A guide rail bolt assembly process optimization method considering the relationship between interaction stiffness and residual pretightening force

Abstract

The application discloses a guide rail bolt assembly process optimization method considering the relationship between interactive stiffness and residual pretightening force, first, based on the guide rail pressure stress cone distribution assumption, the guide rail bolt interactive stiffness function model under different intervals is constructed. The stiffness model of the bolt connection structure is established, the mapping relationship between the bolt pretightening force change and the interactive stiffness value is derived, and the theoretical analysis obtains that the pretightening force change of the pre-tightened bolt is negatively correlated with the subsequent bolt assembly interval. Secondly, the finite element model of the cross beam of a vertical machining center is established, and the theoretical analysis result is verified through multi-load step simulation analysis. Finally, the assembly process of the cross beam guide rail bolt is optimized, and the comprehensive evaluation method of the standard deviation and the mean value is adopted, so that the bolt residual pretightening force discreteness under the new process is reduced, and the consistency is improved.

Description

Technical Field

[0001] This invention belongs to the field of machine tool assembly technology and relates to an assembly process optimization method, specifically a guide rail bolt assembly process optimization method that takes into account the relationship between interaction stiffness and residual preload. Background Technology

[0002] Machine tools, often referred to as the "mother machines" of industry, are a crucial indicator of a nation's industrial level. my country's manufacturing sector is currently undergoing industrial restructuring, with advanced manufacturing gradually replacing traditional manufacturing. As the machine tool industry continues to develop, the requirements for assembly precision and accuracy retention are becoming increasingly stringent, highlighting the growing demand for mid-to-high-end machine tools.

[0003] A CNC machine tool is a complex integrated system, mainly consisting of hardware and software. Its hardware components primarily include functional parts and basic components. Functional parts include guideways, lead screws, and motors, while basic components include the bed, crossbeam, and column. Among these components, the guideways play a crucial role, and their service condition is key to ensuring the normal operation of the machine tool. Guideways are generally connected to key components such as the bed, column, and crossbeam using pre-tightened group bolts, serving both load-bearing and guiding functions within the machine tool. However, due to the elastic interaction between the bolts, pre-tightening the bolts can disturb the already pre-tightened bolts, thus affecting the service performance of the guideways.

[0004] The guide rail is directly connected to the worktable via a slider, and the machine tool uses the guide rail slider to position and process the workpiece during operation. After the guide rail bolts are assembled, if the residual preload of the bolts on the guide rail mating surface is unevenly distributed, it will exacerbate the friction and wear between the guide rail and the base components during machine tool operation, causing the guide rail to deviate from its ideal working state. Therefore, the quality of guide rail assembly directly affects the geometric accuracy of the linear axes of the CNC machine tool. To improve the uniformity of the residual preload of the guide rail bolts, it is necessary to optimize the assembly process of the guide rail bolts. Summary of the Invention

[0005] To address the problem of uneven distribution of residual preload in CNC machine tool guide rail bolt assembly, this invention provides a guide rail bolt assembly process optimization method that takes into account the relationship between interactive stiffness and residual preload.

[0006] An optimization method for guide rail bolt assembly process considering the relationship between interaction stiffness and residual preload includes the following steps:

[0007] Step 1: Based on the assumption of tapered distribution of compressive stress in the guide rail, construct the interactive stiffness function model of the guide rail bolts under different spacings, plot the interactive stiffness value curve with distance as the variable, establish the stiffness model of the bolt connection structure, and derive the mapping relationship between the change in bolt preload and the interactive stiffness value.

[0008] Assume the screw length is L b The vertical distance from the bottom of the guide rail countersunk hole to the mating surface is l1, the length of the screw below the mating surface is l2, the elastic modulus of the guide rail is E1, the elastic modulus of the critical component is E2, the maximum radius of action of the compressive stress on the guide rail is X1, the maximum radius of action of the compressive stress on the critical component is X2, the pressure distribution on the guide rail is σ1, the pressure distribution on the critical component is σ2, and the pressure angle is α. Assume that after the guide rail bolts are pre-tightened, the compressive stress is distributed in a conical shape, and in different pressure layers, the compressive stress satisfies a fourth-order polynomial relationship regarding the radial distance dimension.

