CN-121995844-A - Conjugate characteristic line-based five-axis machining tool path planning method for spiral bevel gear universal tool

CN121995844ACN 121995844 ACN121995844 ACN 121995844ACN-121995844-A

Abstract

The invention discloses a conjugate characteristic line-based five-axis machining tool path planning method for a spiral bevel gear universal tool, which comprises the steps of designing a conjugate characteristic line calculation and solving method for tooth surfaces of the spiral bevel gear, designing a tool path planning method taking the maximum residual height of adjacent tool paths as an optimization target, and designing a strategy for tool path optimization by controlling the maximum residual height according to the distribution condition and geometric structure characteristics of the conjugate characteristic lines. According to the position information of the tooth surface points of the spiral bevel gear, the tooth surface points are divided and discretized, and the tooth surface processing conjugate characteristic line is obtained after calculation according to the information such as the coordinate system of the cutter and the gear. And optimizing the machining tool path planning based on the conjugate characteristic line by taking the residual height as a target, thereby realizing the establishment of a more efficient and more accurate five-axis machining tool path planning method for the universal tool. The method has strong innovation, and can be used for processing the tooth surface of the spiral bevel gear more efficiently according to the requirement on the meshing performance of the gear.

Inventors

WANG PENG
LI DUO
ZHANG CHUNQI
SONG YI
Qiao Baofang
ZHANG LIANG
CHEN YANG

Assignees

北京工业大学

Dates

Publication Date: 20260508
Application Date: 20260106

Claims (10)

