Modeling method for tooth profile error of forming gear grinding machine based on multi-error coupling

Abstract

The invention provides a forming gear grinding machine tooth profile error modeling method based on multi-error coupling, and the method specifically comprises the following steps: 1, building a complete geometric error model based on a homogeneous coordinate transformation principle and a full kinematic chain of a gear grinding machine; 2, according to the relation between the full kinematic chain and the tool nose position in the tool coordinate system, a geometric error-tool pose error model of the forming gear grinding machine is established; and 3, according to an envelope principle, revealing an error mapping rule from the tool error to the tooth profile error, so that a coupling mapping model from the geometric error to the tool error and then to the tooth profile error is established, and a complete multi-error coupling model is obtained. According to the method, the mapping rule of the geometric error and the tooth profile error can be revealed, the influence of the machine tool error on grinding can be comprehensively analyzed, and the limitation of a single error is avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of error modeling of numerically controlled form grinding machines, and particularly relates to a method for modeling the tooth profile error of a form grinding machine based on multi-error coupling, which is a method for modeling the whole-process tooth profile error under the coupling action of multiple geometric errors of a form grinding machine. Background Technique

[0002] Gear transmission has the advantages of smooth transmission, accurate transmission ratio, high efficiency, compact and reliable structure, etc., and is one of the most important and widely used transmission forms in mechanical devices. Therefore, the manufacturing level of gears determines the service performance and core competitiveness of high-end equipment in China's industry, national defense, and strategic emerging industries, and has become a key bottleneck restricting the development of China's high-end equipment.

[0003] As the last process of gear machining, form grinding directly affects the stability and accuracy of gear transmission. However, due to the large number of machine tool geometric error elements and complex coupling effects, the error elements can reach dozens or even over a hundred, resulting in difficulties in error modeling and traceability compensation for large-scale numerically controlled form grinding machines. At present, the research on the influence of form grinding machines on the tooth profile error accuracy mainly focuses on single errors or several errors, and there is less research on the overall coupling effect, making the mapping law and quantitative influence between the geometric error of the form grinding machine and the grinding tooth profile error unclear, resulting in the lack of reliable theoretical basis and model support for ensuring and improving the gear grinding accuracy, and restricting the research and development of high-grade numerically controlled form grinding machines in China.

[0004] Therefore, how to establish a geometric error coupling mapping model for a form grinding machine and reveal the mapping law from geometric error to tooth profile error is one of the research directions for improving grinding accuracy at present. Summary of the Invention

[0005] The present invention provides a method for modeling the tooth profile error of a form grinding machine based on multi-error coupling. This error model can not only reveal the mapping law between geometric error and tooth profile accuracy, but also comprehensively analyze the influence of machine tool errors on grinding, avoid the limitations of single errors, and provide a reliable theoretical basis for subsequent tooth profile error analysis and compensation.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for modeling the tooth profile error of a form grinding machine based on multi-error coupling, comprising the following steps:

[0008] Step 1: Establish a complete geometric error model:

[0009] According to the homogeneous coordinate transformation principle, a geometric error module for each motion axis is established; based on the motion conditions of each axis during the grinding process of the gear grinding machine, the complete motion chain of the machine tool is derived; according to this motion chain, the error modules of each axis are connected in series to obtain a complete geometric error model.

[0010] Step 2: Establish a geometric error-tool pose error model:

[0011] According to the relationship between the complete motion chain and the tool tip position in the tool coordinate system, substitute the tool position to establish a geometric error-tool pose error model for the form grinding gear machine.

[0012] Step 3: Establish a complete multi-error coupling model;

[0013] According to the envelope principle, reveal the error mapping law from tool error to tooth profile error, thereby establishing a coupling mapping model from geometric error to tool error and then to tooth profile error, and obtaining a complete multi-error coupling model.

