Dynamic analysis and optimization method of high-speed stamping hybrid mechanism with lubricated clearance considering impact load

Abstract

The present invention relates to a dynamic analysis and optimization method for a high-speed stamping hybrid mechanism with a lubricated gap considering impact loads, which includes the following steps: S1, defining structural parameters and design parameters; S2, establishing a lubricated gap motion model, a contact force model, and an oil film bearing capacity model; S3, introducing a flexible beam unit model; S4, judging the relative motion state of the bearing and the shaft at the rotating pair element; S5, establishing a dynamic equation; S6, solving the dynamic equation; S7, optimizing and improving the structural parameters of the mechanism; S8, looping the above process, iteratively solving, and thus completing the dynamic analysis and parameter optimization. The rigid-flexible coupling dynamic equation with a lubricated gap established by the present invention can more accurately predict the dynamic response characteristics of the high-speed stamping hybrid mechanism when it is subjected to impact loads during actual working operation. The modeling method is suitable for the dynamic response characteristic analysis and optimization design of high-speed stamping mechanisms of other configurations, and has the advantages of wide applicability.

Description

Technical Field

[0001] The present invention belongs to the technical field of parallel mechanisms, and in particular relates to a dynamic analysis and optimization method for a high-speed stamping hybrid mechanism with a lubricating gap taking impact load into consideration. Background Art

[0002] As a high-efficiency, "low-cutting" machine tool, the multi-link ultra-precision servo press meets the requirements of clean and green production and is widely used in fields such as automotive manufacturing and aerospace. Under the forming conditions of a multi-link ultra-precision servo press, the punching pressure and inertial forces will cause elastic vibration deformation in the transmission system, seriously damaging the dimensional accuracy of the closing height between the upper and lower dies and affecting the forming processing accuracy of the stamped parts. At the same time, the clearance and wear effects of the kinematic pairs of the mechanism can easily cause the separation and collision of the kinematic pair elements, which can lead to chaos and uncertainty in the movement of the end-actuator slider, significantly reducing the accuracy of the relative position of the die and sheet metal in the stamping process and sharply increasing the workpiece size and geometric errors. Therefore, it is necessary to establish a dynamic model of a planar flexible multi-link mechanism with clearance under impact load and estimate its dynamic performance. Furthermore, it is necessary to analyze the influence of the dynamic errors of the multi-link mechanism, realize the multi-objective optimization design of the mechanism clearance size, and break through the technical bottleneck of multi-link ultra-precision. Summary of the Invention

[0003] In response to the problems existing in the prior art, the present invention provides a dynamic analysis and optimization method for a high-speed stamping hybrid mechanism with a lubricated gap that takes impact loads into consideration. This method solves the problem of excessive loss of the gap rotating pair and the end effector caused by errors such as the gap size of the mechanism during the high-speed stamping operation of the high-speed stamping hybrid mechanism. This method is beneficial to improving the load impact capacity of the high-speed stamping hybrid mechanism and extending the service life of the mechanism.

[0004] The technical solution adopted by the present invention is a dynamic analysis and optimization method of a high-speed stamping hybrid mechanism with a lubricating gap considering impact loads, which includes the following steps:

[0005] S1. Define the structural parameters and design parameters of the high-speed stamping hybrid mechanism;

[0006] S2. Establish a lubrication gap motion model for a high-speed stamping hybrid mechanism. Based on the contact force model between the rotating pair elements and the oil film bearing capacity model, calculate the contact force at the gap between the rotating pair elements and the oil film bearing capacity;

[0007] S3, introduce the flexible beam unit model into the system using the absolute coordinate point method;

[0008] S4. Determine the relative motion state of the bearing and the shaft at the rotating pair element based on the lubrication clearance motion model and perform mechanical analysis, specifically including the following steps:

[0009] S41. When e < r, the bearing and the pin shaft are not in contact, and the acting force is the oil film bearing capacity. Then, establish an oil film bearing capacity model and solve the oil film bearing capacity at the clearance of the revolute pair.

[0010] S42. When e > r + e0, the bearing and the pin shaft are in a dry friction contact and collision state, and the acting force is the contact and collision force. Then, establish a contact force model between the elements of the revolute pair and solve the contact and collision force between the elements of the revolute pair.