1. A conjugate characteristic line-based five-axis machining tool path planning method for a spiral bevel gear universal tool is characterized by comprising the following steps: Step A, planning a cutter path based on a machining conjugate characteristic line; Taking the moment when a cutter is used for machining a gear workpiece and is exactly tangent as a starting point, setting the radial vector of a tooth surface as R w =r w (Z, R) under a workpiece coordinate system, solving the position information of the tooth surface point at any moment according to a meshing equation and a mathematical model of a general cutter for machining the gear, discretizing the tooth surface and the excessive rounded corner part by adopting a Newton iteration method until a complete working tooth surface point set is finally obtained, reversely solving coordinate points in the form of (s, theta, phi) on the tooth surface according to Z, R coordinates, and calculating to obtain phi lines, namely paths when the cutter is used for cutting a spiral bevel gear; step B, calculating the tooth surface residual height; The residual height is the protrusion height formed by the material residues which are not completely cut off by the cutting edge between the adjacent tool tracks after the processing along the planned tool path and the maximum normal deviation between the processed residual tooth surface and the theoretical tooth surface; determining an initial machining direction and a cutter pose based on machining conjugate feature phi lines, determining a running distance through optimization calculation, wherein key constraint is a machining residual height, establishing an optimization model, solving the optimal running distance on the premise of meeting constraint, and planning a cutter machining path based on the conjugate feature lines; Step C, optimizing a cutter path by taking the control residual height as a target; Based on a residual height calculation formula, the conjugate characteristic line is processed by the minimum number of feeding times through a planning method of an encryption tool path, so that redundant cutting paths are avoided; Step D, calculating cutter position points of the general cutter; Converting the planned tooth surface coordinate point of the spiral bevel gear into a cutter point during processing, selecting the cutter point as a cutter center point, guiding the cutter point into CAM software for cutter path analysis after conversion, establishing the position relationship between the tooth surface coordinate point and the cutter point center during processing, and then establishing the position information of the cutter point and the cutter axis according to the tooth surface point information.
2. The conjugate characteristic line-based five-axis machining tool path planning method for the spiral bevel gear universal tool, which is disclosed in claim 1, is characterized in that in the step A, the radial vector of the tooth surface is r w =r w (s, θ, φ)=(x w , y w , z w ), and the method is obtained according to an engagement equation: (1) Wherein Z is the axial projection coordinate of a tooth surface point, R is the radial projection coordinate of a tooth surface point, x w ,y w ,z w is the coordinate of a tooth surface point under a workpiece coordinate system, The method is a conjugate engagement equation of a cutter and a tooth surface, wherein s is a cutter edge arc length parameter, theta is a cutter rotation motion parameter, and phi is a cutter generation motion parameter.
3. A five-axis machining tool path planning method for spiral bevel gears based on conjugate characteristic lines is characterized in that a Newton iteration method is adopted to discretize tooth surfaces, namely, a working tooth surface is divided into grids according to tooth width and tooth height directions, tooth surface Z and R coordinates are obtained through coordinate conversion by taking grid midpoints as iteration initial values in projection planes, the tooth surfaces are discretized into m multiplied by n points, wherein m is a discrete value in the tooth height direction, n is a discrete value in the tooth width direction, the working tooth surfaces are discretized into m 1 multiplied by n points, the initial values are continuously updated through bidirectional iteration, the validity of projection areas of the points is verified, and finally a complete working tooth surface point set is obtained.
4. A five-axis machining tool path planning method of a spiral bevel gear universal tool based on conjugate characteristic lines is characterized in that a transition fillet part is discretized into m 2 multiplied by n points, the m 2 multiplied by n points are combined with a working tooth surface to form a complete (m 1+ m 2 ) multiplied by n tooth surface, the tooth surface points obtained through iteration are coordinate points in the form of (s, theta, phi) on the tooth surface according to Z and R coordinates, phi lines are obtained through combination and solving of a tool and the tooth surface in a conjugate meshing equation and coordinate transformation, phi represents different conjugate characteristic lines, phi represents different points on the conjugate characteristic lines for a designated conjugate characteristic line theta, s represents different positions of contact points of the tool and the tooth surface on the tool.
5. The conjugate characteristic line-based five-axis machining tool path planning method for the spiral bevel gear universal tool, which is disclosed in claim 1, is characterized in that in the step B, a calculation formula of the residual height between every two machining conjugate characteristic phi lines is determined, and the method is as follows: (1) When the cutter cuts the gear, the cutter position vector of each point on the processing conjugate feature phi i line is intersected with the cutter position vector of each point on the processing conjugate feature phi i+1 line, and the distance between the intersection point and the tooth surface is the residual height; (2) Based on the tooth surface information of each point on the processing conjugate feature phi i+1 line, calculating the position vector of each intersection point, wherein the position vector of each intersection point is determined by the formula (2); (2) Wherein p 0 is the position vector of the tooth point on phi i , l 0 is the position vector parameter of the tool on phi i , tau 0 is the position vector direction of the tool on phi i , p 1 is the position vector of the tooth point on phi i+1 , l 1 is the position vector parameter of the tool on phi i+1 , tau 1 is the position vector direction of the tool on phi i+1 ; (3) After the position vector of the intersection point is determined, the intersection point projects to the tooth surface to obtain a projection point on the tooth surface, the projection point is set as O, the intersection point is set as C, and the residual height value is obtained 。
6. The five-axis machining tool path planning method for the spiral bevel gear universal tool based on the conjugate characteristic lines is characterized in that in the step C, the interval between every two machining conjugate characteristic phi lines is regarded as a running distance on the basis of the machining conjugate characteristic lines on the tooth surfaces of the spiral bevel gear, and the value of the running distance is set according to different parameters of gears and tools by adjusting the generating angle of the conjugate tooth surfaces.
7. The method for planning the five-axis machining tool path of the spiral bevel gear universal tool based on the conjugated characteristic lines, according to claim 1 or 6, is characterized in that on the concave-convex surface of the large gear and the convex surface of the small gear, the residual height between every two machining conjugated characteristic phi lines is reduced along with the increase of a theta value and is a decreasing function, and for the concave surface of the small gear, the residual height between every two machining conjugated characteristic phi lines is increased along with the increase of the theta value and is an increasing function.
8. The conjugate characteristic line-based five-axis machining tool path planning method for the spiral bevel gear universal tool is characterized in that the encryption tool path planning method is suitable for the approximation of the initial running distance setting which meets the residual height requirement, and because of the non-uniform condition characteristics of the characteristic line distribution, the residual height requirement is partially not met, an additional part of conjugate characteristic line is needed to be inserted in a place with sparse conjugate characteristic line distribution, and encryption part tool paths are optimized.
9. The method of claim 1, further comprising a ball-end cutter, wherein the ball-end cutter is configured to set a position relationship between a tooth surface coordinate point and a cutter tip center during machining, and the tooth surface coordinate point is set as an O point, and a position vector of the O point is Obtaining the position vector of the knife tip center through conversion ; (3) Wherein r is the radius of the universal cutter, s is 1/2-1/5;l r of the arc length of the selected cutter point, the radial direction of the cutter is the normal vector n when the cutter is tangential to the tooth surface, and l s is the generatrix direction T of the cutter.
10. The method for planning the five-axis machining tool path of the spiral bevel gear universal tool based on the conjugate characteristic line, which is characterized by further comprising a flat bottom end mill, wherein the tool position calculation of the flat bottom end mill is performed by adopting a flat bottom milling cutter side edge milling method, and the solution of the milling tool position of the flat bottom end mill side edge is as follows: (4) Wherein n P is the normal vector of the tooth surface and the cutter tangential point, i m is the vector of the cutter shaft direction, l is the distance between the cutter tangential point and the cutter end face, r P and r CL are the position vectors of the point P and the point C L in space respectively, and the distance d between the point A and the adjacent tooth surface should be ensured to take a safety value in processing.

