DISC TOOL PROFILING FOR COMPLEX HELICAL SURFACES MACHINING USING BOOLEAN ENVELOPE METHOD WITH UNDERC

International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN (P): 2249–6890; ISSN (E): 2249–8001 Vol. 10, Issue 3, Jun 2020, 1007-1016 © TJPRC Pvt. Ltd.

DISC TOOL PROFILING FOR COMPLEX HELICAL SURFACES MACHINING USING BOOLEAN ENVELOPE METHOD WITH UNDERCUTTING PROBLEM LONG HOANG Senior Lecturer, Ph.D., Hanoi University of Science and Technology, Hanoi, Vietnam ABSTRACT Helical cylindrical surfaces with constant pitch are widely used in industry, such as helical teeth gears, air compressor screws, or cutting tools. One of the best practical methods for machining these surfaces is using the disc tool to mill or to grind. This paper presents with detail proposed methods for disc tool profiling and a simulative machining algorithm to evaluate the precision of the disc tool. The machining simulation algorithm has provided a reliable method for assessing the correctness of the cutting tool and confirmed that the disc-tool determined by the proposed method achieves a high accuracy of 0.0076 mm.

KEYWORDS: Disc Tool, Profiling, Envelope & Undercutting

1. INTRODUCTION Helical cylindrical surfaces with constant pitch are widely used in industry as helical slots on the active surfaces of helical screws, helical teeth gears, air compressor screws or cutting tools, etc.

For machining helical cylindrical surfaces, one of the best effective methods is using the disc tool to mill

Original Article

Received: Apr 04, 2020; Accepted: Apr 24, 2020; Published: Jun 06, 2020; Paper Id.: IJMPERDJUN202088

or to grind. The traditional methods for disc tool profiling include: determining the contact conditions and specifying the characteristic curve. The analytical methods [1-4] for disk tool profiling based on surface enveloping, have been widely used for a long time. Besides, numerical-analytical methods [5] has also been proposed recently.

The mathematics involved in the above methods is quite complex, so it cannot be solved directly but requires a dedicated algorithm. Besides, these methods require a representation of the machined surface by mathematical equations and without any singular points and undercutting. Actually, the disk tool profiling is often supported by expensive dedicated software based on advanced methods, which are still confidential and only suitable for large companies.

Nowadays, advanced trend used is CAD approach, which makes use of "Projection" command on CATIA to project the disc-tool axis onto the machined surface to get characteristic curve [6] or machining simulation and identification of contact lines by Boolean operation[7], but these works were not written in detail and almost ignored the problem undercutting.

In order to overcome the limitations mentioned above, this paper presents with detail proposed methods for disc tool profiling and a simulative machining algorithm to evaluate the precision of the disc tool.

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2. DISK TOOL PROFILING 2.1. Fundamental Theory in Brief The helical surface generation kinematics using a disc tool involves three motions (See Figure 1): I – rotating of the worked piece; II – moving along the worked piece rotation axis; III – cutting motion – tool rotation around its axis.

XYZ is the system attached to the generated helical surface, having the

axis coincident to the the axis of the

helical surface.

X1Y1Z1 is the system attached to the disc-tool.

Nikolaev theorem applied to find the characteristic curve of both surfaces, Σ, to be generated, and the disc-tool surface is [6]: 0 Where:

(1)

is the vector of the disc-tool rotation axis;

is generated surface normal, into the XYZ system;

is the

position vector of the current point from the generated surface referred to X1Y1Z1 system

Figure 1 : Disc-Tool Primary Peripheral Surface and Helical Surface [6].

2.2. Proposed Methods 2.2.1. Section Method a) CAD Method Use many cutting planes that are perpendicular to the axis of the disk tool. For each cutting plane, the intersection between the plane and the helical surface (see Figure 2: EF) must be tangent to the circle, which is the intersection between the cutting plane and the disk toll, the contact point can be found. The characteristic curve (BTCT on Figure 2) is specified by a set of contact points.

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Disc Tool Profiling for Complex Helical Surfaces Machining using Boolean Envelope Method with Undercutting Problem

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Figure 2: The Characteristic Curve.

Using 3D CAD software such as Inventor, it is easy to draw the intersection between any cutting plane and 3D solid model of the given part that contains helical surfaces (see Figure 3). Drawing File needs tto be exported to AutoCAD, and in AutoCAD, contact points need to be specified by using perpendicular Osnap mode (see also Figure 3).

After determining the number of contact points, it is not difficult to specify the axial section of the disc tool. Then use the "Revolve" command to create the primary peripheral surface of the disk tool.

This method is not applied automatically but can be used to avoid undercutting phenomena.

Figure 3: Specifying a Contact Point on the Cutting Plane.

B)Computational Method The intersection between the cutting plane and the helical surface is determined as follows: The Given:(see Figure 4) 

The profile BC of cross-section N-N of the helical surface.



Position of a cutting plane P-P.

