Bolt tightening planning method based on mathematical mechanism

Abstract

The invention discloses a bolt tightening planning method based on a mathematical mechanism, and relates to the field of intelligent assembling and manufacturing. According to the method, tightening parameters are obtained through a bolt pre-tightening force measuring method under set working conditions, and an expansion matrix is obtained through assembly parameters according to a given calculation method; using a preset tightening sequence to obtain a change matrix; performing matrix calculation on the change matrix and the expansion matrix to obtain an elastic coefficient matrix; and carrying out matrix multiplication on the elastic coefficient matrix and the target residual pre-tightening force to obtain an optimized initial pre-tightening force so as to realize bolt tightening planning. According to the invention, the uniform distribution of the bolt load can be realized, and the bolt loosening phenomenon caused by non-uniform load distribution is avoided.

Description

Technical Field

[0001] This invention belongs to the field of engine bolt connection assembly, specifically a bolt tightening planning method based on mathematical mechanisms. Background Technology

[0002] Solid rocket engines and other aerospace products that experience high stress and require high precision necessitate careful planning of bolt tightening during assembly to prevent leaks in the gas sealing system caused by uneven bolt load distribution. However, the elastic interaction between bolts can lead to bolt loosening, resulting in uneven load distribution. Overcoming this elastic interaction presents significant challenges to engine assembly. Summary of the Invention

[0003] To improve the assembly quality of compartment sections, the present invention aims to provide a bolt tightening planning method based on mathematical mechanisms. By measuring the change in preload before and after bolt tightening in a specific tightening sequence, elastic interaction coefficients are obtained, and an elastic coefficient matrix is ​​constructed. Then, based on the target residual preload, the required initial preload is calculated, thus enabling the planning of bolt tightening.

[0004] The technical solution adopted by the present invention to achieve the above objectives is as follows:

[0005] The bolt tightening planning method based on mathematical mechanisms includes the following steps:

[0006] 1) Measure the tightening coefficient of the bolts to be tested in a given sequence;

[0007] 2) Obtain the extended matrix of the connectors by using the bolt tightening coefficient;

[0008] 3) Based on the preset bolt tightening sequence, perform the same elementary row transformations on the identity matrix as the tightening sequence to obtain the transformation matrix;

[0009] 4) Based on the transformation matrix, perform row and column transformations on the expanded matrix to obtain the elastic coefficient matrix for the preset tightening sequence;

[0010] 5) Invert the elastic coefficient matrix, multiply it by the target residual preload to obtain the optimized initial load, and plan the bolt tightening based on the optimized initial load.

[0011] Step 1) includes the following steps:

[0012] 1.1) Apply torque to the bolt to be tested, and convert the magnitude of the applied torque into an equivalent preload, which is then used as the reference preload.

[0013] 1.2) Apply the same torque to the adjacent bolts on the right side of the bolt to be tested, measure the preload of the bolt to be tested as the first preload, subtract the reference preload from the first preload, divide the difference by the reference preload to obtain the tightening coefficient 1;

[0014] 1.3) Apply the same torque to the right side of the bolt to be tested, one bolt apart, and measure the preload of the bolt to be tested as the second preload. Subtract the first preload from the second preload, divide the difference by the first preload, and obtain the tightening coefficient 2.

[0015] 1.4) Apply the same torque to the bolts adjacent to the bolt on the left side of the bolt to be tested, measure the preload of the bolt to be tested as the third preload, subtract the second preload from the third preload, divide the difference by the second preload to obtain the tightening coefficient 3;

[0016] 1.5) Apply the same torque to the left side of the bolt to be tested, one bolt apart, and measure the preload of the bolt to be tested as the fourth preload. Subtract the third preload from the fourth preload and divide the difference by the third preload to obtain the tightening coefficient 4.

[0017] Step 2) includes the following steps:

[0018] 2.1) Based on the positional relationship between the bolts, fill the tightening coefficient of the bolt to be tested into the row vector corresponding to bolt 1 in the elastic coefficient matrix, and set the remaining elements of the row vector corresponding to bolt 1 to 0;

[0019] 2.2) Based on the expansion logic in step 2.1) and the tightening coefficient of the bolt to be tested, obtain the row vector elements corresponding to all bolts, and then obtain the expansion matrix.

[0020] Step 2.1) includes the following steps:

[0021] 2.1.1) Number the bolts clockwise, starting from 1, for a total of n bolts;

[0022] 2.1.2) Fill the element corresponding to bolt 2 in the row vector corresponding to bolt 1, fill the element corresponding to bolt 3 in the row vector corresponding to bolt n-1, fill the element corresponding to bolt n in the row vector corresponding to bolt n, and fill the element corresponding to the bolt n in the row vector corresponding to bolt n. The elements corresponding to the other bolts are all 0.

[0023] Step 2.2) includes the following steps:

[0024] 2.2.1) Based on the extended logic of step 2.1), obtain the row vectors corresponding to all bolts from bolt 1 to bolt n;

[0025] 2.2.2) Combine all row vectors in the order of bolt 1 to bolt n to obtain the extended matrix.

