CN115609088A - Gear and method for machining and back-adjusting and correcting tooth surface of gear - Google Patents
Gear and method for machining and back-adjusting and correcting tooth surface of gear Download PDFInfo
- Publication number
- CN115609088A CN115609088A CN202211402213.8A CN202211402213A CN115609088A CN 115609088 A CN115609088 A CN 115609088A CN 202211402213 A CN202211402213 A CN 202211402213A CN 115609088 A CN115609088 A CN 115609088A
- Authority
- CN
- China
- Prior art keywords
- tooth surface
- gear
- axis
- machine tool
- transformation matrix
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F13/00—Making worms by methods essentially requiring the use of machines of the gear-cutting type
Landscapes
- Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Numerical Control (AREA)
Abstract
The invention discloses a gear tooth surface machining back-adjustment correcting method, which comprises the following steps: the method comprises the following steps: calculating parameters of a motion axis of the machine tool: 11 Obtaining a first coordinate transformation matrix from a tool coordinate system to a workpiece coordinate system by taking the relative position relation of the tool and the gear tooth surface as a research object; taking a machine tool motion axis as a research object, and obtaining a second coordinate transformation matrix from a tool coordinate system to a workpiece coordinate system; 12 The first coordinate transformation matrix is equal to the second coordinate transformation matrix, the parameters of the machine tool motion axis are obtained through solving, and the theoretical tooth surface equation of the gear is obtained through derivation according to the parameters of the machine tool motion axis obtained through solving; step two: measuring the tooth surface error; step three: correcting the high-order inverse adjustment of the machine tool motion axis based on the gear tooth surface error: 31 Representing the motion axis of the machine tool in a high-order polynomial form, obtaining the deviation between the corrected tooth surface and the theoretical tooth surface, and establishing a target function for reducing the error of the tooth surface; 32 Solving the inverse tuning correction objective function. The invention also discloses a gear.
Description
Technical Field
The invention belongs to the technical field of gear machining, and particularly relates to a gear and a tooth surface machining back-adjustment correcting method thereof.
Background
The numerical control worm grinding wheel gear grinding machine is a special machine tool for precisely machining the hard tooth surface of a face gear, directly determines the tooth surface precision of the face gear, further influences the performance of the whole machine adopting face gear transmission, improves the tooth grinding precision of the face gear, greatly increases the popularization and application of the face gear, and has great significance for the whole face gear manufacturing industry. However, in the process of grinding the gear by the face gear, a plurality of movement axes of the worm grinding wheel gear grinding machine participating in grinding linkage are provided, the machining precision is affected by geometric errors including quasi-static and thermal errors and force-induced deformation errors of dynamic changes, and the cost and difficulty of identifying, tracing and compensating the geometric errors of the gear grinding machine and the thermal errors and the force-induced deformation in the process of grinding the gear are extremely high.
In order to improve the grinding precision of the face gear, the prior art mainly carries out research from two aspects. Firstly, geometric errors of the numerical control gear grinding machine are identified, traced to sources and compensated, or geometric errors of the machine tool, which have great influence on the precision of a gear grinding tooth surface in the process of grinding the gear of the face gear, are identified and compensated; and the other is to perform reverse adjustment and correction on the tooth surface, but is only suitable for the tooth surface of the face gear adopting a grinding method of a disc grinding wheel. The influence of the thermal coupling effect on the tooth surface precision in the tooth grinding process is not fully considered in the identification and compensation of the geometric errors of the machine tool, and a back-adjustment correction method with high efficiency for the face gear worm grinding wheel tooth grinding method does not exist at present. In the prior art, a method of multiple iteration is mostly adopted for improving the gear grinding precision of the face gear, the experience of an operator is seriously relied on, the gear grinding efficiency is greatly reduced, and the qualified rate is low.
Disclosure of Invention
In view of the above, the present invention provides a gear and a method for correcting a tooth surface machining backstepping thereof, which perform a high-order backstepping on a machine tool motion cycle based on a measurement result of a tooth surface error, thereby reducing the tooth surface error and improving machining accuracy.
