CN-118734482-B - Tooth profile inclination deviation correction method based on grinding wheel initial position deviation

CN118734482BCN 118734482 BCN118734482 BCN 118734482BCN-118734482-B

Abstract

The invention relates to the technical field of numerical control, in particular to a tooth profile inclination deviation correction method based on grinding wheel initial position deviation, which realizes tooth profile inclination correction by adjusting the grinding wheel initial position. The method comprises the steps of establishing a tooth profile deviation correction coordinate system, obtaining a transformation relation between a grinding wheel coordinate system and a workpiece coordinate system, solving a grinding wheel contact line equation, obtaining coordinates of corresponding contact points in the grinding wheel coordinate system, transforming contact line coordinate points into the workpiece coordinate system, solving gear end surface profiles, calculating tooth profile inclination deviations on the left side and the right side according to the obtained end surface profiles, and solving optimal grinding wheel position deviation by adopting a particle swarm optimization algorithm with the least square sum of tooth profile inclination deviations on the left side and the right side as a target. The tooth profile inclination deviation correction is carried out by adopting a method for shifting the initial position of the grinding wheel, so that the calculation amount is small, the method is simple and efficient, and the result stability is high.

Inventors

SUN XIAOMIN
SHEN MIN
YU CHUNJIAN
ZHANG HU
CUI JUNJUN

Assignees

南京工大数控科技有限公司

Dates

Publication Date: 20260512
Application Date: 20240624

Claims (4)

1. The tooth profile inclination deviation correction method based on the initial position deviation of the grinding wheel is characterized by comprising the following steps of: step one, establishing a tooth profile deviation correction coordinate system according to the position offset of a grinding wheel to obtain a transformation relation between the grinding wheel coordinate system and a workpiece coordinate system; calculating a grinding wheel contact line, and obtaining coordinates of discrete points on the contact line in a grinding wheel coordinate system; step three, obtaining coordinates of a contact line in a workpiece coordinate system, and solving a gear end surface profile; step four, calculating the inclination deviation of the tooth profiles at the left side and the right side according to the obtained end surface profile; Step five: Establishing a mathematical model which takes X-axis radial offset d x , Y-axis tangential offset d y and A-axis offset d A of the initial position of the grinding wheel as independent variables and takes the least square sum of the corrected left and right tooth profile inclination offset as a target, and obtaining a target equation as follows: (1) In order to solve the model, a particle swarm optimization algorithm is adopted to solve a target equation, and optimal d x 、d y and d A are obtained.
2. The tooth profile inclination deviation correcting method based on the initial position deviation of the grinding wheel according to claim 1, wherein in the first step, a tooth profile deviation correcting coordinate system is established according to the initial position deviation of the grinding wheel, the coordinate system S p (O p -x p y p z p ) is fixedly connected with the workpiece, the coordinate system S w (O w -x w y w z w ) is fixedly connected with the grinding wheel, and the transformation matrix of the workpiece coordinate system S p (O p -x p y p z p ) and the grinding wheel coordinate system S w (O w -x w y w z w ) is as follows: (2) In the formula (2), , , , ; In the above method, d x is the X-axis radial offset of the initial position of the grinding wheel, d y is the Y-axis tangential offset, d A is the A-axis offset, a x0 is the distance between the grinding wheel and the gear in the X-axis direction, and a z is the distance between the grinding wheel and the gear in the z-axis direction; the mounting angle of the grinding wheel is set; The rotation angle of the workpiece around the x axis is given, and p is the spiral parameter.
3. The method for correcting tooth profile inclination deviation based on initial position deviation of grinding wheel according to claim 1, wherein in the second step, normal vectors of any point on the grinding wheel rotation surface and the grinding wheel curved surface can be respectively marked as And The expression of the curved surface of the grinding wheel and the normal vector is converted from a grinding wheel coordinate system to a gear coordinate system as follows: (3) (4) In the above , According to the space curved surface meshing principle, any point on the forming grinding wheel and the contact line meets the condition that the normal vector of the tooth surface is perpendicular to the direction of the relative motion speed of the grinding wheel and the gear, so that the following conditions can be obtained: (5) In the above Representation matrix V p (phi) is the relative motion speed of the grinding wheel and the gear; The grinding wheel contact equation can be found as follows: (6) in the formula (6) of the present invention, , The axial profile of the grinding wheel is expressed as a plurality of discrete points according to the parameter R, and the parameter corresponding to the parameter R can be obtained according to a contact line equation Then will Substituting the contact line equation to obtain the coordinate of the corresponding contact point in the grinding wheel coordinate system, and marking as 。
4. The method for correcting tooth profile inclination deviation based on initial position deviation of grinding wheel as claimed in claim 1, wherein in said step three, coordinates of the contact line in the workpiece coordinate system, which can be obtained based on the transformation relation between the grinding wheel coordinate system S w (O w -x w y w z w ) and the workpiece coordinate system S p (O p -x p y p z p ), are recorded as ; The contact line is projected to the end face of the gear in a spiral way, and the profile of the end face of the gear can be obtained as follows: (7) In the fourth step, according to the difference between the gear end surface profile and the theoretical tooth profile obtained in the third step, namely the normal distance from the point on the involute to the gear end surface profile curve obtained in the third step, the accuracy evaluation is carried out, so as to obtain the inclination deviation of the tooth profiles at the left side and the right side And Let the measured left and right tooth profile tilt deviations be respectively And 。

