Finite element modeling of a cutting edge temperature in high speed turning of unalloyed steel.

Ceau, Gheorghe ; Popovici, Victor ; Tanase, Ioan 等

1. INTRODUCTION

The heat generated during cutting has been studied by a large number of researchers using experimental techniques (Komanduri, 2000; Molinari & Moufki, 2004; Young & Chou, 1994; Daschievici, 2006; Patrascu, 2004). The determination of the maximum temperature and temperature distribution along the rake face of the cutting tool is of particular importance because of its controlled influence on tool life, as well as on the quality of the machined part and on the production costs.

The purpose of this project was to investigate the influence of the cutting parameters on the temperature at the edge of the cutting tool (Davies, 2007). The development of the experiment as well as the processing of the results have been done using the modern method of the response surfaces. The temperature has been measured experimentally using a montage with natural thermocouple between the work-piece and cutting tool. The data acquisition has been accomplished using the LabVIEW instrumentation. The model, as well as the temperature profiles, have been obtained through analytical calculus using the MATLAB program and the mathematic regression method. There was created a model of the thermal field of the cut area using the module cutting software package Deform-3D.

2. THEORETICAL ASPECTS

The researches that have been fulfilled have shown that the mechanical work of the cutting process turns almost completely into heat. According to the accomplished studies, with a certain approximation, it is considered that 75% of the heat generated by cutting comes from the distortion and the detachment from the cutting edge, and 25% from the friction process. From these distortion and friction areas, the heat is transmitted to the areas with lower temperature, being distributed between the chip, the tool, the work-piece and the environment. The share of distributions changes depending on the processing procedure. The quantity of heat generated during the cutting process, depending on the cutting parameters, can be determined using a mathematical model based on the equation of the thermal balance between the chip, the tool, the work-piece and the environment. According to this balance, the general function of the temperature can be determined using the following formula:

[theta] = [C'.sub.[theta] x [e.sup.[summation], [[degrees]C]; [summation] = [x.sub.a]/m [a.sup.m.sub.p] + [y.sub.f]/n [f.sup.n] + [z.sub.v]/q [v.sup.q.sub.c], (1)

where [x.sub.a], [y.sub.f], [z.sub.v] are variables dependent on the parameters of the cutting process [a.sub.p], f and [v.sub.c], [C'.sub.[theta]]--constant which expresses the conditions of the heat transfer in steady thermal conditions, dependent as value on the thermo-physical properties of the material of the work-piece, on the geometry of the active part of the tool and on the wear grade of the edge of the cutting tool. Particularly, [x.sub.a], [y.sub.f], [z.sub.v] being independent variables on [a.sub.p], f and [v.sub.c] there are the relations: m=n=q; [x.sub.a]=[x.sub.[theta]], [y.sub.f]=[y.sub.[theta]], [z.sub.v]=[z.sub.[theta]]. Therefore the relation (1) becomes (Ceau & Predincea, 2008):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)

3. EXPERIMENTAL SETUP AND PROCEDURE

For the determination of the analytical model of the temperature at the cutting edge, depending on the cutting speed ([v.sub.c]), on the rotation feed (f) and on the cutting depth ([a.sub.p]), defined by the equation (2), there has been organized a factorial experimental program, in which, for every variable, there have been chosen three values, taking account of the technological limits restricted by the work conditions and of the recommendations of the cutting inserts' producer.

Experimental setup (fig. 1) and measurement conditions:

* Machine-tool: SN 400x1000 lathe;

* Cutting tool: PDJNL 2525M 15 with DNMG 15 06 04-PM cutting insert;

* Work-piece: Ck 45 rectified bar ([[empty set].sub.ext]=98 mm) according to the DIN 17200 norm.;

* The data acquisition: Measurement and Automation Software National Instruments LabVIEW with Multifunction DAQ PCI-6024E;

* The signal for measurement of the temperature of the cutting edge: natural thermocouple;

* Settings for the measurement channels:

--channel 2 (natural thermocouple): number of scans/sec.: 5; number of acquisitions: 20; measurement range: 0...-10V; measurement without scale; factor of amplification of the operational amplifier: 250;

--channel 1 (environment temp.) thermocouple CuCt: conditioner 5B47; measurement range (0/200)[degrees]C.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

4. RESULTS AND DISCUSSION

The analytical model of the cutting edge temperature depending of the cutting process parameters, obtained by regression of experimental data is:

[theta] = 243.283 x [v.sup.0.242.sub.c] x [f.sup.0.078] x [a.sub.p.sup.0.021] [[degrees]C] (3)

For modeling the cutting process there was used the cutting module of the software package programs Deform-3D with the following settings: convection coefficient: 0.02 N/s/mm/[degrees]C, heat transfer coefficient: 45N/s/mm/[degrees]C, shear friction: factor: 0.4. Modeling results are presented in figure 2 for parameters of the cutting process: n = 1200 rpm, f = 0.24 mm / rev., [a.sub.p]= 1mm.