[0009] σ=k1x 4 +k2x 3 +k3x 2 +k4x+k5(1)

[0010] In the above formula, k1-k5 are undetermined coefficients, which can be obtained by solving according to a specific relationship.

[0011] Based on the different material properties and dimensional parameters of the structural components, the magnitudes of k1-k5 can be solved. Substituting the solved k1-k5 into equation (1) yields the distribution characteristics of the compressive stress of the guide rail. By integration, the magnitude of the deformation is obtained, and the interaction stiffness value is calculated. Based on this, the interaction stiffness curve of the bolt can be plotted. Connecting with the derivation results of the relationship between interaction stiffness and residual preload in the following text, the variation law and trend of the residual preload of the bolt under different spacings are analyzed. The guide rail bolt assembly is analyzed and deduced, and the bolt hole structure is simplified to a spring node unit. For the elastic interaction stiffness K l When i≠j, K (i,j) Defined as the interactive stiffness between nodes i and j, it represents the ability of the guide rail at bolt i to resist deformation when bolt j is pre-tightened; when i = j, K (i,i) Defined as the axial stiffness of bolt hole i, it means the ability of the guide rail at bolt i to resist deformation when bolt i is pre-tightened. Based on this and in conjunction with the bolt pre-tightening force and the change in pre-tightening force, the guide rail assembly process is theoretically derived and analyzed to obtain the relationship between the bolt residual pre-tightening force and the interaction stiffness.

[0012] Step Two: To ensure the rationality of the theoretical model established in Step One, verification is conducted through simulation and experimentation. A finite element model of the machine tool structural components is established, and modal testing is used to verify the correctness of the finite element modeling. Based on the ANSYS Workbench simulation platform, multi-load step simulation analysis is used to verify the theoretical analysis results. After theoretical verification, the assembly process of the guide rail bolts can be optimized based on the theoretical model.

[0013] During finite element model verification, the first six natural frequencies of the structural components were extracted, and the experimental values ​​were compared with the simulation values. Multi-load step simulation analysis was performed on the assembly process of the guide rail bolts of the structural components. A material library was established in the simulation environment, and corresponding material properties were assigned to the structural components, guide rails, and bolts. Appropriate boundary conditions were added to the machine tool structural components, and suitable contact relationships were set for each mating surface. Multiple load steps were set in the simulation environment to simulate the pre-tightening process of the bolts.

[0014] Step 3: Optimize the assembly process of the guide rail bolts in the machine tool structure. This involves adjusting the preload sequence of the guide rail bolts to optimize the distribution characteristics of the residual preload force in the bolt group after assembly, making it as close as possible to the target value and mitigating the uneven distribution of compressive stress in the guide rail. Based on Step 1, a theoretical model of the corresponding assembly environment is established and verified using Step 2. The assembly process is optimized through theoretical analysis combined with finite element simulation. A comprehensive evaluation method using standard deviation and mean is employed to compare the advantages and disadvantages of the old and new processes by examining the distribution of residual preload force.

[0015] This invention employs a combined approach of theoretical analysis, experimental verification, and simulation analysis, providing strong support for the rationality of the established theoretical model. By combining the relationship between interactive stiffness and residual preload, it reveals the elastic interaction relationship during the guide rail bolt assembly process at a deeper level. It provides an effective solution to the problem of uneven compressive stress distribution after guide rail assembly. Compared with methods that only analyze one aspect, this invention is more convincing and reliable, and considers a more comprehensive range. The comprehensive evaluation method using standard deviation and mean values ​​allows for effective assessment of the optimization results. This method can improve the assembly quality of guide rail bolts and reduce the later-stage operating costs of machine tools. Attached Figure Description

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0017] Figure 1 This is a schematic diagram of the bolt connection of the crossbeam guide rail of the present invention;

[0018] Figure 2 This is a diagram showing the compressive stress distribution area of ​​the bolted connection according to the present invention;

[0019] Figure 3 This is a curve showing the compressive stress distribution of the connector in this invention;

[0020] Figure 4 This is a model diagram of the spring node unit of the present invention;

[0021] Figure 5 This is the bolt interaction stiffness curve diagram of the present invention;

[0022] Figure 6 This is a schematic diagram of the testing principle of the present invention:

[0023] Figure 7 These are the modal test diagrams of the beam of this invention;

[0024] Figure 8 This is a diagram showing the results of the modal tests on the beam of this invention;

[0025] Figure 9 This is the beam grid division diagram of the present invention;

[0026] Figure 10 This is the boundary condition diagram of the present invention;

[0027] Figure 11 This is a diagram illustrating the change in preload force according to the present invention.

