A tooth profile tilt deviation correction method based on initial position offset of a grinding wheel

Abstract

The present application relates to the technical field of numerical control, in particular to a gear profile tilt deviation correction method based on initial position offset of grinding wheel, which realizes gear profile tilt correction by adjusting initial position of grinding wheel. The steps are as follows: a gear profile deviation correction coordinate system is established to obtain transformation relationship between grinding wheel coordinate system and workpiece coordinate system; a grinding wheel contact line equation is solved to obtain coordinates of corresponding contact point in grinding wheel coordinate system; the contact line coordinate point is transformed to workpiece coordinate system to solve gear end surface profile; according to the obtained end surface profile, left and right gear profile tilt deviations are calculated; and the particle swarm optimization algorithm is used to solve optimal grinding wheel position offset with the minimum sum of squares of left and right gear profile tilt deviations as the target. The present application uses the method of offsetting initial position of grinding wheel to correct gear profile tilt deviation, which is small in calculation, simple and efficient, and high in result stability.

Description

Technical Field

[0001] This invention relates to the field of CNC machinery technology, specifically to a method for correcting tooth profile tilt deviation based on the initial position offset of the grinding wheel. Background Technology

[0002] CNC profile grinding machines are widely used in high-precision gear machining, including grinding spur / helical cylindrical gears, gears with complex tooth profiles, and gears with complex tooth direction profiles. For tooth profile tilt correction, the sand profile correction method is commonly used. However, this method relies heavily on designing a correction curve based on discrete data points. Common curve design methods include NURBS interpolation and B-spline fitting, which are complex in practice, easily affecting the stability of the calculation results, and are overly cumbersome, leading to low computational efficiency. Therefore, a tooth profile tilt correction method based on the initial position offset of the grinding wheel is proposed. Summary of the Invention

[0003] The purpose of this invention is to provide a method for correcting tooth profile tilt deviation based on the initial position offset of the grinding wheel, so as to solve the problems of complex calculation, large amount of calculation, low efficiency and unstable effect in the process of correcting tooth profile tilt deviation.

[0004] To achieve the above objectives, the present invention provides a method comprising the following steps:

[0005] A method for correcting tooth profile tilt deviation based on initial position offset of grinding wheel includes the following steps:

[0006] Step 1: Based on the grinding wheel position offset, establish a tooth profile deviation correction coordinate system to obtain the transformation relationship between the grinding wheel coordinate system and the workpiece coordinate system;

[0007] Step 2: Calculate the contact line of the grinding wheel and obtain the coordinates of discrete points on the contact line in the grinding wheel coordinate system;

[0008] Step 3: Obtain the coordinates of the contact line in the workpiece coordinate system and solve for the gear end face profile;

[0009] Step 4: Calculate the inclination deviation of the tooth profiles on the left and right sides based on the obtained end face profile;

[0010] Step 5: Establish a mathematical model with the grinding wheel position offset as the variable and the goal of minimizing the sum of the squares of the tilt deviations of the tooth profiles on the left and right sides, and use the particle swarm optimization algorithm to solve for the optimal grinding wheel position offset.

[0011] In step one, a tooth profile deviation correction coordinate system is established based on the initial position offset of the grinding wheel. Coordinate system S p (O p -x p y p z p(Fixed to the workpiece, coordinate system S) w (O w -x w y w z w If the workpiece coordinate system S is fixed to the grinding wheel, then... p (O p -x p y p z p ) and grinding wheel coordinate system S w (O w -x w y w z w The transformation matrix is:

[0012] M wp =M w4 M 43 M 31 M 1p (1)

[0013] In formula (1),

[0014]

[0015] In the above formula, d x d represents the radial offset of the grinding wheel's initial position along the X-axis. y d is the tangential offset along the Y-axis. A This is the A-axis offset; a x0 a is the distance along the x-axis between the grinding wheel and the gear; z The distance between the grinding wheel and the gear along the z-axis; ∑0 is the grinding wheel installation angle; The x-axis represents the rotation angle of the workpiece around the x-axis; p represents the helical parameters of the helix.

