Guide rail surface straightness modeling method based on bolt pretightening force prediction

Abstract

The invention discloses a guide rail surface straightness modeling method based on bolt pre-tightening force prediction, and the method mainly comprises the steps: firstly, building a prediction model of the pre-tightening force of each bolt of a bolt group after the assembly based on the Saint-Venant principle and the deformation coordination condition of the surface of a structural member; secondly, on the basis of the elastic deformation theory, a relation model of guide rail surface node deformation and final bolt pre-tightening force after assembly is completed is established; by combining the two models, the deformation of each node on the surface of the assembled guide rail can be solved. And then, calculating the straightness error of the surface of the guide rail by adopting a three-pole connecting line method. And finally, verifying the effectiveness of the established model through deformation data obtained through finite element and theoretical calculation. The method belongs to the field of machine tool assembly precision, and realizes accurate control of the bolt pre-tightening force by establishing a relation model of the guide rail surface deformation and the pre-tightening force initially applied by the bolt, thereby improving the assembly precision of the guide rail surface. The method solves the technical problem that the surface assembly precision of the guide rail is difficult to predict and control after assembly is completed.

Description

Technical Field

[0001] The present invention relates to a guide rail surface straightness modeling method based on bolt preload prediction, and belongs to the field of machine tool assembly accuracy. Background Art

[0002] The guide rail is an important functional component in the linear feed system of the machine tool. Its surface deformation will act on the worktable through the slider, thereby affecting the motion accuracy and positioning accuracy of the workpiece during the processing. Therefore, the surface assembly accuracy of the guide rail when it is assembled has a great influence on the performance of the machine tool. The guide rail is connected to the bed, columns and other basic parts through bolts. The bolts will be affected by elastic interactions during the assembly process, such as Figure 1 As shown in the figure, the preload force gradually changes with the assembly process, which in turn affects the deformation of each node on the surface of the guide rail. At present, the deformation of each node on the surface of the guide rail is mainly measured by manual detection. Before the guide rail reaches the required assembly accuracy, it needs to be corrected repeatedly, which leads to a series of defects such as long guide rail assembly cycle and high cost. Therefore, a method is needed to accurately predict the deformation of the nodes on the surface of the guide rail after the bolt group is assembled. By adjusting the initial preload force applied by each bolt, the deformation of the guide rail surface can be corrected, thereby improving its assembly accuracy. Summary of the invention

[0003] The present invention provides a guide rail surface straightness modeling method based on bolt preload prediction, the purpose of which is to predict the deformation of each node on the guide rail surface after the bolt group is assembled, and then adjust the initial preload applied by the bolt, so as to improve the guide rail assembly accuracy, shorten the assembly cycle, etc.

[0004] The above technical objectives of the present disclosure are achieved through the following technical solutions:

[0005] A guide rail surface straightness modeling method based on bolt preload prediction includes:

[0006] Based on Saint-Venant's principle and the deformation coordination condition of the structural surface, a prediction model for the preload of each bolt in the bolt group after assembly is established.

[0007] Based on the elastic deformation theory, a relationship model between the deformation of the guide rail surface nodes and the final bolt preload after assembly is established. Combining the above two models, the deformation of each node on the guide rail surface after assembly can be solved.

[0008] The “three-pole connection method” is used to calculate the straightness error of the guide rail surface.

[0009] The effectiveness of the above-mentioned prediction method is verified by finite element. In the finite element, the preload is applied to the bolts according to the assembly process of sequential tightening. The elastic interaction stiffness and axial stiffness between the bolts are obtained by combining the change of the preload during the assembly process and the deformation of each node on the surface. Substituting it and the initial preload applied by the bolt into the prediction model, the theoretical calculation results of the deformation of each node on the surface after the guide rail is assembled are obtained. The results of the finite element and theoretical calculations are compared to verify the effectiveness of the method.

[0010] A guide rail surface straightness modeling method based on bolt preload prediction is disclosed. The deformation of each node on the guide rail surface after the bolt group is assembled is predicted by the method disclosed in the present invention, thereby providing certain guidance for the correction of its assembly accuracy.

[0011] The beneficial effect of the present disclosure is that the guide rail surface straightness modeling method based on bolt preload prediction described in the present invention can accurately predict the deformation of each node on the surface of the guide rail bolt group after assembly, from the perspective of elastic interaction and coordination conditions of structural component surface deformation, making it more convenient to correct the assembly accuracy of the guide rail, thereby improving the processing performance of the machine tool. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a schematic diagram of the elastic interaction of bolts.

[0013] Figure 2 It is a flow chart of the method of the present invention.

[0014] Figure 3 The process of applying preload to a three-bolt connection structure; (a) applying preload to bolt 2; (b) applying preload to bolt 3.