In order to achieve the purpose, the invention provides the following technical scheme:
the invention firstly provides a gear tooth surface machining back-adjusting correction method, which comprises the following steps:
the method comprises the following steps: calculating parameters of motion axis of machine tool
11 Taking the relative position relation between the cutter and the gear tooth surface as a research object, and transforming a cutter tooth surface equation to a workpiece coordinate system along a cutter coordinate system to obtain a gear tooth surface equation and a first coordinate transformation matrix from the cutter coordinate system to the workpiece coordinate system;
taking a machine tool motion axis as a research object, and obtaining a second coordinate transformation matrix from a tool coordinate system to a workpiece coordinate system;
12 The first coordinate transformation matrix is equal to the second coordinate transformation matrix, the parameters of the machine tool motion axis are obtained through solving, and the theoretical tooth surface equation of the gear is obtained through derivation according to the parameters of the machine tool motion axis obtained through solving;
step two: measuring tooth surface errors;
step three: high-order reverse adjustment correction for machine tool motion shaft based on gear tooth surface error
31 Representing the motion axis of the machine tool in a high-order polynomial form, obtaining the deviation between the corrected tooth surface and the theoretical tooth surface, and establishing a target function for reducing the error of the tooth surface;
32 Solving the inverse adjustment modified objective function.
Further, in the step 11), in the process of processing the tooth surface, the gear rotates at a constant speed
The tool rotating about the axis divided by the gear ratio
In addition, it is fed linearly in a direction at an angle λ to its X-axis w (ii) a Specifically, the first coordinate transformation matrix is:
wherein the content of the first and second substances,
representing a first coordinate transformation matrix;
indicating rotation of a gear about an axis
The transformation matrix of (2); m 20s0 (l w ) Indicating linear feed l of the tool in a direction at an angle λ to its X-axis w The transformation matrix of (2); m is a group of s0w0 Representing an auxiliary matrix;
indicating rotation of the tool about an axis
The transformation matrix of (2);
the machine tool has three linear axes and three rotational axes, and the second coordinate transformation matrix is:
wherein, T x 、T y And T z Respectively representing the moving distances of the three linear axes in the tooth surface machining process;
and
respectively showing the rotation angles of the three rotating shafts during the tooth surface machining;
representing a second coordinate transformation matrix;
indicating rotation of gear about axis C
The transformation matrix of (2); m is a group of f0g (T x ,T z ) Indicating that the tools are moved T along the X, Z axes, respectively x ,T z The transformation matrix of (2);
indicating rotation of the tool about axis A
The transformation matrix of (2); m ec0 (T y ) Indicating movement of tool T along Y-axis y The transformation matrix of (2);
indicating rotation of the tool about axis B
The transformation matrix of (2).
Further, in the step 12), let:
M fc ＝M 2w
the parameters of the machine tool motion axis obtained by solving are as follows:
wherein i w2 Representing the tool and gear ratio; e 2s Expressed as an inherent constant related to the gear radius, also as the end position of the linear feed of the tool; k 1 And K 2 Are all machine tool inherent constants;
the theoretical tooth surface equation of the gear is obtained by derivation according to the parameters of the motion axis of the machine tool:
wherein r is f Representing a gear tooth surface equation;
representing an engagement equation between the cutter and the gear when the cutter rotates;
representing an engagement equation between the gear and the tool when the tool moves; r is w Is the tool tooth surface equation; u. of r 、
All represent variables of the tool equation.
Further, in the second step, the measuring points are divided on the tooth surface by a grirson measuring point dividing method, and the tooth surface error is measured by a tooth surface three-coordinate measuring instrument.
