Pergamon 0045-7949(95)00024-O Computers & Struc/ures Vol. 56, No. Z/3, pp. 313-320, 1995 Copyright 0 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0045.7949/95 $9.50 + 0.00 zyxwvut THE FINITE ELEM ENT THERMAL ANALYSIS OF GRINDING PROCESSES BY ADINA M. Mahdi and Liangchi Zhang Centre for Advanced Material Technology, Department of Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia Abstract-Most grinding problems cannot be solved analytically, therefore extensive numerical solutions are required by using appropriate numerical techniques such as the finite element method (FEM). In this study, the well-known finite element software, ADINA, was used to predict the phase transformation of a workpiece subjected to surface grinding. The process was considered to be two-dimensional and the properties of the workpiece material were temperature dependent. To gain practically acceptable results, the induced temperature field ati the associated phase transformation were analysed by different element meshes. Some efficient solution strategies were proposed to obtain reliable predictions for different grinding conditions and workmaterial properties. The user coding facilities of the code were used to achieve the above performances. c zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA D d H h k I 6 4 4 % 4, Pe r T T T, TCW t i u x,x x, z x',z' 5 a co NOTATION specific heat capacity per unit volume of ground components non-dimensional martensite depth (d/l) depth of martensite non-dimensional heat transfer coefficient (2cth/ku) heat transfer coefficient of coolant thermal conductivity of ground components half length of grinding zone, see Fig. 1 relative peak locaion of a heat flux (x,/l), see Fig. 1 heat flux per unit grinding width average heat flux peak value of the heat flux heat transferred by convection (hT), see Fig. 1 Peclet number (VI/Z&) (x2 + 22)‘iZ temperature rise (T, - T,), with respect to ambient temperature non-dimensional temperature (xkuT/Zaq) workmaterial temperature ambient temperature time non-dimensional time (u*r/2cc,) moving speed of the heat source, equal to the table speed set of the grinding machine, see Fig. 1 non-dimensional horizontal coordinate, i.e. x/l and x,/l, respectively coordinates of the stationary reference frame, see Fig. 1 coordinates of the moving reference frame, see Fig. 1 horizontal coordinate of peak heat flux location, see Fig. 1 thermal diffusivity at room temperature 1. INTRODUCTION Grinding requires an extremely high energy input per unit volume of material removal compared with other machining processes, and almost all of the energy is converted to heat which is concentrated in the grinding zone. This usually leads to an elevated temperature rise in both the wheel and workpiece. It is well-known that such temperature rise plays an important role in the formation of residual stresses in a ground component which is a key factor of surface integrity. A main cause of residual stresses is the phase transformation of the surface material, characterized by critical grinding temperature histories. Fundamen- tally, as summarised by Ref. [l], there are four problems in the thermal analysis of phase transform- ation associated with grinding: (1) the strength and distribution of the heat source generated, which relates to the material removal mechanisms of grind- ing; (2) the convection of cooling media, which reflects the effect of coolant; (3) the thermal proper- ties of the workmaterial; and (4) the moving speed of the heat source. Most of the relevant studies of grinding tempera- ture (e.g. Refs [2-71) were based on Jaeger’s model [8] proposed in the 194Os, where a heat source of con- stant strength moving on the surface of a half-plane was considered. Isenberg and Malkin [9] considered the effects of variable thermal properties of work- material and presented a set of numerical results of grinding temperature induced by a moving band source of constant strength. However, the depen- dence of thermal properties on temperature was assumed to be linear. Li and Chen [lo] developed an improved model to investigate grinding temperature and residual stresses due to both mechanical and thermal factors, but the workmaterial properties considered were temperature-independent and the moving heat sources were of constant strength. Recently, Zhang et al. reviewed the previous work [l zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO 11, discussed the relevant problem of moving heat sources of constant and triangular input profiles and studied their effects in terms of grinding conditions [l, 121. They analysed grinding temperature using 313