A Prediction Modeling Method for the Vertical Straightness and Angular Error of the Linear Axis of a Machine Tool

Abstract

The present invention discloses a method for predicting and modeling the vertical straightness and angular error of a linear axis of a machine tool. First, through probability statistics and the "3σ" product qualification inspection criterion, a sine function with manufacturing error as the amplitude is used to characterize the surface curve of the guide rail during manufacturing. Based on finite element analysis, the pre-tightening force distribution law of the guide rail group bolts under specific assembly processes is revealed, and a deformation model of the guide rail assembly with statically indeterminate analysis is proposed. Finally, considering the superposition effect of manufacturing and assembly, the spatial profile curve equation of the guide rail is established. Furthermore, according to the geometric transformation relationship, the vertical straightness and angular error of the linear axis of the machine tool are calculated. By carrying out uncertainty analysis on the relevant design parameters in the manufacturing and assembly processes of the guide rail, the spatial profile curve of the guide rail obtained by the present invention is more accurate than the regular and periodic sine function assumption in traditional research, which lays a theoretical foundation for the optimization of the original design scheme of the machine tool and the improvement of geometric accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of research on the precision design of machine tools, and particularly relates to a method for predicting and modeling the vertical straightness and angular error of a linear axis of a machine tool. Background Art

[0002] In the machine tool design stage, how to accurately predict and systematically analyze the straightness and angular error of the linear axis is a difficult problem that puzzles designers. Due to the low prediction accuracy of the final part geometric deviation, about 70% of the design schemes need to be adjusted or even fail. Therefore, this research is of great significance for optimizing the initial design scheme of the machine tool, implementing effective error compensation technology, and improving geometric accuracy. For the linear error of the linear axis, there are generally two types: horizontal direction (i.e., in the same plane as the two side guide rails) and vertical direction (perpendicular to the guide rail plane). When the straightness and angular error values are comparable to the positioning error or are key error parameters due to a high sensitivity coefficient, the machining accuracy of the machine tool will be severely reduced. Generally, the traditional method of adjusting the anchor bolts can be used to reduce the straightness error in the horizontal direction of the machine tool. However, this method has little effect on the straightness error in the vertical direction. Therefore, a method for predicting and modeling the vertical straightness and angular error of a linear axis of a machine tool is needed. It is expected to accurately predict the error parameters and distribution at the design stage of the linear axis of the machine tool. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for predicting and modeling the vertical straightness and angular error of a linear axis of a machine tool, which can accurately predict the vertical straightness and angular error of the machine tool based on the design parameters related to the structure and assembly process in the detailed design stage of the linear axis system of the machine tool, and provide a theoretical basis for optimizing the machine tool structure design scheme, improving the guide rail assembly efficiency and technology, and enhancing the overall geometric accuracy of the machine.

[0004] To achieve the above purpose, the technical solution adopted by the present invention is a method for predicting and modeling the vertical straightness and angular error of a linear axis of a machine tool, and the method includes the following steps:

[0005] S1 Based on the uncertainty analysis of the manufacturing error of the machine tool guide rail, an absolute value sine function equation with the manufacturing error of the machine tool guide rail as the amplitude is established. The absolute value sine function equation is a first-order Fourier series, and the absolute value sine function equation is used to describe the manufacturing surface curve of the machine tool guide rail:

[0006] S2 Based on finite element simulation; reveal the pre-tightening force distribution law under a specific assembly order of the bolts of the machine tool guide rail group, and conduct an uncertainty analysis of the thread torque coefficient η;

[0007] Taking the assembly reference plane of the machine tool guide rail as the research object, a mechanical model of a statically indeterminate beam is proposed. Analyze the uniformly distributed load q received by the assembly reference plane of the machine tool guide rail under the combined action of the gravity G of all components and the pre-tightening of the group bolts, and the pre-tightening force F at the assembly thread bi , and the unknown supporting force F of the rib plate sk (k = 1, 2, 3, 4) of the statically indeterminate mechanical equation, analyze and obtain the analytical formula of the assembly deformation curve of the reference plane