[0011] S43. When r < e < r + e0, the bearing and the pin shaft are in a transitional state, and the acting force is a combined force of the oil film bearing capacity and the contact and collision force. Then, solve the combined force of the oil film bearing capacity and the contact and collision force, and its expression is:

[0012]

[0013] In the formula, F l represents the contact and collision force, F d represents the oil film bearing capacity, e represents the eccentricity value of the pin shaft relative to the bearing, r represents the clearance value between the bearing and the pin shaft, and e0 represents the eccentricity coefficient.

[0014] S5. Calculate the mass matrix, Jacobian matrix and generalized external force matrix of the system, and establish a rigid-flexible coupling dynamic equation of the mechanism with lubrication clearance considering the impact load, and its expression is;

[0015]

[0016] In the formula, Φ q represents the Jacobian matrix form of the constraint equation, represents the generalized acceleration vector, τ represents the right side of the acceleration constraint equation, M le represents the mass matrix, λ represents the Lagrange multiplier, ζ le represents the generalized external force matrix, γ and η represent the default parameters, and τ represents the product of the generalized acceleration vector and the Jacobian matrix.

[0017] S6. Based on the Baumgarte default stability algorithm, use the Runge-Kutta method to solve the dynamic equation of the mechanism and obtain the generalized coordinates, generalized velocities and generalized accelerations.

[0018] S7. Through the genetic optimization algorithm, optimize and improve the structural parameters of the high-speed stamping hybrid mechanism under the impact load.

[0019] S8. Loop the above process, perform iterative solution until the final solution time is reached, and thus complete the dynamic optimization analysis of the high-speed stamping hybrid mechanism under the impact load.

[0020] Preferably, the step S2 of establishing the contact force model between the revolving pair elements specifically includes the following steps:

[0021] S211. The Lancarani-Nikravesh model is used to calculate the normal collision force between the elements of each rotation pair. The expression is:

[0022]

[0023] Where, Indicates the relative contact speed between the rotating pairs, δ n represents the embedding depth between the shaft and the bearing, K represents the stiffness coefficient, and D represents the damping coefficient. Their expressions are:

[0024]

[0025] Where R i Indicates the curvature radius of the bearing at the collision contact point; R j Indicates the curvature radius of the pin at the collision contact point; δ i represents the shear modulus of the bearing, δ j represents the shear modulus of the pin, v represents Poisson's ratio; E represents elastic modulus; represents the initial contact velocity; c δ represents the coefficient of restitution;

[0026] S212. The tangential friction force between the rotating pair elements is calculated using the modified Coulomb friction model. The expression is:

[0027]

[0028] Where c f represents the coefficient of kinetic friction, c n represents the dynamic correction coefficient, v t Indicates the speed value at time t, F n Indicates positive pressure;

[0029] S213. Calculate the contact force between the elements of the revolving pair. The expression is:

[0030] F d =F n n+F t t

[0031] Where n represents the normal unit vector, and t represents the tangential unit vector;

[0032] Preferably, the step S2 of establishing the oil film bearing capacity model between the rotating pair elements specifically includes the following steps:

[0033] S221, Based on the Gümbel boundary condition, assuming the same fluid temperature, viscosity and density, when the radial velocity between the pin and the bearing in the lubrication gap is The normal oil film bearing capacity and tangential oil film bearing capacity between each rotating pair element are expressed as follows:

[0034]

[0035] When the radial velocity between the pin and the bearing in the lubrication gap The normal oil film bearing capacity and tangential oil film bearing capacity between each rotating pair element are expressed as follows:

[0036]

[0037] Where L is the bearing width, η is the deflection angle, and ε is the eccentricity. represents the first-order derivative of the eccentricity ε with respect to time, represents the deflection angle, Indicates the deflection angle The first derivative with respect to time, μ l represents the dynamic viscosity of the lubricant, ω represents the relative angular velocity; r represents the clearance between the bearing and the pin, where r = R i -R j ; R q represents the radius of the pin; k represents the definition parameter, which can be expressed as

[0038]

[0039] S222. Determine whether the eccentricity ε between the bearing and the pin is close to zero. If the eccentricity ε between the bearing and the pin is close to zero, then the oil film bearing capacity can be obtained by introducing the correction coefficient m, which is expressed as follows:

[0040]

[0041] Where, ε0 represents the correction interval;

[0042] S223. Obtain the component of the oil film bearing capacity at the gap of each rotating pair element on each axis, and its expression is:

[0043]

[0044] When the oil film bearing capacity at the gap between the rotating pair elements is less than the force between the elements, the oil film formed by the lubricant will fail, and the rotating pair elements will be in a contact and collision state. For the transition between the dry friction state and the lubricated state, the eccentricity coefficient e0 is introduced to improve the force model at the gap between the rotating pair elements. Its expression is:

[0045]

[0046] Where, e represents the eccentricity between the bearing and the pin, and e0 represents the eccentricity coefficient.