[0028] Figure 12 This is the original bolt pre-tightening process diagram of the present invention;

[0029] Figure 13 This is a diagram showing the distribution of residual preload in the original process of this invention;

[0030] Figure 14 This is a diagram illustrating the optimized bolt pre-tightening process of this invention;

[0031] Figure 15 This is a diagram showing the distribution of residual preload in the new process of this invention. Detailed Implementation

[0032] Examples of the present invention are described in detail below, with examples shown in the accompanying drawings. The specific implementation process is as follows:

[0033] Step 1: Assembly status of the crossbeam guide rail of a vertical five-axis machining center as follows Figure 1 As shown, apply preload to the hex bolts using a torque wrench, and then preload the guide rail group bolts in sequence to complete the guide rail assembly.

[0034] After applying a preload to the bolt, the compressive stress in the connector exhibits a conical distribution, such as... Figure 2 As shown. The screw length is set to L. b The vertical distance from the bottom of the guide rail countersunk hole to the mating surface is l1, the length of the screw below the mating surface is l2, the elastic modulus of the guide rail is E1, the elastic modulus of the critical component is E2, the maximum radius of action of the compressive stress on the guide rail is X1, the maximum radius of action of the compressive stress on the critical component is X2, the pressure distribution on the guide rail is σ1, the pressure distribution on the critical component is σ2, and the pressure angle is α. Assuming that after the guide rail bolts are pre-tightened, the compressive stress is distributed in a conical shape, and that in different pressure layers, the compressive stress satisfies a fourth-order polynomial relationship on the radial distance dimension, such as... Figure 3 As shown.

[0035] Before proceeding with the theoretical derivation, we make the following assumptions: the guide rail is only subjected to the axial load of the bolts and the guide rail only undergoes elastic deformation. Let the fourth-order polynomial expression of the compressive stress be...

[0036] σ=k1x 4 +k2x 3 +k3x 2 +k4x+k5 (1)

[0037] Where k1, k2, k3, k4, and k5 are undetermined coefficients, and x is the distance from the point to the bolt axis. For the compressive stress curve, at point x1, we have... At point x2, σ = 0. Substituting, we can obtain

[0038] 4k1x1 3 +3k2x1 2 +2k3x1+k4=0 (2)

[0039] k1x2 4 +k2x2 3 +k3x2 2 +k4x2+k5=0 (3)

[0040] 4k1x2 3 +3k2x2 2 +2k3x2+k4=0 (4)

[0041] 12k1x2 2 +6k2x2+2k3=0 (5)

[0042] If the bolt remains stationary along the axial direction, then by the equilibrium condition, we can obtain...

[0043]

[0044] In the above formula, F is the bolt preload, x1 = d2 / 2, x2 = d1 / 2 + l1tanα, where d2 is the bolt hole diameter, d1 is the bolt head diameter, l1 is the guide rail connection thickness, and α is the pressure angle. Solving the above formulas simultaneously, we can obtain k1 = 3A, k2 = -4Ax1 + 2x2, k3 = 6Ax22x1 + x2, and k4 = -12Ax1x2 2 k5 = Ax2 3 4x1-x2, A=5F / πx1-x2 5 3x1+x2.

[0045] Calculate the elastic interaction stiffness K of the bolt according to different x values. l .

[0046] When d² / 2 ≤ x ≤ d¹ / ², the total deformation at the contact point is ε.

