Gantry machine tool multi-guide rail linear shaft stress uniformity evaluation method based on information entropy

Abstract

The present application relates to a kind of gantry machine tool multi-guide rail linear axle stress uniformity evaluation method based on information entropy, comprising: S1, by stress average, standard deviation and maximum stress calculation stress uniformity index SUI;S2, extract the equivalent stress of all nodes on the worktable surface, convert stress field into discrete probability distribution, by calculating the information entropy of discrete probability distribution and normalizing, obtain normalized stress entropy, determine stress uniformity by the size of normalized stress entropy;S3, stress uniformity quantitative evaluation is carried out to different guide rail error combination, combine stress entropy and pose error, verify optimal guide rail error form combination to realize precision and stress uniformity collaborative optimization.The present application has the advantages of accurate evaluation, strong applicability, clear physical meaning, and quantitative comparison of multiple working conditions, and is suitable for stress uniformity detection, structure optimization and assembly process evaluation of various gantry machine tool multi-guide rail linear feeding system.

Description

Technical Field

[0001] This invention relates to the field of performance testing and structural optimization technology for CNC machine tools, specifically to a method for evaluating the stress uniformity of multiple guide rail linear axes in a gantry milling machine based on information entropy. Background Technology

[0002] As the modern CNC machine tool industry develops towards higher speed, higher precision, greater intelligence, and higher reliability, the requirements for the precision of CNC machine tools and the performance of their core components are becoming increasingly stringent. The multi-guideway linear feed system of a gantry milling machine is a core actuator of high-end CNC machine tools, directly determining the overall positioning accuracy, motion smoothness, and machining quality. In large-scale precision machining processes, key technical challenges remain, including guideway geometric error coupling, worktable position deviation, uneven stress distribution, and long-term precision maintenance. These demands are particularly significant in ultra-precision machining fields such as aerospace and high-end mold making.

[0003] To address this issue, traditional guideway precision design only focuses on error amplitude control, lacking analysis of the impact of guideway error morphological coupling on the stress uniformity of the linear shaft. It cannot accurately predict the influence of multi-guideway error morphological coupling on the stress distribution of the linear shaft, and heavily relies on manual scraping and assembly / adjustment experience. These shortcomings have driven the development of morphological matching for the geometric precision of multi-guideway linear shaft guideways in gantry milling machines.

[0004] The geometric error matching method of multi-guide linear axis guideways for gantry milling machines is driven by the uniformity of stress distribution and accuracy stability of linear axes. It establishes an intrinsic mapping relationship between guideway geometric errors and worktable posture errors and stress distribution. It develops a top-down design method that takes into account both linear axis stress distribution and motion accuracy, thereby enabling the linear feed system of gantry milling machines to meet the requirements of high precision while maintaining accuracy. Summary of the Invention

[0005] The purpose of this application is to overcome the shortcomings of the prior art and provide a method for evaluating the stress uniformity of linear axes in multi-guide rails of gantry milling machines based on information entropy. This method solves the problems of traditional stress evaluation methods that rely only on low-order statistics, lack information dimensions, have biased physical meaning, and cannot quantitatively characterize the disorder and uncertainty of stress distribution. It has the advantages of accurate evaluation, strong applicability, clear physical meaning, and quantitative comparison under multiple working conditions. It is applicable to stress uniformity detection, structural optimization, and assembly process evaluation of multi-guide rail linear feed systems of various gantry milling machines.

[0006] The technical problem solved by this application is achieved through the following technical solution: A method for evaluating the stress uniformity of linear shafts in multiple guideways of a gantry milling machine based on information entropy, the method comprising the following steps: S1. Calculate the stress uniformity index SUI by using the average stress, standard deviation and maximum stress to quickly and initially screen multiple sets of guide rail error combinations; S2. Extract the equivalent stress of all nodes on the workbench surface, transform the stress field into a discrete probability distribution, calculate the information entropy of the discrete probability distribution and normalize it to obtain the normalized stress entropy, and use the magnitude of the normalized stress entropy to determine the stress uniformity. S3. Quantitatively evaluate the stress uniformity of different guide rail error combinations, combine stress entropy with pose error, and verify that the optimal guide rail error shape combination achieves coordinated optimization of accuracy and stress uniformity.

[0007] Furthermore, the formula for calculating the stress uniformity index SUI is: ; Where: μ is the average stress at all nodal points on the worktable surface, σ is the standard deviation of the stress at all nodal points, and σ max It is the maximum value among all stresses.