Further, in the step 31), the motion axis of the machine tool is expressed in a high-order polynomial form:
wherein, C a 、C b And C c Motion expressions representing A, B and the C axis, respectively; c x 、C y And C z Motion expressions representing X, Y and the Z axis, respectively; dC (direct current) 0 ～dC 6 Expressing each item coefficient of a C-axis motion higher-order expression; dX 0 ～dX 6 Expressing the coefficients of the X-axis motion high-order expression; dY 0 ～dY 6 Expressing the coefficients of the high-order expression of the Y-axis motion; dZ 0 ～dZ 6 Representing the coefficients of the Z-axis motion higher-order expression;
represents the i power of the rotation angle of the gear;
the power of i represents the moving distance of the tool in the Y direction; i =1,2, …,6;
the high-order polynomial coefficient of the motion axis of the machine tool is expressed as follows by adopting a matrix:
ξ＝[ξ 1 ,ξ 2 ,…,ξ m ] T ＝[dC 0 ,dC 1 ,…,dC 6 ,…,dZ 0 ,dZ 1 ,…,dZ 6 ] T
wherein xi represents a machine tool motion axis high-order polynomial coefficient matrix; xi j J =1,2, …, m, m represents a polynomial coefficient number;
the deviation between the corrected tooth surface and the theoretical tooth surface is obtained as follows:
wherein, delta 2q (ξ j ) Representing the relationship xi between the modified and theoretical tooth surfaces j A deviation of (a);
indicating corrected information about xi j The tooth surface of (a);
representing a theoretical tooth surface;
a j-th term representing a theoretical tooth surface high-order polynomial coefficient;
a normal vector representing a theoretical tooth surface;
the objective function for decreasing tooth surface error is then:
where n represents the total number of measurement points.
Further, in the step 32), a back-tuning correction objective function is solved by adopting a Gauss-Newton method (Gauss-Newton method), an L-M method (Levenberg-Marquardt method) or a Dog-Leg method.
Further, an L-M method is adopted to solve the inverse adjustment correction objective function, and the Jacobian matrix of the inverse adjustment correction objective function is solved as follows:
wherein, J k (ξ (k) ) Representing a Jacobian matrix;
representing the deviation between the k-th corrected tooth surface and the theoretical tooth surface, q =1,2, …, n.
The invention also provides a gear which is processed by the above gear tooth surface processing inverse adjustment method.
Further, the gear is a face gear or a cylindrical gear.
The invention has the beneficial effects that:
the principle of the gear tooth surface machining back-adjustment correction method is as follows: firstly, deducing motion axis parameters based on a machine tool structure, and calculating three-dimensional coordinates of a theoretical tooth surface and a measuring point; then, constructing a machine tool motion axis high-order polynomial, deducing the deviation between the gear tooth surface and the theoretical tooth surface, and establishing a machine tool motion axis inverse adjustment correction objective function; finally, converting the motion axis back-tuning correction into a nonlinear least square problem based on the gear tooth surface deviation obtained by three-coordinate actual measurement, and solving to obtain a high-order polynomial coefficient after the machine tool motion axis back-tuning correction; the reverse adjustment correction of the tooth surface machining can be realized, and the tooth surface precision is improved; the method for machining and reversely adjusting and correcting the gear tooth surface of the gear can be suitable for reversely adjusting and correcting the moving shaft of the machine tool in the processes of hobbing of a face gear and a cylindrical gear and grinding the gear by a worm grinding wheel, and has the remarkable advantages of high solving speed and stability.
Drawings
In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
FIG. 1 is a relative position relationship diagram of a face gear and a worm grinding wheel;
FIG. 2 is a coordinate system of a motion axis of the worm grinding wheel gear grinding machine;
FIG. 3 is a tooth surface measurement point on a plane;
FIG. 4 is a three-dimensional spatial coordinate of a face gear tooth face measurement point on a tooth face;
FIG. 5 is a diagram of a three-coordinate measuring machine for measuring tooth surface errors; (a) a cylindrical gear; (b) a face gear;
FIG. 6 is a graph of measured tooth surface deflection for a face gear;
FIG. 7 illustrates tooth surface deviations before and after the surface modification of a face gear; before correction, (a) carrying out correction; and (b) after correction.
Detailed Description
The present invention is further described with reference to the following drawings and specific examples so that those skilled in the art can better understand the present invention and can practice the present invention, but the examples are not intended to limit the present invention.
The method for machining and reversely adjusting and correcting the gear tooth surface of the gear can be suitable for reversely adjusting and correcting the moving shaft of the machine tool in the process of hobbing of a face gear and a cylindrical gear and grinding the gear by a worm grinding wheel. The present embodiment will address the most complex processing among them: a grinding process of a worm wheel for a face gear is performed as an example, and a specific embodiment of the method of the present invention for correcting the tooth surface of a gear will be described in detail. The reverse adjustment and correction of the other three machining methods can be performed by referring to the machining method to adjust the moving shaft of the machine tool in the machining process, so that the machining precision of the tooth surface is improved.
