Eqs. 8 and 9, the varying upper limit and cutting loads is solved by the iterative algorithm.

For the global iteration scheme, the initial calculated cutting loads are applied on each cutting unit, and the real deflection along current cutting location can be obtained from the FEA solver. Then the tool is rotated to the next feed position, and the cutting loads are corrected by revising the radial cutting depth and immersion angle. The updated cutting loads are applied on the new cutting unit to perform the subsequent simulation, so that corrected part deflection can be obtained.

This routine will be repeated until the required precision is achieved, and analyses of all cutting locations are obtained.

After the deformation results of the main cutting positions are obtained, the interpolation method is employed to find out the complete displacement error of the part.

To improve iteration efficiency and reduce the time to achieve the convergence condition, a more effective iterative algorithm is employed in this study [30]. As shown in Fig. 5, the oblique blue lines represent tool-workpiece engagement boundaries, and red oblique lines represent the in-cutting edge at each iteration step.

Fig. 5 Modelling of tool-workpiece engagement boundaries

At the first axial position, the initial position of the first iteration is D01 E01 . Once the iteration begins, the cutting edge will move repeatedly and get closer to its actual position after each iterative step. After kth step, the cutting tooth reach the convergence position Dk11 Fk11 , and the point Fk11 will be the corrected in-cutting position. After the first iteration convergence, CA1 and DB becomes the new engagement boundary.

Then D02 F02 is taken as initial position for the iteration process instead of D02 E02 . Based on this method, the first iteration step of cutting tooth at nth (n ≥ 2) iteration is defined as D0n F0n , n−1 n−1 Fkn−1 . This method could improve which satisfied D0n F0n =Dkn−1 the algorithm efficiency since the initial position of each iteration is closer to the final convergence position. In Fig. 5,

Dknn Eknn represents the in-cutting edge at nth iteration, δknn and aknn are the deflection of workpiece and actual radial cutting depth at kth iteration step. During the iterative process, the actual radial cutting depth aknn is iteratively updated as: aknn ¼ ae −δknn −Δδ

ð16Þ

where Δδ can be solved by the geometrical relationship as:

ae −δknn cosλs sinγ Δδ ¼ ð17Þ ðγ þ sin λ s Þ D

A kn −1 γ ¼ tan δn −δn = ap −hn δnA and hD n are the displacement value of upper point A and distance from Dkn to D01 at nth cutting position, respectively.

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Cutting Forces

Cutting Heat

Workpiece Deforma on

Proper es of Workpiece Material

Actual Radial Cu ng Depth

proposed cutting load model and FE model. The iteration of each step would stop when the following condition is achieved, namely, the in-cut edge is close enough to its convergence position, k k −1 a n −a n ≤ ε n n

Fig. 6 Interrelation of cutting loads and part deformation

where ε is the tolerance that is applied to control the precision of the calculation.

Meanwhile, the actual immersion starting angle ϕkn is corrected as:

2ak ϕkn ¼ π−cos−1 1− n ð18Þ R

3 FE modelling of thin-wall machining process

Based on above equations, workpiece deflection δkn and corrected cutting loads can be obtained iteratively using Fig. 7 Outline of flexible cutting load model and thermalmechanical coupling

Based on the established theoretical model, the instantaneous cutting loads acting on the workpiece can be obtained, which are then applied as the inputs for the FE model to simulate the deflection of the workpiece. MATLAB programs have been

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4652 Table 1

Temperature-dependent properties of Ti-6Al-4V

Temperature (°C)

Density Thermal expansion (10−6/ ° (Kg/m3) C)

Thermal conductivity (w/m°C)

Heat capacity (J/Kg°C)

Young’s modulus (GPa)