[0016] In step two, the normal vector of any point on the grinding wheel's rotating surface and curved surface is in the grinding wheel coordinate system S. w (O w -x w y w z w The following can be denoted as r respectively. w (R,γ) and n w (R,γ), the expressions for the grinding wheel surface and normal vector, transformed from the grinding wheel coordinate system to the gear coordinate system, are as follows:

[0017] r p =M pw r w (2)

[0018] n p =M pw n w (3)

[0019] In the above formula, M pw =M wp -1

[0020] According to the principle of spatial curved surface meshing, the forming grinding wheel and any point on the contact line satisfy the condition that the normal vector of the tooth surface is perpendicular to the direction of the relative motion velocity of the grinding wheel and the gear. Therefore, we can obtain:

[0021]

[0022] In the above formula, M pw T Representation matrix M pw Transpose of; The relative speed of the grinding wheel to the gear;

[0023] The contact equation of the grinding wheel can then be obtained as follows:

[0024] acos(γ) + bsin(γ) = c (5)

[0025] In formula (5),

[0026]

[0027] The axial profile of the grinding wheel is represented by several discrete points according to the parameter R. The parameter γ corresponding to parameter R can be obtained using the contact line equation. Then, substituting (R, γ) into the contact line equation, the coordinates of the corresponding contact point in the grinding wheel coordinate system can be obtained, denoted as (x...). w ,y w ,z w ).

[0028] In step three, according to the grinding wheel coordinate system S w (O w -x w y w z w ) and workpiece coordinate system S p (O p -x p y p z p The transformation relationship between (x, y) and (x, y) can be used to obtain the coordinates of the contact line in the workpiece coordinate system, denoted as (x, y). p ,y p ,z p );

[0029] By projecting the contact line helically onto the end face of the gear, the profile of the gear end face can be obtained as follows:

[0030]

[0031] In step four, the difference between the gear end face profile obtained in step three and the theoretical tooth profile, i.e., the normal distance from a point on the involute to the curve, is used to evaluate the accuracy, thereby determining the tilt deviation f of the tooth profiles on the left and right sides. hαl and f hαr Let the measured tilt deviations of the left and right tooth profiles be f respectively. hαl0 and f hαr0 .

[0032] In step five, the radial offset d along the X-axis of the initial position of the grinding wheel is established. x Y-axis tangential offset d y A-axis offset d A Using the independent variable as the objective and minimizing the sum of the squares of the corrected left and right tooth profile tilt deviations, the objective equation can be obtained as follows:

[0033]

[0034] To solve this single-objective multivariate optimization model, the particle swarm optimization algorithm is used to find the optimal d. x d y and d A .

[0035] This invention uses the method of offsetting the initial position of the grinding wheel to correct the tooth profile tilt deviation. This method has low computational cost, is simple and efficient, and the results are highly stable. Attached Figure Description

[0036] Figure 1 This is the tooth profile deviation correction coordinate system of the present invention;

[0037] Figure 2 This is a structural diagram of the SKMC-3000 / 20 gear grinding machine of the present invention. Detailed Implementation

[0038] The present invention will now be further described with reference to the accompanying drawings.

[0039] The purpose of this invention is to provide a method for correcting tooth profile tilt deviation based on the initial position offset of the grinding wheel. Taking the SKMC-3000 / 20 gear grinding machine as an example, the preferred embodiment includes:

[0040] Step 1: Based on the initial position offset of the grinding wheel, establish a coordinate system for tooth profile deviation correction. Coordinate system S p (O p -x p y p z p (Fixed to the workpiece, coordinate system S) w (O w -x w yw z w If the workpiece coordinate system S is fixed to the grinding wheel, then... p (O p -x p y p z p ) and grinding wheel coordinate system S w (O w -x w y w z w The transformation matrix is:

[0041] M wp =M w4 M 43 M 31 M 1p (1)

[0042] In the formula,

[0043]

[0044]

[0045] In the above formula, d x d represents the radial offset of the grinding wheel's initial position along the X-axis. y The offset is d in the Y-axis tangential direction; the offset is d in the A-axis direction. A a x0 a is the distance along the x-axis between the grinding wheel and the gear; z The distance between the grinding wheel and the gear along the z-axis; ∑0 is the grinding wheel installation angle; The x-axis represents the rotation angle of the workpiece around the x-axis; p represents the helical parameter of the helix.