[0008] S4 Considering the spatial superposition effect of the deformation equations in the manufacturing and assembly stages, establish an accurate spatial contour curve equation of the machine tool guide rail; according to the geometric transformation relationship between the contour curve equation and the straightness error and angular error, calculate and predict the geometric error related parameters of the machine tool

[0009] The said S1 specifically includes the following steps:

[0010] The design parameter Me of the manufacturing error of the machine tool guide rail, the size of Me is determined by the upper deviation a and the lower deviation b of the manufacturing error, and is described as In actual production activities, the qualified quantity of products is often sampled and inspected with a probability of "3σ" in the normal distribution. When the performance parameter X of the product satisfies the probability P(μ - 3σ ≤ X ≤ μ + 3σ) = 0.9973, it is considered that the product production line is fault-free and the product quality is qualified. Therefore, it is considered that the manufacturing error parameter Me of the qualified production machine tool guide rail follows a normal distribution. The mean value μ of the manufacturing error g , standard deviation σ g and probability density function are expressed as:

[0011]

[0012] According to the above formula, multiple groups of initial data of the manufacturing error of the machine tool guide rail are obtained by the normal sampling method. To meet the production requirements of precision parts products, the probability P of the data Me g needs to satisfy formula (3). By calculating the mean value of 3 groups of data that satisfy P g ≥0.9973, the manufacturing error data of the machine tool guide rail that meet the production requirements are obtained

[0013]

[0014] Thus, an absolute value sine function equation with the manufacturing error as the amplitude is established to describe the manufacturing surface curve f of the machine tool guide rail Msc :

[0015]

[0016] Among them, f Msc is the microscopic curve morphology of the manufacturing surface of the guide rail, λ represents the error wavelength, Lwp is the length of the linear axis slide, z j is the stroke displacement of the slide.

[0017] The specific steps of S2 are as follows:

[0018] Apply a certain amount of pre-tightening force to a group of normal bolts through a torque wrench, and assemble the guide rail on the linear axis of the machine tool. To reduce the convex deformation of the guide rail and make the guide rail fit tightly with the reference surface, the pre-tightening assembly sequence generally starts from the middle and goes to both sides in turn. Due to the influence of bolt spacing and guide rail material properties, etc., the elastic stiffness of the bolts will indirectly affect the residual pre-tightening force after assembly. Therefore, with the help of the Workbench2022 R1 software platform, the distribution law of the pre-tightening force of the guide rail assembly is studied through the following steps:

[0019] S2.1 Create a model. Based on Creo3.0, establish a 3D assembly model of the guide rail - group bolts - reference surface; import the model into the workbench2021R1 software and set the material properties of each part.

[0020] S2.2 Define the contact. Define the guide rail - reference surface as a frictional contact with a friction coefficient of 0.2; define the remaining contact surfaces as fixed connections;

[0021] S2.3 Apply the load. According to the number of bolts m, define m analysis steps. Apply the pre-tightening force within the bolt design strength in turn according to the assembly order of the bolts from the middle to both sides.

[0022] S2.4 Analyze the results. Obtain the average values of the bolt deformation and pressure for each analysis step. Analyze the change law of the bolt pre-tightening force under the influence of a specific assembly order.

[0023] Analysis shows that under this assembly order, the average values of the bolt deformation and pressure increase with the analysis step, which means that the bolts tightened later will weaken the pre-tightening force of the bolts tightened in the previous assembly. In the normal direction of the guide rail installation reference surface, the bolt pre-tightening force shows a gradually increasing trend from the middle to both sides.

[0024] The S2 also includes the following steps:

[0025] Under the known design parameter - torque T b the pre-tightening force F of the guide rail bolts bIs inversely proportional to the torque η, as shown in Equation (5). The symbol D is the nominal diameter of the bolt. During the design phase, for the threads machined on the guide rail installation reference surface, the torque coefficient η is often taken as a certain value for consideration. Affected by various thread structure parameters and lubrication processes, even under the same machining process, the torque coefficients η of each thread are not the same. Similar to the uncertainty analysis of manufacturing errors, it is considered that the thread torque coefficient η closely related to the manufacturing process follows a normal distribution. According to conventional design experience, the value range of η is [0.15, 0.20]. The mean value μ of η η And the standard deviation σ of η η Can be obtained from the following Equation (6), and based on this, data sampling of the normal distribution of η is carried out. Multiple sets of thread torque coefficient η values are obtained.