[0047]

[0048]

[0049] When d1 / 2<x≤d1 / 2+l2tanα, the total deformation at the contact point is ε

[0050]

[0051]

[0052] When x>d1 / 2+l2tanα, the total deformation at the contact point is ε

[0053]

[0054]

[0055] According to different material properties and dimensional parameters of the structural members, the interaction stiffness value curve of the bolt can be plotted. By analyzing and deriving the guide rail bolt assembly, the bolt hole structure is simplified into a spring node unit, as Figure 4 shown. For the elastic interaction stiffness K l , when i≠j, K (i,j) is defined as the interaction stiffness between node i and node j, which means the deformation resistance of the guide rail at bolt i when bolt j is preloaded; when i=j, K (i,i) is defined as the axial stiffness of bolt hole i, which means the deformation resistance of the guide rail at bolt i when bolt i is preloaded.

[0056] Apply a preload force F to the i-th assembled bolt i on the guide rail i , let the displacement at node i be ε i , it can be obtained that

[0057]

[0058] K (i,i) —Axial stiffness of bolt hole i

[0059] Then apply a preload force F to the j-th assembled bolt j on the guide rail j , the change of the preload force of bolt i due to the preloading of bolt j is set as △F (i,j) , the displacement change at node i is set as ε (i,j) , it can be obtained that

[0060]

[0061] K (i,j) —Interaction stiffness between bolt i and bolt j

[0062] Axial stiffness K of bolt i bi for

[0063]

[0064] E bi —The elastic modulus of bolt i;

[0065] A bi —The cross-sectional area of ​​the bolt or screw;

[0066] L bi —The length of the bolt / screw;

[0067] At this time, the change in elastic deformation ε of bolt i (bi,j) It can be represented as

[0068]

[0069] According to the elastic deformation compatibility condition, the elastic deformation deformation of bolt i is the same as that of node i, that is...

[0070] ε (i,j) +ε (bi,j) =0(17)

[0071] By combining equations (13) and (17), the change in bolt preload ΔF can be obtained. (i,j) for

[0072]

[0073] The machine tool beam is made of marble, the guide rails are made of bearing steel, and the bolts are made of alloy steel. M8 diameter socket head cap screws with a performance grade of 12.9 are selected. The safety factor is K = 1.5, and the preload is F = πd. 2 σ s / 4K = 36191N. Substituting the material and structural parameters of the beam, guide rail, and bolts, the bolt cross-stiffness curves at different spacings can be plotted, such as... Figure 5 As shown.

[0074] Depend on Figure 5 It can be seen that the bolt interaction stiffness increases continuously with increasing distance. Given that the materials and structural parameters of the beam, guide rail, and bolts are all fixed, K... (i,i) K bi Both the preload force F and the preload force are constant values. According to the formula derived above, the change in preload force of a preloaded bolt gradually decreases as the assembly spacing of subsequent bolts increases. That is, for a preloaded bolt, the bolts that are closer to it in subsequent assembly have a greater impact on its preload force, while the bolts that are farther away have little impact on its preload force.

[0075] Step Two: To ensure the accuracy and reliability of the simulation results, the effectiveness of the established finite element model is verified through a crossbeam free modal test. The schematic diagram of the crossbeam modal test is shown below. Figure 6 As shown.

[0076] When conducting free modal tests on the crossbeam, a crane was used to suspend it using elastic ropes to simulate a free state. The test site diagram is shown below. Figure 7 As shown in the figure, the experimental equipment used is labeled.

[0077] The physical environment required for the experiment was established, and a multi-point test model of the crossbeam was set up in the software, connecting each data acquisition line to the channel. Modal testing was conducted to obtain the first six natural frequencies of the crossbeam. The experimental results are as follows: Figure 8 As shown.

[0078] The Polymax modal analysis method was used to identify the modal parameters. According to the modal parameter identification principle, the more steady-state poles "s", the richer the modal information. The "s" poles that are basically consistent near the peak value of the horizontal axis were selected to extract the first 6 natural frequencies of the beam. The experimental results of the beam and the simulation analysis results were compared, as shown in Table 1.

[0079] Table 1 Comparison of simulation results of beam test

[0080]

[0081] The comparison results show that the error between the experimental and simulated values ​​of the first six natural frequencies of the beam is within 4%, which verifies the accuracy of the finite element modeling of the beam. The simulation analysis results obtained based on this model are reliable.

