Method for detecting deformation of flexible constant force clamping mechanism under displacement input

Abstract

A kind of deformation detection method of flexible constant force clamping mechanism under displacement input, after the two-dimensional grid model of the flexible constant force clamping mechanism to be measured is constructed, based on the Mooney-Rivlin second-order strain energy function model of super-elastic material and initialization model parameters are generated according to boundary constraint condition and load setting;Based on the virtual work principle discretization equation under the static equilibrium state of continuum, using the displacement control method based on displacement increment iteration, the action point of load application, i.e. control point is handled by displacement application and the displacement increment of corresponding non-constrained point is solved, then the node position coordinates and model coefficients are updated until the convergence criterion is met;Finally, the node deformation solution meeting the equilibrium equation is obtained, and the node displacement, internal stress and other data of the process are processed and charted.The present application can quickly and conveniently model similar examples with simple parameter setting, and obtain the structure deformation condition and force-displacement output characteristic results with high precision.

Description

Technical Field

[0001] This invention relates to the field of flexible constant force clamping mechanisms, specifically a method for detecting deformation of a flexible constant force clamping mechanism under displacement input. Background Technology

[0002] Passive flexible constant force clamping mechanisms possess excellent elastic deformation capabilities and constant force output characteristics. However, due to their strong structural nonlinearity, traditional incremental iterative methods struggle to perform deformation analysis and detection in the constant force section during the design and analysis of their configurations, resulting in iterative failures and low computational efficiency. Summary of the Invention

[0003] To address the aforementioned shortcomings of existing technologies, this invention proposes a deformation detection method for a flexible constant-force clamping mechanism under displacement input. It specifically models and solves the nonlinear deformation problem of structures under long displacement, performs iterative analysis based on displacement increments for the constant-force segment loading unique to the constant-force clamping mechanism, and provides an interface for load analysis through visualization. This allows for rapid and convenient problem modeling of similar examples with simple parameter settings, yielding highly accurate results on structural deformation and force-displacement output characteristics.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to a deformation detection method for a flexible constant-force clamping mechanism under displacement input. After constructing a two-dimensional mesh model of the flexible constant-force clamping mechanism to be tested, a second-order strain energy function model based on the hyperelastic material Mooney-Rivlin is generated and the model parameters are initialized according to boundary constraints and load settings. Based on the virtual work principle of the continuum in static equilibrium, the equations are discretized, and a displacement control method based on displacement increment iteration is adopted. The displacement of the load application points (i.e., control points) is applied cyclically, and the displacement increments of the corresponding unconstrained points are solved. Then, the node position coordinates and model coefficients are updated until the convergence criterion is met. Finally, the nodal deformation solution conforming to the equilibrium equation is obtained, and the nodal displacement, internal stress, and other data are processed and plotted.

[0006] The method includes:

[0007] Step 1: Initialize the 2D model. Set the length and width of the model according to the geometry of the flexible constant force clamping mechanism under test. Divide the model into small square elements and create vectors for the displacement and internal force values ​​of the element nodes, initializing them all to 0. Step 2: Number the degrees of freedom of the elements in the horizontal and vertical directions. Based on their connection to the square elements and their spatial distribution, generate a batch table of correspondence between cells and their contained nodes, and an initial coordinate table for the nodes. Specifically: {x1, y1, ..., x4, y4} = (2N+1)*1 + {0, 1, 2*nely + {2, 3, 0, 1}, -2, -1}, {X1, Y1, ..., X4, Y4} = {N X N Y N X +l, N Y N X +l, N Y +l;N X N Y +l}, where: x i y i Let N be the horizontal and vertical degrees of freedom number of the i-th node traversed counterclockwise starting from the bottom left node, N be the element number, 1 be a vector of all 8 ones, and nely be the number of grid cells in the vertical direction of the structure; X i Y i Let N be the coordinates of the i-th node traversed counterclockwise starting from the bottom left node. x and N Y , where are the horizontal and vertical coordinates of the lower left node of the cell, and l is the side length of the square grid.

[0008] Step 3: Set the boundary constraints, the application point of the displacement load, and the direction of displacement application for the flexible constant force clamping mechanism under test;

[0009] Step 4: By applying the Mooney-Rivlin second-order material model, a hyperelastic material strain energy model is constructed for the flexible constant-force clamping mechanism under test. Specifically: Among them: J i The right Cauchy-Green deformation tensor C = F for mesh deformation T The invariant eigenvalues ​​of F, A 10 A 01 And K is a material-related parameter constant, deformation tensor Where: x and y are the horizontal and vertical displacement values ​​of the node relative to its initial position, respectively, and X and Y are the initial horizontal and vertical coordinate values ​​of the node.

