A machine tool power tool holder geometric accuracy forward design method based on multi-body theory

Abstract

The present application relates to a kind of machine tool power tool rest geometric accuracy forward design method based on many-body theory, comprising S1, the end precision design index of power tool rest is determined;S2, the mapping relationship between machining error and geometric error is determined;S3, the mapping relationship between pose error, assembly error and geometric accuracy is determined, and the final error transfer model considering the coupling of machining error and many-body geometric error is obtained;S4, positioning accuracy and repeatability accuracy sensitivity analysis and parameter weight identification of end tooth disc machining error;S5, find the maximum machining error and assembly error tolerance range;S6, calculate the assembly clearance tolerance and end face runout tolerance that meet the positioning accuracy and repeatability accuracy requirement.Based on the target direction of the present application is stronger, make power tool rest can adapt to user process and working condition environment requirement, and make that tolerance distribution is more accurate, improve the positioning accuracy and repeatability accuracy of power tool rest.

Description

Technical Field

[0001] This invention belongs to the field of high-end equipment manufacturing technology, specifically relating to a forward design method for the geometric accuracy of a power tool holder. Background Technology

[0002] The modern CNC machine tool industry is developing towards higher speed, higher precision, greater intelligence, and higher reliability. Therefore, the requirements for the precision of CNC machine tools and the performance of their components are becoming increasingly stringent. The power tool turret is one of the core components of a CNC machining center, enabling functions such as tool storage, automatic tool changing, and tool positioning.

[0003] To address the stringent requirements for positioning accuracy and repeatability during machining of powered tool holders, traditional geometric accuracy design methods, lacking clear performance objectives, struggle to achieve quantitative accuracy control and rely excessively on assembly experience. To resolve this issue, an error propagation model is established based on multibody system theory. By analyzing the geometric error relationships between the moving parts of the powered tool holder, a forward design approach is implemented, from overall machine accuracy indicators to component tolerances. This provides theoretical support for accurately controlling the positioning accuracy and repeatability of the powered tool holder. Summary of the Invention

[0004] The purpose of this application is to overcome the shortcomings of the prior art and provide a forward design method for the geometric accuracy of the power tool post based on multibody theory. Based on multibody system theory, an error transmission model is established. By analyzing the geometric error relationship between various moving parts of the power tool post, forward design from the overall machine accuracy index to the tolerance of the parts is realized, providing theoretical support for accurately controlling the positioning accuracy and repeatability of the power tool post.

[0005] The technical problem solved by this invention is achieved through the following technical solution: A forward design method for the geometric accuracy of a machine tool power tool holder based on multibody theory, comprising the following steps: S1. Determine the end-effector accuracy design parameters based on the machining process requirements; S2. Establish a geometric error propagation model that considers the machining error of the end gear plate, and determine the mapping relationship between machining error and geometric error; S3. Based on the multibody system theory, construct the theoretical pose transformation matrix and error transformation matrix between adjacent bodies, establish an error transmission model for the geometric accuracy of the power tool holder, and determine the mapping relationship between pose error, assembly error and geometric accuracy; take the various geometric errors caused by machining errors as inputs and substitute them into the error transmission model established based on the multibody system theory, so as to obtain the final error transmission model that comprehensively considers the coupling effect of machining error and multibody geometric error. S4. Based on the established final error propagation model, perform sensitivity analysis and parameter weight identification for positioning accuracy and repeatability accuracy. S5. Based on genetic algorithms and Monte Carlo methods, the allowable ranges of machining errors and assembly errors are designed to find the maximum allowable range of machining errors and assembly errors. S6. Based on the obtained assembly error tolerance range, calculate the assembly clearance tolerance and end face runout tolerance that meet the positioning accuracy and repeatability requirements.

[0006] Furthermore, the error propagation model includes end gear plate machining error and end gear plate geometric error. The end gear plate machining error includes cumulative tooth pitch error, tooth direction error, tooth profile half angle error and tooth width error. The end gear plate geometric error includes x-direction straightness error, y-direction straightness error, z-direction straightness error, roll error, yaw error and pitch error.