[0008] Furthermore, the stress values ​​σ={σ1,σ2,……,σn} of all effective nodes on the surface of the worktable extracted by S2 are the equivalent stress values ​​of each node. w This is the sum of all nodal stresses; w i The ratio of stress at a given point to the total stress is calculated using the following formula: ; ; The equivalent stress value of each node is regarded as an independent sample observation of a random variable X. All possible values ​​of the random variable X constitute the stress value {σ1,σ2,……,σn}, where n is the total number of extracted nodes. The ratio Pi of a given stress value to the sum of stresses at all nodes is defined as the empirical probability of that stress sample occurring, and the calculation formula is as follows: ; The information entropy H(X) is: ; The theoretical maximum value Hmax is: ; The normalized stress entropy H0 is: .

[0009] Furthermore, the overall stress entropy value obtained by S3 is closer to 1, indicating a more uniform stress distribution on the workbench surface; conversely, the closer it is to 0, the more concentrated the stress distribution and the greater the local differences.

[0010] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention uses information entropy to characterize the disorder and uncertainty of stress distribution, which can reflect high-order characteristics such as skewness, kurtosis, and multimodality that traditional stress uniformity indices cannot capture, and avoid evaluation bias caused by low-order statistical approximations, making stress uniformity evaluation more realistic and accurate.

[0011] 2. This invention transforms a complex three-dimensional stress field into a single value in the [0,1] interval by normalizing the stress entropy H0. The index is simple, comparable, and easy to understand, solving the problem of traditional multi-index complexity and difficulty in comprehensive judgment.

[0012] 3. Under the premise of ensuring optimal positional error, the present invention simultaneously obtains the guide rail error combination with the most uniform stress distribution, thereby achieving a dual improvement in accuracy and reliability, extending the service life of the machine tool and improving processing stability.

[0013] 4. This invention does not rely on a specific structure and can be directly applied to multi-guide rail linear feed systems such as gantry milling machines, machining centers, and precision platforms, providing a unified evaluation tool for guide rail design, assembly debugging, and performance testing. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of a non-coplanar four-guide-rail, eight-slider linear shaft in the gantry milling machine of the present invention; Figure 2 These are diagrams illustrating the geometric error morphologies of the three guide rails of this invention. Figure 3 This is a finite element model diagram of the non-coplanar four-guide rail eight-slider linear axis gantry milling machine of the present invention; Figure 4 Stress distribution cloud diagram for applying horizontal guide rail geometric error to the present invention; Figure 5 Stress distribution cloud map of the vertical guide rail geometric error applied to this invention. Detailed Implementation

[0015] The present application 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 application.

[0016] An innovative method for evaluating the stress uniformity of linear axes in multi-guideways of a gantry milling machine based on information entropy is described, with the following steps: This embodiment takes a non-coplanar four-guide-rail, eight-slider linear shaft in a gantry milling machine as the research object, such as... Figure 1 As shown, the method of the present invention is used to evaluate the uniformity of linear axial stress.

[0017] During simulation, the error values ​​at the slider-guide rail connection points at different positions are varied to simulate the error changes of the linear axis feed platform at different locations. Taking a four-guide-rail, eight-slider supported feed platform as the object, quasi-static simulation is used to equivalently characterize the platform's dynamic travel posture error. The focus is on investigating the influence of multi-guide-rail error coupling on posture deviation, while neglecting external load fluctuations. Simulation constraint: 9.8 m / s² 2 The guide rail is subjected to a fully fixed constraint due to gravitational acceleration; the coordinate system is defined as follows: X-axis is horizontal, Y-axis is vertical, and Z-axis is the feed direction, as shown below. Figure 2 As shown.

[0018] The geometric errors of the non-coplanar four-guide linear shafts in a gantry milling machine exhibit complex coupling relationships. Based on error propagation theory, the error at a single slider can be decomposed into horizontal and vertical components. During simulation, the error vectors of the four raceway surfaces corresponding to each slider are summed to obtain the combined horizontal and vertical errors, which are then used as the equivalent errors of the guide rail in these two directions. Guide rail straightness errors mainly include three types: monotonic, arched, and chordal (e.g.,...). Figure 3 As shown in the figure, the monotonic error is a special form of the arch error: the arch error has a curved shape similar to an arch bridge, which can easily lead to uneven contact between the slider and the guide rail, and aggravate local wear; the chord error has a wavy shape similar to a chord line, which can cause unevenness of the contact surface, resulting in contact interruption, vibration and noise.