[0010] Step 5: Initialize the load factor λ and input displacement value x of the solution algorithm;

[0011] Step 6, initialize the ideal number of iterations J required for the iteration. d And the iterative smoothing coefficient γ;

[0012] Step 7: Based on the deformation of the flexible constant force clamping mechanism under test in this iteration, calculate the linear displacement-strain matrix B of each element. G and the nonlinear displacement-strain matrix B N This allows for the calculation of the element stiffness matrix of each element, ultimately assembling it into the overall stiffness matrix K of the mechanism under its current deformation. E Specifically, the interpolation points are selected as the four points (±0.57735, ±0.57735) in the reference mesh mapped to the four vertices (-1, -1), (1, -1), (1, 1), and (-1, 1) after deformation, respectively. i And based on the geometric mapping relationship of the square unit, the linear interpolation function N is obtained. i Make N i (n j )=δ ij The value is 1 when i = j; linear displacement strain matrix B G There are column vectors in: j = mod(k, 2), k = 1, ..., 8. The column components of the nonlinear displacement-strain matrix are... Where: i = mod(k, 2), N j，x For interpolation function N i The partial derivatives with respect to the x-component; finally, the components of the stiffness matrix of each element are added together according to the node labels generated in step 2 to obtain the overall stiffness matrix.

[0013] Step 8: Take one displacement application as a new round. In the first iteration of each round, only the control points are applied with displacement, and the other unconstrained free points are not updated. After the first iteration of each round, the displacement of the control points remains unchanged.

[0014] Step 9: Keeping the displacement of the control points constant, calculate the displacement increment of the unconstrained points in this iteration, and update the node position coordinates and load coefficient λ. Specifically: Unconstrained point displacement increment Δd = Δλ·Δd b +Δd a Where: Δλ is the increment of the reference load factor, Δd b To correct for the reference load P based on the current structural stiffness, Δd a The residual R is corrected based on the current structural stiffness, and the residual value of internal and external forces R = f is calculated from the results of the previous iteration. ext -f int f ext The product of the reference load factor and the reference load is used as the external force vector, f. int The internal force vector after node deformation is obtained by multiplying the element stress vector with the nonlinear displacement-strain matrix and adding the corresponding vectors.

[0015] Step 10: Calculate the residual vector R between the updated model internal force values ​​and the applied external force;

[0016] Step 11: If the convergence criterion is met, proceed to step 9; otherwise, if the control point reaches the target displacement value, proceed to step 12; otherwise, record the number of iterations J, node deformation and output force value in this round, and proceed to step 7.

[0017] The convergence criterion stated above is: the average error of the nodes is less than the set threshold, i.e. Where: N E The total number of nodes in the model is represented by Tol, which is the convergence threshold and has a value of 1*10. -4 .

[0018] Step 12: Based on the node deformation recorded in the process and the output force value of the control point, draw the structural deformation stress distribution diagram and the force-displacement relationship diagram of the displacement loading process for analysis.

[0019] This invention relates to a system for implementing the above-mentioned method, comprising: a mesh generation unit, an overall stiffness matrix construction unit, a deformation solving unit, and a deformation result visualization unit, wherein: the mesh generation unit generates unit nodes and corresponding node coordinates in batches according to the set mesh quantity and distribution and unit size information, for subsequent calculations; the overall stiffness matrix construction unit calculates the corresponding unit stiffness matrix according to the input node deformation information and the material parameter model, and assembles the overall stiffness matrix of the clamping mechanism under current deformation according to the node connection relationship; the deformation solving unit iteratively solves the displacements and output forces of the remaining nodes to be determined according to the applied displacement of the control points in each round, and obtains the deformation result after the current round of loading; the deformation result visualization unit calculates the stress within the unit according to the node information and unit stiffness matrix after iteration, and presents the unit deformation result and stress distribution in a visual manner by plotting the stress distribution in a graph.

[0020] Technical effect

[0021] This invention addresses the iterative solution of deformation analysis using the displacement control method of nonlinear finite element under long displacement loads. Analogous to solving general differential equation problems, it requires only the computational workload of a first-order precision differential equation solution method, and has deformation analysis accuracy close to that of a second-order precision method. Furthermore, it achieves a computational accuracy improvement of more than 10% when the maximum strain of the mechanism reaches 50%. Attached Figure Description

[0022] Figure 1 This is a flowchart of the present invention;

[0023] Figure 2 This is a schematic diagram illustrating the boundary conditions and load application in the embodiment;

[0024] Figure 3 This is a schematic diagram of the grid division and node numbering in the embodiment;

[0025] Figure 4 This is a schematic diagram of mesh deformation in the embodiment;

[0026] Figure 5 This is a graph showing the relationship between the applied force and the input displacement in the embodiment.

[0027] Figure 6 This is a schematic diagram of the structural stress distribution in the embodiment.