[0007] Furthermore, the error propagation model between the machining error and geometric error of the locking gear disc in the locked state is as follows: (a) Mathematical model of straightness error and machining error: Cumulative tooth pitch error: Cumulative tooth pitch error is a static error along the x-axis. ; In the formula: The angle through which the gear disc rotates; Tooth direction error: Tooth direction error causes displacement in the x-direction and tilting about the y-axis. ; In the formula: The radius of the pitch circle; Tooth profile half-angle error: Tooth profile half-angle error causes x-axis translation: ; Tooth width error: Tooth width error causes tilting about the y-axis ; Therefore, the spatial geometric relationship between straightness error in the x-direction and machining error is as follows: ; (b) Mathematical model of straightness error in the Y direction and machining error: Cumulative tooth pitch error: Cumulative tooth pitch error is a static error along the x-axis. ; Tooth direction error: Tooth direction error causes displacement in the y-axis and tilting about the x-axis. ; Tooth profile half-angle error: No displacement in the y-direction (tooth profile shape deviation, displacement occurs on the tangent): ; Tooth width error: Tooth width error causes axial dimensional deviation. ; Therefore, the spatial geometric relationship between the straightness error in the y-direction and the machining error is as follows: ; (c) Mathematical model of z-axis straightness error and machining error: Cumulative tooth pitch error: Cumulative tooth pitch error does not cause axial offset. ; Tooth direction error: Tooth direction error is the error in the direction of the meshing line and does not cause axial offset. ; Tooth profile half-angle error: This is a deviation in the tooth profile shape, resulting in displacement along the tangent line but not axial offset. ; Tooth width error: Tooth width error causes axial dimensional deviation. ; Therefore, the spatial geometric relationship between the z-axis straightness error and the machining error is as follows: ; (d) Mathematical model of pitch error and machining error: Cumulative tooth pitch error: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: ; Therefore, the spatial geometric relationship between pitch error and machining error is as follows: ; (e) Mathematical model of runout error and machining error: Cumulative tooth pitch error: Cumulative tooth pitch error along the xy plane: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: Tooth width error causes axial dimensional deviation. ; Therefore, the spatial geometric relationship between pitch error and machining error is as follows: ; (f) Mathematical model of rolling error and machining error: Cumulative tooth pitch error: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: ; Therefore, the spatial geometric relationship between roll error and machining error is as follows: ; (g) Error propagation model of machining error and geometric error of locking gear disc in locking state ; The geometric error propagation model for machining error and geometric error of the moving gear disk during rotational positioning in the power tool post end gear disk structure is as follows: (a) Mathematical model of straightness error and machining error: Cumulative tooth pitch error: Cumulative tooth pitch error is a static error along the x-axis. ; In the formula: The angle through which the gear disc rotates; Tooth direction error: Tooth direction error causes displacement in the x-direction and tilting about the y-axis. ; In the formula: The radius of the pitch circle; Tooth profile half-angle error: Tooth profile half-angle error causes x-axis translation: ; Tooth width error: Tooth width error causes tilting about the y-axis ; Therefore, the spatial geometric relationship between straightness error in the x-direction and machining error is as follows: ; (b) Mathematical model of straightness error in the y-direction and machining error: Cumulative tooth pitch error: Cumulative tooth pitch error is a static error along the x-axis. ; Tooth direction error: Tooth direction error causes displacement in the y-axis and tilting about the x-axis. ; Tooth profile half-angle error: ; Tooth width error: Tooth width error causes axial dimensional deviation. ; Therefore, the spatial geometric relationship between the straightness error in the y-direction and the machining error is as follows: ; (c) Mathematical model of z-axis straightness error and machining error: Cumulative tooth pitch error: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: Tooth width error causes axial dimensional deviation. ; Therefore, the spatial geometric relationship between the z-axis straightness error and the machining error is as follows: ; (d) Mathematical model of pitch error and machining error: Cumulative tooth pitch error: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: ; Therefore, the spatial geometric relationship between pitch error and machining error is as follows: ; (e) Mathematical model of runout error and machining error Cumulative tooth pitch error: Cumulative tooth pitch error along the xy plane: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: Tooth width error causes axial dimensional deviation. ; Therefore, the spatial geometric relationship between pitch error and machining error is as follows: ; (f) Mathematical model of rolling error and machining error Cumulative tooth pitch error: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: ; Therefore, the spatial geometric relationship between roll error and machining error is as follows: ; The specific transmission model of machining error and geometric error during indexing of the moving gear disc is as follows: .

[0008] Furthermore, the solution process for the transformation matrix and geometric error model of the dynamic tool holder coordinate system based on multibody system theory in S3 is as follows: (1) Establish the multi-body system topology of the power tool post, including the coordinate system and transformation matrix of the housing, spindle, rear piston, moving gear plate, fixed gear plate, and locking gear plate; The position transformation matrix and static error matrix between adjacent objects are represented as follows: (a) Change from the housing to the rear piston: The theoretical position transformation matrix is: ; The error position transformation matrix is: ; The theoretical motion transformation matrix is: ; The error motion transformation matrix is: ; (b) Transition from the rear piston to the main shaft: The theoretical position transformation matrix is: ; The error position transformation matrix is: ; The theoretical motion transformation matrix is: ; The error motion transformation matrix is: ; (c) Transition from main spindle to moving gear plate: The theoretical position transformation matrix is: ; The error position transformation matrix is: ; The theoretical motion transformation matrix is: ; The error motion transformation matrix is: ; (d) Transition from housing to locking gear: The theoretical position transformation matrix is: ; The error position transformation matrix is: ; The theoretical motion transformation matrix is: ; The error motion transformation matrix is: ; (e) Transition from locking gear plate to fixed gear plate: The theoretical position transformation matrix is: ; The error position transformation matrix is: ; The theoretical motion transformation matrix is: ; The error motion transformation matrix is: ; (2) Establish a geometric error propagation model based on the transformation matrix. The specific process is as follows: (a) Determination of the relative position error of the indexing point between the moving gear plate and the fixed gear plate The coordinate system of the moving gear is The coordinates of the meshing point in the coordinate system of the moving gear disk are represented by a column vector: ; To predict the positional error of the indexing engagement point, both the actual and theoretical position coordinates of the moving gear plate must be transformed into the same coordinate system, namely the box coordinate system. middle; In an ideal scenario, i.e., when there is no error, the expression for the indexing engagement point in the tool post coordinate system is: ; However, when there are geometric errors in the tool post, the coordinates of the indexing engagement point will deviate from the ideal position. The coordinate expression of the indexing engagement point in the tool post coordinate system after deviating from the ideal position is: ; Similarly, suppose the coordinates of the pitch engagement point of the fixed gear plate are as follows in the coordinate system of the fixed gear plate: ; In an ideal scenario, where there is no error, the coordinate expression of the fixed gear meshing point in the tool post coordinate system is: ; However, when there are geometric errors in the tool post, the actual position of its meshing point will deviate from the ideal position. After deviating from the ideal position, the coordinate expression of the meshing point of the fixed gear plate in the tool post coordinate system is: ; At this point, both the moving gear and the fixed gear have been transformed into the tool post coordinate system, and the theoretical positional relationship of the indexing engagement point can be obtained: ; The relationship between position error and position error is: ; (b) Determination of the relative motion error at the indexing point of the moving gear plate and the fixed gear plate Assume the orientation vector of the indexing engagement point of the moving gear plate in the coordinate system of the moving gear plate is: ; To predict the position and orientation error of the moving gear disk, the vector of the moving gear disk must be... The required position and orientation of the moving gear disk are all transformed into the same coordinate system, specifically the box coordinate system. middle; In an ideal scenario, i.e., when there is no error, the expression for the position vector of the moving gear disk in the moving gear disk coordinate system is: ; In the formula , Each is a two adjacent body and The ideal positions between them, and the rotation transformation matrix of the motion; However, when the tool post has geometric errors, the actual pose of the moving gear disc deviates from the theoretical pose. The expression for the actual pose is: ; In the formula , Each is a two adjacent body and The ideal positions between them, and the rotation transformation matrix of the motion; Assume the orientation vector of the indexing engagement point of the fixed gear plate in the coordinate system of the fixed gear plate is: ; For the pose of a fixed gear disk, ideally, when there is no error, the vector of the fixed gear disk... The expression in the coordinate system of the fixed gear disk is: ; However, when the tool post has geometric errors, the actual pose of the fixed gear disc deviates from the theoretical pose. The expression for the actual pose is: ; At this point, both the moving gear and the fixed gear have been transformed into the tool post coordinate system, and the theoretical motion relationship of the indexing engagement point can be obtained: ; The relationship between motion error and motion error is: ; Substituting the transformation matrix of the tool post into the theoretical positional relationship, we can obtain the theoretical positional relationship between the moving gear plate coordinate system and the fixed gear plate coordinate system of the power tool post: ; Substituting the above equation and the transformation matrix of the tool post into the error position relationship and the error motion relationship, we can obtain the relative pose error relationship between the moving gear plate coordinate system, the fixed gear plate coordinate system and the locking gear plate coordinate system of the power tool post: ; Combining the two equations yields the specific relationship between the machining error and geometric error of the end gear disc: .

[0009] Furthermore, the positioning accuracy sensitivity and repeatability sensitivity analysis of S4 are specifically as follows: Let the geometric error be represented by the six-degree-of-freedom pose error vector of the geometric error model: ; Machining errors and assembly errors are expressed as follows: ; Positioning accuracy sensitivity and repeatability sensitivity are defined as follows: ; This represents the partial derivative of the j-th machining error component with respect to the i-th geometric error component; From the specific formula relating machining error and geometric error, it can be seen that... It is a variable A continuously differentiable function of each error component. right The partial derivatives of each error component are generally expressed as: Assuming If it is continuously differentiable, then for Expand the first-order Taylor series and remove higher-order terms: ; in: It is a small component of geometric error; This is the sensitivity matrix; For higher-order terms, after removing the higher-order terms: ; Therefore, the sensitivity analysis model for error X can be obtained as follows: ; in: This is the sensitivity matrix; By calculating the positioning accuracy sensitivity and repeatability sensitivity, the degree of influence of machining error and assembly error on the pose error can be obtained, thereby reducing machining error and assembly error and improving the overall accuracy of the power tool holder.

[0010] Furthermore, S5 performs geometric accuracy design based on an optimization problem model with chance programming constraints, first determining the design variables, objective function, and constraints of the geometric accuracy optimization problem: (1) Design variables: For high-precision tool holders, the geometric error can generally be assumed to follow a uniform distribution, and its vertical deviation is assumed to be symmetrical. It is the fourth of the four geometric errors. The error value of the term error, then ; in: Sure If the upper and lower limits are defined, then the design variables are: ; (2) Objective function: The objective function used in the design must relax the error sources to the maximum feasible region. Since there are 14 machining error sources, it is essentially a multi-objective optimization problem, which needs to be transformed into a single-objective optimization problem. Since geometric errors have different sensitivities to machining errors, the assigned results should satisfy the condition that the error term with the greater error sensitivity should have a smaller tolerance, that is, a smaller standard deviation. Construct an objective function based on the differences in sensitivity: ; in: The weighting coefficient is determined based on the sensitivity coefficient, as shown in the following formula: ; For machining error terms with relatively high sensitivity, the maximum allowable error range will be smaller. (3) Constraints: (a) Constraints on design variables ; in: This is the lower limit value. This is the upper limit value; (b) Constraints on machining errors The previous section presented the functional relationship between the machining error and the geometric pose error of the end gear disk. However, in precision design, since only the tolerance of the machining error sources is designed, a different approach is adopted. ; The computational function serving as the terminal function; Where: A is the sensitivity matrix of the error transfer function. ; Since any variable in X follows a uniform distribution And they are independent of each other. Y and X have a linear relationship. When there are enough statistical values, the row vector of Y follows a normal distribution with a mean of 0. The constraint on the error range is transformed into a constraint on statistical parameters, that is, a constraint on the standard deviation of the processing error. ; in, Let be the statistical variance of each vector, and represent the statistical variance of the processing error, respectively. Designed to meet precision requirements; The steps for optimizing design variables by combining Monte Carlo simulation and genetic algorithm are as follows: Step 1: Determine the population size and initial population. The number of individuals in the population will affect the convergence speed and convergence accuracy. Generally, the population size is determined based on the number of design variables. Step 2: Within the range of each individual in the population, randomly generate N sets of variables X, each of which meets the allowed range requirements. Substitute the variables into the equation to calculate the terminal error. Statistically analyze each term of the terminal error Y and calculate the standard deviation to determine whether the constraints are met. Step 3: Retain individuals in the population that meet the constraints, calculate their fitness, and select individuals with better fitness for crossover and mutation. Step 4: When the calculation process reaches the preset number of iterations or iteration precision, the algorithm terminates and obtains the optimal solution; otherwise, it returns to step 2 to continue iterating.

[0011] Furthermore, S6 specifically involves: based on the obtained assembly error tolerance range, calculating the assembly clearance tolerance and end face runout tolerance that meet the requirements of positioning accuracy and repeatability. Clearance tolerance: ; in: For clearance tolerance, For assembly error angle, The length of the hole-shaft fit End face runout tolerance: ; in: For end face runout tolerance, For end face assembly error angle, This is the diameter for the end face fit.

[0012] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention determines the positioning accuracy and repeatability design indicators of the power tool holder based on specific process requirements, making the target more targeted and enabling the power tool holder to adapt to the user's process and working environment requirements.

[0013] 2. The present invention is based on the full-link geometric error transmission model established by the multibody system theory. It comprehensively considers the precision positioning process of the power tool holder, and the transmission mechanism and internal relationship of the geometric error of each component to the final accuracy index are clear and explicit.

[0014] 3. The forward design method for the geometric accuracy of the power tool holder proposed in this invention makes the tolerance allocation of positioning accuracy and repeatability more precise, effectively improving assembly efficiency. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the power tool holder topology of the present invention; Figure 2 This is a bar chart showing the sensitivity of the positioning accuracy x-axis straightness error in this invention. Figure 3 This is a bar chart showing the sensitivity of the positioning accuracy y-axis straightness error in this invention. Figure 4 This is a bar chart showing the sensitivity of the positioning accuracy z-axis straightness error in this invention. Figure 5 This is a bar chart showing the positioning accuracy pitch error sensitivity of the present invention. Figure 6 This is a bar chart showing the sensitivity of the positioning accuracy yaw error of the present invention. Figure 7 This is a bar chart showing the sensitivity of the positioning accuracy roll error of the present invention. Figure 8 This is a bar chart showing the overall positioning accuracy error sensitivity of the present invention. Figure 9 This is a bar chart showing the sensitivity of repeatability positioning accuracy x-axis straightness error in this invention. Figure 10 This is a bar chart showing the sensitivity of repeatability positioning accuracy y-axis straightness error in this invention. Figure 11 This is a bar chart showing the sensitivity of the repeatability positioning accuracy z-axis straightness error in this invention. Figure 12 This is a bar chart showing the repeatability accuracy pitch difference sensitivity of the present invention. Figure 13 This is a bar chart showing the repeatability accuracy deviation sensitivity of the present invention. Figure 14 This is a bar chart showing the repeatability accuracy roll difference sensitivity of the present invention. Figure 15 This is a bar chart showing the sensitivity of the comprehensive error in repeatability positioning accuracy according to the present invention. Figure 16 This is a simulation verification diagram of the positioning accuracy x-axis straightness error of the present invention; Figure 17This is a simulation verification diagram of the positioning accuracy y-direction straightness error of the present invention; Figure 18 This is a simulation verification diagram of the positioning accuracy z-axis straightness error of the present invention; Figure 19 This is a simulation verification diagram of the positioning accuracy pitch error of the present invention; Figure 20 This is a simulation verification diagram of the positioning accuracy yaw error of the present invention; Figure 21 This is a simulation verification diagram of the positioning accuracy roll error of the present invention; Figure 22 This is a simulation verification diagram of the repeatability accuracy x-axis straightness error of the present invention; Figure 23 This is a simulation verification diagram of the repeatability positioning accuracy y-direction straightness error of the present invention; Figure 24 This is a simulation verification diagram of the repeatability positioning accuracy z-axis straightness error of the present invention; Figure 25 This is a simulation verification diagram of the pitch error for repeatability positioning accuracy of the present invention; Figure 26 This is a simulation verification diagram of the repeatability positioning accuracy skew error of the present invention; Figure 27 This is a simulation verification diagram of the repeatability accuracy roll error of the present invention. Detailed Implementation

[0016] The present invention will be further described in detail below through specific embodiments. The following embodiments are merely descriptive and not limiting, and should not be used to limit the scope of protection of the present invention.

[0017] This invention discloses a forward design method for the geometric accuracy of a machine tool power tool post based on multibody theory. Taking a T33 power tool post as an example (center height 160mm, 24 teeth on both the moving gear plate and the locking gear plate, pitch circle radius 220mm), its innovation lies in the following steps: S1. Determine the end-effector accuracy design parameters based on the machining process requirements; S2. Establish an error propagation model that considers the geometric error caused by the machining error of the end gear plate, and determine the mapping relationship between machining error and geometric error; The transmission model of machining and geometric errors of the end gear plate includes the error transmission model of cumulative tooth pitch error, tooth direction error, tooth profile half angle error, and tooth width error and geometric errors (x-direction straightness error, y-direction straightness error, z-direction straightness error, roll error, yaw error, pitch error).

[0018] S3. Based on the multibody system theory, the theoretical pose transformation matrix and error transformation matrix between adjacent bodies were constructed, and an error propagation model for the geometric accuracy of the power tool holder was established. The mapping relationship between pose error, assembly error and geometric accuracy was determined. The various geometric errors caused by machining errors were taken as inputs and substituted into the error propagation model established based on the multibody system theory, so as to obtain the final error propagation model that comprehensively considers the coupling effect of machining error and multibody geometric error.

[0019] Establish the multibody system topology of the powered tool post, such as Figure 1 As shown, the coordinate system and transformation matrix include the housing, main shaft, rear piston moving gear disk, locking gear disk, and fixed gear disk.

[0020] S4. Based on the established comprehensive error propagation model, perform sensitivity analysis and parameter weight identification of positioning accuracy and repeatability accuracy. S5. Based on genetic algorithms and Monte Carlo methods, the allowable ranges of machining errors and assembly errors are designed to find the maximum allowable range of machining errors and assembly errors. S6. Based on the obtained assembly error tolerance range, the assembly clearance tolerance and end face runout tolerance that meet the requirements of positioning accuracy and repeatability are calculated.

[0021] Furthermore, the final error propagation model obtained from the propagation model of the end gear disk machining error and geometric error of S2 is as follows: The transmission model of machining error and geometric error during locking of the locking gear disc: ; The specific transmission model of machining error and geometric error during indexing of the moving gear disc is as follows: ; Furthermore, the geometric error model obtained by solving the transformation matrix of the dynamic tool holder coordinate system based on multibody system theory in S3 is as follows: The relative error pose relationship between the fixed gear plate coordinate system and the moving gear plate coordinate system is as follows: ; By combining the two equations, we can obtain the specific relationship between the machining error and the geometric error of the end gear plate: .

[0022] Furthermore, the positioning accuracy sensitivity and repeatability sensitivity analysis of S4 are specifically as follows: (1) Set the rotation angle of the end toothed disk to 30° and use it as the benchmark for its positioning accuracy. Based on this, conduct a positioning accuracy sensitivity analysis and obtain the analysis results. After substituting the known parameters, the sensitivities of each component of the geometric error to each machining error component and assembly error component are shown below. A sensitivity bar chart is also plotted as follows. Figure 2-7 As shown; ; This allows us to obtain the overall error sensitivity under the given positioning accuracy and then plot a sensitivity histogram. For example... Figure 8 As shown: ; (2) Set the rotation angle of the end toothed disk to 360° and use it as the benchmark for its repeatability. Based on this, conduct a sensitivity analysis of the positioning accuracy and obtain the analysis results. After substituting the known parameters, the sensitivities of each component of the geometric error to each component of the machining error and assembly error are shown below, and a sensitivity bar chart is plotted as follows. Figure 9-14 As shown.

[0023] ; This allows us to obtain the comprehensive error sensitivity under repeatability accuracy and plot a sensitivity histogram. For example... Figure 15 As shown: ; Furthermore, the S5 genetic algorithm and the Monte Carlo method are specifically as follows: (1) Genetic algorithm solution and Monte Carlo method verification under positioning accuracy: Each generation of the population randomly generates 1860 data points within its range, and Monte Carlo methods are used for calculation and statistics. After 1000 iterations, the optimized design results for the four machining error tolerances and assembly error tolerances can be obtained, as shown in Table 1. Monte Carlo simulation verification shows that the optimized error allocation scheme can effectively control the end-effector error and achieve positive design of the tool holder geometric accuracy. The verification results are as follows: Figure 16-21 As shown.

[0024] Table 1. Optimization Design Results for Positioning Accuracy

[0025] (2) Genetic algorithm solution and Monte Carlo method verification under repeated positioning accuracy: Each generation of the population randomly generates 1860 data points within its range, and Monte Carlo methods are used for calculation and statistics. After 1000 iterations, the optimized design results for the four machining error tolerances and assembly error tolerances can be obtained, as shown in Table 2. Monte Carlo simulation verification shows that the optimized error allocation scheme can effectively control the end-effector error and achieve positive design of the tool holder's geometric accuracy. Verification results are as follows: Figure 22-27 As shown.

[0026] Table 2 Results of Repeatability Accuracy Optimization Design

[0027] Furthermore, the S6 clearance tolerance and end face runout tolerance are specifically as follows: (1) Clearance tolerance under positioning accuracy: Based on the positioning accuracy assembly error tolerance calculated above, the clearance tolerance and end face runout tolerance for different fits during assembly can be obtained, as shown in Table 3.

[0028] Table 3 Results of Positioning Accuracy Clearance Tolerance and End Face Runout Tolerance

[0029] (2) Clearance tolerance under repeatability accuracy: Based on the assembly error tolerance of repeatability accuracy calculated above, the clearance tolerance and end face runout tolerance of different fits during assembly can be obtained, and the results are shown in Table 4.

[0030] Table 4 Results of Repeatability Accuracy Clearance Tolerance and End Face Runout Tolerance

[0031] Although embodiments and drawings of the present invention have been disclosed for illustrative purposes, those skilled in the art will understand that various substitutions, variations and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A forward design method for the geometric accuracy of a machine tool power tool post based on multibody theory, characterized in that: The steps of the method are as follows: S1. Determine the end-effector accuracy design parameters based on the machining process requirements; S2. Establish a geometric error propagation model that considers the machining error of the end gear plate, and determine the mapping relationship between machining error and geometric error; S3. Based on the theory of multibody systems, construct the theoretical pose transformation matrix and error transformation matrix between adjacent bodies, establish the error transmission model of the dynamic tool holder's geometric accuracy, and determine the mapping relationship between pose error, assembly error and geometric accuracy. By taking the various geometric errors caused by machining errors as inputs and substituting them into the error propagation model based on multibody system theory, a final error propagation model that comprehensively considers the coupling effect of machining errors and multibody geometric errors is obtained. S4. Based on the established final error propagation model, perform sensitivity analysis and parameter weight identification for positioning accuracy and repeatability accuracy. S5. Based on genetic algorithms and Monte Carlo methods, the allowable ranges of machining errors and assembly errors are designed to find the maximum allowable range of machining errors and assembly errors. S6. Based on the obtained assembly error tolerance range, calculate the assembly clearance tolerance and end face runout tolerance that meet the positioning accuracy and repeatability requirements.

2. The forward design method for the geometric accuracy of a power tool post based on multibody theory according to claim 1, characterized in that: The geometric error propagation model includes end gear plate machining error and end gear plate geometric error. The end gear plate machining error includes cumulative tooth pitch error, tooth direction error, tooth profile half angle error and tooth width error. The end gear plate geometric error includes x-direction straightness error, y-direction straightness error, z-direction straightness error, roll error, yaw error and pitch error.

3. The forward design method for the geometric accuracy of a power tool post based on multibody theory according to claim 2, characterized in that: The geometric error propagation model for the machining error and geometric error of the locking gear disc in the locked state is as follows: (a) Mathematical model of straightness error and machining error: Cumulative tooth pitch error: Cumulative tooth pitch error is a static error along the x-axis. ; In the formula: The angle through which the gear disc rotates; Tooth direction error: Tooth direction error causes displacement in the x-direction and tilting about the y-axis. ; In the formula: The radius of the pitch circle; Tooth profile half-angle error: Tooth profile half-angle error causes x-axis translation: ; Tooth width error: Tooth width error causes tilting about the y-axis ; Therefore, the spatial geometric relationship between straightness error in the x-direction and machining error is as follows: ； (b) Mathematical model of straightness error in the Y direction and machining error: Cumulative tooth pitch error: Cumulative tooth pitch error is a static error along the x-axis. ; Tooth direction error: Tooth direction error causes displacement in the y-axis and tilting about the x-axis. ; Tooth profile half-angle error: No displacement in the y-direction (tooth profile shape deviation, displacement occurs on the tangent): ; Tooth width error: Tooth width error causes axial dimensional deviation. ; Therefore, the spatial geometric relationship between the straightness error in the y-direction and the machining error is as follows: ； (c) Mathematical model of z-axis straightness error and machining error: Cumulative tooth pitch error: Cumulative tooth pitch error does not cause axial offset. ; Tooth direction error: Tooth direction error is the error in the direction of the meshing line and does not cause axial offset. ; Tooth profile half-angle error: This is a deviation in the tooth profile shape, resulting in displacement along the tangent line but not axial offset. ; Tooth width error: Tooth width error causes axial dimensional deviation. ; Therefore, the spatial geometric relationship between the z-axis straightness error and the machining error is as follows: ; (d) Mathematical model of pitch error and machining error: Cumulative tooth pitch error: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: ; Therefore, the spatial geometric relationship between pitch error and machining error is as follows: ; (e) Mathematical model of runout error and machining error: Cumulative tooth pitch error: Cumulative tooth pitch error along the xy plane: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: Tooth width error causes axial dimensional deviation. ; Therefore, the spatial geometric relationship between pitch error and machining error is as follows: ; (f) Mathematical model of rolling error and machining error: Cumulative tooth pitch error: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: ; Therefore, the spatial geometric relationship between roll error and machining error is as follows: ； (g) Error propagation model of machining error and geometric error of locking gear disc in locking state ； The geometric error propagation model for machining error and geometric error of the moving gear disk during rotational positioning in the power tool post end gear disk structure is as follows: (a) Mathematical model of straightness error and machining error: Cumulative tooth pitch error: Cumulative tooth pitch error is a static error along the x-axis. ; In the formula: The angle through which the gear disc rotates; Tooth direction error: Tooth direction error causes displacement in the x-direction and tilting about the y-axis. ； In the formula: The radius of the pitch circle; Tooth profile half-angle error: Tooth profile half-angle error causes x-axis translation: ; Tooth width error: Tooth width error causes tilting about the y-axis ; Therefore, the spatial geometric relationship between straightness error in the x-direction and machining error is as follows: ； (b) Mathematical model of straightness error in the y-direction and machining error: Cumulative tooth pitch error: Cumulative tooth pitch error is a static error along the x-axis. ; Tooth direction error: Tooth direction error causes displacement in the y-axis and tilting about the x-axis. ; Tooth profile half-angle error: ; Tooth width error: Tooth width error causes axial dimensional deviation. ; Therefore, the spatial geometric relationship between the straightness error in the y-direction and the machining error is as follows: ； (c) Mathematical model of z-axis straightness error and machining error: Cumulative tooth pitch error: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: Tooth width error causes axial dimensional deviation. ; Therefore, the spatial geometric relationship between the z-axis straightness error and the machining error is as follows: ； (d) Mathematical model of pitch error and machining error: Cumulative tooth pitch error: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: ; Therefore, the spatial geometric relationship between pitch error and machining error is as follows: ； (e) Mathematical model of runout error and machining error Cumulative tooth pitch error: Cumulative tooth pitch error along the xy plane: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: Tooth width error causes axial dimensional deviation. ; Therefore, the spatial geometric relationship between pitch error and machining error is as follows: ； (f) Mathematical model of rolling error and machining error Cumulative tooth pitch error: ; Tooth direction error: ; Tooth profile half-angle error: ; Tooth width error: ; Therefore, the spatial geometric relationship between roll error and machining error is as follows: ; The specific transmission model of machining error and geometric error during indexing of the moving gear disc is as follows: 。 4. The forward design method for the geometric accuracy of the power tool post according to claim 1, characterized in that: The solution process for the dynamic tool holder coordinate system transformation matrix and geometric error model based on multibody system theory in S3 is as follows: (1) Establish the multi-body system topology of the power tool post, including the coordinate system and transformation matrix of the housing, spindle, rear piston, moving gear plate, fixed gear plate, and locking gear plate; The position transformation matrix and static error matrix between adjacent objects are represented as follows: (a) Change from the housing to the rear piston: The theoretical position transformation matrix is: ； The error position transformation matrix is: ； The theoretical motion transformation matrix is: ； The error motion transformation matrix is: ； (b) Transition from the rear piston to the main shaft: The theoretical position transformation matrix is: ； The error position transformation matrix is: ； The theoretical motion transformation matrix is: ； The error motion transformation matrix is: ； (c) Transition from main spindle to moving gear plate: The theoretical position transformation matrix is: ； The error position transformation matrix is: ； The theoretical motion transformation matrix is: ； The error motion transformation matrix is: ； (d) Transition from housing to locking gear: The theoretical position transformation matrix is: ； The error position transformation matrix is: ； The theoretical motion transformation matrix is: ； The error motion transformation matrix is: ； (e) Transition from locking gear plate to fixed gear plate: The theoretical position transformation matrix is: ； The error position transformation matrix is: ； The theoretical motion transformation matrix is: ； The error motion transformation matrix is: ； (2) Establish a geometric error propagation model based on the transformation matrix. The specific process is as follows: (a) Determination of the relative position error of the indexing point between the moving gear plate and the fixed gear plate The coordinate system of the moving gear is The coordinates of the meshing point in the coordinate system of the moving gear disk are represented by a column vector: ； To predict the positional error of the indexing engagement point, both the actual and theoretical position coordinates of the moving gear plate must be transformed into the same coordinate system, namely the box coordinate system. middle; In an ideal scenario, i.e., when there is no error, the expression for the indexing engagement point in the tool post coordinate system is: ； However, when there are geometric errors in the tool post, the coordinates of the indexing engagement point will deviate from the ideal position. The coordinate expression of the indexing engagement point in the tool post coordinate system after deviating from the ideal position is: ； Similarly, suppose the coordinates of the pitch engagement point of the fixed gear plate are as follows in the coordinate system of the fixed gear plate: ； In an ideal scenario, where there is no error, the coordinate expression of the fixed gear meshing point in the tool post coordinate system is: ； However, when there are geometric errors in the tool post, the actual position of its meshing point will deviate from the ideal position. After deviating from the ideal position, the coordinate expression of the meshing point of the fixed gear plate in the tool post coordinate system is: ； At this point, both the moving gear and the fixed gear have been transformed into the tool post coordinate system, and the theoretical positional relationship of the indexing engagement point can be obtained: ； The relationship between position error and position error is: ； (b) Determination of the relative motion error at the indexing point of the moving gear plate and the fixed gear plate Assume the orientation vector of the indexing engagement point of the moving gear plate in the coordinate system of the moving gear plate is: ； To predict the position and orientation error of the moving gear disk, the vector of the moving gear disk must be... The required position and orientation of the moving gear disk are all transformed into the same coordinate system, specifically the box coordinate system. middle; In an ideal scenario, i.e., when there is no error, the expression for the position vector of the moving gear disk in the moving gear disk coordinate system is: ； In the formula , Each is a two adjacent body and The ideal positions between them, and the rotation transformation matrix of the motion; However, when the tool post has geometric errors, the actual pose of the moving gear disc deviates from the theoretical pose. The expression for the actual pose is: ； In the formula , Each is a two adjacent body and The ideal positions between them, and the rotation transformation matrix of the motion; Assume the orientation vector of the indexing engagement point of the fixed gear plate in the coordinate system of the fixed gear plate is: ； For the pose of a fixed gear disk, ideally, when there is no error, the vector of the fixed gear disk... The expression in the coordinate system of the fixed gear disk is: ； However, when the tool post has geometric errors, the actual pose of the fixed gear disc deviates from the theoretical pose. The expression for the actual pose is: ； At this point, both the moving gear and the fixed gear have been transformed into the tool post coordinate system, and the theoretical motion relationship of the indexing engagement point can be obtained: ； The relationship between motion error and motion error is: ； Substituting the transformation matrix of the tool post into the theoretical positional relationship, we can obtain the theoretical positional relationship between the moving gear plate coordinate system and the fixed gear plate coordinate system of the power tool post: ； Substituting the above equation and the transformation matrix of the tool post into the error position relationship and the error motion relationship, we can obtain the relative pose error relationship between the moving gear plate coordinate system, the fixed gear plate coordinate system and the locking gear plate coordinate system of the power tool post: ； Combining the two equations yields the specific relationship between the machining error and geometric error of the end gear disc: 。 5. The forward design method for the geometric accuracy of the power tool post according to claim 1, characterized in that: The positioning accuracy sensitivity and repeatability sensitivity analysis of S4 are as follows: Let the geometric error be represented by the six-degree-of-freedom pose error vector of the geometric error model: ； Machining errors and assembly errors are expressed as follows: ； Positioning accuracy sensitivity and repeatability sensitivity are defined as follows: ； This represents the partial derivative of the j-th machining error component with respect to the i-th geometric error component; From the specific formula relating machining error and geometric error, it can be seen that... It is a variable A continuously differentiable function of each error component. right The partial derivatives of each error component are generally expressed as: Assuming If it is continuously differentiable, then for Expand the first-order Taylor series and remove higher-order terms: ； in: It is a small component of geometric error; This is the sensitivity matrix; For higher-order terms, after removing the higher-order terms: ； Therefore, the sensitivity analysis model for error X can be obtained as follows: ； in: Sensitivity matrix By calculating the positioning accuracy sensitivity and repeatability sensitivity, the degree of influence of machining error and assembly error on the pose error can be obtained, thereby reducing machining error and assembly error and improving the overall accuracy of the power tool holder.

6. The forward design method for the geometric accuracy of a power tool post based on multibody theory according to claim 1, characterized in that: The S5 method performs geometric accuracy design based on an optimization problem model with chance programming constraints. First, it determines the design variables, objective function, and constraints for the geometric accuracy optimization problem: (1) Design variables: For high-precision tool holders, the geometric error can generally be assumed to follow a uniform distribution, and its vertical deviation is assumed to be symmetrical. It is the fourth of the four geometric errors. The error value of the term error, then ； in: Sure If the upper and lower limits are defined, then the design variables are: ; (2) Objective function: The objective function used in the design must relax the error sources to the maximum feasible region. Since there are 14 machining error sources, it is essentially a multi-objective optimization problem, which needs to be transformed into a single-objective optimization problem. Since geometric errors have different sensitivities to machining errors, the assigned results should satisfy the condition that the error term with the greater error sensitivity should have a smaller tolerance, that is, a smaller standard deviation. Construct an objective function based on the differences in sensitivity: ； in: The weighting coefficient is determined based on the sensitivity coefficient, as shown in the following formula: ； For machining error terms with relatively high sensitivity, the maximum allowable error range will be smaller. (3) Constraints: (a) Constraints on design variables ； in: This is the lower limit value. This is the upper limit value; (b) Constraints on machining errors The above describes the functional relationship between the machining error and the geometric pose error of the end gear disk. However, in precision design, since only the tolerance of the machining error sources is designed, a different approach is adopted. ； The computational function serving as the terminal function; Where: A is the sensitivity matrix of the error transfer function. ; Since any variable in X follows a uniform distribution And they are independent of each other. Y and X have a linear relationship. When there are enough statistical values, the row vector of Y follows a normal distribution with a mean of 0. The constraint on the error range is transformed into a constraint on statistical parameters, that is, a constraint on the standard deviation of the processing error. ； in, Let be the statistical variance of each vector, and represent the statistical variance of the processing error, respectively. Designed to meet precision requirements; The steps for optimizing design variables by combining Monte Carlo simulation and genetic algorithm are as follows: Step 1: Determine the population size and initial population. The number of individuals in the population will affect the convergence speed and convergence accuracy. Generally, the population size is determined based on the number of design variables. Step 2: Within the range of each individual in the population, randomly generate N sets of variables X, each of which meets the allowed range requirements. Substitute the variables into the equation to calculate the terminal error. Statistically analyze each term of the terminal error Y and calculate the standard deviation to determine whether the constraints are met. Step 3: Retain individuals in the population that meet the constraints, calculate their fitness, and select individuals with better fitness for crossover and mutation. Step 4: When the calculation process reaches the preset number of iterations or iteration precision, the algorithm terminates and obtains the optimal solution; otherwise, it returns to step 2 to continue iterating.

7. The forward design method for the geometric accuracy of the power tool post according to claim 1, characterized in that: Specifically, S6 involves calculating the assembly clearance tolerance and end face runout tolerance that meet the requirements of positioning accuracy and repeatability based on the obtained assembly error tolerance range. Clearance tolerance: ； in: For clearance tolerance, For assembly error angle, The length of the hole-shaft fit End face runout tolerance: ； in: For end face runout tolerance, For end face assembly error angle, This is the diameter for the end face fit.

Images