[0047] Furthermore, the flexible beam unit model is established in step S3, which specifically includes the following steps:

[0048] S31. Define the generalized coordinates of the flexible beam, which are expressed as:

[0049]

[0050] Where, (r ax r ay )、(r bx r by ) represent the position vectors of nodes a and b respectively, denote the slope vectors of nodes a and b respectively;

[0051] S32. Establish the mass matrix of the flexible beam, which is expressed as:

[0052] M e =∫ V ρS T SdV

[0053] Where ρ and V represent the density and volume of the flexible beam, respectively, S is the shape function, and S T is the transposed matrix of the shape function, where the shape function expression is:

[0054] S=[S1I,S2I,S3I,S41I]

[0055] Where, in, l is the length of the flexible beam, x represents the mapping of the flexible beam in the x-axis direction, and I is the unit matrix;

[0056] S33. Calculate the total strain energy ψ of the flexible beam element e , whose expression is:

[0057] ψ e =ψ p +ψ q

[0058] Where, ψ p , ψ q are the bending strain energy and axial strain energy of the flexible beam element, respectively, and their expressions are:

[0059]

[0060] Where B e is the cross-sectional area of ​​the flexible beam element, Ee and I e is the Young's modulus and section moment of inertia of the beam element, κ e is the curvature of the beam, ε e is the flexible beam element strain;

[0061] S34. Calculate the total elastic force F of the flexible beam e , whose expression is:

[0062] F e =F p +F q =K p q e +K q q e

[0063] Where, F p and F q are the bending elastic force and the axial tensile elastic force, respectively, and their expressions are:

[0064]

[0065]

[0066] Where K p and K q are the bending stiffness and axial tensile stiffness of the flexible beam, respectively.

[0067] Furthermore, the generalized external force model is established in step S5, which specifically includes the following steps:

[0068] S51. Based on the element shape function of the flexible beam element and the principle of virtual work, the virtual work generated by the generalized distributed gravity is obtained, and its expression is:

[0069]

[0070] Where ρ represents the density of the flexible beam, g represents the acceleration of gravity, S represents the shape function, and q f represents the generalized coordinates of the beam element, l represents the length of the flexible beam, q e represents generalized coordinates;

[0071] S52. Calculate the generalized distributed gravity of the flexible beam element. The expression is:

[0072]

[0073] S53. Calculate the equivalent elastic force of the flexible beam element. The expression is:

[0074] F f =K p q e +Kq q e

[0075] Where K p represents the bending stiffness of the flexible member, K q represents the axial tensile stiffness of the flexible rod;

[0076] S54, consider the impact load F on the end of the high-speed stamping hybrid mechanism i Therefore, the generalized force of the high-speed stamping hybrid mechanism with lubricated clearance considering the impact load is obtained, and its expression is:

[0077] ζ e =g e +F z -F f +F i

[0078] Where, F z It represents the generalized force generated at the clearance of the revolving pair, F i Indicates the impact load value received by the end effector during its stroke.

[0079] The characteristics and beneficial effects of the present invention are:

[0080] The present invention provides a method for dynamic analysis and optimization of a high-speed stamping hybrid mechanism with a lubricated clearance that takes into account impact loads. The rigid-flexible coupling dynamic model with a lubricated clearance that takes into account impact loads, the lubricated clearance of the rotating pair, and the flexible rods can accurately predict the dynamic response characteristics of the high-speed stamping hybrid mechanism in actual working operation. At the same time, the dynamic optimization design method considering impact loads provided by the present invention is used to optimize the structural parameters of the rods in the high-speed stamping hybrid mechanism, which can effectively reduce the adverse effects of the clearance effect of the mechanism during high-speed stamping operation, improve the dynamic performance and dynamic accuracy of the mechanism, and enhance the design accuracy of the overall machine parameters. Considering the impact of impact loads in the design stage can make the high-speed stamping hybrid mechanism more reliable and extend the life of the mechanism. The modeling method and structural parameter optimization method of this dynamic model are applicable to the dynamic response characteristic analysis and optimization design of high-speed stamping mechanisms of other configurations. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 This is a flow chart of the method for dynamic analysis and optimization of a high-speed stamping hybrid mechanism with a lubricating gap considering impact loads according to the present invention;

