Spindle Thermal Error Optimization Modeling of a Five-axis Machine Tool

Chinese Journal of Mechanical Engineering

Table 2 Grey relational degree between thermal errors and 24 heat sources

Grey relational degree	Initial transform	Average transform	Polar difference transform	Sum of different transform
\(\gamma_{25,\,1}\)	0.255	0.314	0.287	0.856
\(\gamma_{25,\,2}\)	0.813	0.725	0.711	2.249
\(\gamma_{25,\,3}\)	0.327	0.404	0.398	1.129
\(\gamma_{25,\,4}\)	0.521	0.302	0.278	1.101
\(\gamma_{25,\,5}\)	0.412	0.544	0.459	1.415
\(\gamma_{25,\,6}\)	0.654	0.791	0.549	1.994
\(\gamma_{25,\,7}\)	0.695	0.683	0.799	2.177
\(\gamma_{25,\,8}\)	0.390	0.627	0.515	1.532
\(\gamma_{25,\,9}\)	0.529	0.384	0.425	1.338
\(\gamma_{25,\,10}\)	0.587	0.644	0.637	1.868
\(\gamma_{25,\,11}\)	0.491	0.505	0.487	1.483
\(\gamma_{25,\,12}\)	0.526	0.488	0.571	1.585
\(\gamma_{25,\,13}\)	0.722	0.689	0.667	2.078
\(\gamma_{25,\,14}\)	0.333	0.471	0.286	1.090
\(\gamma_{25,\,15}\)	0.663	0.492	0.525	1.680
\(\gamma_{25,\,16}\)	0.621	0.511	0.529	1.661
\(\gamma_{25,\,17}\)	0.632	0.818	0.655	2.105
\(\gamma_{25,\,18}\)	0.756	0.803	0.664	2.223
\(\gamma_{25,\,19}\)	0.575	0.596	0.747	1.918
\(\gamma_{25,\,20}\)	0.515	0.357	0.476	1.348
\(\gamma_{25,\,21}\)	0.375	0.466	0.583	1.424
\(\gamma_{25,\,22}\)	0.568	0.485	0.609	1.662
\(\gamma_{25,\,23}\)	0.598	0.687	0.724	2.009
\(\gamma_{25,\,24}\)	0.429	0.394	0.443	1.266