Analysis and modeling of error of spiral bevel gear grinder based on multi-body system theory

Abstract

Six-axis numerical control spiral bevel gear grinder was taken as the object, multi-body system theory and Denavit-Hartenberg homogeneous transformed matrix (HTM) were utilized to establish the grinder synthesis error model, and the validity of model was confirmed by the experiment. Additionally, in grinding wheel tool point coordinate system, the errors of six degrees of freedom were simulated when the grinding wheel revolving around C-axis, moving along X-axis and Y-axis. The influence of these six errors on teeth space, helix angle, pitch, teeth profile was discussed. The simulation results show that the angle error is in the range from −0.148 4 rad to −0.241 9 rad when grinding wheel moving along X, Y-axis; the translation error is in the range from 0.866 0 μm to 3.605 3 μm when grinding wheel moving along X-axis. These angle and translation errors have a great influence on the helix angle, pitch, teeth thickness and tooth socket.

Keywords

six-axis / grinder / spiral bevel gear / error model / analysis

References

[1] ShihY. P., FongZ. H.. Flank modification methodology for face-hobbing hypoid gears based on ease-off topography [J]. Journal of Mechanical Design, 2007, 129(12): 1294-1302

[2] LinC. Y., TsayC. B., FongZ. H.. Computer-aided manufacturing of spiral bevel and hypoid gears with minimum surface deviation [J]. Mech Mach Theory, 1998, 33(6): 785-803

[3] LinC. Y., TsayC. B., FongZ. H.. Computer-aided manufacturing of spiral bevel and hypoid gears by applying optimization techniques [J]. Journal of Materials Processing Technology, 2001, 114: 22-35

[4] FanS.-b., WangT.-y., WangW.-j., WangW.-j., LengY.-gang.. Prediction of diameter errors compensation in bars turning [J]. Journal of Central South University of Technology, 2005, 12(S2): 264-268

[5] LeiW. T., SungM. P.. NURBS-based fast geometric error compensation for CNC machine tools [J]. Inter Mach Tools Manufact, 2008, 48: 1199-1213

[6] SrivastavaA. K., VeldhuisS. C., ElbestawitM. A.. Modeling geometric and thermal errors in a five-axis CNC machine tool [J]. Inter J Mach Tools Manufact, 1995, 35(9): 1321-1337

[7] LinY., ShenY.. Modeling of five-axis machine tool metrology models using the matrix summation approach [J]. The International Journal of Advanced Manufacturing Technology, 2003, 21: 243-248

[8] BohezE. L. J.. Compensating for systematic errors in 5-axis NC machining [J]. Computer-Aided Dsign, 2002, 34: 391-403

[9] OkaforA. C., ErtekinY. M.. Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics [J]. Inter J Mach Tools Manufact, 2000, 40: 1199-1213

[10] LeeJ. H., YangS. H.. Measurement of geometric errors in a miniaturized machine tool using capacitance sensors [J]. Journal of Materials Processing Technology, 2005, 165: 1402-1409

[11] YangH., NiJ.. Dynamic neural network modeling for nonlinear, nonstationary machine tool thermally induced error [J]. Inter J Mach Tools Manufact, 2005, 45: 455-465

[12] YangH., NiJ.. Adaptive model estimation of machine-tool thermal errors based on recursive dynamic modeling strategy [J]. Inter J Mach Tools Manufact, 2005, 45: 1-11

[13] ZhaoH.-t., YangJ.-g., ShenJ.-hua.. Simulation of thermal behavior of a CNC machine tool spindle [J]. Inter J Mach Tools Manufact, 2007, 47: 1003-1010

[14] FlorussenG. H. J., DelbressineF. L. M., Van De MolengraftM. J. G., SchellekensP. H. J.. Assessing geometrical errors of multi-axis machines by three-dimensional length measurements [J]. Measurement, 2001, 30: 241-255

[15] TongH.-c., YangJ.-g., LiuG.-l., WangX.-s., LiY.-xiang.. The volumetric error modeling technique of the two-axis system in an NC lathe [J]. Journal of Shanghai Jiaotong University, 2006, 40(7): 1213-1217