[0082] A multi-load step simulation analysis was conducted on the assembly process of the crossbeam guide rail bolts to study the influence of subsequent bolts on the preload of pre-tightened bolts during multi-bolt assembly. A material library was established in the simulation environment, and the material properties are shown in Table 2. Corresponding material properties were assigned to the crossbeam, guide rail, and bolts. The bottom of the crossbeam was fixedly constrained, and frictional contact was used between the bolts and the crossbeam, the bolts and the guide rail, and the guide rail and the crossbeam, with a friction coefficient of 0.15. Tetrahedral elements were used to mesh the finite element model, and the meshing results are shown below. Figure 9 As shown. A single guide rail is fixed to the crossbeam by 36 bolts, numbered 1 to 36 from left to right for ease of explanation. 36 load steps are set in the simulation environment to simulate the bolt pre-tightening process. During bolt pre-tightening, pre-tightening begins sequentially from the first bolt on the left, with a pre-tightening force of 36191 N. The assembly boundary conditions for the crossbeam and guide rail are as follows. Figure 10 As shown.

[0083] Table 2 Material Parameters and Properties

[0084]

[0085] After solving the problem using the finite element method, the change in preload force of bolt 1 after bolts 2 to 36 were preloaded sequentially was extracted. The influence of subsequent preloaded bolts on the preload force of the preloaded bolts on the crossbeam guide rail was analyzed. The change process of the preload force of bolt 1 during assembly is as follows: Figure 11 As shown.

[0086] observe Figure 11 After bolt 1 is pre-tightened, bolts 2 through 36 are pre-tightened sequentially. The adjacent bolt 2 has the greatest impact on the pre-tightening force of bolt 1, while the impact of the remaining bolts on the pre-tightening force of bolt 1 decreases sequentially, approaching zero at a certain distance. Therefore, it can be concluded that as the spacing between the guide rail bolts increases, the change in pre-tightening force due to elastic interaction between the bolts gradually decreases, while the interaction stiffness gradually increases, consistent with theoretical analysis results.

[0087] Step 3: As analyzed above, during the assembly of linear guide bolts, the pre-tightened bolts will be affected by the subsequent pre-tightened bolts, resulting in a partial loss of pre-tightening force. Simultaneously, the uneven load distribution due to differences in pre-tightening force affects the straightness of the guide rail. Therefore, it is necessary to compensate for the bolt pre-tightening force and optimize the pre-tightening sequence to ensure a uniform distribution of residual pre-tightening force among the assembled bolt group.

[0088] The original bolt pre-tightening sequence is as follows: Figure 12 As shown, F n This represents the preload sequence, i.e., preloaded sequentially from left to right. The standard deviation of the group of bolts for a given preload is defined as σ, and the average preload loss as τ. σ and τ are used to comprehensively evaluate the distribution of residual preload in the group of bolts. Calculations show that under the original assembly process, σ1 = 491 and τ1 = -453. The distribution of residual preload is shown in [the original text]. Figure 13 .

[0089] As shown in the figure above, the residual preload of each bolt is almost entirely far from the target value and is quite dispersed. According to theoretical model analysis, the preload of bolts will fluctuate due to the influence of subsequent preloaded bolts, and this fluctuation increases with the increase of load steps. Therefore, the new process reduces the number of load steps and compensates for the average preload loss. The optimized bolt preload process is shown below. Figure 14 That is, pre-tightening is done sequentially from the middle to both sides.

[0090] Through simulation analysis, the calculated values ​​of σ² = 253 and τ² = -20 under the new process are shown in the figure. Figure 15 .

[0091] After process optimization, σ1=491>σ2=253, |τ1|=453>|τ2|=20. The standard deviation and average preload loss of the group of bolts for the given preload are reduced to some extent, and the residual preload distribution becomes relatively concentrated. (In summary...) Figure 13 and Figure 15 After process optimization, the residual preload of each bolt is compensated to a certain extent, and the uniformity of the distribution of residual preload of bolts is improved.

