Kinematic error modeling and analysis of the loading device based on multi-body theory and stream of variation theory
Because of some reasons such as machining error and assembly clearance, the loading device will produce kinematic error during movement. While kinematic error will have a great significance on the position accuracy of the loading device. For the above reasons, firstly, the topological structure of the loading device was described based on lower body arrays. The kinematic error matrices of adjacent parts in the loading device were obtained by multi-body system kinematic theory and homogeneous translation matrix (HTM). Then an improved error modeling method was put forward, which combined multi-body system theory with stream of variation theory. And the kinematic error model of the loading device was set up with this method. Numerical results could clearly display the error transformation and propagation among components. Finally, the effect of every kinematic error on final deviation was analyzed, and error sources of a greater effect on the final deviation were obtained. This method can provide a theoretical basis to improve the accuracy of the loading device.
Analysis and modeling of error of spiral bevel gear grinder based on multi-body system theory
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.
Flank Modification Methodology for Face-Hobbing Hypoid Gears Based on Ease-Off Topography
The fundamental design of spiral bevel and hypoid gears is usually based on a local synthesis and a tooth contact analysis of the gear drive. Recently, however, several flank modification methodologies have been developed to reduce running noise and avoid edge contact in gear making, including modulation of tooth surfaces under predesigned transmission errors. This paper proposes such a flank modification methodology for face-hobbing spiral bevel and hypoid gears based on the ease-off topography of the gear drive. First, the established mathematical model of a universal face-hobbing hypoid gear generator is applied to investigate the ease-off deviations of the design parameters-including cutter parameters, machine settings, and the polynomial coefficients of the auxiliary flank modification motion. Subsequently, linear regression is used to modify the tooth flanks of a gear pair to approximate the optimum ease-off topography suggested by experience. The proposed method is then illustrated using a numerical example of a face-hobbing hypoid gear pair from Oerlikon's Spiroflex cutting system. This proposed flank modification methodology can be used as a basis for developing a general technique of flank modification for similar types of gears.