Method for optimizing mounting angle of tooth-direction modification grinding wheel

Abstract

The invention provides a method for optimizing an installation angle of a tooth-direction modification grinding wheel, which is based on a forming grinding principle and considers that the tooth surface condition can be influenced by changing the installation angle of the grinding wheel and the form, height and position of a contact line under the tooth-direction modification condition, and the optimal installation angle enabling the tooth surface deviation to be minimum exists. The method comprises the following steps: firstly, establishing a theoretical modification tooth surface model through an involute tooth surface equation and a modification equation, then determining a grinding wheel profile by combining grinding wheel parameters and mounting parameters, determining an envelope curved surface during grinding of a grinding wheel, and ensuring that a mounting angle is within a non-interference range during grinding through contact line solving and induced curvature calculation; discrete points on the addendum circle, the reference circle and the dedendum circle are used for deviation calculation, and the minimum deviation quadratic sum is used as an optimization target for continuous optimization so as to obtain the optimal grinding wheel installation angle. According to the optimization method provided by the invention, the universality of forming grinding tooth direction modification is expanded; the non-interference angle range of the grinding wheel mounting angle can be efficiently obtained; and the tooth surface modification error can be reduced to the greatest extent.

Description

Technical Field

[0001] The invention belongs to the field of gear precision machining, and in particular relates to the field of machining high-precision tooth profile modified helical gears. Background Art

[0002] Gear shaping has the advantages of good grinding quality and high grinding efficiency. It is a widely used gear finishing hard tooth surface modification process. In order to reduce the impact of meshing in and out of gear transmission, improve the phenomenon of uneven load distribution, and improve the gear transmission accuracy, load-bearing capacity and service life, it is necessary to perform gear tooth modification in actual production to improve the contact characteristics. In theory, different section-shaped grinding wheels should be used for profile grinding tooth modification, but in actual processing, only one section-shaped grinding wheel can be used to grind the entire tooth surface, resulting in tooth surface errors.

[0003] In the case of no tooth profile modification, the installation angle and the corresponding grinding wheel section are changed at the same time, and the envelope tooth surface produced by grinding remains unchanged. In the case of tooth profile modification, the shape, height and position of the contact line will affect the tooth surface condition by changing the grinding wheel installation angle, so the tooth surface error can be reduced by optimizing the grinding wheel installation angle. Summary of the invention

[0004] The purpose of the present invention is to provide a method for optimizing the installation angle of a tooth profile grinding wheel so as to reduce the tooth surface error during gear grinding.

[0005] In order to achieve the above technical objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for optimizing the installation angle of a tooth profile grinding wheel, characterized by comprising the following steps:

[0007] Step 1: Establish a modified tooth surface model based on the basic parameters of the gear and the tooth modification parameters;

[0008] Step 2: According to the given grinding wheel parameters and installation parameters, the grinding wheel profile is calculated in combination with the basic parameters of the gear and the shaping parameters;

[0009] Step 3: Based on the calculated contour of the modified sand and the spatial motion of the grinding wheel, the envelope surface formed by the modification motion of the grinding wheel teeth is inversely solved;

[0010] Step 4: Calculate the adjustment range of the installation angle based on the numerical calculation of the grinding interference verification conditions;

[0011] Step 5: Compare the deviations of the tooth profile modification grinding wheel envelope surface and the theoretical modified tooth surface on the tooth addendum circle, pitch circle and tooth root circle discrete points, and optimize with the minimum sum of squares of discrete point deviations as the optimization target to obtain the best grinding wheel installation angle.

[0012] The step 1 specifically includes the following steps:

[0013] The standard involute tooth surface equation of helical gear is as follows:

[0014]

[0015] In the formula, r b is the base circle diameter; u and θ are variable parameters; σ0 is the base circle tooth groove half angle; p is the helical parameter; after the tooth profile is modified, the tooth profile position of the end section will change, and the modified profile can be regarded as the standard tooth profile obtained by rotating an additional angle γ around the center of the pitch circle;

[0016] Then the relationship between the additional rotation angle γ and the modification amount ΔL is:

[0017]

[0018] Where r is the pitch circle radius; β is the helix angle of the helical gear;

[0019] After superimposing the additional rotation angle into the standard spiral motion, the following theoretical tooth profile modification tooth surface equation can be obtained:

[0020]