[0019] The formula for the guide rail arch error is defined as follows: ; The formula for the guide rail chord error is defined as follows: ; in: Z It is the position of the center of the worktable during the stroke, in mm. By using the arch error calculation formula and the chord error calculation formula, the error value at different positions when the guide rail has arch straightness error or chord straightness error can be calculated. The guide rail error shape at that position can be simulated by changing the spring length at the four sliders.

[0020] This embodiment employs orthogonal experimental design to efficiently reduce the experimental scale. Guide rails one to four are defined as four experimental factors, and the level of each factor is one of four error forms: positive arch, negative arch, sine, and negative sine, which includes a total of 16 core error combinations, thereby significantly improving the analysis efficiency.

[0021] Table 1. Horizontal (Vertical) Direction Four-Guide Rail Error Morphological Coupling Orthogonal Test Table

[0022] S1. Calculate the stress uniformity index SUI using the average stress, standard deviation, and maximum stress. To quantitatively compare the stress distribution uniformity of a non-coplanar four-rail linear feed system under different guide rail error combinations, this study first employs the stress uniformity index evaluation method to quantitatively score sixteen sets of orthogonal test results. This method constructs a composite index—the Stress Uniformity Index (SUU). SUI The three statistical characteristics of stress distribution are taken into account: average level, dispersion (such as standard deviation), and extreme peak value.

[0023] Stress uniformity index SUI : ; in: μ This represents the average stress at all nodes on the worktable surface. σ The standard deviation of stress at all nodes, σ max It is the maximum value among all stresses. SUI The larger the calculated value, the better the stress value of this set of tests.

[0024] The calculated SUI values ​​in the horizontal direction are shown in Table 2. The vertical direction... SUI The values ​​are shown in Table 3: Table 2 Horizontal Direction SUI value

[0025] Table 3 Vertical direction SUI value

[0026] S2. Construct an entropy-based stress uniformity evaluation model and calculate the stress entropy. Extract the stress values ​​σ of all effective nodes on the surface of the worktable from the finite element model. σ 1,σ2,……,σ n} represents the equivalent stress value of each node. w This is the sum of all nodal stresses; w i This is the ratio of the stress at a given point to the total stress. The formula is as follows: ; ; The steady-state stress field of the worktable structure under specific guide rail error and load coupling conditions was obtained through simulation calculation using finite element analysis software (Abaqus). To focus on the load-bearing and deformation-sensitive areas, the equivalent stress values ​​of all effective nodes on the upper surface of the worktable were extracted, yielding a total of [value missing]. w Stress data for 3075 nodes, denoted as set { σ 1, σ 2,……, σ 3075}

[0027] To construct a stress distribution evaluation model based on information entropy, this study treats the equivalent stress value of each node on the workbench surface as a random variable. X The independent sample observations of the random variable. X All possible values ​​constitute the sample space { σ 1, σ 2,……, σ N},in N This represents the total number of extracted nodes. To characterize the relative frequency of occurrence of different stress levels, the ratio of a node stress value to the sum of stresses at all nodes is used. P i Defined as the empirical probability of the occurrence of this stress sample, i.e.: ; in: P i Satisfies the basic properties of probability distribution: P i ∈[0,1], thus, the stress distribution on the worktable surface can be transformed into a discrete probability distribution. P= { p 1, p 2…… p N Based on this distribution, the information entropy of the workbench surface... H (X) can be calculated as follows: ; According to the maximum entropy principle, when the stress values ​​of all nodes are exactly equal (i.e., ... P 1= P 2=……= P N =1 / N When the system exhibits maximum disorder, the stress entropy of the worktable reaches its theoretical maximum value H. max : ; To eliminate sample size N To minimize the impact of the absolute magnitude of the entropy value and facilitate direct comparisons across different sample sizes or operating conditions, the entropy value needs to be normalized to obtain the normalized stress entropy. H 0: ; HThe value of 0 ranges from [0,1]. The closer the value is to 1, the more uniform the stress distribution on the worktable surface; conversely, the closer the value is to 0, the more concentrated the stress distribution and the greater the local differences.

[0028] Based on the constructed stress entropy evaluation method, two working conditions were set up to investigate the stress distribution of a non-coplanar four-rail linear feed system with guideway errors applied in different directions: Condition 1: Apply horizontal guide rail geometric error to the four guide rails; In working condition two, vertical guide rail geometric errors were applied to the four guide rails, and stress distribution cloud diagrams of the linear feed system under two different working conditions were obtained, as shown below. Figure 4 and Figure 5 As shown, this provides a data basis for subsequent quantitative evaluation of stress uniformity.

[0029] The orthogonal test conditions under the aforementioned sixteen groups of different guide rail error coupling conditions were analyzed, and the normalized entropy value of the stress distribution on the worktable surface was calculated respectively.