[0028] Figure 7 This diagram illustrates the comparison of the number of computational cycles and computational accuracy required between the DCM example and conventional differential equation solving methods, specifically the first-order precision method (Euler) and the second-order precision method (P_Euler). Detailed Implementation

[0029] like Figure 1 The illustration shows a deformation detection method for a flexible constant force clamping mechanism under displacement input, based on an embodiment of this method. It utilizes a simplified model of a constant force clamping mechanism made of a 40-hardness rubber superelastic material as the body material and a strip-shaped structure as the mechanism. The embodiment analyzes the deformation and output force under an applied external displacement of 50 mm. The steps of this embodiment are as follows:

[0030] Step 1: Prepare a two-dimensional model. Based on the geometry of the mechanism, set the model to be 100mm long and 10mm wide. Divide the model into small square elements with a side length of 1mm. Create vectors for the nodal displacement and internal force values ​​of the elements and initialize them to 0.

[0031] Step 2: Number the degrees of freedom of the cells in the horizontal and vertical directions, and generate a table of correspondence between cells and their contained nodes and an initial coordinate table of nodes in batches according to their connection relationship with the cells and their spatial distribution.

[0032] Step 3: Set the boundary constraints of the mechanism, the application point of the displacement load, and the direction of displacement application; set the upper nodes of the mechanism as fixed constraints, set the lower nodes of the mechanism as symmetrical constraints, with only horizontal degree of freedom, and set the displacement load application point as the lower right vertex, with the displacement application direction as the positive direction of horizontal to the right.

[0033] Step four: Establish the material model of the mechanism. By applying the Mooney-Rivlin second-order material model, mathematical modeling is performed on the strain energy of the hyperelastic material used in the mechanism; where a rubber material with a hardness of 40 is used, with parameters A... 10 =1.95e^5, A 01 =1.62e^4, K = 1e^3;

[0034] Step 5: Initialize the load factor λ = 3 and the input displacement value x = 50 mm for the solution algorithm;

[0035] Step 6: Initialize the ideal number of iterations J required for the iteration. d =3, and the iterative smoothing coefficient γ = 0.5;

[0036] Step 7: Assemble the stiffness matrix. Based on the deformation of this mechanism, calculate the linear displacement-strain matrix B of each element. G and the nonlinear displacement-strain matrix B N This allows for the calculation of the element stiffness matrix of each element, ultimately assembling it into the overall stiffness matrix K of the mechanism under its current deformation. E ;

[0037] Step 8: Apply displacement in a new round. In the first iteration of this round, displacement is applied only to the control points, and the other unconstrained free points are not updated.

[0038] Step 9: In subsequent iterations after the displacement is applied, keep the displacement of the control points unchanged, solve for the displacement increment of the non-constrained points in this iteration, and update the node position coordinates and load coefficient λ.

[0039] Step 10: Calculate the residual vector R between the updated model internal force values ​​and the applied external force;

[0040] Step 11: Determine whether the current calculation has converged based on the residual. If it has not converged, proceed to step 9. Otherwise, further determine whether the target displacement value has been reached. If it has, proceed to step 12. Otherwise, record the number of iterations J, node deformation, and output force value experienced in this round, and proceed to step 7.

[0041] Step 12: Based on the node deformation recorded in the process log and the output force values ​​of the control points, draw the following diagram: Figure 4 and Figure 6 The structural deformation stress distribution diagram shown, and as shown in the figure Figure 5 The force-displacement relationship diagram for the displacement loading process is shown.

[0042] Compared with existing technologies, this method, through the displacement control iterative approach used in steps eight to ten, achieves an accuracy level similar to that of second-order methods with only 20% of the computational cost of equivalent second-order accuracy solutions. Figure 7 The accuracy shown is 10% higher than that of the equivalent first-order method.

