英语翻译
2.Thermal Modelling of Grinding
The finite element model proposed is based on Jaeger's model [2]; it is a 2D model and the grinding wheel is considered to be a moving heat source,see Fig.1.The heat source is characterised by a physical quantity,the heat flux,q,that represents the heat entering an area of workpiece per unit time and is considered to be of the same density along its length,which is taken equal to the geometrical contact length,l.which is calculated from the relation where a is the depth of cut and d ,is the diameter of the gringing wheel .The real contact length is expected to be large owing to the deflection of the grinding wheel and the workpiece in the contact area.Nevertheless,as a first approximation,the geometrical and real contact lengths are considered to be equal.The heat flux can be calculated from the following equation Where is the percentage of heat flux entering the workpiece,the tangential force per unit width of the workpiece,the peripheral wheel speed and the geometrical contact length.The proportion of the heat flux entering the workpiece can be calculated by a formula suggested by Malkin [3,4] for grinding with aluminium oxide wheels,as where is the energy required for chip formation,having a constant value of about 13.8 J mm-3 for grinding all ferrous materials and u is the total specific grinding energy required for grinding,calculated from where is the workspeed and,consequently,as in Jaeger's model,the speed of the moving heat source.Note that,in both Eqs (2) and (4),the value of ,is required in order to calculate the heat flux and the total specific grinding energy,respectively; it can be calculated from where is the power per unit width of the workpiece,which was measured during the testing of the different grinding wheels.Therefore,from Eqs (2)一(5),the heat flux can be calculated for every case.The kind of modelling suggested in this paper is suitable for a grinding process with a very small depth of cut,since there is no modelling of the chip.In any other case,other assumptions must be made for the chip in order to provide a valid model,since the heat carried away by the chip cannot be neglected.Furthermore,the two coef- ficients of the workpiece material that are related to temperature,i.e.the thermal conductivity and the specific heat capacity,along with the density of the workpiece must be inserted as inputs to the program.For the material used in the wheel testing,those quantities were taken from the FEM program data bank.The first two were considered to be temperature dependent.