[0026]

[0027] According to the obtained pre-tightening force change trend, and combined with the inverse proportional relationship between η and the pre-tightening force F in Equation (5) b , map the change law of the bolt pre-tightening force to the sorting method of the sampling results of the torque coefficient η. It is considered that on the basis of η satisfying the probability P η ≥0.9973, the η of the entire set of bolts of the machine tool guide rail ① , η ② ,…, η m Follow an arrangement where the middle is large and the two sides are small. The constraint conditions that η should satisfy can be expressed as:

[0028]

[0029] Among them, η middle Is the torque coefficient of the middle assembled thread (i.e., the first assembly site) of the bolts in the guide rail group.

[0030] The specific steps of S3 are as follows:

[0031] Under the support of the straight axis rib plate, the installation reference surface of the machine tool guide rail bears the gravity and external load of all components on it. Assume that after assembly, the machine tool guide rail is in close contact with the reference surface and deforms synchronously. In the present invention, the reference surface is abstracted as a uniformly distributed load q and the unknown support force F of the rib plate bi Under the combined action of the pre-tightening force F sk (k = 1, 2, 3,…n) acting on the simply supported beam model. Since the number n of unknown support forces is often more than the number of static equilibrium equations, therefore, the installation reference surface of the machine tool guide rail is actually a hyperstatic beam model. Equation (8) gives the deformation coordination condition in the hyperstatic mechanics equation. w k Is the bending deflection at the k-th straight axis rib plate. K s Is the stiffness coefficient of the straight axis rib plate.

[0032]

[0033] According to the bending deformation formula, the bending deflection caused by the uniformly distributed load q at k (k = 1, 2, 3, ... n) is expressed as (w k )q is expressed as,

[0034]

[0035] Among them, L AB The end of the rail closest to the edge mounting bolts is set as end A, and the other end is set as end B. As is the distance between the rib plate closest to end A and end A, l s is the spacing between ribs, z k is the distance from the kth rib to the A end, E is the elastic modulus of the selected metal material of the linear axis, and I is the moment of inertia of the mounting reference surface.

[0036] Preload F bi The bending deflection caused by the stiffener at k (k = 1, 2, 3, ... n) is expressed as (w k )F bi It is expressed as,

[0037]

[0038] Symbol a bi is the distance from the preload position of the i-th bolt to end A, d b is the bolt spacing.

[0039] Support force F sk The bending deflection caused by the stiffener at k (k = 1, 2, 3, ... n) is expressed as (w k )F sk It is expressed as,

[0040]

[0041] Symbol a sk is the distance from the kth rib support force position to end A.

[0042] Based on the superposition principle, each load and bending moment are linearly related. Therefore, w k are the algebraic sum of the bending deflections caused by each load acting on the kth rib plate individually. It can be expressed as:

[0043]

[0044] By combining formulas (8) and (13), we can obtain n mechanical equations containing n unknown support forces. From this, we can calculate the total load on the guide rail installation reference surface. j)q,(w j )F bi ,(w j )F sk respectively represent the uniformly distributed load q, the pre-tightening force F bi and the supporting force F sk at the position z j under the action of the deflection. Then the guide rail assembly deformation curve f Adc can be expressed by Equation (15).

[0045] f Adc =(w j )q+(w j )F bi +(w j )F sk (15)

[0046] The specific steps of S4 are as follows:

[0047] According to the uncertainty analysis of the guide rail manufacturing and assembly information, the manufacturing surface curve f Msc and the assembly deformation curve f Adc are obtained respectively. Considering the spatial superposition effect of the deformation equations in the manufacturing and assembly stages, the actual profile curve function f At (z j ) can be obtained from Equation (16).

[0048] f At (z j ) = f Msc +f Adc (16)

[0049] By analyzing the geometric transformation relationship between the guide rail profile curve and the straightness and angular errors, the vertical straightness error δ y (z) of the machine tool linear axis and its corresponding angular error ε α (z) are calculated and predicted by using Equation (17).