[0015] Figure 4 This is a schematic diagram of the principle of the three-pole connection method.

[0016] Figure 5 It is a finite element simulation model.

[0017] Figure 6 It is a diagram showing the relationship between deformation and force.

[0018] Figure 7 It is a comparison between bolt preload simulation and theoretical calculation.

[0019] Figure 8 It is the deformation cloud map of the guide rail surface.

[0020] Fig. 9 It is the three-pole connection method to solve the straightness. DETAILED DESCRIPTION

[0021] The present invention will be further described in detail below with reference to the accompanying drawings.

[0022] Figure 2 Flow chart of the disclosed method. Figure 2 As shown in the figure, based on the Saint-Venant principle and the deformation coordination condition of the surface of the structural part, a prediction model for the preload of each bolt after the bolt group is assembled is established. On this basis, based on the elastic deformation theory, a relationship model between the deformation of each node on the guide rail surface and the final preload of the bolt after assembly is established. Combining the above two models, the deformation of each node on the guide rail surface after assembly can be predicted and solved. Then, the straightness error of the guide rail surface is calculated using the three-pole connection method. Finally, the effectiveness of the above-mentioned prediction method is verified by finite element. In the finite element method, the preload is applied to the bolt according to the assembly process of sequential tightening. Combined with the change of the preload of the bolt during the assembly process and the deformation of each node on the surface, the elastic interaction stiffness and axial stiffness between the bolts are obtained. Substituting it and the initial preload applied by the bolt into the prediction model, the theoretical calculation results of the deformation of each node on the surface after the guide rail is assembled can be obtained. The results of the finite element and theoretical calculations are compared to verify their effectiveness.

[0023] For a linear bolt connection mechanism, the bolt preload will gradually change during the assembly process due to the influence of elastic interaction. Based on the Saint-Venant principle (bolt i only has elastic interaction with bolt i+1 and bolt i-1), the derivation process of the bolt preload expression during the assembly process is as follows:

[0024] After bolt j is assembled, the expression of the preload force on bolt i is:

[0025] F i,j =F i 0 +ΔF i,j (1)

[0026] Among them, F i,j is the preload force of bolt i after bolt j is assembled. i 0 is the initial preload applied by bolt i, ΔF i,j is the change in preload force of bolt i.

[0027] According to the deformation coordination conditions of the bolts and the surface nodes of the structural parts, it can be obtained:

[0028]

[0029] According to formulas (1) and (2), the residual preload model on bolt i is:

[0030]

[0031] Among them, Ki,j is the elastic interaction stiffness between bolts i and j, K i,i is the axial stiffness of the structural surface node i to resist deformation, E bi is the elastic modulus of bolt i, A bi is the axial area of ​​bolt i, L bi is the length of bolt i. It is not difficult to see that the change in bolt preload is mainly related to the physical parameters, geometric parameters, equivalent node stiffness of the bolt hole, elastic interaction stiffness and initial preload.

[0032] Due to the complexity of the coefficients in formula (3), let C i =K i,i E bi A bi / [K i,j (E bi A bi +K i,i L bi )], the above formula (3) can be simplified as:

[0033] F i,j =F i 0 -C i F j 0 (4)

[0034] Take the assembly process of the three-bolt connection structure as an example. Figure 3 As shown. After the bolt 2 has applied the preload, Figure 3 As shown in (a), the preload force expression on bolt 1 is:

[0035] F 1,2 =F1 0 -C1F2 0 (5)

[0036] After the bolt 3 is preloaded, Figure 3 (b). At this time, the expression of the preload force on bolt 2 is:

[0037] F 2,3 =F2 0 -C2F3 0 (6)

[0038] Change in preload force on bolt 1 ΔF 1,3 The expression is:

[0039] ΔF 1,3 =C1C2F3 0 (7)

[0040] By integrating the above formulas, the preload force expression on each bolt after assembly is obtained as follows:

[0041]

[0042] Among them, F i,final is the final preload force on bolt i, F i 0 is the initial preload applied to bolt i.

[0043] For a linear group bolt connection structure containing n bolts, an iterative solution method can be used to establish a prediction model for the preload distribution of each bolt in the bolt group under the sequential tightening method:

[0044]

[0045] According to Saint-Venant's principle, bolts only interact elastically with adjacent bolts. Therefore, based on the elastic deformation theory of structural parts, when the preload F1 is applied to bolt 1 0 When , the deformation of the surface node 1 and the surface node 2 of the connected part is:

[0046]

[0047]

[0048] Among them, δ i,j is the deformation of node i on the surface of the structural member when bolt j applies preload.

