Design of a torque multiplying device based on the calculation of clamping and cutting force.

Park, Hong Seok ; Thai, N.N. Dien ; Kim, Jong Su 等

Abstract: This paper presents the development of a device that helps reduce clamping force required for workpiece fixturing. Based on the analysis of ball-end milling process applied in die manufacturing, a mechanics model for determining appropriate value of clamping force is developed. Cutting force for the determination of clamping force is calculated through the simulation of machining process using finite element method. The device is then designed so that power needed for workpiece constraining decreases to a suitable value for human working. It releases workers from heavy load and industrial diseases.

Keywords: Clamping force, Machining simulation, Jigs and fixtures, Ball-end milling

1. INTRODUCTION

Workpiece positioning and constraining is an important issue in many manufacturing operations. Unfortunately, clamping force much larger than needed is likely to be used because the optimal value is unknown. This makes fixturing system complicated and workers have to work under heavy load. In the long term, it will be harmful to health and cause some industrial diseases related to musculoskeletal system.

These factors have motivated researchers to develop new method to estimate and reduce clamping force. Calculation of clamping force can be operated using an elastic contact model (Li & Melkote, 2001) or by a min-max load model (DeMeter, 1995). Intelligent algorithms such as GA (Melkote et al., 2002) or ANN (Zuperl & Cus, 2003) are also utilized for the optimization of clamping force. In this paper, a mechanics model built on the analysis of ball-end milling process for die manufacturing is considered. Machining process is simulated by mean of FEM software and then clamping force is calculated. Based on that result, the development of new fixture system which can reduce clamping force is formerly the objective of this study. However, such system is impossible because of constraints such as machining environment, shape of workpiece or machine tool. Hence, a jointing tool that helps reduce clamping force is developed as an alternative.

2. CLAMPING FORCE CALCULATION

In case of die manufacturing, workpiece is usually in large dimension. Therefore, it is difficult to locate and constrain workpiece using 3-2-1 principle, which requires three locators plane and one locator on the third locating plane. A common way is that workpiece is located on one plane and is held in its place with clamping forces applied at four positions. Displacements in unconstrained directions will be fixed by friction between the workpiece and machine table.

[FIGURE 1 OMITTED]

Forces applied on workpiece during the process of milling are described in Fig. 1, in which:

[R.sub.x], [R.sub.y], [R.sub.z]--components of cutting force (N) [F.sub.i] (i = 1 ... 4)--reactions acting at locating positions (N) [F.sub.ci] (i = 1 ... 4)--clamping forces at locating positions (N) [f.sub.ix], [f.sub.iy], [f.sub.iz] (i = 1 ... 4)--components of friction forces at locating points (N)

G--gravity

The equations of equilibrium are:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where:

[r.sub.i]--vectors defining locating points r--tool radius Friction forces can be calculated as follows:

[f.sub.i] - [mu]([F.sub.i] + [F.sub.ci]) (3)

[f.sub.ix] - [mu]cos[[theta].sub.i]([F.sub.i] + [F.sub.ci]) (4)

[f.sub.iy] - [mu]sin[[theta].sub.i]([F.sub.i] + [F.sub.ci]) (5)

where:

[mu]--friction coefficient [theta]--angle of displacement Due to real demand in design, [F.sub.c1] = [F.sub.c3] = [F.sub.a] and [F.sub.c2] = [F.sub.c4] = [F.sub.b]. Then, the equations of equilibrium can be rewritten in on the first locating plane, two locators on the second locating matrix form:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

or [A][F] = [B] (7)

The value of vector [F] can be obtained using following equation:

[F] = [[A].sup.-1][B] (8)

As shown in the equations, if the value of cutting force and the position of tool at which cutting force reaches maximum value are determined, clamping forces [F.sub.a] and [F.sub.b] can be easily calculated.

3. CUTTING FORCE ESTIMATION USING FEM

As presented in above section, value of maximum cutting force and position at which it occurs are required for the calculation of clamping forces. In this paper, these parameters are obtained by simulating machining process in FEM tool. Tool chosen in this study is Deform3D, an engineering software to analyze the deformation of metal in forming and machining process.

First, machining tool path was generated by a CAM software CATIA in this case. Then, the stock was split along the path into small pieces. These pieces as well as tool geometry were exported to STL format to be recognized by Deform3D. After that, simulation was run for each split piece.

The simulation of machining operation result in the stress generated during cutting process. By comparing these results, value of maximum stress and the position where it occurs are determined.

As maximum stress obtained from the simulation, cutting force can be calculated using the equation:

R = [[sigma].sub.max] = A (9)

in which

[[sigma].sub.max]--maximum stress (MPa) A--cross section of chip ([mm.sup.2])

[FIGURE 2 OMITTED]

As shown in Fig. 2, it is easy to find out that cross section of the chip can be obtained by the product of feed rate and axial depth of cut.

A = [a.sub.a]f (10)

[a.sub.a]--axial depth of cut (mm) f--feed rate (mm/tooth) Then, the value of cutting force in each direction can be calculated.

[R.sub.x] = Rsin([gamma]) (11)

[R.sub.y] Rcos([psi])cos([gamma]) (12)

[R.sub.x] = Rsin([gamma]) (13)

where

[psi]--angle that inserts are mounted on tool body

[gamma]--rake angle of cutter

4. DEVELOPMENT OF JOINTING DEVICE

The main objective of the device is to increase torque applied by workers. For that purpose, the planetary gear system is an ideal choice because of its high ratio and compact size. The device is constructed from two stages of planetary gear system (Fig. 3). Each stage increases applied torque by a factor of 5, allows the device to produce output torque at 25 times larger.

[FIGURE 3 OMITTED]

Input torque is applied to the sun gear of the first stage. Four planet gears engaged to the sun gear are held by a carrier which also holds the sun gear of the second stage. The output square drive is held by the carrier of the second planetary gear system. A reaction arm connected to both annulus gears prevents them from rotating. This causes the planet gears to orbit around the sun, transfer and increase torque from input to output.

[FIGURE 4 OMITTED]

5. CONCLUSION

In this paper, a mechanics model to calculate appropriate value of clamping force for large workpiece fixturing used in die manufacturing was developed. Applying FEM to the simulation of machining process, cutting force was estimated to be used in the model. From calculation result, a tool that increases torque applied by an operator was designed to reduce loads. Its benefits are saving workers energy, protecting them from industrial diseases due to the reduction of clamping force, offering safer and more convenient working condition.

The study was based on the analysis of ball-end milling process for die manufacturing. The developed technique can be extended to other processes.

Acknowledgements: This research was supported by the Ministry of Commerce, Industry and Energy under the development program of next generation manufacturing supervised by the Korea Institute of Industrial Technology Evaluation and Planning.

6. REFERENCES

DeMeter, E.C. (1995) Min-Max Load Model of Optimizing Machining Fixture Performance, Transaction of the ASME, Journal of Engineering for Industry, Vol. 117, pp. 186-193.

Li, B. & Melkote, S.N. (2001). Fixture clamping force optimization and its impact on workpiece location accuracy, International Journal of Advanced Manufacturing Technology, 17, pp. 104-113.

Melkote, S.N. et al.(2002). Iterative Fixture Layout and Clamping Force Optimization Using the Genetic Algorithm, Journal of Manufacturing Science and Engineering, Vol. 124, No. 1, pp. 119-125.

Zuperl, Uros & Cus, Franci (2003). A model for analyzing and optimizing fixtures, Journal of Mechanical Engineering.