[0050]

[0051] Compared with the prior art, the beneficial effects of the present invention are:

[0052] A method for predicting and modeling the vertical straightness and angular error of a machine tool linear axis proposed by the present invention establishes a mathematical relationship between the geometric errors of the machine tool and product information, and has a guiding effect on the complex theoretical modeling of the vertical straightness. In addition, this method predicts the errors of the linear axis based on known design parameters. This is more conducive for engineers to understand the error distribution of the machine tool during the design stage. Thus, targeted error prevention technologies can be formulated and implemented to reduce the original errors of the machine tool. At the same time, the method of the present invention considers the elastic deformation caused by the gravity load in the assembly deformation analysis. Due to different structural machine tools, design parameters such as the gravity load of the linear axis and the assembly pre-tightening force are different, and the proposed inventive method has universality in the assembly accuracy analysis. Other objects and advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to make the objectives, technical solutions, and beneficial effects of the present invention clearer and more understandable, the present invention provides the following drawings for elaboration.

[0054] Figure 1 It is a schematic diagram of the structure and design parameters of the machine tool linear axis.

[0055] Figure 2 It is a schematic diagram of the machining data and probability distribution of the guide rail manufacturing error.

[0056] Figure 3 It is a flowchart of the finite element analysis under a specific assembly sequence of the guide rail group bolts.

[0057] Figure 4 It is a diagram of the bolt pre-tightening force value calculated by formula (5).

[0058] Figure 5 It is an effect diagram of the simply supported beam model and the action of the rib plate on the bearing surface. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0059] The following further illustrates the present invention in conjunction with the Figures 1-5 drawings and embodiments. In order to deepen the intuitive understanding of the method of the present invention by those in the machine tool design field, taking the linear axis (named Z-direction in the present invention) system where the machine tool bed structure is located as an example, the inventive method is introduced, but the examples given are not intended to limit the present invention.

[0060] A method for predicting and modeling the vertical straightness and angular error of a machine tool linear axis includes the following steps:

[0061] 1) Based on the uncertainty analysis of manufacturing errors, establish an absolute value sine function (first-order Fourier series) equation with manufacturing errors as the amplitude to describe the manufacturing surface curve of the machine tool guide rail:

[0062] 2) Based on finite element simulation; reveal the pre-tightening force distribution law of the guide rail group bolts under a specific assembly sequence; and conduct an uncertainty analysis of the thread torque coefficient η;

[0063] 3) Taking the guide rail assembly reference plane as the research object, propose a mechanical model of a statically indeterminate beam. Analyze the uniform load q, the pre-tightening force F at the assembly thread, and the unknown supporting force F of the rib plate bi , of the statically indeterminate mechanical equations under F sk (k = 1, 2, 3, 4), and analyze and obtain the analytical formula of the assembly deformation curve of the reference plane.

[0064] 4) Considering the spatial superposition effect of the deformation equations in the manufacturing and assembly stages, establish an accurate guide rail spatial profile curve equation; calculate and predict the geometric error-related parameters of the machine tool according to the geometric transformation relationship between the profile curve and the straightness error and angular error.

[0065] The specific steps of step 1) include the following steps:

[0066] As Figure 1 shown, the upper (a) and lower (b) deviations of the manufacturing error where a = -0.01mm, b = 0.03mm, for the selected "p"-level precision guide rail, the machining error requirement in the height direction is The mean μ of the manufacturing error g , and the standard deviation σ g can be expressed as:

[0067]

[0068] Calculated from the above formula, μ g = 0.01, σ g = 0.02 / 3, then the probability density function of Me can be expressed as

[0069]

[0070] According to the above formula, multiple groups of initial data of the guide rail manufacturing error can be obtained by the normal sampling method. To meet the production requirements of precision parts products, the probability P of the data Me g needs to satisfy formula (3). By calculating the mean of 3 groups of data that satisfy P g ≥ 0.9973, the manufacturing error data that meet the production requirements can be obtained. As Figure 2 shown is the manufacturing error data and its probability distribution.

[0071]

[0072] Thus, an absolute value sine function equation with manufacturing error as the amplitude is established to describe the manufacturing surface curve f of the machine tool guide rail Msc :

[0073]

[0074] where f Msc is the microscopic curve morphology of the guide rail manufacturing surface, λ represents the error wavelength, L wp is the length of the linear axis slide, and z j is the slide stroke displacement.