[0046] Therefore, the following transformation matrix can be obtained.

[0047]

[0048] Step two allows us to obtain the normal vectors of any point on the grinding wheel's rotating surface and curved surface in the grinding wheel coordinate system S. w (O w -x w y w z w The following can be represented as:

[0049] r w (R,γ)=[Rcos(γ),Rsin(γ),f(R),1] T (4)

[0050] n w (R,γ)=[Rf'(R)cosγ,Rf'(R)sinγ,-R,0] T(5)

[0051] In formulas (4) and (5), R is the radius of any point on the cross section of the grinding wheel; γ is the rotation angle of the grinding wheel; f(R) is the equation for the grinding wheel profile; r w (R,γ) represents the rotating surface of the grinding wheel; n w (R,γ) represents the normal vector of any point on the surface of the grinding wheel.

[0052] Transform the expressions for the grinding wheel surface and normal vector from the grinding wheel coordinate system to the gear coordinate system.

[0053] r p =M pw r w (6)

[0054] n p =M pw n w (7)

[0055] The relative speed of the grinding wheel and the gear for,

[0056]

[0057] According to the gear meshing principle, the forming grinding wheel and any point on the contact line satisfy the condition that the normal vector of the tooth surface is perpendicular to the direction of the relative motion velocity of the grinding wheel and the gear. Therefore, we can obtain:

[0058]

[0059] In the formula,

[0060]

[0061] Based on the above conditions, the contact equation can be derived as follows:

[0062] acos(γ) + bsin(γ) = c (10)

[0063] In the formula,

[0064]

[0065] The axial profile of the grinding wheel is represented by several discrete points according to the parameter R. The parameter γ corresponding to parameter R can be obtained using the contact line equation. Then, substituting (R, γ) into the contact line equation, the coordinates of the corresponding contact point in the grinding wheel coordinate system can be obtained, denoted as (x...). w ,y w ,z w );

[0066] Step 3, based on the grinding wheel coordinate system S from Step 1 above.w (O w -x w y w z w ) and workpiece coordinate system S p (O p -x p y p z p The transformation relationship between (x, y) and (x, y) can be used to obtain the coordinates of the contact line in the workpiece coordinate system, denoted as (x, y). p ,y p ,z p );

[0067] By projecting the contact line helically onto the end face of the gear, the corrected gear end face profile can be obtained as follows:

[0068]

[0069] Step four, the theoretical gear end face profile is represented as:

[0070]

[0071] Solve for the normal vector on the theoretical tooth profile, denoted as In the formula, m = x' g , l = y' g ;

[0072] Then the unit vector of the normal vector is

[0073] The difference between the corrected gear end face profile and the theoretical tooth profile is calculated based on the above normal vector, which is the normal distance from the point on the involute to the curve. The accuracy of this calculation is then evaluated to obtain the tilt deviation f of the tooth profile on both sides. hαl and f hαr Let the measured tilt deviations of the left and right tooth profiles be f respectively. hαl0 and f hαr0 ;

[0074] In step five, the radial offset d along the X-axis of the initial position of the grinding wheel is established. x Y-axis tangential offset d y A-axis offset d A Using the independent variable as the objective and minimizing the sum of the squares of the corrected left and right tooth profile tilt deviations, the objective equation can be obtained as follows:

[0075]

[0076] To solve this single-objective multivariate optimization model, the particle swarm optimization algorithm is used to find the optimal d. x d y and dA .

[0077] The beneficial effects of this invention are as follows: This invention provides a method for correcting tooth profile tilt deviation based on the initial position offset of the grinding wheel, thereby solving the problems of complex calculations, large computational load, low efficiency, and unstable results in the process of correcting tooth profile tilt deviation. This invention uses the method of offsetting the initial position of the grinding wheel to correct tooth profile tilt deviation. This method has a small computational load, is simple and efficient, and the results are highly stable.