Poisson’s ratio

25 100 200 300

4420 4406 4395 4381

2.9 3.0 3.4 3.8

7.0 7.45 8.75 10.15

546 562 584 606

114.7

0.34

105.3

0.35

400 500 600 700 800 900 1000 1100 1200

4366 4350 4336 4324 4309 4294 4282 4267 4252

4.1 4.4 4.8 5.4 5.7 6.3 6.9 7.3 7.65

11.35 12.6 14.2 15.5 17.8 20.2 19.3 21 22.9

629 651 673 694 714 734 641 660 678

89

0.37

developed to calculate the cutting loads for different cutter geometries and machining conditions. The finite element model of thermal-mechanical coupling can be developed using the finite element solver ABAQUS. For simplification, the thinwall part is assumed to be a low-rigidity rectangular part with the same geometries and material properties of the real workpiece. The inputs to the FEM model are the material properties, calculated cutting loads, various cutting parameters and

75 72.3

0.43

64.6

boundary conditions. The cutting loads are treated as movingdistributed loads and discretised to the relevant nodes of the machined surface. Consequently, the deflection and dynamic characteristic of the machined part could be obtained.

3.1 Application of cutting loads and material removal In the FE analysis, the calculated cutting forces and heat sources were applied as input to the current cutting units in each time step, and the cutting loads were unloaded from the previous cutting units when the tool moves to the next cutting position. The thermal-mechanical coupling analysis was performed to obtain the coordinates changes of cutting units in the current step, and then the cutting conditions were modified with the corrected cutting loads for the next step. Figure 6 presents the complex schematic of cutting loads and workpiece deformation.

Due to the continuous removal of workpiece materials in the cutting process, the dynamic characteristics and static stiffness of the part changes simultaneously, which further affects the calculation of thin-walled part deformation. In order to simulate the influences of material removal, a set of elements that equivalent to the cutter swept volume at each feed step was deactivated when cutting tool passes from one discrete cutting position to the next.

The detailed analysis process of the established thermalmechanical coupling model is shown in Fig. 7:

3.2 Workpiece material properties and basic setup of FE model

Fig. 8 Mesh strategy of the FEA mode

During the simulation, temperature-dependent thermo-physical properties of Ti-6Al-4V material were implemented in this model and its detailed properties are listed in Table 1 [34, 35].

Int J Adv Manuf Technol (2020) 107:4645–4659 Table 2 Parameters of the FEA model

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Material model

Temperature-dependent and elastic-plastic material model

Material removal model Mesh type Fine mesh size (mm) Coarser mesh size (mm) Boundary conditions

Model change interaction C3D8T 1.8 (X) × 1.0 (Y) × 0.02 (Z) 1.8 (X) × 1.0 (Y) × 0.6 (Z) Encastre and surface film condition interaction 25 2000

Ambient temperature (° C) Heat transfer coefficient (W/m2/K)

The workpiece was defined as elastic-plastic model and meshed into 99,889 elements and 108,784 nodes. The element type of workpiece was simplified and set as solid element (C3D8T). The influence of material removal was achieved by the model change interaction. The mesh sizes were calculated based on real cutting parameters. Variable mesh density was implemented for the model, and the mesh elements within the finished part were refined to obtain better simulation results. The mesh strategy is shown in Fig. 8. Structural boundary condition was applied on the bottom portion of the workpiece to model the fixture constrains; the degree-of-freedom of the bottom part was fixed along the feed, axial and radial directions, respectively. Thermal boundary condition was applied on the workpiece surface and the initial temperature of the workpiece was set to be the room temperature. The effect of cutting fluid on the workpiece was equivalent to the forced heat exchange process and modelled by applying the relevant

Fig. 9 Experimental setup and the equipment

convective film coefficient. Detailed parameters of the FEA model are listed in Table 2.

4 Experimental analysis and verification A series of milling experiments were conducted to verify the predictive model of cutting force and workpiece deformation. The experimental setup is presented in Fig. 9.