Description

Conjugate characteristic line-based five-axis machining tool path planning method for spiral bevel gear universal tool Technical Field The invention relates to the technical field of spiral bevel gear machining, and provides a conjugate characteristic line-based five-axis machining tool path planning method for a spiral bevel gear universal tool. Background Spiral bevel gears are a collective term for conical gears with curved tooth surface pitch lines, and include so-called spiral bevel gears, spiral hypoid gears, cycloidal bevel gears, and cycloidal hypoid gears. The spiral bevel gear can realize the transmission of the movement and power between intersecting or staggered shafts, has the characteristics of stable transmission, high bearing capacity and good meshing performance, and is widely applied to key transmission parts in large heavy-duty equipment of national post industries such as aeroengines, helicopter reducers, large ships, vehicle rear axle transmission systems, mines, metallurgy, building materials, energy sources and the like. The common processing method for spiral bevel gear processing is carried out by adopting a special machine tool and a special cutter. The special machining mode is suitable for mass production, and has the advantage of low average cost of single-piece products. The special machining mode has the defects of more matched equipment, complex cutters, higher initial investment of a machine tool and daily consumption cost of special cutters, and long preparation period of the special cutters. Along with the rapid iteration requirement in the product research and development process and the design trend of integrated components in large-scale complex equipment, the special machining mode based on the special cutter has obvious defects, and is difficult to meet the market processing technology requirement. The gear is machined by using the machining center and the universal cutter, the flexibility is high, a long-time special cutter preparation period is not needed, the gear development period can be greatly shortened, and large-scale and special complex gears can be machined by using the machining center However, in the existing main processing method, NURBS curved surface fitting is difficult for modeling a theoretical tooth surface of a complex tooth surface such as a spiral bevel gear during processing, the complex tooth surface is regarded as a common complex curved surface by the existing CAM to carry out processing tool path planning, and information such as curvature of the curved surface is lost, so that processing precision is not ideal. In addition, aiming at the processing of complex modified tooth surfaces of spiral bevel gears and the like with respect to the performance requirements of different occasions, the high-precision processing is carried out by considering the modified geometric information of the tooth surfaces, and the internal geometric characteristics of the complex tooth surfaces are considered by carrying out tool path planning based on the geometric information of conjugate characteristic lines of the tooth surfaces, so that the processing precision and the processing efficiency can be better improved. Publication number CN 108568567A discloses a spiral bevel gear machining method based on a universal four-axis numerical control machine tool and a ball end mill, in which a universal cutter ball end mill is used for machining a spiral bevel gear, a layered cutting path of a cutter from a tooth top to a tooth bottom to the tooth top is realized through tooth surface calculation, modeling and cutter path creation, publication number CN 117548744A discloses a method for machining a line contact tapered spiral bevel gear pair, which is based on the principle of a conjugate tooth surface, a shaping method for a large wheel and a generating method for a small wheel by taking a cutter head cutting surface as a shaping surface are designed, a high-efficiency method for machining the line contact tapered spiral bevel gear pair is realized through meshing and a cutting tooth model, publication number CN 120115763A discloses a spiral bevel gear machining method based on error compensation, after the spiral bevel gear is machined to a preset number, a distance error is measured on line, a cutter displacement compensation value is calculated by detecting the deformation amount when the deviation exceeds the distance error, and a method for improving the precision by the cutter tool is designed by a machine tool. The internal geometric characteristics of the tooth surface conjugate characteristic line are not considered in the above patents, and the processing precision and the processing efficiency are difficult to improve. Aiming at given processing precision requirements, the processing method provided by the invention can further greatly improve the processing efficiency compared with the existing processing method. Disclosure of Invention The invention ai