[0075] The specific steps of step 2) include the following steps:

[0076] Apply a certain amount of pre-tightening force to a group of normal bolts through a torque wrench and assemble the guide rail on the linear axis of the machine tool. To reduce the convex deformation of the guide rail and make the guide rail fit tightly with the reference surface, the pre-tightening assembly sequence generally starts from the middle and goes to both sides in turn. Due to the influence of bolt spacing and guide rail material properties, etc., the elastic stiffness of the bolts will indirectly affect the residual pre-tightening force after assembly. Therefore, with the help of the Workbench2022 R1 software platform, the following steps are used to study the distribution law of the pre-tightening force of the guide rail assembly.

[0077] S2.1 Create a model. Based on Creo3.0, establish a 3D assembly model of the guide rail-group bolts-reference surface; import the model into the workbench2021R1 software and set the material properties of each part.

[0078] S2.2 Define the contact. Define the guide rail-reference surface as a frictional contact with a friction coefficient of 0.2; define the remaining contact surfaces as fixed connections;

[0079] S2.3 Apply the load. According to Figure 1 the number of bolts in the instance, define 20 analysis steps. Apply the pre-tightening force in turn according to the assembly order of the bolts from the middle to both sides. Assume that the pre-tightening force of each bolt is 25000N.

[0080] S2.4 Analyze the results. Obtain the average values of the bolt deformation and pressure for each analysis step. Analyze the change law of the bolt pre-tightening force under the influence of a specific assembly order.

[0081] As shown in the Figure 3 attachment, it is analyzed that under this assembly order, the average values of the bolt deformation and pressure increase with the analysis step, which means that the bolts tightened later will weaken the pre-tightening force of the bolts tightened earlier. In the normal direction of the guide rail installation reference surface, the bolt pre-tightening force shows a gradually increasing trend from the middle to both sides.

[0082] Step 2) also includes the following steps:

[0083] In the example, the relevant structural design and assembly process parameters of the linear axis of the machine tool are shown in Table 1.

[0084] Table 1 Symbols and Meanings of Design Parameters Related to the Linear Axis

[0085]

[0086] Similar to the uncertainty analysis of manufacturing errors, it is considered that the thread torque coefficient η, which is closely related to the manufacturing process, follows a normal distribution. According to conventional design experience, the value range of η is [0.15, 0.20]. The mean value μ of η η and the standard deviation σ η can be obtained from the following formula (6), and based on this, data sampling of the normal distribution of η is carried out. Multiple sets of thread torque coefficient η values are obtained.

[0087]

[0088] According to the changing trend of the pre-tightening force obtained by the above steps, and combined with the inverse proportional relationship between η and the pre-tightening force F in formula (5). b In the present invention, the changing law of the bolt pre-tightening force is mapped to the sorting method of the sampling results of the torque coefficient η. It is considered that when η satisfies the probability P η ≥0.9973, among the η values of the bolts of the entire guide rail group ① , η ② , …, η m are arranged in a pattern where the middle is large and the two sides are small. The constraint conditions that η should satisfy can be expressed as:

[0089]

[0090] Among them, η middle is the torque coefficient of the middle assembly thread (i.e., the first assembly site) of the bolts of the guide rail group. Table 2 shows the sampling results of the η values. Figure 4 Shows the bolt pre-tightening force values calculated by formula (5).

[0091] Table 2 Thread Torque Coefficient η Values

[0092]

[0093] Step 3) specifically includes the following steps:

[0094] Under the support of the stiffeners of the linear axis, the installation reference surface of the guide rail bears the gravity of all components on it and the external load. It is assumed that after assembly, the guide rail is in close contact with the reference surface and deforms synchronously. In the present invention, the reference surface is abstracted as a uniformly distributed load q and an unknown support force F of the stiffeners under the combined action of the pre-tightening force F bi at the assembly thread, the gravity G, and the pre-tightening of the group bolts. sk(k = 1, 2, 3, 4) acting simply supported beam model, as shown in the appendix Figure 5 (a). The support force F sk (k = 1, 2, 3, 4) represents the effect of the rib plate on the bearing surface, as shown in the appendix Figure 5 (b). Since the number of unknown support forces is often more than the number of static equilibrium equations (4 > 3), therefore, the guide rail installation reference surface is actually a statically indeterminate beam model. Equation (8) gives the deformation compatibility condition in the statically indeterminate mechanics equation. w k is the bending deflection at the rib plate of the k-th linear axis. K s is the stiffness coefficient of the linear axis rib plate.