The thin-wall milling tests were carried out using a 3-axis HAAS CNC milling machine. Thin-wall parts with the dimension of 150 mm (length) × 15 mm (height) × 120 mm (width) and 2 mm thickness were clamped on a Kistler 9257B three-component dynamometer. The Lion Precision ECL 130 inductive displacement sensors were employed for on-line measuring of the part deflection, the sensors were placed at three different locations with an

CNC Tool Displacement Sensors

Nozzle Thin-wall Part

Dynamometer Machine table

NI DAQ Card

Driver

Charge Amplifier

DAQ Card

LabVIEW SignalExpress

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4654 Table 3 L9(34) orthogonal array of cutting conditions for milling experiments

Parameters Test no.

RDOC (mm)

Spindle speed (r/min)

Feed rate (mm/z)

Length of flank wear land (mm)

ADOC (mm)

1 2 3 4 5 6

0.2 0.2 0.2 0.4 0.4 0.4

2500 3500 4500 2500 3500 4500

0.01 0.02 0.03 0.02 0.03 0.01

0 0.035 0.06 0.06 0 0.035

10 10 10 10 10 10

7 8 9

0.6 0.6 0.6

2500 3500 4500

0.03 0.01 0.02

0.035 0.06 0

10 10 10

equal interval (L1 = 0, L2 = 1/2 L and L3 = L) at the back of the workpiece and mounted on customised brackets.

Tungsten Carbide end mill with 4 flutes, 6 mm diameter and 38° helix angle were used to machine the thin-wall components. Moreover, the Kistler 5070A eight-channel charge amplifier was used to amplify and convert the signals from the dynamometer and displacement sensors, then these signals were transferred to the NI DAQ card and the obtained signals were analysed using LabView.

The contrast tests were performed when the tools were with different wear conditions, the widths of flank wear (VB) were measured using a Leica Optical microscope before each milling test. In the cutting tests, the collected cutting force signals include high frequency chaotic signals or background noise due to external interferences in the measurement process or internal disturbances of the tool-workpiece system. Therefore, the signal filtering was performed with low-pass filters to remove high frequency noise and undesired dynamic effects, and facilitate the

Fig. 10 Comparison of calculated and measured cutting forces in Test 1

visualization and readability of cutting force waveforms.

Different cutting speeds, feed rates and cutting depths were selected orthogonally, as listed in Table 3.

5 Results and discussions In the following section, experimental results and FE model of thin-wall milling are presented and discussed. Tests 1, 7 and 9 were randomly selected as examples to show the experimental results.

5.1 Cutting forces Figure 10 shows the comparison of cutting forces between the experimental result and calculated outcome. Force component in the normal direction Fy was mainly considered as it plays a dominant role in the workpiece deflection, and the evolution of calculated and measured milling forces of cutting Test 1 in

120

Measured force Fy Predicted force Fy

Cutting force (N)

100

80

60

40

20

Rotation of the cutter (°)

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Fig. 11 Comparison of calculated and measured cutting forces in Test 7

300

Predicted force Fy Measured force Fy

Cutting force (N)

250

200

150

100

50

Rotation of the cutter (°)

the sample window is given as an example. It can be seen in Fig. 10 that the cutting forces calculated by the flexible force model are in good agreement in magnitude as well in trend with the measured results. The maximum calculated cutting force Fy is 93 N, while the measured data is found to be 91 N. The percentage errors are less than 3%. The differences between the simulated and measured results are attributed to some possible factors including process damping, the changes of workpiece material property and tool run-out.

Fresh tools and tools with different degrees of wear were selected to analyse the effects of tool flank wear.

Figure 11 presents the variations of measured and calculated forces in Test 7 (VB = 0.035 mm) in a stable state. In this case, it can be observed that the calculated results are well consistent with the experimental results with errors less than 7%, and the trend of evolutions also matches well. It is also shown in Fig. 11 that the maximum calculated force is lower than the measured force. One possible reason leading to the difference is that the length and width of tool flank wear land were not uniform during

Fig. 12 Modelling of thin-wall deformation

the milling process, while the tool was considered as to be in an ideal condition in the predictive model. Secondly, other types of tool wear would occur during the milling process, and this led to the increase of cutting forces while only tool flank wear was considered in the proposed model. Additionally, the tool wear rate was treated as a constant in each cutting test, which can also cause prediction errors. All these errors would have uncertain influences on the evolution of cutting forces. It could also be found that the amplitude variation of each force component varies slightly in each rotation period. The main reason is that the cutting forces are affected by different dynamic factors in the milling process, especially in cutting of titanium alloy, factors such as chatter and the wear degree of the tool may affect the cutting forces.