Specifically, the method for back-adjusting and correcting gear tooth surface machining of the present embodiment includes the following steps:
the method comprises the following steps: calculating parameters of motion axis of machine tool
11 The relative position relation between the cutter and the gear tooth surface is taken as a research object, so that the cutter tooth surface equation is transformed from the cutter coordinate system to the workpiece coordinate system along the cutter coordinate system, and a first coordinate transformation matrix from the gear tooth surface equation and the cutter coordinate system to the workpiece coordinate system is obtained.
The relative positional relationship between the face gear and the worm grinding wheel is shown in FIG. 1, and the coordinate system S 2 And S w Respectively fixedly connected with the face gear and the worm grinding wheel. In the process of grinding teeth, the face gear rotates at a constant speed
Worm wheel rotating about axis divided by gear ratio
In addition, it is fed linearly in a direction at an angle λ to its X-axis w . Specifically, the first coordinate transformation matrix is:
wherein the content of the first and second substances,
representing a first coordinate transformation matrix;
indicating rotation of a gear about an axis
The transformation matrix of (2); m is a group of 20s0 (l w ) Indicating linear feed l of the tool in a direction at an angle λ to its X-axis w The transformation matrix of (2); m s0w0 Representing an auxiliary matrix;
indicating rotation of the tool about an axis
The transformation matrix of (2);
and taking the motion axis of the machine tool as a research object to obtain a second coordinate transformation matrix from the tool coordinate system to the workpiece coordinate system. As shown in fig. 2, it is a coordinate system of the motion axis of the face gear worm grinding wheel gear grinding machine. The gear grinding machine has three linear shafts (X, Y, Z) and three rotating shafts (A, B, C), and moves correspondingly for a distance (T) in the gear grinding process x 、T y 、T z ) And the angle of rotation
Coordinate system S f And S c Respectively a workpiece (face gear) and a cutter (worm grinding wheel), and a coordinate system S g And S e Is an auxiliary coordinate system. K 1 And K 2 Are all machine tool inherent constants. The face gear is installed on the C shaft of the machine tool, and the worm grinding wheel is installed on the B shaft of the machine tool. The second coordinate transformation matrix is then:
wherein, T x 、T y And T z Respectively showing the moving distances of the three linear axes in the tooth surface machining process;
and
respectively showing the rotation angles of the three rotating shafts during the tooth surface machining;
representing a second coordinate transformation matrix;
indicating rotation of gear about axis C
The transformation matrix of (2); m f0g (T x ,T z ) Indicating that the tools are moved T along the X, Z axes, respectively x ,T z The transformation matrix of (2);
indicating rotation of the tool about axis A
The transformation matrix of (2); m is a group of ec (T y ) Indicating movement of tool T along Y-axis y The transformation matrix of (2);
indicating rotation of the tool about axis B
The transformation matrix of (2).
12 The first coordinate transformation matrix is equal to the second coordinate transformation matrix, the parameters of the machine tool motion axis are obtained through solving, and the theoretical tooth surface equation of the gear is obtained through derivation according to the parameters of the machine tool motion axis obtained through solving. Namely, let:
M fc ＝M 2w
the parameters of the machine tool motion axis obtained by solving are as follows:
wherein i w2 Representing the tool and gear ratios; e 2s Expressed as an inherent constant related to the gear radius, and is also the end position of the linear feeding of the cutter; k 1 And K 2 Are all machine tool inherent constants;
the theoretical tooth surface equation of the gear is obtained by derivation according to the parameters of the motion axis of the machine tool:
wherein r is f Representing a gear tooth surface equation;
representing an engagement equation between the cutter and the gear when the cutter rotates;
representing an engagement equation with the gear when the tool moves; r is w Is the tool tooth surface equation; u. of r 、
All represent variables of the tool equation.