[0030] Based on the normalized stress entropy at seven different locations from the sixteen orthogonal experiments shown in Table 4 ( H 0) The evaluation results can quantitatively analyze the influence of the horizontal guide rail error shape on the uniformity of stress distribution: (1) When the horizontal guide rail error is applied, the stress entropy value of all positions in the first group of tests is close to 0.99, which is significantly higher than that of other groups. This indicates that when the error shape of the four guide rails of the non-coplanar four-rail linear feed system is all positive arch error, the stress distribution of the worktable is the most uniform and is the optimal solution in the horizontal direction.

[0031] (2) Error morphology coupling of non-coplanar four-rail linear feed system at different positions in steps 5, 6, 7, 11, 12, 15, and 16 H With minimal fluctuations in the zero value (standard deviation < 0.01), these error patterns enable the linear feed system to maintain a high degree of stability in stress uniformity throughout the entire stroke.

[0032] (3) The non-coplanar four-rail linear feed system with error morphology coupling in groups 3, 4, and 8 during the stroke H A large fluctuation in the value of 0 (standard deviation > 0.01) indicates sensitivity to changes in location.

[0033] (4) Based on the systematic analysis of the stress entropy values ​​obtained from the sixteen orthogonal experiments, the conclusion is that the stress entropy values ​​satisfy the following conditions. H For the test group with a stress entropy value greater than 0.97, the standard deviation of the stress entropy value fluctuation across the seven measurement locations was generally less than 0.01, indicating uniformity and stability of stress distribution during the journey; and the upper quartiles of the average stress entropy sequence of the sixteen test groups were calculated. Q3) Approximately 0.97. For operating conditions with a surface entropy value greater than 0.97, the uniformity level is within the top 25% of all test results, and can be defined as the critical point for good stress uniformity in a non-coplanar four-rail linear feed system.

[0034] Table 4 Entropy values ​​of horizontal error stress distribution ( H 0) Evaluation Results

[0035] Based on the normalized stress entropy at seven different locations from the sixteen orthogonal experiments with vertical errors shown in Table 5, H The evaluation results (0) allow for a quantitative analysis of the impact of vertical guide rail error morphology on stress distribution uniformity. (1) Normalized stress entropy of the sixteen groups of experiments H The 0 values ​​are mostly concentrated between 0.96 and 0.99, and the entropy fluctuations at the seven positions are minimal in most tests. Compared with the horizontal error condition, the overall entropy level is higher and the distribution is more concentrated under the vertical error condition, and the worktable exhibits better stress uniformity.

[0036] (2) When the vertical guide rail error is applied, the stress entropy value of the first group of tests is close to 0.99 at all positions, which is significantly higher than that of the other groups. This indicates that when all four guide rails of the non-coplanar four-rail linear feed system are in a positive arch error shape combination, the stress distribution of the worktable is the most uniform.

[0037] (3) The H0 values ​​of the error-mode coupled non-coplanar four-rail linear feed systems in groups 6, 7, 10, 11, 12, 14, 15, and 16 fluctuate very little at different positions (standard deviation < 0.01), and the error-mode combination enables the linear feed system to maintain a high degree of stability in stress uniformity throughout the entire stroke. The H0 values ​​of the error-mode coupled non-coplanar four-rail linear feed systems in groups 2, 5, and 13 fluctuate more significantly during the stroke (standard deviation > 0.01), showing sensitivity to position changes.

[0038] (4) Vertical test data show that it meets the requirements. H The experimental groups with a stress entropy value greater than 0.97 accounted for 87.5% of all experiments, significantly higher than the 56.3% in the horizontal direction. The upper quartiles of the average stress entropy sequence of the sixteen vertical experimental groups ( Q 3) Also approximately 0.97, if the stress entropy value of the error pattern combination throughout the entire stroke... H A value greater than 0.97 indicates that the linear feed system has good stress uniformity.

[0039] Table 5 Entropy values ​​of vertical error stress distribution ( H 0) Evaluation Results

[0040] S3. Perform stress uniformity verification. When horizontal and vertical errors are applied respectively, the combinations H (sine-negative sine-sine-negative sine) and V (negative arch-sine-positive arch-negative sine) exhibit optimal motion accuracy. However, the motion accuracy of the feed system in actual working conditions is affected by multiple factors, and a single accuracy evaluation index cannot fully reflect the comprehensive performance of the non-coplanar four-guide linear feed system under complex stress conditions. To further verify the correctness of the range analysis results, the stress entropy evaluation method is used to study the stress distribution characteristics of the two combinations under combined loads.