[0021] The step 2 specifically includes the following steps:

[0022] Establish the grinding wheel fixed coordinate system and gear coordinate system respectively o -X o Y o Z o and O-XYZ, the distance between the origins of the two coordinate systems is the center distance a, and the grinding wheel installation angle is Σ (note β is the pitch circle helix angle);

[0023] According to the coordinate transformation principle, the transformation matrix between the gear coordinate system and the grinding wheel coordinate system can be obtained as follows:

[0024]

[0025] By combining equations (5) and (3), we can obtain the tooth surface equation in the grinding wheel coordinate system:

[0026]

[0027] During profile grinding, the instantaneous contact line between the grinding wheel and the gear is the key to connecting the grinding wheel profile and the tooth profile. Therefore, according to the basic law of gear meshing, every point on the contact line between the profile grinding wheel and the gear satisfies the condition that the tooth surface normal vector is perpendicular to the direction of the grinding wheel's rotation speed, which can be obtained: v·n=0.

[0028] According to the condition that the normal vector of the tooth surface is perpendicular to the speed direction of the grinding wheel rotation, the contact condition can be obtained as follows: (z g +y g cotΣ)n x +(ax g )(n y cotΣ+n z )=0.

[0029] Substituting (x, y, z) into the tooth surface equation of the helical gear tooth profile, the tooth profile contact line condition formula can be obtained as follows:

[0030]

[0031] The Newton iteration method is used to solve the problem, and the discrete points of the contact line can be obtained by substituting it into the above formula (5), which constitutes the contact line;

[0032] The forming grinding wheel is a rotating tool, so the grinding wheel rotating surface can be obtained by rotating the contact line around the grinding wheel axis. The axial section of the grinding wheel can be obtained by projecting the contact line onto the grinding wheel calculation plane;

[0033] The mathematical expression of the axial section of the grinding wheel is as follows:

[0034]

[0035] The step three specifically includes the following steps:

[0036] According to the grinding wheel cross-section obtained in step 2 above, the following grinding wheel rotation surface equation is established in the grinding wheel coordinate system:

[0037] r w (R,γ)=[Rcos(γ),Rsin(γ),f(R),1] T (8)

[0038] n w (R,γ)=[Rf'(R)cosγ,Rf'(R)sinγ,-R,0] T (9)

[0039] Transform the grinding wheel surface from the grinding wheel coordinate system to the gear coordinate system.

[0040] r p =M pw r w (10)

[0041] n p =M pw n w (11)

[0042] The relative motion speed between the grinding wheel and the gear is:

[0043]

[0044] Substituting into the meshing equation (2-22), we get:

[0045]

[0046] In the formula,

[0047]

[0048] The dynamic contact equation between the grinding wheel and the tooth surface is obtained as follows:

[0049] acos(γ)+bsin(γ)=c (14)

[0050] In the formula,

[0051]

[0052] The tooth surface contact line thus obtained forms the envelope surface.

[0053] The step 4 specifically includes the following steps:

[0054] By studying the induced normal curvature of the contact point between the two surfaces, it can be determined whether the two surfaces interfere with each other. When the induced normal curvature of any point on the contact line between the gear surface and the grinding wheel envelope surface in any direction is When the surfaces do not interfere, on the contrary, interference occurs;

[0055] The gear tooth surface equation is r = r (u, θ), and the grinding wheel surface equation is r0 = r0 (R, φ);

[0056] Then the calculation formula for the normal curvature of any point M on the gear tooth surface is expressed as:

[0057]

[0058] In the formula, L, M, N are called the first basic form coefficients of the surface; E, F, G are called the second basic form coefficients of the surface;

[0059] The first basic form coefficient of the surface can be obtained by the dot product of the partial derivatives of the surface equation. For example, if the tooth surface equation is r = r(u,θ), then the first basic form coefficient of the surface is: L = r u ·r u ,M=r u ·r v ,N=r v ·r v , where r u , r v is the first-order partial derivative;

[0060] Similarly, the coefficient of the second basic form of the surface is E = ruu n,F=r uv n,G=r vv n, where r uu , r uv , r vv is the second-order partial derivative,

[0061] Then the difference in normal curvature of the two surfaces along the same direction at the tangent point is called the induced normal curvature in that direction, which can be expressed as:

[0062]

[0063] In the formula, is the angle between any direction and the principal normal curvature direction of the gear surface; a n11 is the angle between the principal curvatures of the two surfaces; Q1 is the sum of the two principal curvatures of the gear surface; Q2 is the sum of the two principal curvatures of the grinding wheel surface; P1 is the difference between the two principal curvatures of the gear surface; P2 is the difference between the two principal curvatures of the grinding wheel surface;

[0064] Will Directed Angle The induced normal curvature is solved for the one-dimensional independent variable function of the variable, and the maximum and minimum values ​​of the induced normal curvature are solved;

[0065] The induced normal curvature is used as the basis, and the grinding wheel installation angle is used as the variable to calculate the size of the induced normal curvature value of the point on the contact line. The grinding wheel installation angle is updated with a certain step size, and the induced normal curvature is calculated to determine whether interference occurs in grinding at this installation angle, thereby obtaining the value range of the grinding wheel installation angle under non-interference conditions.

[0066] The step five specifically includes the following steps:

[0067] Solve the equations of the grinding wheel envelope surface and the modified tooth surface, and discretize the deviations of the discrete points on the tooth top circle, pitch circle and root circle. Let a discrete point on the modified tooth surface be a ij , the corresponding discrete point of the tooth profile grinding wheel envelope surface is b ij , then its modification deviation is:

[0068] ζ ij =a ij -b ij (15)

[0069] The error evaluation function is calculated by calculating the sum of squared deviations, that is:

[0070]

[0071] The value of the grinding wheel installation angle is continuously changed within the non-interference range, and the above steps are repeated to find the grinding wheel installation angle with the smallest error evaluation function value by a given step length, and the installation angle at this time is determined to be the optimal grinding wheel installation angle;

[0072] The technical effects of the present invention have the following advantages:

[0073] 1. The present invention establishes a profile grinding tooth modification model, which is suitable for modification trajectories of any modification amount, and expands the versatility of profile grinding tooth modification.

[0074] 2. During the motion of the grinding wheel, the present invention can reversely obtain the envelope surface of the grinding wheel in the gear coordinate system, and can quickly obtain the envelope motion trajectory of the grinding wheel;

[0075] 3. The present invention determines the grinding interference range by studying the positive and negative values ​​of the induced curvature, and adopts program cycle determination to efficiently obtain the non-interference angle range;

[0076] 4. The present invention uses the sum of squared deviations as an evaluation criterion to optimize the grinding wheel installation angle to minimize the tooth surface modification error. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 The present invention is a flow chart for optimizing the grinding wheel installation angle.

[0078] Figure 2 Schematic diagram of helical gear tooth profile parameters.

[0079] Figure 3 Schematic diagram of the relative position of the workpiece and the grinding wheel.

[0080] Figure 4 It is a sand contour diagram. DETAILED DESCRIPTION

[0081] In order to enable those skilled in the art to better understand the present invention, Figure 1-4 Further explanation of the technical solution of the present invention: Without departing from the above-mentioned thought and technology of the present invention, various substitutions and changes are made according to the common technical knowledge and conventional means in the field, which should be included in the protection scope of the present invention.

[0082] A method for optimizing the installation angle of a tooth profile grinding wheel comprises the following steps:

[0083] According to the basic parameters of the gear and the tooth modification parameters, a modified tooth surface model is established;

[0084] The step 1 specifically includes the following steps:

[0085] The standard involute tooth surface equation of helical gear is as follows;

[0086]

[0087] In the formula, r b is the base circle diameter; u and θ are variable parameters; σ0 is the base circle tooth groove half angle; p is the helical parameter; after the tooth profile is modified, the tooth profile position of the end section will change, and the modified profile can be regarded as the standard tooth profile obtained by rotating an additional angle γ around the center of the pitch circle;

[0088] Then the relationship between the additional rotation angle γ and the modification amount ΔL is:

[0089]

[0090] Where r is the pitch circle radius; β is the helix angle of the helical gear;

[0091] After superimposing the additional rotation angle into the standard spiral motion, the following theoretical tooth profile modification tooth surface equation can be obtained:

[0092]

[0093] The step 2 specifically includes the following steps:

[0094] Establish the grinding wheel fixed coordinate system and gear coordinate system respectively o -X o Y o Z o and O-XYZ, the distance between the origins of the two coordinate systems is the center distance a, and the grinding wheel installation angle is Σ (note β is the pitch circle helix angle);

[0095] According to the coordinate transformation principle, the transformation matrix between the gear coordinate system and the grinding wheel coordinate system can be obtained as follows:

[0096]

[0097] By combining equations (5) and (3), we can obtain the tooth surface equation in the grinding wheel coordinate system:

[0098]

[0099] During profile grinding, the instantaneous contact line between the grinding wheel and the gear is the key to connecting the grinding wheel profile and the tooth profile. Therefore, according to the basic law of gear meshing, every point on the contact line between the profile grinding wheel and the gear satisfies the condition that the tooth surface normal vector is perpendicular to the direction of the grinding wheel's rotation speed, which can be obtained: v·n=0.

[0100] According to the condition that the normal vector of the tooth surface is perpendicular to the speed direction of the grinding wheel rotation, the contact condition can be obtained as follows: (z g +y g cotΣ)n x +(axg )(n y cotΣ+n z )=0.

[0101] Substituting (x, y, z) into the tooth surface equation of the helical gear tooth profile, the tooth profile contact line condition formula can be obtained as follows:

[0102]

[0103] The above contact line condition is a transcendental equation, so the Newton iteration method is used to solve it. Let u take a series of discrete values ​​within a certain range, and substitute it into the contact line condition to solve the corresponding θ value. Finally, it is substituted into the above formula to obtain the discrete points of the contact line to form the contact line.

[0104] The forming grinding wheel is a rotating tool, so the grinding wheel rotating surface can be obtained by rotating the contact line around the grinding wheel axis. The axial section of the grinding wheel can be obtained by projecting the contact line onto the grinding wheel calculation plane;

[0105] The mathematical expression of the axial section of the grinding wheel is as follows:

[0106]

[0107] The step three specifically includes the following steps:

[0108] According to the grinding wheel cross-section obtained in step 2 above, the following grinding wheel rotation surface equation is established in the grinding wheel coordinate system:

[0109] r w (R,γ)=[Rcos(γ),Rsin(γ),f(R),1] T (8)

[0110] n w (R,γ)=[Rf'(R)cosγ,Rf'(R)sinγ,-R,0] T (9)

[0111] Transform the grinding wheel surface from the grinding wheel coordinate system to the gear coordinate system.

[0112] r p =M pw r w (10)

[0113] n p =M pw n w (11)

[0114] The relative motion speed between the grinding wheel and the gear is:

[0115]

[0116] Substituting into the meshing equation (2-22), we get:

[0117]

[0118] In the formula,

[0119]

[0120] The dynamic contact equation between the grinding wheel and the tooth surface is obtained as follows:

[0121] acos(γ)+bsin(γ)=c (14)

[0122] In the formula,

[0123]

[0124] The tooth surface contact line thus obtained forms the envelope surface.

[0125] The step 4 specifically includes the following steps:

[0126] By studying the induced normal curvature of the contact point between the two surfaces, it can be determined whether the two surfaces interfere with each other. When the induced normal curvature of any point on the contact line between the gear surface and the grinding wheel envelope surface in any direction is When the surfaces do not interfere, on the contrary, interference occurs;

[0127] The gear tooth surface equation is r = r (u, θ), and the grinding wheel surface equation is r0 = r0 (R, φ);

[0128] Then the calculation formula for the normal curvature of any point M on the gear tooth surface is expressed as:

[0129]

[0130] In the formula, L, M, N are called the first basic form coefficients of the surface; E, F, G are called the second basic form coefficients of the surface;

[0131] The first basic form coefficient of the surface can be obtained by the dot product of the partial derivatives of the surface equation. For example, if the tooth surface equation is r = r(u,θ), then the first basic form coefficient of the surface is: L = r u ·r u ,M=r u ·r v ,N=r v ·r v , where r u , r v is the first-order partial derivative;

[0132] Similarly, the coefficient of the second basic form of the surface is E = r uu n,F=r uv n,G=rvv n, where r uu , r uv , r vv is the second-order partial derivative,

[0133] Then the difference in normal curvature of the two surfaces along the same direction at the tangent point is called the induced normal curvature in that direction, which can be expressed as:

[0134]

[0135] In the formula, is the angle between any direction and the principal normal curvature direction of the gear surface; a n11 is the angle between the principal curvatures of the two surfaces; Q1 is the sum of the two principal curvatures of the gear surface; Q2 is the sum of the two principal curvatures of the grinding wheel surface; P1 is the difference between the two principal curvatures of the gear surface; P2 is the difference between the two principal curvatures of the grinding wheel surface;

[0136] Will Directed Angle The induced normal curvature is solved for the one-dimensional independent variable function of the variable, and the maximum and minimum values ​​of the induced normal curvature are solved;

[0137] The induced normal curvature is used as the basis, and the grinding wheel installation angle is used as the variable to calculate the size of the induced normal curvature value of the point on the contact line. The grinding wheel installation angle is updated with a certain step size, and the induced normal curvature is calculated to determine whether interference occurs in grinding at this installation angle, thereby obtaining the value range of the grinding wheel installation angle under non-interference conditions.

[0138] The step five specifically includes the following steps:

[0139] Solve the equations of the grinding wheel envelope surface and the modified tooth surface, and discretize the deviations of the discrete points on the tooth top circle, pitch circle and root circle. Let a discrete point on the modified tooth surface be a ij , the corresponding discrete point of the tooth profile grinding wheel envelope surface is b ij , then its modification deviation is:

[0140] ζ ij =a ij -b ij (15)

[0141] The error evaluation function is calculated by calculating the sum of squared deviations, that is:

[0142]

[0143] The value of the grinding wheel installation angle is continuously changed within the non-interference range, and the above steps are repeated to find the grinding wheel installation angle with the smallest error evaluation function value with a given step size, and the installation angle at this time is determined to be the optimal grinding wheel installation angle.

Claims

1. A method for optimizing the installation angle of a tooth profile grinding wheel, characterized in that The steps include: Step 1: Establish a tooth profile modification tooth surface model based on the basic parameters of the gear and the tooth profile modification parameters; Step 2: Calculate the grinding profile according to the given grinding wheel parameters and installation parameters; Step 3: Based on the calculated sand contour and grinding wheel spatial motion, solve the envelope surface formed by the grinding wheel tooth modification motion; Step 4: Calculate the adjustment range of the installation angle based on the numerical calculation of the grinding interference verification conditions; Step 5: Compare the deviations of the tooth profile modification grinding wheel envelope surface and the theoretical modified tooth surface on the tooth addendum circle, pitch circle and tooth root circle discrete points, and optimize with the minimum sum of squares of discrete point deviations as the optimization target to obtain the best grinding wheel installation angle.

2. The method for optimizing the installation angle of a tooth profile grinding wheel according to claim 1, characterized in that The step 1 specifically includes the following steps: The standard involute tooth surface equation of helical gear is as follows; In the formula, r b is the base circle diameter; u and θ are variable parameters; σ0 is the base circle tooth groove half angle; p is the helical parameter; after the tooth profile is modified, the tooth profile position of the end section will change, and the modified profile can be regarded as the standard tooth profile obtained by rotating an additional angle γ around the center of the pitch circle; Then the relationship between the additional rotation angle γ and the modification amount ΔL is: Where r is the pitch circle radius; β is the helix angle of the helical gear; After superimposing the additional rotation angle into the standard spiral motion, the following theoretical tooth profile modification tooth surface equation can be obtained:

3. The method for optimizing the installation angle of a tooth profile grinding wheel according to claim 1, characterized in that The step 2 specifically includes the following steps: Establish the grinding wheel fixed coordinate system and gear coordinate system respectively o -X o Y o Z o and O-XYZ, the distance between the origins of the two coordinate systems is the center distance a, and the grinding wheel installation angle is Σ (note β is the pitch circle helix angle); According to the coordinate transformation principle, the transformation matrix between the gear coordinate system and the grinding wheel coordinate system can be obtained as follows: By combining equations (5) and (3), we can obtain the tooth surface equation in the grinding wheel coordinate system: During profile grinding, the instantaneous contact line between the grinding wheel and the gear is the key to connecting the grinding wheel profile and the tooth profile. Therefore, according to the basic law of gear meshing, every point on the contact line between the profile grinding wheel and the gear satisfies the condition that the tooth surface normal vector is perpendicular to the direction of the grinding wheel's rotation speed, which can be obtained: v·n=0. Then the contact line condition of the profile grinding can be obtained as follows: The Newton iteration method is used to solve the problem, and the obtained data is put into formula (5) to obtain the discrete points of the contact line to form the contact line; The forming grinding wheel is a rotating tool, so the grinding wheel rotating surface can be obtained by rotating the contact line around the grinding wheel axis. The axial section of the grinding wheel can be obtained by projecting the contact line onto the grinding wheel calculation plane; The mathematical expression of the axial section of the grinding wheel is as follows:

4. The method for optimizing the installation angle of a tooth profile grinding wheel according to claim 1, characterized in that The step three specifically includes the following steps: According to the grinding wheel cross-section obtained in step 2 above, the following grinding wheel rotation surface equation is established in the grinding wheel coordinate system: r w (R,γ)=[Rcos(γ),Rsin(γ),f(R),1] T (8) n w (R,γ)=[Rf'(R)cosγ,Rf'(R)sinγ,-R,0] T (9) Transform the grinding wheel surface from the grinding wheel coordinate system to the gear coordinate system. r p ＝M pw r w (10) n p =M pw n w (11) The relative motion speed between the grinding wheel and the gear is: Substituting into the meshing equation (2-22), we get: In the formula, The dynamic contact equation between the grinding wheel and the tooth surface is obtained as follows: acos(γ)+bsin(γ)=c (14) In the formula, The tooth surface contact line thus obtained forms the envelope surface.

5. The method for optimizing the installation angle of a tooth profile grinding wheel according to claim 1, characterized in that The step 4 specifically includes the following steps: By studying the induced normal curvature of the contact point between the two surfaces, it can be determined whether the two surfaces interfere with each other. When the induced normal curvature of any point on the contact line between the gear surface and the grinding wheel envelope surface in any direction is When the surfaces do not interfere, on the contrary, interference occurs; The gear tooth surface equation is r = r (u, θ), and the grinding wheel surface equation is r0 = r0 (R, φ); Then the calculation formula for the normal curvature of any point M on the gear tooth surface is expressed as: In the formula, L, M, N are called the first basic form coefficients of the surface; E, F, G are called the second basic form coefficients of the surface; The first basic form coefficient of the surface can be obtained by the dot product of the partial derivatives of the surface equation. For example, if the tooth surface equation is r = r(u,θ), then the first basic form coefficient of the surface is: L = r u ·r u ,M=r u ·r v ,N=r v ·r v , where r u , r v is the first-order partial derivative; Similarly, the coefficient of the second basic form of the surface is E = r uu n,F=r uv n,G=r vv n, where r uu , r uv , r vv is the second-order partial derivative, Then the difference in normal curvature of the two surfaces along the same direction at the tangent point is called the induced normal curvature in that direction, which can be expressed as: In the formula, is the angle between any direction and the principal normal curvature direction of the gear surface; a n11 is the angle between the principal curvatures of the two surfaces; Q1 is the sum of the two principal curvatures of the gear surface; Q2 is the sum of the two principal curvatures of the grinding wheel surface; P1 is the difference between the two principal curvatures of the gear surface; P2 is the difference between the two principal curvatures of the grinding wheel surface; Will Directed Angle The induced normal curvature is solved for the one-dimensional independent variable function of the variable, and the maximum and minimum values ​​of the induced normal curvature are solved; The induced normal curvature is used as the basis, and the grinding wheel installation angle is used as the variable to calculate the size of the induced normal curvature value of the point on the contact line. The grinding wheel installation angle is updated with a certain step size, and the induced normal curvature is calculated to determine whether interference occurs during grinding at this installation angle, thereby obtaining the value range of the grinding wheel installation angle under non-interference conditions.

6. The method for optimizing the installation angle of a tooth profile grinding wheel according to claim 1, characterized in that The step five specifically includes the following steps: Solve the equations of the grinding wheel envelope surface and the modified tooth surface, and discretize the deviations of the discrete points on the tooth top circle, pitch circle and root circle. Let a discrete point on the modified tooth surface be a ij , the corresponding discrete point of the tooth profile grinding wheel envelope surface is b ij , then its modification deviation is: g ij =a ij -b ij (18) The error evaluation function is calculated by calculating the sum of squared deviations, that is: The value of the grinding wheel installation angle is continuously changed within the non-interference range, and the above steps are repeated to find the grinding wheel installation angle with the smallest error evaluation function value with a given step size, and the installation angle at this time is determined to be the optimal grinding wheel installation angle.

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