[0043] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A method for detecting deformation of a flexible constant force clamping mechanism under displacement input, characterized in that, After constructing a two-dimensional mesh model of the flexible constant-force clamping mechanism under test, a second-order strain energy function model based on the hyperelastic material Mooney-Rivlin is generated and the model parameters are initialized according to the boundary constraints and load settings. Based on the virtual work principle of the continuum in static equilibrium, the equations are discretized. A displacement control method based on displacement increment iteration is used to iteratively apply displacement to the points of application of the load, i.e., the control points, and solve for the displacement increments of the corresponding unconstrained points. Then, the nodal coordinates and model coefficients are updated until the convergence criterion is met. Finally, the nodal deformation solution that conforms to the equilibrium equation is obtained, and the nodal displacement and internal stress data of the process are processed and plotted, specifically including: Step 1: Initialize the two-dimensional model. Set the length and width of the model according to the geometric configuration of the flexible constant force clamping mechanism to be tested. Divide the model into small square elements and create vectors for the displacement values ​​and internal force values ​​of the element nodes, and initialize them to 0. Step 2: Number the degrees of freedom in the horizontal and vertical directions of the unit. Based on its connection relationship with the square unit and its spatial distribution, generate a batch table of correspondence between the unit and its contained nodes, as well as an initial coordinate table of the nodes. Specifically: ， ， in: The first node is the 1st node of the counter-clockwise traversal starting from the bottom left node. The horizontal and vertical degrees of freedom of each node are numbered. For unit number, For length equal to The whole vector, This represents the number of grid cells in the vertical direction of the structure. The first node is the 1st node of the counter-clockwise traversal starting from the bottom left node. The coordinates of each node. and These are the x and y coordinates of the lower left node of the element, respectively. The side length of the square grid; Step 3: Set the boundary constraints, the application point of the displacement load, and the direction of displacement application for the flexible constant force clamping mechanism under test; Step 4: By applying the Mooney-Rivlin second-order material model, a hyperelastic material strain energy model is constructed for the flexible constant-force clamping mechanism under test. Specifically: The right Cauchy-Green deformation tensor of the mesh deformation invariant characteristic quantities, , as well as For material-related constant parameters, the deformation tensor ,in: and These are the lateral and longitudinal displacements of the nodes relative to their initial positions, respectively. and These are the initial x and y coordinates of the node; Step 5, Initialize load factor and input displacement value ; Step 6: Initialize the ideal number of iterations required for the iteration. and iterative smoothing coefficient ; Step 7: Based on the deformation of the flexible constant force clamping mechanism under test in this iteration, calculate the linear displacement-strain matrix of each element. and nonlinear displacement-strain matrix The element stiffness matrix of each element is calculated, and finally assembled into the overall stiffness matrix of the mechanism under the current deformation. Specifically, the interpolation points are selected as the points mapped to the four vertices of the deformed element. , , , Reference grid ( Four points And obtain the linear interpolation function based on the geometric mapping relationship of the square unit. Make ,when Time value Linear displacement-strain matrix There are column vectors ,in: , , The column components of the nonlinear displacement-strain matrix are ,in: , , , interpolation function right The partial derivatives of the components; finally, the components of the stiffness matrix of each element are added together according to the node labels generated in step 2 to obtain the overall stiffness matrix; Step 8: Take one displacement application as a new round. In the first iteration of each round, only the control points are applied with displacement, and the other unconstrained free points are not updated. After the first iteration of each round, the displacement of the control points remains unchanged. Step 9: Keeping the displacement of the control points constant, solve for the displacement increment of the unconstrained points in this iteration, and determine the node position coordinates and load coefficients. The update will be performed specifically: displacement increment of unconstrained points. ,in: As an increment of the reference load factor, To apply the reference load to the current structural stiffness The correction, Based on the current structural stiffness and residual The correction is made by calculating the residual values ​​of internal and external forces based on the results of the previous iteration. , The external force vector is obtained by multiplying the reference load factor and the reference load. The internal force vector after node deformation is obtained by multiplying the element stress vector and the nonlinear displacement-strain matrix and adding them accordingly. Step 10: Calculate the residual vector between the updated model internal force values ​​and the applied external force. ; Step 11: If the convergence criterion is not met, proceed to step 9; otherwise, further determine if the control point reaches the target displacement value, then proceed to step 12; otherwise, record the number of iterations in this round. Analyze the node deformation and output force values, and then proceed to step 7; Step 12: Based on the node deformation recorded in the process and the output force value of the control point, draw the structural deformation stress distribution diagram and the force-displacement relationship diagram of the displacement loading process for analysis.

2. The deformation detection method for the flexible constant force clamping mechanism under displacement input according to claim 1, characterized in that, The convergence criterion stated above is: the average error of the nodes is less than the set threshold, i.e. ,in: This represents the total number of nodes. The convergence threshold is set to a value of [value to be filled in]. .

3. A deformation detection system for a flexible constant force clamping mechanism under displacement input, implementing the method of claim 1 or 2, characterized in that, include: The system comprises a mesh generation unit, an overall stiffness matrix construction unit, a deformation solving unit, and a deformation result visualization unit. Specifically: the mesh generation unit generates element nodes and their corresponding coordinates in batches according to the set mesh quantity, distribution, and element size information; the overall stiffness matrix construction unit calculates the corresponding element stiffness matrix based on the input node deformation information and material parameter model, and assembles the overall stiffness matrix of the clamping mechanism under current deformation according to the node connection relationships; the deformation solving unit iteratively solves the displacements and output forces of the remaining nodes based on the applied displacements of the control points in each round, obtaining the deformation results after this round of loading; and the deformation result visualization unit calculates the stress within the element based on the node information and element stiffness matrix after iteration, and then plots the element deformation results and stress distribution in a visual manner.

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