[0095]

[0096] According to the bending deformation formula, the bending deflection caused by the uniformly distributed load q at the rib plate at k (k = 1, 2, 3, 4) is expressed by (w k )q as,

[0097]

[0098] where, L AB is the full length of the guide rail. The end closest to the edge assembly bolt at both ends of the guide rail is set as end A, and the other end is end B. l As is the distance between the rib plate closest to end A and end A, l s is the rib plate spacing, z k is the distance from the k-th rib plate to end A. The symbol E is the elastic modulus of the selected metal material of the linear axis, and I is the moment of inertia of the installation reference surface.

[0099] The pre-tightening force F bi causes the bending deflection at the rib plate at k (k = 1, 2, 3, 4) to be expressed by (w k )F bi as,

[0100]

[0101] The symbol a bi is the distance from the pre-tightening force position of the i-th bolt to end A. d b is the bolt spacing.

[0102] The support force F sk causes the bending deflection at the rib plate at k (k = 1, 2, 3, 4) to be expressed by (w k )F sk as,

[0103]

[0104] The symbol a skis the distance from the kth rib support force position to end A.

[0105] Based on the superposition principle, each load and bending moment are linearly related. Therefore, w k are the algebraic sum of the bending deflections caused by each load acting on the kth rib plate individually. It can be expressed as:

[0106]

[0107] By combining formulas (8) and (13), we can obtain four mechanical equations containing four unknown support forces. From this, we can calculate the total load on the guide rail installation reference surface. j )q,(w j )F bi ,(w j )F sk They represent the uniform load q and the preload F respectively. bi and support force F sk Position z under action j The deflection at the point. Then the guide rail assembly deformation curve f Adc It can be expressed by formula (15).

[0108] f Adc =(w j )q+(w j )F bi +(w j )F sk (15)

[0109] The step 4) specifically comprises the following steps:

[0110] According to the uncertainty analysis of guide rail manufacturing and assembly information, the manufacturing surface curves f Msc and the assembly deformation curve f Adc Considering the spatial superposition effect of the deformation equations in the two stages of manufacturing and assembly, the actual contour curve function of the guide rail is At (z j ) can be obtained by formula (15).

[0111] f At (z j ) = f Msc +f Adc (16)

[0112] By analyzing the geometric transformation relationship between the guide rail profile curve and the straightness and angle errors, the vertical straightness error δ of the machine tool linear axis is calculated and predicted using formula (16): y (z) and its corresponding angular error ε α (z).

[0113]

[0114] The above has introduced in detail a method for predicting and modeling the vertical straightness and angular error of a linear axis of a machine tool provided by the present invention. Since the method of the present invention starts from the relevant design parameters of the linear axis of the machine tool and conducts predictive analysis on the vertical straightness and angular error of the machine tool. For different design parameters of different machine tools, the method of the present invention has a certain wide applicability. At the same time, in the analysis of the assembly deformation of the guide rail, the influence of its actual assembly process on the accuracy of the machine tool is considered, and the established model is closer to the engineering reality. This theoretical analysis has guiding significance for the optimization of the guide rail assembly process and the improvement of the overall accuracy of the machine tool, which is also a significant advantage of this technology.