[0014] 2. The method for modeling the tooth profile error of a form grinding gear machine based on multi-error coupling according to claim 1, characterized in that: in the step 1, the motion chain of the form grinding gear machine is: gear G - C axis - bed R - X axis - Z axis - A axis - Y axis - tool W. Then the motion matrices of each axis are:

[0015]

[0016] T GC = T WY = I;

[0017] where T GC is the transformation matrix of the gear relative to the C axis, and T WY is the transformation matrix of the tool relative to the Y axis. Therefore, in the ideal case, the homogeneous transformation matrix of the tool coordinate system relative to the gear coordinate system is:

[0018]

[0019] In the step 1, the numerically controlled form grinding gear machine includes five axes: X axis, Y axis, Z axis, A axis, and C axis. In addition to the position-related geometric errors (PDGEs) existing in each axis itself, there are also position-independent geometric errors (PIGEs) caused by assembly deviations; as shown in the following table:

[0020]

[0021] Represent the single position-independent error of the motion axis with a matrix, and then multiply all the matrices to obtain the PDGEs of a single axis as:

[0022]

[0023] Similarly, the position-independent geometric errors caused by assembly deviations can be expressed as:

[0024]

[0025] Based on the above formula, the complete geometric error model for a single axis is:

[0026] T(N) = T PDGEs (N)T PIGEs (N)T m (N);

[0027] Therefore, considering the actual coordinate transformation with all errors, that is, the complete geometric error model is:

[0028]

[0029] In the second step, according to the relationship between the full motion chain and the tip position in the tool coordinate system, a geometric error-tool pose error model of the form grinding machine is established. If the tip position in the tool coordinate system is [a, b, c] T , the geometric error-tool pose error model can be obtained as:

[0030]

[0031] In the third step, according to the envelope principle, the error mapping law from tool error to tooth profile error is revealed, so as to establish a coupling mapping model from geometric error to tool error and then to tooth profile error, and a complete multi-error coupling model is obtained; it is known that the grinding wheel is a double bevel-shaped grinding wheel, composed of two symmetric inclined planes, and the angle between the inclined plane and the axis is The radius of the grinding wheel is R and the thickness is W. Its surface is divided into left and right inclined planes, and the parametric equations are:

[0032]

[0033] where u is the axial parameter and θ is the circumferential angle. Therefore, the surface of the grinding wheel in the global coordinate system can be obtained as:

[0034] S L = T GW ·S L (u, θ), S R = T GW ·S R (u, θ);

[0035] To meet the envelope condition, the contact point needs to satisfy that the normal vector is orthogonal to the relative velocity:

[0036]

[0037] where the velocity v is:

[0038]

[0039] The normal vector n is as follows:

[0040]

[0041] Solve the envelope equation for each inclined plane respectively:

[0042]

[0043] Use the iterative method to solve and obtain the set of contact points (u, θ), and this set is also the actual tooth profile. Solve the involute gear according to the gear design parameters to obtain the theoretical tooth profile, and subtract the two tooth profiles to obtain the tooth profile error containing the complete error, that is, the complete multi-error coupling model.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0045] The tooth profile error modeling method of the form grinding machine based on multi-error coupling of the present invention first establishes the pose transformation relationship containing errors between the axes of the grinding machine based on the homogeneous coordinate transformation principle and the motion chain of the machine tool, so as to obtain a complete geometric error model; then substitute the tool position to establish a geometric error-tool pose error model of the form grinding machine; then, based on the envelope principle, considering the characteristics of the contact points, obtain the set of contact points, and this set is also the actual tooth profile. Then subtract the actual tooth profile from the theoretical tooth profile to obtain the tooth profile error containing the complete error. Through this model, the mapping relationship between the geometric error of the grinding machine and the tooth profile can be intuitively obtained, and it can also provide a comprehensive theoretical basis for subsequent analysis and compensation. Brief Description of the Drawings

[0046] Figure 1 is the flow chart of error modeling;

[0047] Figure 2 is the coordinate axis structure diagram of the five-axis form grinding machine;

[0048] Figure 3 is the schematic diagram of the machine tool motion chain. Detailed Embodiments

[0049] To clarify the technical problems, technical solutions, implementation processes and performance demonstrations, the present invention will be further described in detail below with reference to the drawings and embodiments, but the described embodiments are only a part of the embodiments of the present invention, not all of them.

[0050] The tooth profile error modeling method of the form grinding machine based on multi-error coupling in this embodiment includes the following steps:

[0051] Step 1: Establish a complete geometric error model:

[0052] According to the homogeneous coordinate transformation principle, a geometric error module for each motion axis is established; based on the motion conditions of each axis during the grinding of the gear grinding machine, the full motion chain of the machine tool is derived; according to this motion chain, the error modules of each axis are connected in series to obtain a complete geometric error model.