The comparison between the measured and the calculated values of the average temperature at the chip-tool interface, for three values of the cutting speed, is presented in table 1 (T1--calculated with the analytical relation (3), T2--measured values with natural thermocouple and T3--FEM analysis results) and graphic representation in figure 3.

[FIGURE 3 OMITTED]

It has been observed that the FEM model was underestimating the analytical model results and the experimental determinations for the considered values of the friction coefficient for the couple of steel-steel materials. Consequently, the friction coefficient has been modified in the field given by the professional pieces of work, in order to obtain validated results by the experimental measurements. For the value of 0.4 for the friction coefficient, there were obtained results with a maximum margin of 10%.

5. CONCLUSIONS

The temperature of the cutting edge measured with the natural thermocouple represents the actual temperature of the cutting edge during the cutting process, without any approximation or simplifying hypothesis. The measurement of this temperature by other measurement means is not possible without considering certain work hypotheses.

The successful checking of the determined model for other cutting conditions (see Fig. 3), has shown the validity of the applied theory, the one of the response surfaces method and the accuracy of the accomplished experiments.

The results have emphasized the major influence of the cutting speed. The cutting feed and cutting depth have smaller influence on the cutting temperature according to their exponents in the determined model (3). Some researchers found statistically insignificant the influence of the cutting depth. The temperature of the cutting edge can reach high values even for conventional cutting conditions or for the lower limit of the HSC domain. Future research will be oriented towards establishing a more precise average coefficient of friction between the chip and the tool rake face based on the comparison between experimental results and simulation results to deform 3D software package.

6. REFERENCES

Davies, M. A., Ueda, T., M'Saoubi, R., Mullany, B., Cooke, A. L. (2007). On The Measurement of Temperature in Material Removal Processes. Annals of the CIRP Vol. 56/2/2007, pp. 581-604

Daschievici, L., Ghelase, D., Diaconescu, I. (2006). Thermal area in cutting tool, Proceedings of the 15th International Conference on Manufacturing Systems, Ed. Academiei Romane, ISSN 1842-3183, Romania, 26-27 October, 2006

Komanduri, R., Hou. (2000). Thermal modeling of the metal cutting process. Part I-Temperature rise distribution due to shear plane heat source, International Journal of Mechanical Sciences, Vol. 42, issue 9, sept. 2000, p. 1715-1752

Molinari, A., Moufki, A. (2004). A new thermomechanical model of cutting, applied to turning operations. Part. I. Theory. International Journal of Machine Tools&Manufacture, vol. 45, feb. 2005, p. 166-180

Patrascu, G., (2004), 3D Simulation of Turning Process Using FEM Software. Proceedings of the International Conference on Manufacturing Systems ICMaS 2004, Romanian Journal of Tehnical Sciences Applied Mechanics, Tome 49, Editura Academiei Romane, p. 297-300

Ceau, Gh., Predincea, N., Tanase, I., (2008). Researches about the Cuting Edge Temperature in High Speed Turning of Quqlity Steel. Proceedings of ICMaS, University POLITEHNICA of Bucharest, 13-14 November 2008. Editura Academiei Romane, p. 218-222, ISSN 1842-3183

Young, H., Chou, T.L. (1994). Modelling of tool/chip interface temperature distribution, International Journal of Mechanical Sciences, Vol. 36, issue 10, p. 931-943

Tab. 1. Values of the temperature according to the cutting speed

 [v.sub.c] f [a.sub.p] [T.sub.1]
Exp. [m/min] [mm/rev] [mm] [[degrees]C]

1 235.4 0.24 1 816.11
2 293.8 0.24 1 861.11
3 369.3 0.24 1 910.04

 [T.sub.2] [T.sub.3]
Exp. [[degrees]C] [[degrees]C]

1 818.1 807
2 849.5 819
3 911.8 976