[0041] The calculated overall stress entropy values ​​for combinations H and V are shown in Tables 6 and 7, respectively. Table 6 Overall Stress Entropy Values ​​of Combination H

[0042] Table 7 Overall Stress Entropy Values ​​of Combination V

[0043] The stress entropy calculation results show that: 1. When a horizontal error is applied to a non-coplanar four-rail linear feed system, and the error patterns of the four rails are as follows: rail one is sinusoidal error, rail two is negative sinusoidal error, rail three is sinusoidal error, and rail four is negative sinusoidal error, the overall stress entropy value of the linear feed system is greater than 0.97, indicating that the stress distribution inside the worktable is relatively uniform and it is in a better mechanical state.

[0044] 2. When a vertical error is applied to the non-coplanar four-rail linear feed system, and the error shapes of the four rails are as follows: rail one has a negative arch error, rail two has a sinusoidal error, rail three has a positive arch error, and rail four has a negative sinusoidal error, the overall stress entropy value of the linear feed system is greater than 0.97, indicating that this combination can also achieve good stress distribution uniformity.

[0045] 3. The overall stress entropy values ​​of both combination H and combination V are greater than 0.97, which confirms the correctness of the range analysis results from the perspective of stress distribution uniformity: the two combinations not only perform best in kinematic accuracy, but also have good stress distribution in structural mechanics.

[0046] Based on the calculation results of the table pose error and the evaluation results of the stress entropy, it can be concluded that in a non-coplanar four-guide-rail eight-slider linear feed system, the optimal error pattern combination in the horizontal direction is: guide rail one sinusoidal, guide rail two negative sinusoidal, guide rail three sinusoidal, and guide rail four negative sinusoidal; the optimal error pattern combination in the vertical direction is: guide rail one negative arch, guide rail two sinusoidal, guide rail three positive arch, and guide rail four negative sinusoidal. Under this error pattern coupling, the table pose error is minimized, the stress distribution uniformity is good, and the overall accuracy and long-term stability of the non-coplanar four-guide-rail eight-slider linear feed system are optimal.

[0047] 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 method for evaluating the stress uniformity of linear axes in multi-guide rails of a gantry milling machine based on information entropy, characterized in that: The steps of the method are as follows: S1. Calculate the stress uniformity index SUI by using the average stress, standard deviation and maximum stress to quickly and initially screen multiple sets of guide rail error combinations; S2. Extract the equivalent stress of all nodes on the workbench surface, transform the stress field into a discrete probability distribution, calculate the information entropy of the discrete probability distribution and normalize it to obtain the normalized stress entropy, and use the magnitude of the normalized stress entropy to determine the stress uniformity. S3. Quantitatively evaluate the stress uniformity of different guide rail error combinations, combine stress entropy with pose error, and verify that the optimal guide rail error shape combination achieves coordinated optimization of accuracy and stress uniformity.

2. The method for evaluating the stress uniformity of linear axes of multi-guide rails in a gantry milling machine based on information entropy as described in claim 1, characterized in that: The formula for calculating the stress uniformity index (SUI) is as follows: ； Where: μ is the average stress at all nodal points on the worktable surface, σ is the standard deviation of the stress at all nodal points, and σ max This is the maximum value among all stresses.

3. The method for evaluating the stress uniformity of linear axes of multi-guide rails in a gantry milling machine based on information entropy as described in claim 1, characterized in that: The stress values ​​σ = {σ1, σ2, ..., σn} of all effective nodes on the surface of the worktable extracted by S2 are the equivalent stress values ​​of each node. w This is the sum of all nodal stresses; w i The ratio of stress at a given point to the total stress is calculated using the following formula: ； ； The equivalent stress value of each node is regarded as an independent sample observation of a random variable X. All possible values ​​of the random variable X constitute the stress value {σ1,σ2,……,σn}, where n is the total number of extracted nodes. The ratio Pi of a given stress value to the sum of stresses at all nodes is defined as the empirical probability of that stress sample occurring, and the calculation formula is as follows: ； The information entropy H(X) is: ； The theoretical maximum value Hmax is: ； The normalized stress entropy H0 is: 。 4. The method for evaluating the stress uniformity of linear axes in multi-guide rails of a gantry milling machine based on information entropy as described in claim 1, characterized in that: The S3 method yields the overall stress entropy value. The closer the value is to 1, the more uniform the stress distribution on the workbench surface. Conversely, the closer the value is to 0, the more concentrated the stress distribution and the greater the local differences.

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