Claims

1. A method for correcting tooth profile tilt deviation based on initial position offset of grinding wheel, characterized in that, Includes the following steps: Step 1: Based on the grinding wheel position offset, establish a tooth profile deviation correction coordinate system to obtain the transformation relationship between the grinding wheel coordinate system and the workpiece coordinate system; Step 2: Calculate the contact line of the grinding wheel and obtain the coordinates of discrete points on the contact line in the grinding wheel coordinate system; Step 3: Obtain the coordinates of the contact line in the workpiece coordinate system and solve for the gear end face profile; Step 4: Calculate the inclination deviation of the tooth profiles on the left and right sides based on the obtained end face profile; Step 5: Establish the radial offset d along the X-axis from the initial position of the grinding wheel. x Y-axis tangential offset d y A-axis offset d A Using the variable as the independent variable, and with the objective of minimizing the sum of squares of the corrected left and right tooth profile tilt deviations, the objective equation is as follows: （1） To solve this model, the particle swarm optimization algorithm is used to solve the objective equation, and the optimal d is obtained. x d y and d A .

2. The tooth profile tilting deviation correction method based on the initial position offset of the grinding wheel according to claim 1, characterized in that, In step one, a tooth profile deviation correction coordinate system is established based on the initial position offset of the grinding wheel. Coordinate system S p (O p -x p y p z p ( ) is fixed to the workpiece, coordinate system S w (O w -x w y w z w If the workpiece coordinate system S is fixed to the grinding wheel, then... p (O p -x p y p z p ) and grinding wheel coordinate system S w (O w -x w y w z w The transformation matrix is: （2） In formula (2), ， ， ， ； In the above formula, d x d represents the radial offset of the grinding wheel's initial position along the X-axis. y d is the tangential offset along the Y-axis. A This is the A-axis offset; a x0 a is the distance along the x-axis between the grinding wheel and the gear; z The distance between the grinding wheel and the gear along the z-axis; Set the angle for the grinding wheel; denoted as the workpiece rotation angle around the x-axis; p is the helical parameter.

3. The tooth profile tilting deviation correction method based on the initial position offset of the grinding wheel according to claim 1, characterized in that, In step two, the normal vector of any point on the grinding wheel's rotating surface and curved surface is in the grinding wheel coordinate system S. w (O w -x w y w z w The following can be denoted as: and The expressions for the grinding wheel surface and normal vector, transformed from the grinding wheel coordinate system to the gear coordinate system, are as follows: （3） （4） In the above formula , According to the principle of spatial curved surface meshing, the forming grinding wheel and any point on the contact line satisfy the condition that the normal vector of the tooth surface is perpendicular to the direction of the relative motion velocity of the grinding wheel and the gear. Therefore, we can obtain: （5） In the above formula Representation matrix transpose; v p (φ) represents the relative speed of the grinding wheel to the gear; The contact equation of the grinding wheel can then be obtained as follows: （6） In formula (6), ， The axial profile of the grinding wheel is represented as several discrete points according to the parameter R. The parameters corresponding to parameter R can be obtained according to the contact line equation. Then Substituting into the contact line equation, we can obtain the coordinates of the corresponding contact point in the grinding wheel coordinate system, denoted as . .

4. The tooth profile tilting deviation correction method based on the initial position offset of the grinding wheel according to claim 1, characterized in that, In step three, according to the grinding wheel coordinate system S w (O w -x w y w z w ) and workpiece coordinate system S p (O p -x p y p z p The transformation relationship between the two can be used to obtain the coordinates of the contact line in the workpiece coordinate system, denoted as . ; By projecting the contact line helically onto the end face of the gear, the profile of the gear end face can be obtained as follows: （7） In step four, the difference between the gear end face profile obtained in step three and the theoretical tooth profile is used, i.e., the normal distance from a point on the involute to the gear end face profile curve obtained in step three. An accuracy evaluation is then performed to determine the tilt deviation of the tooth profiles on the left and right sides. and Let the measured tilt deviations of the left and right tooth profiles be respectively... and .

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