Specify: The section P-P The profile BC on section N-N is given by a number of points, as usual, each point of them is given by a pair r, δ (polar www.tjprc.org

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coordinates), it can be translated into Cartesian coordinates as: x = r sin δ

(2)

y = - r cos δ

(3)

Figure 4: Specify Intersection of a Helix and Cutting Plane.

The equations of the helical surface are written as: x = r sin(δ + dδ)

(4)

y = - r cos (δ + dδ)

(5)

z = p dδ

(6)

Where p is the parameter of the helix, dδ is the angle that the profile N-N rotates about the axis of the helical surface.

The equation of the cutting plane P-P is written as: z = k (x-x0)

(7)

Where k, x0 are parameters of the given cutting plane P-P. So, the intersection point between cutting plane P-P and the helix from any point on cross-section N-N, such as CN, satisfies the equation: p dδ = k (r sin(δ + dδ) – x0)

(8)

The equation (8) can not be solved exactly, but it can be solved approximately by using a subroutine running in Impact Factor (JCC): 8.8746

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AutoCAD, its algorithm as follows (see Figure 5):

Figure 5: The Algorithm for Solving the Equation (8).

Repeating the above subroutine, after specifying intersection points on the cutting plane, contact point needs to be identified, as the nearest point to the disc tool axis.

2.2.2. Boolean Operation Method and Results The algorithm for creating the disc tool is shown in Figure 6(a) and has been implemented by AutoLISP subroutines running in AutoCAD to produce the results in Figure 6(b).

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(a)

(b)

Figure 6: (a) The Algorithm for Disc Tool Profiling ; (b) The Disc Tool was Created.

At first, the cuter is a solid of a cylinder and will become the disc tool after performing the subroutines mentioned above. The statement, cuter = cuter – the helical solid, is executed by the "Subtract" command in AutoCAD. The numbers 100 and 0.5 in Figure 6(a) can be changed to achieve the required accuracy.

3. SIMULATIVE MACHINING AND TESTING RESULTS Verifying the accuracy of the disc tool was performed by simulative machining as follows: The algorithm for simulative machining is shown in Figure 7(a) and has been implemented by an AutoLISP subroutine running in AutoCAD to generate the helical surface, as shown in Figure 7(b). The subroutine is a loop, including the "Subtract" command, to cutout, step by step, unwanted material, keeping the enveloping relative movement between the cuter and the workpiece, as mentioned in section 2.1.

Using Geomagic Control X, 3D comparison of the given helical surface and the helical surface generated by the disc tool is shown in figure 8(a,b).

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Disc Tool Profiling for Complex Helical Surfaces Machining using Boolean Envelope Method with Undercutting Problem

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(b)

Figure 7: (a) The Algorithm for creating the Gate Screw Profile; (b) The helical surface was Simulative Machined

Figure 8(a): The 3D the Accuracy of the Helical Surface Machined by the Disc Tool.

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Figure 8(b): The Cross-section Accuracy of the Helical Surface Machined by the Disc Tool.

4. DISCUSSIONS Figure 8 has shown that the disc-tool primary peripheral surface created by the proposed method is highly accurate (the average error of the helical surface generated by the disc tool is - 0.0076 mm).

Higher accuracy can be achieved by increasing the number of loops and reducing the angle step. Still, the experiment shows that values of 100 and 0.5 are suitable to both meet the required accuracy and reduce the running time.

For avoiding phenomena of undercutting, it is necessary to select the angle formed by the tool axis and the workpiece axis as well as the distance from the tool axis to the workpiece axis appropriately by the method presented in section 2.2.1a.

If any small undercutting occurs, the analytical methods [1-5] and the projection method [6] are no longer valid because equation (1) is no longer satisfied (in Figure 9a, the disc tool is not generated completely at the root of the screw).

However, it is still possible to use the proposed method (see Figure 9b), which is one of the advantages of this approach.

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Disc Tool Profiling for Complex Helical Surfaces Machining using Boolean Envelope Method with Undercutting Problem

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(b)

Figure 9: (a) The Disc Tool Generated by the Projection Method in CATIA; (b) The Disc Tool Generated by the Proposed Method

5. CONCLUSIONS The proposed method for the determination of the helical surface machining disc-tool overcomes the limitations of the analytical methods with advantages as follows : 

It accepts the undercutting phenomena and singularity point on the helical surface.



It can be used for variable complex helical surface shapes such as air compressor rotor profiles,



It does not require the representation of the helical surface by complex math equations.



The machining simulation algorithm has provided a reliable way of evaluating the precision of the cutting tool and confirmed that the disc-tool determined by the proposed method achieves a high accuracy of 0.0076 mm.



The algorithms are described in detail such that it is easy to apply by the subroutine written in Autolisp. It can be the basis to study the impact of tool wear and tool positioning error on the generated surface deviation.

ACKNOWLEDGMENTS This work was supported by Hanoi University of Science and Technology in the project T2016-PC-077.

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