Step two: measuring tooth flank error
In the embodiment, the measuring points are divided on the tooth surface by a gleason measuring point dividing method, and the tooth surface error is measured by a tooth surface three-coordinate measuring instrument. Specifically, as shown in fig. 3, the solved face gear tooth surface points are shrunk according to the grirson measurement point division rule, wherein the shrinkage in the tooth length direction is 10% of the entire tooth length, and the shrinkage in the tooth height direction is 5% of the entire tooth height. It is also important to note that the contracted measurement points are kept clear of the flank chamfer and that the width of the tooth flank at the measurement point near the tooth root is greater than the ball diameter. The tooth surface points of the face gear projected on the plane are as follows:
wherein X represents the X coordinate of the projected tooth surface point; z represents the Z coordinate of the projected tooth surface point; x is the number of f An x-coordinate representing a spatial flank point; y is f A y-coordinate representing a spatial tooth face point; z is a radical of f Representing the z-coordinate of the spatial flank point.
The process of planning the measuring points comprises the following steps:
(1) Projecting the surface points of the surface gear teeth to a plane;
(2) Contracting the tooth surface points according to the Gleason rule to obtain contracted tooth surface points, namely measuring points on a plane;
(3) Based on the plane coordinates of the measuring points, the spatial three-dimensional coordinates on the tooth surface corresponding to the measuring points can be solved by combining the two formulas. The solved measurement points of the tooth surface of the face gear are shown in fig. 4.
Specifically, the measurement of the tooth surface errors of the spur gear and the face gear using the coordinate measuring machine is shown in fig. 5 (a) and 5 (b).
Step three: high-order reverse adjustment correction for machine tool motion shaft based on gear tooth surface error
A worm grinding wheel is adopted to grind the face gear based on the parameters of the motion axis of the machine tool obtained by calculation, and due to the comprehensive influence of errors such as geometric errors, thermal errors, force-induced deformation errors and the like of the machine tool, a certain deviation exists between the tooth surface of the face gear obtained by grinding and a theoretical tooth surface, so that the tooth surface of the face gear hardly meets the precision requirement. Based on the measured deviation between the actual tooth surface and the theoretical tooth surface of the face gear, the tooth surface machining back-adjustment correction method of the gear can reduce the deviation of the tooth surface of the face gear after grinding and improve the accuracy of the tooth surface. The essence of the inverse adjustment correction is that the motion shaft of the machine tool is inversely adjusted to enable the corrected tooth surface to generate a topological tooth surface opposite to the actual grinding tooth surface deviation direction relative to the theoretical tooth surface, so that the deviation of the processed tooth surface after the motion shaft of the machine tool is corrected and the theoretical tooth surface is reduced, and the requirement of tooth surface precision is met.
31 The motion axis of the machine tool is expressed into a high-order polynomial form, the deviation between the corrected tooth surface and the theoretical tooth surface is obtained, and an objective function for reducing the tooth surface error is established.
Specifically, during grinding, the A shaft is kept still, and the B shaft and the C shaft are rotated by keeping strict transmission ratio. The machine tool motion axes are represented in a higher order polynomial form:
wherein, C a 、C b And C c Motion expressions representing A, B and the C axis, respectively; c x 、C y And C z Motion expressions for X, Y and the Z axis, respectively; dC (direct current) 0 ～dC 6 Representing the coefficients of the C-axis motion high-order expression; dX 0 ～dX 6 Expressing the coefficients of the X-axis motion high-order expression; dY 0 ～dY 6 Expressing each item coefficient of a Y-axis motion higher-order expression; dZ 0 ～dZ 6 Representing the coefficients of the Z-axis motion higher-order expression;
represents the i power of the rotation angle of the gear;
the power of i representing the moving distance of the tool in the Y direction; i =1,2, …,6;
the high-order polynomial coefficient of the motion axis of the machine tool is expressed as follows by adopting a matrix:
ξ＝[ξ 1 ,ξ 2 ,…,ξ m ] T ＝[dC 0 ,dC 1 ,…,dC 6 ,…,dZ 0 ,dZ 1 ,…,dZ 6 ] T
wherein xi represents a machine tool motion axis high-order polynomial coefficient matrix; xi j J =1,2, …, m, m represents a polynomial coefficient number;
the deviation between the corrected tooth surface and the theoretical tooth surface is obtained as follows:
wherein, delta 2q (ξ j ) Representing the relationship xi between the modified and theoretical tooth surfaces j A deviation of (a);
indicating a corrected relation xi j The tooth surface of (a);
representing a theoretical tooth surface;
a j-th term representing a theoretical tooth surface high-order polynomial coefficient;
a normal vector representing a theoretical tooth surface;
the objective function for the relieved tooth surface error is then:
where n represents the total number of measurement points.