[0049] When bolt 2 applies preload, the change in deformation value at node 1 on the surface of the connected part is:

[0050]

[0051] The change in deformation value at node 2 on the surface of the connected part is:

[0052]

[0053] The deformation value at the node 3 on the surface of the connected part is:

[0054]

[0055] Among them, Δδ i,j is the change in deformation value of node i on the surface of the structural member when bolt j applies preload. When bolt 3 applies preload, the change in deformation value at node 1 on the surface of the connected member is:

[0056]

[0057] The change in deformation value at node 2 on the surface of the connected part is:

[0058]

[0059] The change in deformation value at node 3 on the surface of the connected component is:

[0060]

[0061] In summary, the deformation value at node 1 on the surface of the connected component is:

[0062]

[0063] The deformation value at node 2 is:

[0064]

[0065] The deformation value at node 3 is:

[0066]

[0067] Integrating equations 18, 19, and 20 yields:

[0068]

[0069] Among them, δ i It is the deformation of the guide rail surface at node i after the bolt group is assembled.

[0070] Furthermore, for a general n-bolt connection structure, the relationship model between the deformation of each node on the guide rail surface and the final preload force on each bolt is:

[0071]

[0072] Combining formula (22) with formula (9), a relationship model between the deformation of each node on the guide rail surface after assembly and the initial preload force applied by each bolt can be established, as shown below:

[0073]

[0074] When the specifications of each bolt are the same as the initial preload applied, formula (23) can be simplified, assuming that the initial preload applied by each bolt is F p 0 .

[0075] For the surface nodes δ1 and δ n Due to the particularity of its surface position, its deformation expression is:

[0076]

[0077]

[0078] For δ i The deformation of (i=2,3,4…n-1), its surface deformation expression is:

[0079]

[0080] Based on the deformation of each node on the guide rail surface, the three-pole connection method is used to solve the straightness error of the guide rail surface. The principle is: according to the definition of the straightness error in a given plane, when two parallel lines enclose the actual measured straight line S, the three poles of "high, low, high" or "low, high, low" are in contact alternately, then the width of the area between the two parallel lines is the straightness of the measured straight line S, which is represented by fmz. The schematic diagram of the principle is as follows Figure 4 shown.

[0081] Therefore, according to the above-mentioned principles and methods of solving the problem, we should first find three points that meet the conditions:

[0082] find[N1,N2,N3…N n ]=[N m ,N p ,N q ] (27)

[0083] Over N m and N q The equation of the straight line between these two points is:

[0084]

[0085] Among them, N ix is the position of pole i on the measured straight line, N iy is the deformation value of pole i, that is, N iy =δ i .

[0086] A little past the middle p Do N m and N q The parallel line between two points, according to the principle and method of the three-pole connection method, the straightness error of the deformation curve is the distance between the two parallel lines, set as fmz, then the expression of fmz is:

[0087]

[0088] Finite element method is used to verify the validity of the above-mentioned model. The specific process is as follows: Establish the guide rail bolt assembly model in the finite element method, such as Figure 5 The material properties of the structural parts are shown in Table 1. In order to obtain the axial stiffness K of the guide rail surface node i i,i, taking the axial stiffness at the surface node 1 as an example. By applying different preloads to bolt 1, the deformation value at the center node 1 of the bolt hole on the rail surface is extracted, as shown in Figure 6 As shown, the axial stiffness K at the surface node 1 can be obtained 1,1 The axial stiffness of the other four nodes on the surface against deformation can be obtained in the same way, and is summarized in Table 2.

[0089] Table 1 Properties of structural material

[0090]

[0091] Table 2 Axial stiffness at surface node i N / mm

[0092]

[0093] In order to obtain the elastic interaction stiffness K between bolt i and bolt j i,j , the elastic interaction stiffness is calculated as follows:

[0094]

[0095] From the above formula, it can be obtained that in addition to the basic specifications of the bolts, the initial preload applied by bolts i and j, as well as the change in preload on bolt i after bolt j is assembled, are also required to obtain the elastic interaction stiffness of the bolts. According to the machine tool guide rail assembly process requirements and the bolt preload-torque conversion formula, the preload corresponding to the M16 bolt at a torque of 140N.m is 37660N.

[0096] In order to obtain the change in the preload force of bolt i, a preload force of 37660 N is first applied to bolt i, and then the same preload force is applied to bolt i+1 to obtain the change in the preload force of bolt i, ΔF i,i+1 , substitute it into formula (31) to solve for the elastic interaction stiffness K between bolt i and bolt i+1 i,i+1 For the finite element model established above, the changes in preload force are summarized, as shown in Table 3. Combined with the axial stiffness at each surface node in Table 2, the elastic interaction stiffness between the bolts can be solved, as shown in Table 4.