5.2 Part deflection and form errors During the machining process, the thin-wall part deflects due to its low rigidity under the action of cutting loads.

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4656 Fig. 13 Comparison of measured and predicted surface form errors in Test 9

8

Measured results of sensor 1 Measured results of sensor 2 Measured results of sensor 3 Predicted results of sensor 1 Predicted results of sensor 2 Predicted results of sensor 3

Displacement (µm)

7 6 5 4

3 2 1 0

Tool movement (mm)

Figure 12 shows the displacement of the thin-wall component under cutting conditions of Test 9, which is selected as an example to present the FEA results. Because the thickness and stiffness of the part in the radial direction are smallest compared with those in other directions, and the deformation in the radial direction is much larger, only the deformation in the radial direction is analysed in this paper.

Figure 13 shows the comparison of surface form errors between modelling and experimental results. In the figure, the simulated and measured surface form errors in Test 9 at feed position of L1 = 0, L2 = 1/2 L and L3 = L are presented; the variation of part deformation was measured along the length direction of the workpiece.

It can be seen in Fig. 13 that the percentage errors of maximum displacement values at L1, L2 and L3 are 5.6%, 5.4% and 5.9%, respectively; the tendencies are

Table 4

found to match very well. It can be observed that the amplitudes of deformation present an increasing trend towards the free ends of the part due to the lower stiffness of thin-wall part at these areas compared with the middle section of the part. Because of the higher stiffness at the middle of the part, cutting loads and the changes of residual stress have smaller effects on the local deformation.

Moreover, the part becomes more flexible in the process due to the unremitting material removal process, which leads to decreasing stiffness and non-uniform residual stress of the part, so the thin-wall part is not symmetrical along the feed direction and relatively larger deformation values were found at the latter half of the part. Due to the influence of part deformation, the actual radial cutting depth decreased and the milling forces were also expected to be lower at the end of the part than those in previous cutting positions. Through FEA results shown in Fig. 12,

Comparison between measured and predicted results for all the milling tests

Test no. Factors A B C D RDOC (mm) Spindle speed (r/min) Feed rate (mm/z) Length offFlank wear (mm)

Maximum measured δw at L2

Maximum predicted δw at L2

Deviation

1

0.2

2500

0.01

0

1.379301758

1.10941071

19.6%

2 3 4 5 6 7 8 9

0.2 0.2 0.4 0.4 0.4 0.6 0.6 0.6

3500 4500 2500 3500 4500 2500 3500 4500

0.02 0.03 0.02 0.03 0.01 0.03 0.01 0.02

0.035 0.06 0.06 0 0.035 0.035 0.06 0

1.096005102 1.494590035 2.578850649 2.350204950 2.621099802 3.578332602 4.005913155 3.179479249

1.18392493 1.25844086 2.06565977 2.11853263 2.17381209 3.06410112 3.19662539 3.00851841

8.0% 15.8% 19.9% 9.8% 17.1% 14.4% 20.2% 5.4%

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Fig. 14 Machined surface in milling Test 8

it can also be found that larger deformation occurred at the top of the part in the axial direction as the stiffness of the upper edge of the part was less than that at the root of the part.

Additionally, through the analysis of results obtained from the orthogonal experiments, the sequence and contribution rate of each experiment factor on target index were determined as radial depth of cut, feed rate, length of flank wear land and spindle speed. Radial cutting depth has a bigger impact on the deformation than other parameters, and with the increase of radial cutting depth, the maximum form error increased significantly. Meanwhile, with the increase of spindle speed, the maximum deformation of the workpiece increased but the gradient tended to be gentle. And it was believed that the workpiece deformation would experience a similar tendency as cutting forces when tool flank wear deteriorated following the typical wear curve because the increased flank wear would lead to softened material and extra thermal-mechanical loads on workpiece. The values and percentage of errors of the measured and predicted results at the middle position L2 are shown in Table 4.