[0053] Step 2: Establish a geometric error-tool pose error model:

[0054] According to the relationship between the full motion chain and the tip position in the tool coordinate system, substituting the tool position, a geometric error-tool pose error model of the form grinding gear grinding machine is established.

[0055] Step 3: Establish a complete multi-error coupling model:

[0056] To meet the enveloping condition, based on the geometric error-tool pose error model in Step 2, the velocity and normal vector of the contact point during grinding are obtained; according to the enveloping principle, the set of contact points between the tool and the tooth profile is solved, and this set is also the actual tooth profile. Then, according to the gear design parameters, the theoretical tooth profile is solved, and the actual one is subtracted from the theoretical one to obtain the tooth profile error containing the complete error, that is, the complete multi-error coupling model.

[0057] The complete geometric error model in Step 1 above, as Figure 2 shown in the coordinate axis structure diagram of the five-axis form grinding gear grinding machine. Based on the motion conditions of each axis during grinding, the motion chain of the form grinding gear grinding machine can be deduced as: gear G - C axis - bed R - X axis - Z axis - A axis - Y axis - tool W, as Figure 3 shown. According to the actual motion of each axis during grinding, its motion matrix is deduced as:

[0058]

[0059] T GC =T WY =I;

[0060] where T GC is the transformation matrix of the gear relative to the C axis, and T WY is the transformation matrix of the tool relative to the Y axis; X, Y, and Z are the distances moved by the X axis, Y axis, and Z axis respectively, and A and C are the distances moved by the A axis and C axis respectively. Therefore, in the ideal case without geometric errors, the homogeneous transformation matrix of the tool coordinate system relative to the gear coordinate system is:

[0061]

[0062] In the first step mentioned above, due to manufacturing errors of the machine tool, six degrees of freedom geometric errors will occur when each axis moves. Since the values of these 6 errors change when moving to different positions, they are called position-dependent geometric errors (PDGEs); in addition, there are also position-independent geometric errors (PIGEs) caused by assembly deviations. The summary is as follows in the table:

[0063]

[0064]

[0065] To obtain the position-dependent geometric errors of each moving axis, each error can be represented by a homogeneous transformation matrix, and then all error matrices are multiplied to obtain the following result:

[0066]

[0067] Similarly, the position-independent geometric errors caused by assembly deviations can be expressed as:

[0068]

[0069] Based on the above formulas, multiplying the position-dependent geometric error matrix, position-independent geometric error matrix and displacement matrix of a single axis, the complete actual geometric error model is obtained:

[0070] T(N) = T PDGEs (N)T PIGEs (N)T m (N);

[0071] Considering the relative position relationship and displacement relationship between axes, the following formula is obtained, that is, the overall actual geometric error model is:

[0072]

[0073] For the geometric error - tool pose error model in the second step mentioned above, according to the relationship between the full motion chain and the tip position in the tool coordinate system, a geometric error - tool pose error model of the form grinding machine is established. If the tip position in the tool coordinate system is [a, b, c] T , the geometric error - tool pose error model can be obtained as:

[0074]

[0075] The complete multi-error coupling model in step three reveals the error mapping law from tool error to tooth profile error according to the envelope principle, thereby establishing a coupling mapping model from geometric error to tool error and then to tooth profile error, and obtaining the complete multi-error coupling model. It is known that the grinding wheel is a double-inclined-sided grinding wheel composed of two symmetric inclined planes, and the angle between the inclined plane and the axis is The radius of the grinding wheel is R and the thickness is W. Its surface is divided into left and right inclined planes, so the parametric equations can be obtained as follows:

[0076]

[0077] where u is the axial parameter and θ is the circumferential angle. Multiplying it with the above geometric error-tool pose error model, the grinding wheel surface in the global coordinate system can be obtained as:

[0078] S L =T GW ·S L (u,θ),S R =T GW ·S R (u,θ);

[0079] To meet the envelope condition, the contact point needs to satisfy that the normal vector is orthogonal to the relative velocity:

[0080]

[0081] Based on the error model obtained in step two, the velocity v of the contact point during grinding can be calculated as:

[0082]

[0083] The normal vector n is:

[0084]

[0085] Therefore, the equation that meets the envelope principle can be obtained as:

[0086]

[0087] Using the iterative method to solve the two equations, the contact point set (u,θ) can be obtained, and this set is also the actual tooth profile. Then, according to the gear design parameters, the involute gear is solved to obtain the theoretical tooth profile. Subtracting the two tooth profiles, the tooth profile error containing the complete error, that is, the complete multi-error coupling model, can be obtained.