Description

Tooth profile inclination deviation correction method based on grinding wheel initial position deviation Technical Field The invention relates to the technical field of numerical control machinery, in particular to a tooth profile inclination deviation correction method based on grinding wheel initial position deviation. Background The numerical control forming gear grinding machine is widely applied to high-precision gear machining, including grinding machining of gears such as straight/helical gear, complex tooth profile modification gear and the like. For tooth profile inclination deviation correction, a sand profile correction method is generally adopted. However, the key point of the method is that a correction curve is designed according to discrete data points, and common curve design methods include NURBS interpolation, B spline fitting and the like, so that the actual use processing method is complex, the stability of the calculation effect is easily affected, and the calculation efficiency is low due to excessive complexity. In view of this, a tooth profile inclination deviation correction method based on the initial position deviation of the grinding wheel is proposed. Disclosure of Invention The invention aims to provide a tooth profile inclination deviation correction method based on grinding wheel initial position deviation, which aims to solve the problems of complex calculation, large calculated amount, low efficiency and unstable effect in the tooth profile inclination deviation correction process. To achieve the above object, the present invention provides a method comprising the steps of: A tooth profile inclination deviation correction method based on grinding wheel initial position deviation comprises the following steps: step one, establishing a tooth profile deviation correction coordinate system according to the position offset of a grinding wheel to obtain a transformation relation between the grinding wheel coordinate system and a workpiece coordinate system; calculating a grinding wheel contact line, and obtaining coordinates of discrete points on the contact line in a grinding wheel coordinate system; step three, obtaining coordinates of a contact line in a workpiece coordinate system, and solving a gear end surface profile; step four, calculating the inclination deviation of the tooth profiles at the left side and the right side according to the obtained end surface profile; Establishing a mathematical model with the grinding wheel position offset as a variable and with the minimum sum of squares of tooth profile inclination offset values at the left side and the right side as a target, and solving the optimal grinding wheel position offset by adopting a particle swarm algorithm. In the first step, a tooth profile deviation correction coordinate system is established according to the initial position offset of the grinding wheel, the coordinate system S p(Op-xpypzp) is fixedly connected with the workpiece, the coordinate system S w(Ow-xwywzw) is fixedly connected with the grinding wheel, and the transformation matrix of the workpiece coordinate system S p(Op-xpypzp) and the grinding wheel coordinate system S w(Ow-xwywzw) is as follows: Mwp＝Mw4M43M31M1p (1) In the formula (1), In the above, d x is the X-axis radial offset of the initial position of the grinding wheel, d y is the Y-axis tangential offset, d A is the A-axis offset, a x0 is the distance between the grinding wheel and the gear in the X-axis direction, a z is the distance between the grinding wheel and the gear in the z-axis direction, and Sigma 0 is the mounting angle of the grinding wheel; The angle of rotation of the workpiece around the x-axis is given by p, which represents the spiral parameter of the spiral line. In the second step, normal vectors of any point on the grinding wheel rotation surface and the grinding wheel curved surface can be respectively marked as R w (R, gamma) and n w (R, gamma) under a grinding wheel coordinate system S w(Ow-xwywzw, and then the grinding wheel curved surface and the normal vector expression are transformed from the grinding wheel coordinate system to a gear coordinate system as follows: rp＝Mpwrw (2) np＝Mpwnw (3) M in the above pw＝Mwp-1 According to the space curved surface meshing principle, any point on the forming grinding wheel and the contact line meets the condition that the normal vector of the tooth surface is perpendicular to the direction of the relative motion speed of the grinding wheel and the gear, so that the following conditions can be obtained: Wherein M pwT represents the transpose of matrix M pw; is opposite to the gear of the grinding wheel is a relative movement speed of the two; The grinding wheel contact equation can be found as follows: acos(γ)+bsin(γ)=c (5) In the formula (5) of the present invention, The axial profile of the grinding wheel is expressed as a plurality of discrete points according to the parameter R, the parameter gamma corresponding