Fig. 15 Comparison of surface form errors with and without considering cutting heat

7

Displacement (Âľm)

6 5 4

According to the proposed model, the additional cutting force components and rubbing heat source due to tool flank wear have great effects on the amplitude of part deformation.

The deterioration of tool flank wear would lead to increasing cutting force components and extra thermal stress at the toolworkpiece interface, resulting in poor surface quality. Thus, the prediction of thin-wall deformation at the presence of tool flank wear is necessary before actual machining operations.

It should be noted that significant chatter vibration occurred in Test 8, which seriously affects the surface quality of the finished workpiece, and the cutting forces in this case cannot be accurately calculated by the developed model. The chatter marks on the workpiece surface are shown in Fig. 14. At the beginning and end of the cutting process, both the tool and part were inflicted to larger mechanical impact, so the chatter marks were relatively obvious, while the vibration in the middle part was relatively weak. The chatter is mainly due to the relatively large radial cutting depth and low feed rate so that the ploughing force component is dominant while the rigidity of thin-wall part is low, which causes larger force-induced coupling defection of the tool-workpiece system, and resulted in a significant calculation error which is as high as 20.2%. From the aspect of avoiding chatter damage on the machined surface, properly choice of cutting parameters based on the stability lobe diagram (SLD) method is also required [36].

To confirm the effects of thermal load, two FEA processes with and without applying cutting heat were carried out based on the established FEM model and the cutting conditions of cutting Test 9. As shown in Fig. 15, it is observed that cutting heat has a great impact on the magnitude of maximal form error as it can change the properties of workpiece material and the distribution of thermal stress. A maximum percentage difference of 19% was found between these two analyses. Therefore, cutting heat cannot be ignored in thin-wall milling, and it is essential for the prediction and control of thin-wall deflection.

Predicted results of sensor 1 Predicted results of sensor 2 Predicted results of sensor 3 Predicted results of sensor 1 without applying cutting heat Predicted results of sensor 2 without applying cutting heat Predicted results of sensor 3 without applying cutting heat

3 2 1 0

Tool movement (mm)

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6 Conclusions

3.

In this paper, a new predictive model was developed to analyse the interaction between the cutting loads and part deformation in milling thin-wall parts. The development of tool wear and the thermal effects were taken into account when calculating the flexible milling loads, and an efficient iterative algorithm was employed to improve the accuracy and efficiency of calculation. In the predicting process, the results of the flexible cutting force model and relevant cutting heat sources were applied as the input of the FEA model. Validation experiments of Ti-6Al-4V thin-wall milling were performed to verify the analytical model and simulation results. The main conclusions can be summed up as following:

4.

1. It has been demonstrated that the new model was not only reliable but also robust. The deviations between the measured and calculated cutting forces were within the errors of 14%, 10% and 5% in the radial, feed and axial directions, respectively. The errors of cutting cases with a sharp tool were relatively small and within the range of 2 to 7%.

Moreover, the maximum predicted deformation errors at the initial, middle and end portions of the workpiece were less than 20%.

2. Tool wear effect is critical for predicting cutting loads in milling of difficult-to-machine materials like Ti-6Al-4V. The wear-induced loads and thermal stress could further deteriorate the finished surface and cutting tool. And cutting force components have an increasing trend along with the propagation of tool flank wear.

3. By comparing the deformation of thin-wall under the effects of cutting forces and multi-loads, it was found that the deformation caused by multi-loads was about 10–19% larger than that of the deformation caused by milling force. Therefore, it is necessary to study and control the surface form errors caused by thermo-mechanical coupling especially in precision processing of thin-wall parts.

The presented model paves the way for developing new models to estimate surface form errors for machining complex thin-wall parts with the consideration of chatter stability and other cooling strategies.

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