Method for identifying critical error of worm gear machine and method for iteratively compensating critical error of worm gear machine

A method for identifying a critical error of a worm gear machine, comprising the following steps:

• step a):
• analyzing a geometric error of each motion axis of the worm gear machine, and obtaining an actual forward kinematic model T27a and an ideal forward kinematic model T27i from a coordinate system of a worm gear hob to a coordinate system of a worm gear based on a motion chain of the worm gear machine, thereby establishing a geometric error-pose error model of the worm gear machine which contains final geometric errors after comparing between the actual forward kinematic model T27a and the ideal forward kinematic model T27i;
• step b):
• having the geometric error-pose error model of the worm gear machine as a multi-input multi-output (MIMO) nonlinear system, and solving, by taking the geometric error of each motion axis of the worm gear machine as an input feature X, and a pose error between the worm gear hob and the worm gear as an output variable Y, a coefficient of each input feature with a random forest algorithm;
• step c):
• determining, according to the solved coefficient of each input feature, the critical error affecting a machining accuracy of the worm gear machine;
• and
• step d):
• outputting numerical control instruction to the worm gear machine to adjust positions of the worm gear hob to correct the critical error affecting the machining accuracy of the worm gear machine;
• wherein in the step a), a method for establishing the geometric error-pose error model of the worm gear machine is as follows:
• step a1) analyzing the geometric error of the worm gear machine;
• step a2) obtaining the actual forward kinematic model T27a and the ideal forward kinematic model T27i from the coordinate system of the worm gear hob to the coordinate system of the worm gear according to the motion chain of the worm gear machine;
• and
• step a3) establishing the geometric error-pose error model of the worm gear machine from the actual forward kinematic model T27a and the ideal forward kinematic model T27i;
• wherein in the step a1), geometric errors of X-, Y-, Z- and C-motion axes of the worm gear machine are considered, wherein
• each motion axis comprises 6 items of position-dependent geometric errors (PDGEs), respectively comprising:
• an x-direction linear error δx(s) of an S-axis in motion, a y-direction linear error δy(s) of the S-axis in motion, a z-direction linear error δz(s) of the S axis in motion, an x-direction angular error εx(s) of the S-axis in motion, a y-direction angular error εy(s) of the S-axis in motion, and a z-direction angular error εz(s) of the S-axis in motion, wherein s represents a motion instruction of the motion axis S, and s=x, y, z, c;
• position-independent geometric errors (PIGEs) are present between the motion axes, respectively comprising:
• a perpendicularity error φyz between the X axis and the Z axis, a perpendicularity error φzy between the Y axis and the Z axis, and a perpendicularity error φxy between the Y axis and the X axis;
• and
• the C axis has four items of placement errors, respectively comprising:
• an x-direction linear error δxc of the C axis in placement, a y-direction linear error δyc of the C axis in placement, an x-direction angular error φxc of the C axis in placement, and a y-direction angular error φyc of the C axis in placement.