[0097] Table 3 Bolt preload change / N

[0098]

[0099] Substitute the initial preload applied by the bolts, the elastic interaction stiffness between the bolts, and the axial stiffness at the surface nodes into formula (10). Taking the preload on bolt 1 as an example, the results of the finite element and theoretical calculations during the assembly process are compared, as shown in Figure 1. Figure 7As shown in the figure, the effectiveness of the bolt preload prediction model is verified.

[0100] According to formula (24), the theoretical value of the deformation of the central node of each bolt hole on the guide rail surface can be obtained after the bolt group is assembled. After the finite element simulation is completed, the deformation cloud diagram of the guide rail surface is as follows: Figure 8 The deformation values ​​of the central nodes of each bolt hole are extracted. Table 5 is a comparison of the results of finite element simulation and theoretical calculation, which verifies the effectiveness of the model.

[0101] Table 5. Deformation results comparison / mm

[0102]

[0103] The straightness error of each node deformation on the guide rail surface is calculated according to the principle and method of the "three-pole connection method". Taking the result of finite element simulation as an example, Fig. 9 shown.

[0104] It can be concluded that the straightness error of the finite element simulation is 0.4μm, and the straightness error of the theoretical calculation is 0.37μm.

Claims

1. A guide rail surface straightness modeling method based on bolt preload prediction, characterized in that: The steps include: Step 1: Based on Saint-Venant's principle and the deformation coordination condition of the surface of the structural part, a prediction model for the preload force of each bolt after the bolt group is assembled is established; Step 2: Based on the elastic deformation theory, a relationship model between the deformation of the guide rail surface nodes and the final preload force of the bolts after assembly is established; by combining the above two models, the deformation of each node on the guide rail surface after assembly can be solved; Step 3: Based on the deformation of each node on the guide rail surface, according to the principle and method of the "three-pole connection method", the straightness error of the surface is solved.

2. The guide rail surface straightness modeling method based on bolt preload prediction according to claim 1, characterized in that: Step 1 includes the following steps: Step 1.1: Based on Saint-Venant's principle and deformation coordination conditions, bolt i only has elastic interaction with bolt i+1 and bolt i-1. After bolt j is assembled, the preload expression of bolt i is: Among them, F i,j is the preload force of bolt i after bolt j is assembled; F i 0 is the initial preload applied by bolt i, ΔF i,j is the change in preload force of bolt i; Let C i =K i,i E bi A bi / [K i,j (E bi A bi +K i,i L bi )], the above formula is simplified to: F i,j =F i 0 -C i F j 0 (2) Step 1.2: After the bolt group of the three-bolt connection structure is assembled, the relationship model between the final preload force and the initial preload force on each bolt is: Among them, K i,j is the elastic interaction stiffness between bolt i and bolt j, K i,i is the axial stiffness of the structural surface node i to resist deformation, E bi is the elastic modulus of bolt i, A bi is the axial area of ​​bolt i, L bi is the length of bolt i; it is not difficult to see that the change in bolt preload is mainly related to the physical parameters, geometric parameters, equivalent node stiffness of the bolt hole, elastic interaction stiffness and initial preload; For a linear group bolt connection structure containing n bolts, an iterative solution method can be used to establish a prediction model for the final preload force of each bolt after assembly under the sequential tightening process:

3. The guide rail surface straightness modeling method based on bolt preload prediction according to claim 1, characterized in that: Step 2 includes the following steps: Step 2.1: Based on Saint-Venant's principle, deformation coordination condition, elastic deformation theory, and bolt elastic interaction stiffness K i,j (i≠j) and axial stiffness K i,j (i=j), and establish the relationship model between the deformation of the guide rail surface node and the final preload of the bolt after assembly, as shown below: Step 2.2: Combine the mathematical models established in step 1.2 and step 2.1 to establish a relationship model between the deformation of the guide rail surface nodes and the initial preload force applied by the bolts, as shown below: When the initial preload force applied by each bolt is the same, formula (6) can be simplified, assuming that the preload force applied by each bolt is F p 0 ; For δ1 and δ n The deformation of the surface is expressed as: Among them, F i,final is the final preload force on bolt i, F i 0 is the initial preload applied to bolt i; For δ i The deformation of (i=2,3,4…n-1), its surface deformation expression is:

4. The guide rail surface straightness modeling method based on bolt preload prediction according to claim 1, characterized in that: Step 3 includes: The three-pole connection method is used to solve the straightness error of the guide rail surface. According to its principle and method, three points that meet the conditions must be found first: find[N1,N2,N3…N n ]=[N m ,N p ,N q ] (10) Over N m and N q The equation of the line between these two points is: δ i,j is the deformation of node i on the surface of the structural member when the bolt j applies preload; N p Do N m and N q The parallel line between two points, according to the principle and method of the three-pole connection method, the straightness error of the deformation curve is the distance between the two parallel lines, set as fmz, then the expression of fmz is:

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