32 Solving the inverse tuning correction objective function.
The high-order polynomial inverse adjustment correction objective function of the motion axis of the face gear worm grinding wheel gear grinding machine is a typical nonlinear least square problem, and solving methods comprise a Gauss-Newton method, an L-M method (Levenberg-Marquardt method) and a Dog-Leg method. Generally, the GaussNewton method is fast in convergence but unstable, the L-M method is a damped Gauss-Newton method, the Dog-Leg method adopts a trust region to replace a damping term, and the two methods are fast in solving speed and good in stability. In this embodiment, an L-M method is used to solve the inverse tone correction objective function, and the solution of the jacobian matrix is:
wherein, J k (ξ (k) ) Representing a Jacobian matrix;
representing the deviation between the k-th corrected tooth surface and the theoretical tooth surface, q =1,2, …, n.
The tooth surface measuring points of the face gear after tooth grinding are measured by using a three-coordinate measuring machine, and the measured tooth surface deviation is shown in fig. 6. The face gear standard gear is projected, and the tooth surface deviation measured by the three-coordinate measuring machine after the worm grinding wheel is ground is represented on the plane of change, as shown in fig. 7 (a). Based on the tooth surface deviation of the three-coordinate measuring instrument, the machine tool moving shaft is reversely adjusted and corrected in the grinding process by adopting the reverse adjustment and correction method, and the obtained tooth surface deviation of the face gear is shown in fig. 7 (b).
In addition, the gear tooth surface machining inverse adjustment correction method is also suitable for inverse adjustment correction of a machine tool moving shaft in the processes of hobbing of a cylindrical gear, grinding of a worm grinding wheel and hobbing of a face gear, but a 45-point measurement method is needed to measure a machined tooth surface through a three-coordinate measuring instrument, the number of measurement points can be increased according to needs but needs to be guaranteed to be uniformly distributed on the tooth surface, and the method is used for inverse adjustment correction of the machine tool moving shaft according to a measurement result, so that the tooth surface precision is improved.
The embodiment also provides a gear which is obtained by processing the gear surface by the above gear tooth surface processing and back-adjusting correction method, and specifically, the gear is a face gear or a cylindrical gear.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (9)
1. A gear tooth surface machining back-adjustment correction method is characterized in that: the method comprises the following steps:
the method comprises the following steps: calculating parameters of motion axis of machine tool
11 Taking the relative position relation between the cutter and the gear tooth surface as a research object, and transforming a cutter tooth surface equation to a workpiece coordinate system along a cutter coordinate system to obtain a gear tooth surface equation and a first coordinate transformation matrix from the cutter coordinate system to the workpiece coordinate system;
taking a machine tool motion axis as a research object, and obtaining a second coordinate transformation matrix from a tool coordinate system to a workpiece coordinate system;
12 The first coordinate transformation matrix is equal to the second coordinate transformation matrix, the parameters of the machine tool motion axis are obtained through solving, and the theoretical tooth surface equation of the gear is obtained through derivation according to the parameters of the machine tool motion axis obtained through solving;
step two: measuring the tooth surface error;
step three: high-order reverse adjustment correction for machine tool motion shaft based on gear tooth surface error
31 Representing the motion axis of the machine tool in a high-order polynomial form, obtaining the deviation between the corrected tooth surface and the theoretical tooth surface, and establishing a target function for reducing the error of the tooth surface;