Claims

1. A method for optimizing the assembly process of guide rail bolts, considering the relationship between interactive stiffness and residual preload, characterized in that: The modeling method consists of the following three steps: Step 1: Based on the assumption of tapered distribution of compressive stress in the guide rail, construct the interactive stiffness function model of the guide rail bolts under different spacings, plot the interactive stiffness value curve with distance as the variable, establish the stiffness model of the bolt connection structure, and derive the mapping relationship between the change in bolt preload and the interactive stiffness value. The screw length is set to L b The vertical distance from the bottom of the guide rail countersunk hole to the mating surface is l1, the length of the screw below the mating surface is l2, the elastic modulus of the guide rail is E1, the elastic modulus of the critical component is E2, the maximum radius of action of the compressive stress on the guide rail is X1, the maximum radius of action of the compressive stress on the critical component is X2, the pressure distribution on the guide rail is σ1, the pressure distribution on the critical component is σ2, and the pressure angle is α. After the guide rail bolts are pre-tightened, the compressive stress is distributed in a conical shape, and in different pressure layers, the compressive stress satisfies the fourth-order polynomial relationship of the radial distance dimension. σ=k1x 4 +k2x 3 +k3x 2 +k4x+k5 (1) Based on the different material properties and dimensional parameters of the structural components, the interaction stiffness curves of the bolts are plotted; the guide rail bolt assembly is analyzed and derived, simplifying the bolt hole structure into spring node elements; the elastic interaction stiffness K is... l When i≠j, K (i,j) Defined as the interactive stiffness between nodes i and j, it represents the ability of the guide rail at bolt i to resist deformation when bolt j is pre-tightened; when i = j, K (i,i) Defined as the axial stiffness of bolt hole i, it means the ability of the guide rail at bolt i to resist deformation when bolt i is pre-tightened; Step 2: Establish a finite element model of the machine tool structural components, verify the correctness of the finite element modeling using modal tests, and verify the theoretical analysis results through multi-load step simulation analysis based on the ANSYS Workbench simulation platform. During finite element model verification, the first six natural frequencies of the structural components were extracted, and the experimental values ​​were compared with the simulation values. Multi-load step simulation analysis was performed on the assembly process of the guide rail bolts of the structural components. A material library was established in the simulation environment, and corresponding material properties were assigned to the structural components, guide rails, and bolts respectively. Appropriate boundary conditions were added to the machine tool structural components, and appropriate contact relationships were set for each mating surface. Multiple load steps were set in the simulation environment to simulate the pre-tightening process of the bolts. Step 3: Optimize the assembly process of the guide rail bolts of the machine tool structural components. Use a comprehensive evaluation method of standard deviation and mean to compare the advantages and disadvantages of the old and new processes by the distribution of residual preload.

2. The method for optimizing the assembly process of guide rail bolts considering the relationship between interactive stiffness and residual preload as described in claim 1, characterized in that, In step one, based on the assumption of a conical distribution of compressive stress in the guide rail, an interactive stiffness function model of the guide rail bolts under different spacings was constructed, and the interactive stiffness value curve with distance as the variable was plotted.

3. The method for optimizing the assembly process of guide rail bolts considering the relationship between interactive stiffness and residual preload as described in claim 1, characterized in that, In step one, a stiffness model of the bolted connection structure is established, and the mapping relationship between the change in bolt preload and the interaction stiffness value is derived.

4. The method for optimizing the assembly process of guide rail bolts considering the relationship between interactive stiffness and residual preload as described in claim 1, characterized in that, In step one, after the guide rail bolts are pre-tightened, the compressive stress is distributed in a conical shape, and in different pressure layers, the compressive stress satisfies the fourth-order polynomial relationship of the radial distance dimension.

5. The method for optimizing the assembly process of guide rail bolts considering the relationship between interactive stiffness and residual preload as described in claim 1, characterized in that, In step two, a finite element model of the machine tool structural components is established, and the correctness of the finite element modeling is verified by modal testing. Based on the ANSYS Workbench simulation platform, the theoretical analysis results are verified by multi-load step simulation analysis.

6. The method for optimizing the assembly process of guide rail bolts considering the relationship between interactive stiffness and residual preload as described in claim 1, characterized in that, In step three, the assembly process of the guide rail bolts of the machine tool structural components was optimized. A comprehensive evaluation method of standard deviation and mean was adopted, and the advantages and disadvantages between the old and new processes were compared by the distribution of residual preload.

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