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

Patent metadata

Field	Value
Publication number	US-12066809-B2
Application number	US-202117470015-A
Country	US
Kind code	B2
Filing date	Sep 9, 2021
Priority date	Apr 12, 2021
Publication date	Aug 20, 2024
Grant date	Aug 20, 2024

Abstract

A method for identifying a critical error of a worm gear machine, step 1: obtaining an actual forward kinematic model T 27 a and an ideal forward kinematic model T 27 i from a coordinate system of a worm gear hob to a coordinate system of a worm gear, thereby establishing a geometric error-pose error model of the worm gear machine; step 2: regarding 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, an importance coefficient of each input feature with a random forest algorithm; and step 3: determining a critical error affecting a machining accuracy of the worm gear machine.

First claim

What is claimed is:

1. 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 T 27 a and an ideal forward kinematic model T 27 i 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 T 27 a and the ideal forward kinematic model T 27 i ;
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 T 27 a and the ideal forward kinematic model T 27 i 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 T 27 a and the ideal forward kinematic model T 27 i ;
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 δ x (s) of an S-axis in motion, a y-direction linear error δ y (s) of the S-axis in motion, a z-direction linear error δ z (s) of the S axis in motion, an x-direction angular error ε x (s) of the S-axis in motion, a y-direction angular error ε y (s) of the S-axis in motion, and a z-direction angular error ε z (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 φ yz between the X axis and the Z axis, a perpendicularity error φ zy between the Y axis and the Z axis, and a perpendicularity error φ xy 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 δ xc of the C axis in placement, a y-direction linear error δ yc of the C axis in placement, an x-direction angular error φ xc of the C axis in placement, and a y-direction angular error φ yc of the C axis in placement.

2. The method for identifying the critical error of the worm gear machine according to claim 1 , wherein in the step a2), with the worm gear hob as a transfer end point, the worm gear machine has a following motion chain: worm gear→C-axis→bed→X-axis→Z-axis→Y-axis→B-axis→worm gear hob, wherein the worm gear-C axis-bed serves as a workpiece chain, and the bed→X-axis→Z-axis→Y-axis→B-axis→worm gear hob serves as a cutter chain;
during consideration of the geometric errors, an actual kinematic model of the tool chain is:
T 02 a =T 01 T 12 =T p01 T pe01 T m01 T me01 ×T p12 T pe12 T m12 T me12 ;

and
an ideal kinematic model of the tool chain is:
T 02 i =T 01 i T 12 i =T p01 T m01 ×T p12 T m12

wherein, T 02 a and T 02 i respectively represent an actual transformation matrix and an ideal transformation matrix from the worm gear to the bed; T 01 and T 01 i respectively represent an actual transformation matrix and an ideal transformation matrix from the C axis to the bed; T 12 and T 12 i respectively represent an actual transformation matrix and an ideal transformation matrix from the worm gear to the C axis; T p01 represents a placement matrix from the C axis to the bed; T pe01 represents a placement error matrix from the C axis to the bed; T m01 represents a motion matrix from the C axis to the bed; T me01 represents a motion error matrix from the C axis to the bed; T p12 represents a placement matrix from the worm gear to the C axis; T pe12 represents a placement error matrix from the worm gear to the C axis; T m12 represents a motion matrix from the worm gear to the C axis; and T me12 represents a motion error matrix from the worm gear to the C axis; and
during consideration of the geometric errors, an actual kinematic model of the cutter chain is:
T 07 a =T 03 T 34 T 45 T 56 T 67 =T p03 T pe03 T m03 T me03 ×T p34 T pe34 T m34 T me34 ×T p45 T pe45 T m45 T me45 ×T p56 T pe56 T m56 T me56 ×T p67 T pe67 T m67 T me67 ;

and
an ideal kinematic model of the cutter chain is:
T 07 i =T p03 T m03 T p34 T m34 T p45 T m45 T p56 T m56 T p67 T m67

wherein, T 07 a and T 07 i respectively represent an actual transformation matrix and an ideal transformation matrix from the worm gear hob to the bed; T 03 represents an actual transformation matrix from the X axis to the bed; T 34 represents an actual transformation matrix from the Z axis to the X axis; T 45 represents an actual transformation matrix from the Y axis to the Z axis; T 56 represents an actual transformation matrix from the B axis to the Y axis; represents an actual transformation matrix from the worm gear hob to the B axis; T p03 represents a placement matrix from the X axis to the bed; T pe03 represents a placement error matrix from the X axis to the bed; T m03 represents a motion matrix from the X axis to the bed; T me03 represents a motion error matrix from the X axis to the bed; T p34 represents a placement matrix from the Z axis to the X axis; T pe34 represents a placement error matrix from the Z axis to the X axis; T m34 represents a motion matrix from the Z axis to the X axis; T me34 represents a motion error matrix from the Z axis to the X axis; T p45 represents a placement matrix from the Y axis to the Z axis; T pe45 represents a placement error matrix from the Y axis to the Z axis; T m45 represents a motion matrix from the Y axis to the Z axis; T me45 represents a motion error matrix from the Y axis to the Z axis; T p56 represents a placement matrix from the B axis to the Y axis; T pe56 represents a placement error matrix from the B axis to the Y axis; T m56 represents a motion matrix from the B axis to the Y axis; T me56 represents a motion error matrix from the B axis to the Y axis; T p67 represents a placement matrix from the worm gear hob to the B axis; T pe67 represents a placement error matrix from the worm gear hob to the B axis; T m67 represents a motion matrix from the worm gear hob to the B axis; and T me67 represents a motion error matrix from the worm gear hob to the B axis,
thereby obtaining the actual forward kinematic model of the worm gear machine from the coordinate system of the worm gear hob to the coordinate system of the worm gear:
T 27 a =( T 02 a ) −1 T 07 a ;

and
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Assignees

• Univ Chongqing

Inventors

• Wang Shilong
• Ma Chi
• Wang Sibao
• Heng Dechao
• Zeng Lingwan
• Yang Yong
• Yang Canhui

Classifications

• G06N5/01

  Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound · CPC title

• G05B19/406

  characterised by monitoring or safety (G05B19/19 takes precedence) · CPC title

• F16H2057/012

  of gearings · CPC title

• F16H57/01

  Monitoring wear or stress of gearing elements, e.g. for triggering maintenance · CPC title

• G06F2119/02

  Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA] · CPC title