Claims

1. A method for predicting and modeling the perpendicular straightness and angular error of a linear axis of a machine tool, characterized in that, The method includes the following steps: S1 Based on the uncertainty analysis of the manufacturing errors of the machine tool guideways, establish an absolute value sine function equation with the manufacturing errors of the machine tool guideways as the amplitude. The absolute value sine function equation is a first-order Fourier series, and this absolute value sine function equation is used to describe the manufacturing surface curve of the machine tool guideways: S2 Based on finite element simulation; reveal the pre-tightening force distribution law under a specific assembly sequence of the bolts in the machine tool guideway group, and conduct an uncertainty analysis of the thread torque coefficient η; Taking the assembly reference plane of the machine tool guide rail as the research object, a mechanical model of a statically indeterminate beam is proposed; the uniformly distributed load q and the pre-tightening force F at the assembly thread received by the assembly reference plane of the machine tool guide rail under the combined action of the gravity G of all components and the pre-tightening of the group bolts are analyzed bi , and the unknown supporting force F of the rib plate sk The statically indeterminate mechanical equation under is analyzed, and the analytical formula of the assembly deformation curve of the reference plane is obtained; the installation reference plane of the machine tool guide rail is supported by the rib plate of the linear axis and bears the gravity and external load of all components on it; Assume that after assembly, the machine tool guide rail is in close contact with the reference surface and deforms synchronously; abstract the reference surface as being subjected to the pre-tightening force F at the assembly thread bi , the uniformly distributed load q and the unknown supporting force F of the rib plate under the combined action of the gravity G and the pre-tightening of the group bolts sk acting on the simply supported beam model; since the number n of unknown supporting forces is often more than the number of static equilibrium equations, the actual installation reference surface of the machine tool guide rail is a hyperstatic beam model; S4 Consider the spatial superposition effect of the deformation equations in the manufacturing and assembly stages, and establish an accurate spatial contour curve equation of the machine tool guideway; according to the geometric transformation relationship between the contour curve equation and the straightness error and angular error, calculate and predict the geometric error-related parameters of the machine tool.

2. The vertical straightness and angular error prediction and modeling method for a linear axis of a machine tool according to claim 1, characterized in that The specific steps of S1 include the following: The design parameter Me of the manufacturing error of the machine tool guide rail is determined by the upper deviation a and the lower deviation b of the manufacturing error, and is described as The manufacturing error parameter Me of the machine tool guide rail produced by qualified production follows a normal distribution; the mean value μ of the manufacturing error g , the standard deviation σ g and the probability density function are expressed as: Obtain multiple groups of initial data of the manufacturing error of machine tool guideways through the normal sampling method; the probability P of the data Me g needs to satisfy formula (3); by calculating the mean values of 3 groups of data that satisfy P g ≥0.9973, obtain the manufacturing error data of the machine tool guideway that meets the production requirements; Thus, an absolute value sine function equation with the manufacturing error as the amplitude is established to describe the manufacturing surface curve f of the machine tool guide rail Msc : Among them, f Msc is the microscopic curve morphology of the guide rail manufacturing surface, λ represents the error wavelength, L wp is the length of the linear axis slide, z j is the slide stroke displacement, L wp / λ = 0.

25.

3. A method for predicting and modeling the perpendicular straightness and angular error of a linear axis of a machine tool according to claim 1, characterized in that, The specific steps of S2 include the following: Apply a pre-tightening force to a group of normal bolts with a torque wrench and assemble the guideway on the linear axis of the machine tool; with the help of the Workbench2022 R1 software platform, conduct a study on the pre-tightening force distribution law of the guideway assembly through the following steps: S2.1 Create a model; establish a 3D assembly model of the guideway-group bolts-reference plane based on Creo3.0; import the model into the workbench2021R1 software and set the material properties of each part; S2.2 Define the contact; define the guideway-reference plane as a friction contact with a friction coefficient of 0.2; define the remaining contact surfaces as fixed connections; S2.3 Apply the load; according to the number of bolts m, define m analysis steps; in accordance with the assembly sequence of the bolts from the middle to both sides, apply the pre-tightening force within the bolt design strength in turn; S2.4 Analyze the results; obtain the average values of the bolt deformation and pressure for each analysis step; analyze the change law of the bolt pre-tightening force under the influence of a specific assembly sequence; Analysis shows that under this assembly sequence, the average values of the bolt deformation and pressure increase with the analysis step, which indicates that the bolts tightened later will weaken the pre-tightening force of the bolts tightened in the previous assembly; in the normal direction of the guideway installation reference plane, the bolt pre-tightening force shows a gradually increasing trend from the middle to both sides.