[0088] The above-described embodiments are merely preferred examples given to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection of the present invention shall be subject to the claims.

Claims

1. A tooth profile error modeling method for a form grinding machine based on multi-error coupling, characterized in that It includes the following steps: Step 1: Establish a complete geometric error model: According to the homogeneous coordinate transformation principle, establish the geometric error module of each motion axis; based on the motion conditions of each axis during the gear grinding process of the gear grinding machine, deduce the full motion chain of the machine tool; according to this motion chain, connect the error modules of each axis in series to obtain a complete geometric error model; Step 2: Establish a geometric error - tool pose error model: According to the relationship between the full motion chain and the tool tip position in the tool coordinate system, substitute the tool position to establish a geometric error - tool pose error model for the form grinding gear machine; Step 3: Establish a complete multi - error coupling model; According to the envelope principle, reveal the error mapping law from tool error to tooth profile error, so as to establish a coupling mapping model from geometric error to tool error and then to tooth profile error, and obtain a complete multi - error coupling model.

2. The method for modeling the tooth profile error of a form grinding machine based on multi-error coupling according to claim 1, wherein: In the above Step 1, the motion chain of the form grinding gear machine is: gear G - C axis - bed R - X axis - Z axis - A axis - Y axis - tool W. Then the motion matrices of each axis are: T GC = T WY = I; where T GC is the transformation matrix of the gear relative to the C-axis, and T WY is the transformation matrix of the cutting tool relative to the Y-axis. Therefore, ideally, the homogeneous transformation matrix of the cutting tool coordinate system relative to the gear coordinate system is: In the above Step 1, the numerically controlled form grinding gear machine includes five axes: X axis, Y axis, Z axis, A axis, and C axis. In addition to the position - related geometric errors (PDGEs) existing in each axis itself, there are also position - independent geometric errors (PIGEs) caused by assembly deviations; as shown in the following table: Represent the single position - independent error of the motion axis with a matrix, and then multiply all the matrices to obtain the PDGEs of a single axis as: Similarly, the position - independent geometric error caused by assembly deviation can be expressed as: Based on the above formulas, the complete geometric error model of a single axis is: T(N) = T PDGEs (N)T PIGEs (N)T m (N); Therefore, considering the actual coordinate transformation of all errors, that is, the complete geometric error model is:

3. The tooth profile error modeling method of a form grinding machine based on multi-error coupling according to claim 1, characterized in that: In the second step, according to the relationship between the full motion chain and the tip position in the tool coordinate system, a geometric error-tool pose error model of the form grinding machine is established. If the tip position in the tool coordinate system is [a, b, c] T , the geometric error-tool pose error model can be obtained as follows:

4. The method for modeling the tooth profile error of a form grinding machine based on multi-error coupling according to claim 1, wherein: In the third step, according to the envelope principle, the error mapping law from the tool error to the tooth profile error is revealed, so as to establish a coupling mapping model from the geometric error to the tool error and then to the tooth profile error, and a complete multi-error coupling model is obtained; it is known that the grinding wheel is a double trapezoidal grinding wheel, which consists of two symmetric inclined planes, and the angle between the inclined plane and the axis is The radius of the grinding wheel is R and the thickness is W. Its surface is divided into left and right inclined planes, and the parametric equations are: Among them, u is the axial parameter, and θ is the circumferential angle. Therefore, the surface of the grinding wheel in the global coordinate system can be obtained as: S L = T GW ·S L (u, θ), S R = T GW ·S R (u, θ); To meet the envelope condition, the contact point needs to satisfy that the normal vector is orthogonal to the relative velocity: Among them, the velocity v is: The normal vector n is: Solve the envelope equation for each inclined plane respectively: Use the iterative method to solve and obtain the set of contact points (u, θ), and this set is also the actual tooth profile. Solve the involute gear according to the gear design parameters to obtain the theoretical tooth profile, subtract the two tooth profiles to obtain the tooth profile error including complete errors, that is, the complete multi - error coupling model.

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