【正文】
hat of the previous moment and the rotation speed of spindle. So a model representing the behavior of the thermal errors as written is the form where Δ z ( t) ——— Thermal error at time t k , m ——— Order of the model ai , bi ——— Coefficient of the model n ( t i) ——— Spindle rotation speed at time t i The order k and m are determined by the final predictionerror criterion. The coefficients ai and bi are estimated by artificial neural work technique. A neural work is a multiple nonlinear regression equation in which the coefficient s are called weight s and are t rained with an iterative technique called back propagation. It is less sensitive than other modeling technique to individual input failure due to thresholding of the signals by the sigmoid functions at each node. The neural work for this problem is shown in . ( k = 1 , m = 0) . The number of hidded nodes is determined by a trialand error procedure. Using the data obtained (thermal errors and correspondence speed) , four models for the errors at z 1 , z 2 , z 3 and z 4 are established. Thermal errors at positions other than z 1 , z 2 , z 3 , z 4 are calculated by an interpolating function. So the errors at any z coordinates can be obtained. In order to verify the prediction accuracy of the model , a number of new operation conditions are used. Fig14 shows an example of predicted result on a new condition. It shows that the auto regressive model based on speed can descibe thermal errors well in a relative stable environment . A neural work for thermal errors Thermal error predicting results 2Predicting results 3 PRECOMPENSATION FOR THERMAL ERRORS The principle of prepensation for thermal errors is shown in . The spindle rotation speed and the z coordinates are known as soon as the workpiece NC machining program is made. By , for example , every 10 min , the thermal errors Δ z are calculated by the model. Then the program is corrected by adding the calculated Δ z to the original z . So the thermal errors are pensated before machining. The effectiveness of the error pensation is verified by many cutting test s. Several surfaces are milled under cold start and after 1 h run with varying speeds. As shown in , the depth difference of the milled surface is used to evaluate the pensation result of the thermal errors in z direction. It shows that the difference is reduced from 7μ m to 2μ m. Compensation for thermal errors by revising machining program The effectiveness of pensation 4 CONCLUSIONS A novel method for improving the accuracy of CNC machine tools is discussed. The core of the study is an error model based on spindle rotation speed but not on temperature like conventional approach. By revising the NC workpiece machining program , the thermal errors can be pensated before machining but not in realtime. By using the method , the accuracy of machine tools can be increased economically. References 1 Chen J S , Chiou G. Quick testing and modeling of thermallyinduced errors of CNC machine tools. International Journal of Machine Tools and Manufacture , 1995 , 35(7) ∶ 1 063~ 1 074 2 Chen J S. Computeraided accuracy enhancement for multiaxis CNC machine tool. International Journal of Machine Tools and Manufacture , 1995 , 35(4) ∶ 593~ 605 3 Donmez M A. A general methodology for machine tool accuracy enhancement by erro