[0026] Step 3) includes the following steps:

[0027] 3.1) The rows of the identity matrix are swapped according to the preset tightening order, that is, the first two tightening orders are a and b respectively. Then, the first row element of the identity matrix is ​​equal to the a row element of the identity matrix, denoted as P1. Then, the second row element of matrix P1 is equal to the b row element of the identity matrix, denoted as matrix P2.

[0028] 3.2) Based on the logic of step 3.1), the change matrix Pn is finally obtained according to the tightening order.

[0029] Step 4) specifically involves:

[0030] Multiply the extended matrix on the left by the transformation matrix, and on the right by the transpose of the transformation matrix. Retain the upper triangular elements of the transformed extended matrix as the elastic coefficient matrix for the preset tightening order.

[0031] The present invention has the following beneficial effects and advantages:

[0032] 1. This invention is simple to operate and easy to apply in practical engineering;

[0033] 2. Compared with other bolt load optimization methods, the present invention has lower computational cost and has been experimentally verified to achieve a more uniform load distribution;

[0034] 3. This invention can achieve uniform distribution of bolt load, avoiding bolt loosening caused by uneven load distribution. Attached Figure Description

[0035] Figure 1 This is the overall flowchart of the simulation calculation method for the unmeasurable assembly quality of the compartment section of the present invention;

[0036] Figure 2 This is a principle block diagram of step S2 in an embodiment of the present invention. Detailed Implementation

[0037] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0038] like Figure 1 As shown, the bolt tightening planning method based on mathematical mechanisms includes the following steps:

[0039] Step S1: Measure the tightening coefficient of the bolts to be tested in the given sequence;

[0040] Step S2: Obtain the extended matrix of the connector using the bolt tightening coefficient obtained in S1;

[0041] Step S3: According to the preset bolt tightening sequence, perform the same elementary row transformation on the identity matrix as the tightening sequence to obtain the transformation matrix;

[0042] Step S4: Based on the transformation matrix, perform row and column transformations on the expansion matrix, which means multiplying the expansion matrix on the left by the transformation matrix and on the right by the transpose of the transformation matrix, retaining the upper triangular elements of the transformed expansion matrix, and obtaining the elastic coefficient matrix of the preset tightening order.

[0043] Step S5: Invert the elastic coefficient matrix and multiply it by the target residual preload to obtain the optimized initial load and realize the bolt tightening plan.

[0044] Specifically, step S1 includes the following steps:

[0045] Step S1.1: Apply torque to the bolt to be tested, and convert the applied torque into an equivalent preload.

[0046] Step S1.2: Apply the same torque to the adjacent bolts on the right side of the bolt to be tested, measure the preload of the bolt to be tested, subtract the preload obtained in S1.1 from the preload obtained in S1.2, divide the difference by the preload obtained in S1.1 to obtain the tightening coefficient 1;

[0047] Step S1.3: Apply the same torque to the right side of the bolt to be tested, one bolt apart, and measure the preload of the bolt to be tested. Subtract the preload obtained in S1.2 from the preload obtained in S1.3, and divide the difference by the preload obtained in S1.2 to obtain the tightening coefficient 2.

[0048] Step S1.4: Apply the same torque to the bolts adjacent to the bolt on the left side of the bolt to be tested, measure the preload of the bolt to be tested, subtract the preload obtained in S1.3 from the preload obtained in S1.4, divide the difference by the preload obtained in S1.3, and obtain the tightening coefficient 3.

[0049] Step S1.5: Apply the same torque to the left side of the bolt to be tested, one bolt apart, and measure the preload of the bolt to be tested. Subtract the preload obtained in S1.4 from the preload obtained in S1.5, and divide the difference by the preload obtained in S1.4 to obtain the tightening coefficient 4.

[0050] The expansion matrix of the connector is obtained by using the bolt tightening coefficient obtained in step S1.

[0051] like Figure 2 As shown, step S2 includes the following steps:

[0052] Step S2.1: Based on the positional relationship between the bolts, fill the tightening coefficient of the bolt to be tested into the row vector corresponding to bolt 1 in the elastic coefficient matrix, and set the remaining elements of the row vector corresponding to bolt 1 to 0;

[0053] Specifically, step S2.1 includes the following steps:

[0054] S2.1.1: Number the bolts clockwise, starting from 1, for a total of n bolts;

[0055] S2.1.2: Fill the element corresponding to bolt 2 in the row vector corresponding to bolt 1 with tightening coefficient 1, fill the element corresponding to bolt 3 with tightening coefficient 2, fill the element corresponding to bolt n-1 with tightening coefficient 3, fill the element corresponding to bolt n with tightening coefficient 4, and fill the element corresponding to the other bolts with 0.

[0056] Step S2.2: Based on the expansion logic of S2.1 and the tightening coefficient of the bolt to be tested, obtain the row vector elements corresponding to all bolts, and then obtain the expansion matrix;

[0057] Specifically, step S2.2 includes the following steps:

[0058] S2.2.1: Following the same expansion logic, obtain the row vectors corresponding to all bolts from bolt 1 to bolt n;

[0059] S2.2.1: Combine all row vectors in the order of bolt 1 to bolt n to obtain the extended matrix.