32 Solving the inverse tuning correction objective function.
2. Gear tooth flank working back-trimming as claimed in claim 1The squaring method is characterized in that: in the step 11), in the process of processing the tooth surface, the gear rotates at a constant speed
The tool rotating about the axis divided by the gear ratio
In addition, it is fed linearly in a direction at an angle λ to its X-axis w (ii) a Specifically, the first coordinate transformation matrix is:
wherein, the first and the second end of the pipe are connected with each other,
representing a first coordinate transformation matrix;
indicating rotation of a gear about an axis
The transformation matrix of (2); m 20s0 (l w ) Indicating linear feed l of the tool in a direction at an angle λ to its X-axis w The transformation matrix of (2); m s0w0 Representing an auxiliary matrix;
indicating rotation of the tool about an axis
The transformation matrix of (2);
the machine tool has three linear axes and three rotational axes, and the second coordinate transformation matrix is:
wherein, T x 、T y And T z Respectively showing the moving distances of the three linear axes in the tooth surface machining process;
and
respectively showing the rotation angles of the three rotating shafts during the tooth surface machining;
representing a second coordinate transformation matrix;
indicating rotation of gear about axis C
The transformation matrix of (2); m f0g (T x ，T z ) Indicating that the tools are moved T along the X, Z axes, respectively x ，T z The transformation matrix of (2);
indicating rotation of the tool about axis A
The transformation matrix of (2); m ec0 (T y ) Indicating movement of the tool T along the Y-axis y The transformation matrix of (2);
indicating rotation of the tool about axis B
The transformation matrix of (2).
3. The method of gear tooth surface machining back-adjustment correction according to claim 2, characterized in that: in the step 12), let:
M fc ＝M 2w
the parameters of the machine tool motion axis obtained by solving are as follows:
wherein i w2 Representing the tool and gear ratio; e 2s Expressed as an inherent constant related to the gear radius, and is also the end position of the linear feeding of the cutter; k 1 And K 2 Are all machine tool inherent constants;
the theoretical tooth surface equation of the gear is obtained by derivation according to the parameters of the motion axis of the machine tool:
wherein r is f Representing a gear tooth surface equation;
representing an engagement equation between the cutter and the gear when the cutter rotates;
representing an engagement equation with the gear when the tool moves; r is w Is the tool tooth surface equation; u. of r 、
All represent variables of the tool flank equation.
4. The method of gear tooth surface machining back-adjustment correction according to claim 3, characterized in that: in the second step, measuring points are divided on the tooth surface by a measuring point dividing method of the gleason, and a tooth surface error is measured by a tooth surface three-coordinate measuring instrument.
5. The method of gear tooth surface machining back-adjustment correction according to claim 4, characterized in that: in the step 31), the motion axis of the machine tool is expressed in a high-order polynomial form:
wherein, C a 、C b And C c Motion expressions for A, B and the C axis, respectively; c x 、C y And C z Motion expressions for X, Y and the Z axis, respectively; dC (direct current) 0 ～dC 6 Expressing each item coefficient of a C-axis motion higher-order expression; dX 0 ～dX 6 Expressing the coefficients of the X-axis motion high-order expression; dY 0 ～dY 6 Expressing the coefficients of the high-order expression of the Y-axis motion; dZ 0 ～dZ 6 Expressing each item coefficient of a Z-axis motion higher-order expression;
represents the i power of the rotation angle of the gear;
the power of i representing the moving distance of the tool in the Y direction; i =1,2, ·,6;
the high-order polynomial coefficient of the motion axis of the machine tool is expressed as follows by adopting a matrix:
ξ＝[ξ 1 ，ξ 2 ，...，ξ m ] T ＝[dC 0 ，dC 1 ，...，dC 6 ，...，dZ 0 ，dZ 1 ，...，dZ 6 ] T
wherein xi represents a machine tool motion axis high-order polynomial coefficient matrix; xi j J =1,2, j.. The m, m represents a polynomial coefficient of the modified tooth surface high-order polynomial coefficient matrix;
the deviation between the corrected tooth surface and the theoretical tooth surface is obtained as follows:
wherein, delta 2q (ξ j ) Representing the relationship xi between the modified and theoretical tooth surfaces j A deviation of (a);
indicating a corrected relation xi j The tooth surface of (a);
representing a theoretical tooth surface;
a j-th term representing a theoretical tooth surface high-order polynomial coefficient;
a normal vector representing a theoretical tooth surface;
the objective function for the relieved tooth surface error is then:
where n represents the total number of measurement points.
6. The method of gear tooth surface machining back-adjustment correction according to claim 5, characterized in that: in the step 32), a Gaussian Newton method (Gauss-Newton method), an L-M method (Levenberg-Marquardt method) or a Dog-Leg method is adopted to solve the inverse adjustment correction objective function.