4. A method for predicting and modeling the perpendicular straightness and angular error of a linear axis of a machine tool according to claim 1, characterized in that, S2 also includes the following steps: In the case of known design parameters - torque T b The pre-tightening force F of the guide rail bolt assembly b Has an inverse proportional relationship with the torque η, as shown in Equation (5); D is the nominal diameter of the bolt; during the design stage, for the threads machined on the guide rail installation reference surface, the torque coefficient η is considered a fixed value; affected by various thread structure parameters and lubrication processes, even under the same machining process, the torque coefficients η of each thread are not the same; similar to the uncertainty analysis of manufacturing errors, it is considered that the thread torque coefficient η closely related to the manufacturing process follows a normal distribution; according to conventional design experience, the value range of η is [0.15, 0.20]; the mean μ of η η And the standard deviation σ of η η Are obtained from the following Equation (6), and based on this, data sampling of the normal distribution of η is carried out; multiple sets of thread torque coefficient η values are obtained; According to the obtained pre-tightening force change trend and combined with the inverse proportional relationship between η and the pre-tightening force F in formula (5), the change law of the bolt pre-tightening force is mapped to the sorting method of the sampling results of the torque coefficient η. It is considered that on the basis of η satisfying the probability P b ≥0.9973, for the η of the whole set of bolts of the machine tool guide rail η , η ① , η ② , …, η m in the middle, it follows the arrangement of being large in the middle and small on both sides. The constraint conditions that η should satisfy can be expressed as: Among them, η middle is the torque coefficient of the intermediate assembly thread of the guide rail group bolt, i.e., the first assembly site.

5. A prediction and modeling method for the vertical straightness and angular error of a linear axis of a machine tool according to claim 1, characterized in that The specific steps of S3 include the following: Equation (8) gives the deformation compatibility condition in the statically indeterminate mechanical equation; w k is the bending deflection at the k-th straight axial stiffener plate; K s is the stiffness coefficient of the straight axial stiffener plate; According to the bending deformation formula, the bending deflection caused by the uniformly distributed load q at the stiffener at k is expressed as (w k )q, Among them, L AB is the full length of the guide rail. The end closest to the edge assembly bolt at both ends of the guide rail is set as end A, and the other end is end B; l As is the distance between the stiffener closest to end A and end A, l s is the distance between the stiffeners, z k is the distance from the k-th stiffener to end A, E is the elastic modulus of the selected metal material of the linear axis, and I is the moment of inertia of the installation reference surface; Pre-tightening force F bi The bending deflection caused by the rib plate at k is represented by (w k )F bi and is expressed as a bi =(i - 1)d b + l Ab (12) Symbol a bi is the distance from the pre-tightening force position of the i-th bolt to end A, d b is the bolt pitch; i = 1, 2, 3, … m; Support force F sk The bending deflection caused by the rib at k is represented by (w k )F sk as shown below Symbol a sk is the distance from the position of the support force of the k-th rib plate to end A; Based on the superposition principle, each load and the bending moment have a linear relationship; thus, w k is the algebraic sum of the bending deflections generated when each load acts on the k-th stiffener separately; expressed by the formula as: By combining formulas (8) and (13), we can obtain n mechanical equations containing n unknown supporting forces. From this, we can calculate the total load on the guide rail installation reference surface. j )q,(w j )F bi ,(w j )F sk They represent the uniform load q and the preload F respectively. bi and support force F sk Position z under action j The deflection at the guide rail assembly is f Adc It is expressed by formula (15); f Adc = (w j )q + (w j )F bi + (w j )F sk (15).

6. A method for predicting and modeling the perpendicular straightness and angular error of a linear axis of a machine tool according to claim 1, characterized in that, The specific steps of S4 include the following: According to the uncertainty analysis of the manufacturing and assembly information of the guide rail, the manufacturing surface curve f Msc and the assembly deformation curve f Adc are obtained respectively; Considering the spatial superposition effect of the deformation equations in the manufacturing and assembly stages, the actual profile curve function f At (z j ) is obtained from Equation (16); f At (z j ) = f Msc + f Adc (16) By analyzing the geometric transformation relationship between the guide rail contour curve and the straightness and angular errors, the vertical straightness error δ of the machine tool linear axis is calculated and predicted using Equation (17). y (z) and its corresponding angular error ε α (z);

Images