[0060] Step S3 includes the following steps:

[0061] Step S3.1: According to the preset tightening order, the rows of the identity matrix are swapped. That is, the first two tightening orders are a and b respectively. Then, let the first row element of the identity matrix be equal to the a row element of the identity matrix, denoted as P1. Then let the second row element of matrix P1 be equal to the b row element of the identity matrix, denoted as matrix P2.

[0062] Step S3.2: Based on the logic of step 3.1), the change matrix Pn is finally obtained according to the tightening order.

Claims

1. A method for bolt tightening planning based on mathematical mechanism, characterized in that, The method comprises the following steps: 1) measuring the tightening coefficient of the bolt to be tested under a given sequence; 2) obtaining the augmented matrix of the connecting piece through the bolt tightening coefficient; 3) according to the preset bolt tightening sequence, performing the same elementary row transformation on the unit matrix as the tightening sequence to obtain a change matrix; 4) according to the change matrix, performing row and column transformation on the augmented matrix to obtain the elastic coefficient matrix of the preset tightening sequence; 5) inverting the elastic coefficient matrix, multiplying the target residual pretightening force to obtain the optimized initial load, and performing bolt tightening planning according to the optimized initial load.

2. The mathematical mechanism-based bolt-up procedure of claim 1, wherein, The step 1) comprises the following steps: 1.1) applying a torque to the bolt to be tested, and converting the torque size into the pretightening force size as the reference pretightening force; 1.2) applying the same torque to the adjacent bolt on the right side of the bolt to be tested, measuring the pretightening force of the bolt to be tested as the first pretightening force, subtracting the reference pretightening force from the first pretightening force, and dividing the difference by the reference pretightening force to obtain the tightening coefficient 1; 1.3) applying the same torque to the bolt spaced one bolt on the right side of the bolt to be tested, measuring the pretightening force of the bolt to be tested as the second pretightening force, subtracting the first pretightening force from the second pretightening force, and dividing the difference by the first pretightening force to obtain the tightening coefficient 2; 1.4) applying the same torque to the adjacent bolt on the left side of the bolt to be tested, measuring the pretightening force of the bolt to be tested as the third pretightening force, subtracting the second pretightening force from the third pretightening force, and dividing the difference by the second pretightening force to obtain the tightening coefficient 3; 1.5) applying the same torque to the bolt spaced one bolt on the left side of the bolt to be tested, measuring the pretightening force of the bolt to be tested as the fourth pretightening force, subtracting the third pretightening force from the fourth pretightening force, and dividing the difference by the third pretightening force to obtain the tightening coefficient 4.

3. The mathematical mechanism-based bolt-up procedure of claim 1, wherein, The step 2) comprises the following steps: 2.1) according to the position relationship between the bolts, filling the tightening coefficient of the bolt to be tested into the row vector corresponding to the bolt 1 in the elastic coefficient matrix, and setting the remaining elements of the row vector corresponding to the bolt 1 to 0; 2.2) according to the augmented logic of step 2.1) and the tightening coefficient of the bolt to be tested, obtaining the row vector elements corresponding to all the bolts, and further obtaining the augmented matrix.

4. The mathematical mechanism-based bolt-up procedure of claim 3, wherein, The step 2.1) comprises the following steps: 2.1.1) clockwise labeling the bolts, starting from 1, a total of n bolts; 2.1.2) filling the tightening coefficient 1 into the element corresponding to the bolt 2 in the row vector corresponding to the bolt 1, filling the tightening coefficient 2 into the element corresponding to the bolt 3, filling the tightening coefficient 3 into the element corresponding to the bolt n-1, filling the tightening coefficient 4 into the element corresponding to the bolt n, and setting the elements corresponding to the remaining bolts to 0.

5. The bolt tightening planning method based on mathematical mechanism according to claim 3, wherein the step 2.2) comprises the following steps: 2.2.1) according to the augmented logic of step 2.1), obtaining the row vectors corresponding to all the bolts from the bolt 1 to the bolt n; 2.2.2) combining all the row vectors in the order of the bolts from 1 to n to obtain the augmented matrix.

6. The mathematical mechanism-based bolt-up procedure of claim 1, wherein, The step 3) comprises the following steps: 3.1) According to the preset tightening sequence, the rows of the unit matrix are exchanged, that is, the first two sequences of the tightening sequence are a and b in turn, then the first row elements of the unit matrix are equal to the a-th row elements of the unit matrix, denoted as P1, and then the second row elements of the matrix P1 are equal to the b-th row elements of the unit matrix, denoted as the matrix P2; 3.2) According to the logic of step 3.1), the change matrix Pn is finally obtained according to the tightening sequence.

7. The mathematical mechanism-based bolt-up procedure of claim 1, wherein, The step 4) is specifically: The upper triangular elements of the change matrix multiplied by the left and the transpose of the change matrix multiplied by the right of the extended matrix are reserved as the elastic coefficient matrix of the preset tightening sequence.

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