7. The method of gear tooth surface machining back-adjustment correction according to claim 6, characterized in that: and solving a back-tuning correction objective function by adopting an L-M method, wherein the solution of a Jacobian matrix is as follows:
wherein, J k (ξ (k) ) Representing a Jacobian matrix;
represents the deviation between the k-th corrected tooth surface and the theoretical tooth surface, q =1,2.
8. A gear, characterized by: the gear tooth surface machining back-adjustment correction method is adopted to machine the gear tooth surface according to any one of the claims 1 to 7.
9. The gear of claim 8, wherein: the gear is a face gear or a cylindrical gear.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211402213.8A CN115609088A (en) | 2022-11-09 | 2022-11-09 | Gear and method for machining and back-adjusting and correcting tooth surface of gear |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211402213.8A CN115609088A (en) | 2022-11-09 | 2022-11-09 | Gear and method for machining and back-adjusting and correcting tooth surface of gear |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN115609088A true CN115609088A (en) | 2023-01-17 |
Family
ID=84879123
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211402213.8A Pending CN115609088A (en) | 2022-11-09 | 2022-11-09 | Gear and method for machining and back-adjusting and correcting tooth surface of gear |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115609088A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117195604B (en) * | 2023-11-07 | 2024-02-13 | 湖南中大创远数控装备有限公司 | Method for calculating sectional shape of forming tool for machining gear and forming tool |
-
2022
- 2022-11-09 CN CN202211402213.8A patent/CN115609088A/en active Pending
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117195604B (en) * | 2023-11-07 | 2024-02-13 | 湖南中大创远数控装备有限公司 | Method for calculating sectional shape of forming tool for machining gear and forming tool |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111590594B (en) | Robot trajectory tracking control method based on visual guidance | |
| Xiang et al. | Geometric error analysis and compensation for multi-axis spiral bevel gears milling machine | |
| CN109765848B (en) | Method for calculating geometric error contribution value of motion axis of five-axis machine tool and evaluating influence | |
| CN104615083A (en) | Curved surface tool path contour error compensation method based tool location point correction | |
| CN109483322B (en) | Zero calibration method of five-axis numerical control machine tool | |
| WO2019047458A1 (en) | Five-axis double spline curves interpolation speed planning method | |
| CN110899860B (en) | Numerical control machining method for linear contact spiral bevel gear pair | |
| CN108873809B (en) | High-order tooth surface error correction method for spiral bevel gear | |
| CN112558547B (en) | Quick optimization method for geometric error compensation data of translational shaft of five-axis numerical control machine tool | |
| CN111644909B (en) | Method for solving grinding track of rear cutter face of woodworking forming milling cutter | |
| CN109960215B (en) | Off-line compensation method for contour error of machining track of four-axis lathe | |
| CN115609088A (en) | Gear and method for machining and back-adjusting and correcting tooth surface of gear | |
| CN111715947B (en) | Method for forming linear contact gradually-reduced tooth arc tooth bevel gear pair | |
| CN113325802B (en) | Geometric error compensation method for five-axis machine tool | |
| CN111679629A (en) | Idle stroke non-interference track planning method for multi-spindle nose machining | |
| CN116400646A (en) | Universal post-processing method for five-axis numerical control machine tool based on singular compensation | |
| CN104597846B (en) | Lull-closed-loop motion control method for interpolation of multi-shaft coupling pipeline | |
| CN111967096A (en) | Design method of diamond roller and worm grinding wheel | |
| CN109396567B (en) | Digital envelope method for determining profile of worm grinding wheel in generating grinding of shape-modified cycloid gear | |
| CN104035379A (en) | Compensation method for perpendicularity error between feed shafts | |
| CN113359609A (en) | Key geometric error optimization proportioning compensation method for five-axis numerical control machine tool | |
| CN105116840A (en) | Compensation method for slowly varying error of primary interpolation of space curve | |
| CN116562151A (en) | Method for calculating deviation of section shape of rotary envelope shaft of disc milling cutter with rotation axis error | |
| CN113515091B (en) | Real-time track interpolation method and device for corner smoothing spline | |
| CN112346408B (en) | Geometric error compensation method for numerically controlled grinder for constructing binary once equation set |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |