Grinding path error analysis method for eccentric shaft external cylindrical grinder

Abstract

The present invention provides a method for analyzing the grinding trajectory error of an eccentric shaft external cylindrical grinder, comprising the following steps: S1. constructing a grinding wheel local coordinate system W{O}, a workpiece local coordinate system T{O} and a grinder global coordinate system Q{O} of the eccentric shaft external cylindrical grinder; S2. constructing an ideal trajectory model η of the eccentric shaft external cylindrical grinding point: S3. constructing an actual trajectory model τ of the eccentric shaft external cylindrical grinding point; S4. calculating the trajectory error λ of the eccentric shaft appearance grinder: λ=τ‑η. Through the above method, based on the combination of the actual trajectory of the grinding point and the ideal trajectory during the grinding process, the comprehensive geometric error of the grinder can be accurately analyzed, thereby providing accurate data support for the error compensation control during the grinding process, and ensuring the final eccentric shaft product quality.

Description

Technical Field

[0001] The invention relates to a grinding machine error analysis method, in particular to a grinding track error analysis method for an eccentric shaft cylindrical grinder. Background Art

[0002] With the rapid development of science and technology and the level of intelligence, manufacturing companies have increasing requirements for production accuracy and efficiency, and therefore the demand for industrial robots is also increasing.

[0003] RV (Rotary-Vector) reducers are key components in the joints of industrial robots. They have a series of advantages such as small size, high rigidity, and long service life. However, the processing quality of the eccentric shaft, one of its core components, is often an important factor that restricts the service life of the reducer. In the prior art, many achievements have been made in the analysis of its own characteristics such as error. However, compared with the influence of the eccentric shaft itself, the error of the machine tool used to process the part has a greater impact.

[0004] Eccentric shaft processing belongs to high-precision processing. Even the slight error of the grinder itself may have a huge impact on its processing accuracy. The eccentric shaft cylindrical grinding process is mainly divided into two parts: the main journal grinding and the eccentric journal grinding. The main journal grinding method is the same as the ordinary cylindrical grinding method, while the eccentric journal is processed by the follow-up grinding method. In the existing technology, the focus is generally on the parts themselves and process parameters. There is currently no effective means to analyze the impact of the grinder's error on the quality of the eccentric shaft.

[0005] Therefore, in order to solve the above technical problems, it is urgent to propose a new technical means. Summary of the invention

[0006] In view of this, the purpose of the present invention is to provide a method for analyzing the grinding trajectory error of an eccentric shaft external cylindrical grinder. Based on the combination of the actual trajectory of the grinding point and the ideal trajectory during the grinding process, the comprehensive geometric error of the grinder can be accurately analyzed, thereby providing accurate data support for the error compensation control during the grinding process and ensuring the final eccentric shaft product quality.

[0007] The present invention provides a method for analyzing grinding trajectory errors of an eccentric shaft cylindrical grinder, comprising the following steps:

[0008] S1. Construct the grinding wheel local coordinate system W{O}, the workpiece local coordinate system T{O} and the grinding machine global coordinate system Q{O} of the eccentric shaft external cylindrical grinder; wherein the grinding wheel local coordinate system takes the grinding wheel rotation center O3 of the eccentric shaft external cylindrical grinder as the origin, and the workpiece local coordinate system takes the eccentric shaft rotation center O1 as the origin; draw a perpendicular line through the origin of the grinder to the line between the grinding wheel rotation center O3 and the eccentric shaft rotation center O1, and the intersection of the perpendicular line and the line between the grinding wheel rotation center O3 and the eccentric shaft rotation center O1 is taken as the origin of the grinding machine global coordinate system;

[0009] S2. Construct the ideal trajectory model η of the eccentric shaft external grinding point:

[0010] η=H QT ·K T (θ); where: K T (θ) is the motion trajectory of the grinding point p in the local coordinate system T{O} of the workpiece, H QT The transformation matrix from the global coordinate system Q{O} of the grinder to the local coordinate system T{O} of the workpiece;

[0011] L tx and L tz is the spatial position of the eccentric axis rotation center O1 in the global coordinate system Q{O};

[0012] S3. Construct the actual trajectory model τ of the eccentric shaft external grinding point:

[0013] τ=M z ·M x ·H QW ·K W (θ);

[0014] Where: M Z is the comprehensive geometric error of the radial motion axis of the grinder, M x is the comprehensive geometric error of the axial motion axis of the grinding wheel frame, H QW K is the transformation matrix from the global coordinate system Q{O} of the grinding machine to the local coordinate system W{O} of the grinding wheel. W (θ) is the motion trajectory of the grinding point p in the local coordinate system W{O} of the grinding wheel;

[0015] X' is the actual length of the center line O1O3;

[0016] S4. Calculate the trajectory error λ of the eccentric shaft appearance grinder: λ = τ - η.

[0017] Further, in step S2, the motion trajectory K of the grinding point p in the workpiece local coordinate system T{O} T (θ) is determined by the following method:

[0018] Among them: θ is the rotation angle of the eccentric shaft, β is the angle that the grinding wheel rotates relative to the grinding point p, e is the eccentricity of the eccentric shaft, R g R is the eccentric shaft neck radius of the eccentric shaft, w is the grinding wheel radius.

[0019] Further, in step S3, the trajectory of the grinding point p in the local coordinate system W{O} of the grinding wheel is determined by the following method:

[0020] Where: β is the angle of the grinding wheel relative to the grinding point p, e is the eccentricity of the eccentric shaft, R g R is the eccentric shaft neck radius of the eccentric shaft, w is the grinding wheel radius.

[0021] Furthermore, the comprehensive geometric error M of the radial motion axis of the grinding machine Z Determined by:

[0022] in, is the rotation of the radial motion axis of the grinding machine i (z) The corresponding exponential matrix:

[0023] is the unit error rotation of the radial motion axis of the grinding machine ex (z) corresponds to the exponential matrix, is the unit error rotation of the radial motion axis of the grinding machine ey (z) corresponds to the exponential matrix, is the unit error rotation of the radial motion axis of the grinding machine ez (z) The corresponding exponential moment

[0024]

[0025]

[0026] Array; among them:

[0027] Furthermore, the comprehensive geometric error M of the axial motion axis of the grinding wheel frame x Determined by:

[0028]

[0029] in: is the rotation of the radial motion axis of the grinding machine i (x) The corresponding exponential matrix

[0030] is the unit error rotation of the axial motion axis of the grinding wheel frame ξ ex (x) corresponds to the exponential matrix, is the unit error rotation of the axial motion axis of the grinding wheel frame ξ ey (x) corresponds to the exponential matrix, is the unit error rotation of the axial motion axis of the grinding wheel frame ξ ez (x) corresponds to the exponential matrix; where:

[0031] ξ i (x) = [0,0,0,1,0,0] T ;

[0032] S z (x) is the deviation between the ideal position and the actual position of the axial motion axis of the grinding wheel frame of the grinding machine;

[0033]

[0034]

[0035] in:

[0036] δ x (x),δ y (x),δ z (x) are the linear errors of the axial motion axis of the grinding wheel frame in the x, y, and z directions, respectively, and ε x (x),ε y (x),ε z (x) are the angular errors of the axial motion axis of the grinding wheel frame in the x, y, and z directions respectively.

[0037] The beneficial effects of the present invention are as follows: Through the present invention, based on the combination of the actual trajectory of the grinding point during the grinding process and the ideal trajectory, the comprehensive geometric error of the grinding machine can be accurately analyzed, thereby providing accurate data support for the error compensation control during the grinding process, thereby ensuring the final eccentric shaft product quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0039] Figure 1 It is a flow chart of the present invention.

[0040] Figure 2 Schematic diagram of the eccentric shaft structure of the RV reducer.

[0041] Figure 3 Schematic diagram of the eccentric journal following grinding motion.

[0042] Figure 4Schematic diagram of the geometric error of the axial motion axis (translational axis) of the grinding wheel frame of the grinding machine.

[0043] Figure 5 is the verticality error S z (x) Schematic diagram.

[0044] Figure 6 Schematic diagram of the grinding machine topology. DETAILED DESCRIPTION

[0045] The present invention is further described in detail below in conjunction with the accompanying drawings:

[0046] The eccentric shaft external cylindrical grinder is a three-axis CNC machine tool consisting of the grinding wheel frame axial motion axis (X-axis), radial motion axis (Z-axis) and workpiece rotation axis (C-axis). According to the ISO230-1 standard, machine tool geometric errors are mainly divided into two categories: position dependent geometric errors (PDGEs) caused by machine tool manufacturing defects and position independent geometric errors (PIGEs) caused by machine tool assembly defects. From the above analysis, it can be seen that the grinder has a total of 18 PDGEs. It has 2 moving axes and 1 rotation axis, and each moving axis includes 6 PDGEs, including 3 linear errors and 3 angular errors. Taking the X-axis as an example, Figure 3 The PDGEs for the translational axes are described. In addition, the machine tool includes 4 PIGEs, 2 of which are perpendicularity errors and 2 are installation errors for the rotational axes.

[0047] Based on the above principle, the C-axis only drives the workpiece to rotate, and its position is fixed in the entire machine tool space. The error it produces has little effect on the machining accuracy, so the C-axis and the machine tool bed are regarded as a rigid body, and the geometric errors related to it are not considered; therefore,

[0048] The eccentric shaft external cylindrical grinding machine contains 13 geometric errors, as shown in Table 1.

[0049] Table 1 Geometric error elements of eccentric shaft external cylindrical grinder

[0050]

[0051] In Table 1, three different letters, δ, ε, and S, are used to represent different error variables, where δ represents linear error, ε represents angular error, and S represents vertical error. Error variables are represented according to a certain naming rule. The first letter of the subscript represents the direction in which the error occurs, and the letter in the bracket represents the name of the motion axis where the error is located, for example: δ x (x) represents the linear error of the X-axis in the x-direction, S z(x) represents the verticality error between the X-axis and the Z-axis. Based on the above analysis, the present invention proposes the following specific model:

[0052] The present invention provides a method for analyzing grinding trajectory errors of an eccentric shaft cylindrical grinder, comprising the following steps:

[0053] S1. Construct the grinding wheel local coordinate system W{O}, the workpiece local coordinate system T{O} and the grinding machine global coordinate system Q{O} of the eccentric shaft external cylindrical grinder; wherein the grinding wheel local coordinate system takes the grinding wheel rotation center O3 of the eccentric shaft external cylindrical grinder as the origin, and the workpiece local coordinate system takes the eccentric shaft rotation center O1 as the origin; draw a perpendicular line through the origin of the grinder to the line between the grinding wheel rotation center O3 and the eccentric shaft rotation center O1, and the intersection of the perpendicular line and the line between the grinding wheel rotation center O3 and the eccentric shaft rotation center O1 is taken as the origin of the grinding machine global coordinate system;

[0054] S2. Construct the ideal trajectory model η of the eccentric shaft external grinding point:

[0055] η=H QT ·K T (θ); where: K T (θ) is the motion trajectory of the grinding point p in the local coordinate system T{O} of the workpiece, H QT The transformation matrix from the global coordinate system Q{O} of the grinder to the local coordinate system T{O} of the workpiece;

[0056] L tx and L tz is the spatial position of the eccentric axis rotation center O1 in the global coordinate system Q{O};

[0057] S3. Construct the actual trajectory model τ of the eccentric shaft external grinding point:

[0058] τ=M z ·M x ·H QW KW(θ);

[0059] Where: M Z is the comprehensive geometric error of the radial motion axis of the grinder, M x is the comprehensive geometric error of the axial motion axis of the grinding wheel frame, H QW K is the transformation matrix from the global coordinate system Q{O} of the grinding machine to the local coordinate system W{O} of the grinding wheel. W (θ) is the motion trajectory of the grinding point p in the local coordinate system W{O} of the grinding wheel;

[0060] X' is the actual length of the center line O1O3;

[0061] S4. Calculate the trajectory error λ of the eccentric shaft appearance grinder: λ = τ-η. Through the above method, based on the actual trajectory of the grinding point during the grinding process and the combination of the ideal trajectory, the comprehensive geometric error of the grinder can be accurately analyzed, thereby providing accurate data support for the error compensation control during the grinding process and ensuring the final eccentric shaft product quality.

[0062] In this embodiment, in step S2, the motion trajectory K of the grinding point p in the workpiece local coordinate system T{O} is T (θ) is determined by the following method:

[0063] Among them: θ is the rotation angle of the eccentric shaft, β is the angle that the grinding wheel rotates relative to the grinding point p, e is the eccentricity of the eccentric shaft, R g R is the eccentric shaft neck radius of the eccentric shaft, w is the grinding wheel radius.

[0064] In this embodiment, in step S3, the trajectory of the grinding point p in the grinding wheel local coordinate system W{O} is determined by the following method:

[0065] Where: β is the angle of the grinding wheel relative to the grinding point p, e is the eccentricity of the eccentric shaft, R g R is the eccentric shaft neck radius of the eccentric shaft, w is the grinding wheel radius.

[0066] In this embodiment, the radial motion axis comprehensive geometric error M of the grinding machine is Z Determined by:

[0067] in, is the rotation of the radial motion axis of the grinding machine i (z) The corresponding exponential matrix:

[0068] is the unit error rotation of the radial motion axis of the grinding machine ex (z) corresponds to the exponential matrix, is the unit error rotation of the radial motion axis of the grinding machine ey (z) corresponds to the exponential matrix, is the unit error rotation of the radial motion axis of the grinding machine ez (z) The corresponding exponential moment

[0069]

[0070]

[0071] Array; among them:

[0072] The comprehensive geometric error M of the axial motion axis of the grinding wheel frame x Determined by:

[0073]

[0074] in: is the rotation of the radial motion axis of the grinding machine i (x) The corresponding exponential matrix

[0075] is the unit error rotation of the axial motion axis of the grinding wheel frame ξ ex (x) corresponds to the exponential matrix, is the unit error rotation of the axial motion axis of the grinding wheel frame ξ ey (x) corresponds to the exponential matrix, is the unit error rotation of the axial motion axis of the grinding wheel frame ξ ez (x) corresponds to the exponential matrix; where:

[0076] ξ i (x) = [0,0,0,1,0,0] T ;

[0077] S z (x) is the deviation between the ideal position and the actual position of the axial motion axis of the grinding wheel frame of the grinding machine;

[0078]

[0079]

[0080] in:

[0081] δ x (x),δ y (x),δ z (x) are the linear errors of the axial motion axis of the grinding wheel frame in the x, y, and z directions, respectively, and ε x (x),ε y (x),ε z (x) are the angular errors of the axial motion axis of the grinding wheel frame in the x, y, and z directions respectively.

[0082] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A grinding trajectory error analysis method for an eccentric shaft cylindrical grinder, characterized in that: The following steps are involved: S1. Construct the grinding wheel local coordinate system W{O}, the workpiece local coordinate system T{O} and the grinding machine global coordinate system Q{O} of the eccentric shaft external cylindrical grinder; wherein the grinding wheel local coordinate system takes the grinding wheel rotation center O3 of the eccentric shaft external cylindrical grinder as the origin, and the workpiece local coordinate system takes the eccentric shaft rotation center O1 as the origin; draw a perpendicular line through the origin of the grinder to the line between the grinding wheel rotation center O3 and the eccentric shaft rotation center O1, and the intersection of the perpendicular line and the line between the grinding wheel rotation center O3 and the eccentric shaft rotation center O1 is taken as the origin of the grinding machine global coordinate system; S2. Construct the ideal trajectory model η of the eccentric shaft external grinding point: η=H QT ·K T (θ); where: K T (θ) is the motion trajectory of the grinding point p in the local coordinate system T{O} of the workpiece, H QT The transformation matrix from the global coordinate system Q{O} of the grinder to the local coordinate system T{O} of the workpiece; L tx and L tz is the spatial position of the eccentric axis rotation center O1 in the global coordinate system Q{O}; S3. Construct the actual trajectory model τ of the eccentric shaft external grinding point: τ=M z ·M x ·H QW ·K W (i); Where: M Z is the comprehensive geometric error of the radial motion axis of the grinder, M x is the comprehensive geometric error of the axial motion axis of the grinding wheel frame, H QW K is the transformation matrix from the global coordinate system Q{O} of the grinding machine to the local coordinate system W{O} of the grinding wheel. W (θ) is the motion trajectory of the grinding point p in the local coordinate system W{O} of the grinding wheel; X' is the actual length of the center line O1O3; S4. Calculate the trajectory error λ of the eccentric shaft appearance grinder: λ = τ - η.

2. The grinding trajectory error analysis method of an eccentric shaft cylindrical grinder according to claim 1, characterized in that: In step S2, the motion trajectory K of the grinding point p in the workpiece local coordinate system T{O} T (θ) is determined by the following method: Among them: θ is the rotation angle of the eccentric shaft, β is the angle that the grinding wheel rotates relative to the grinding point p, e is the eccentricity of the eccentric shaft, R g R is the eccentric shaft neck radius of the eccentric shaft, w is the grinding wheel radius.

3. The grinding trajectory error analysis method of an eccentric shaft cylindrical grinder according to claim 1, characterized in that: In step S3, the trajectory of the grinding point p in the local coordinate system W{O} of the grinding wheel is determined by the following method: Where: β is the angle of the grinding wheel relative to the grinding point p, e is the eccentricity of the eccentric shaft, R g R is the eccentric shaft neck radius of the eccentric shaft, w is the grinding wheel radius.

4. The grinding trajectory error analysis method of an eccentric shaft cylindrical grinder according to claim 1, characterized in that: The comprehensive geometric error M of the radial motion axis of the grinding machine Z Determined by: in, is the rotational moment of the radial motion axis of the grinding machine i (z) The corresponding exponential matrix: is the unit error rotation of the radial motion axis of the grinding machine ex (z) corresponds to the exponential matrix, is the unit error rotation of the radial motion axis of the grinding machine ey (z) corresponds to the exponential matrix, is the unit error rotation of the radial motion axis of the grinding machine ez (z) The corresponding exponential matrix; where:

5. The grinding trajectory error analysis method of an eccentric shaft cylindrical grinder according to claim 1, characterized in that: The comprehensive geometric error M of the axial motion axis of the grinding wheel frame x Determined by: in: is the rotational moment of the radial motion axis of the grinding machine i (x) The corresponding exponential matrix is the unit error rotation of the axial motion axis of the grinding wheel frame ξ ex (x) corresponds to the exponential matrix, is the unit error rotation of the axial motion axis of the grinding wheel frame ξ ey (x) corresponds to the exponential matrix, is the unit error rotation of the axial motion axis of the grinding wheel frame ξ ez (x) corresponds to the exponential matrix; where: x i (x)=[0,0,0,1,0,0] T ; S z (x) is the deviation between the ideal position and the actual position of the axial motion axis of the grinding wheel frame of the grinding machine; in: δ x (x),δ y (x),δ z (x) are the linear errors of the axial motion axis of the grinding wheel frame in the x, y, and z directions, respectively, and ε x (x),ε y (x),ε z (x) are the angular errors of the axial motion axis of the grinding wheel frame in the x, y, and z directions respectively.

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