[0082] Figure 2 It is a schematic diagram of the lubrication gap motion model of the present invention;

[0083] Figure 3 is a schematic diagram of the flexible beam unit model of the present invention;

[0084] Figure 4a ) is a schematic diagram of a seven-bar mechanism according to embodiment 1 of the present invention;

[0085] Figure 4b ) is a schematic diagram of a triangular plate member in a seven-bar mechanism according to Example 1 of the present invention;

[0086] Figure 4c ) is a schematic diagram of a revolute pair in a seven-bar mechanism according to Example 1 of the present invention;

[0087] Figure 5 2 is a comparison diagram of the displacement dynamic response characteristics of Example 1 of the present invention;

[0088] Figure 6 This is a comparison diagram of the speed dynamic response characteristics of Example 1 of the present invention;

[0089] Figure 7 is a comparison diagram of the acceleration dynamic response characteristics of Example 1 of the present invention;

[0090] Figure 8a ) is a comparison diagram of the dynamic response characteristics of the collision force at the lubrication gap A of Example 1 of the present invention;

[0091] Figure 8b ) is a comparison diagram of the dynamic response characteristics of the collision force at the lubrication gap B of Example 1 of the present invention;

[0092] Figure 9a ) is a comparison diagram of the dynamic response characteristics of the actual motion trajectory of the pin shaft at the lubrication gap A in the bearing according to Example 1 of the present invention;

[0093] Figure 9b ) is a comparison diagram of the dynamic response characteristics of the actual motion trajectory of the pin shaft at the lubrication gap B in the bearing according to Example 1 of the present invention;

[0094] Figure 10 4 is a functional relationship diagram between the number of iterations and the fitness value during the optimization process of the seven-bar mechanism of Example 1 of the present invention.

[0095] Main reference numerals: DETAILED DESCRIPTION

[0096] To fully describe the technical content, structural features, objectives and effects of the present invention, the following is a detailed description with reference to the accompanying drawings.

[0097] The present invention provides a dynamic analysis and optimization method for a high-speed stamping hybrid mechanism with a lubricating gap considering impact loads, such as Figure 1 As shown, it includes the following steps:

[0098] S1. Define the structural parameters and design parameters of the high-speed stamping hybrid mechanism;

[0099] S2. Establish a lubrication clearance motion model for the high-speed stamping hybrid mechanism, and calculate the contact force and oil film bearing capacity at the clearance of the rotating pair elements respectively based on the contact force model between the rotating pair elements and the oil film bearing capacity model.

[0100] S3. Introduce a flexible beam element model into the system using the absolute coordinate point method.

[0101] S4. According to the lubrication clearance motion model, judge the relative motion state between the bearing and the shaft at the rotating pair elements, and conduct a mechanical analysis, which specifically includes the following steps:

[0102] S41. When e < r, the bearing and the pin shaft are not in contact, and the acting force is the oil film bearing capacity. Then establish an oil film bearing capacity model and solve the oil film bearing capacity at the clearance of the rotating pair.

[0103] S42. When e > r + e0, the bearing and the pin shaft are in a dry friction contact and collision state, and the acting force is the contact collision force. Then establish a contact force model between the rotating pair elements and solve the contact collision force between the rotating pair elements.

[0104] S43. When r < e < r + e0, the bearing and the pin shaft are in a transition state, and the acting force is a mixed force of the oil film bearing capacity and the contact collision force. Then solve the mixed force of the oil film bearing capacity and the contact collision force, and its expression is:

[0105]

[0106] In the formula, F l represents the contact collision force, F d represents the oil film bearing capacity, e represents the eccentricity value of the pin shaft relative to the bearing, r represents the clearance value between the bearing and the pin shaft, and e0 represents the eccentricity coefficient.

[0107] S5. Calculate the mass matrix, Jacobian matrix and generalized external force matrix of the system, and establish a rigid-flexible coupling dynamic equation for the mechanism with lubrication clearance considering the impact load, and its expression is;

[0108]

[0109] In the formula, Φ q represents the Jacobian matrix form of the constraint equation, represents the generalized acceleration vector, τ represents the right side of the acceleration constraint equation, M le represents the mass matrix, λ represents the Lagrange multiplier, ζ le represents the generalized external force matrix, γ and η represent the default parameters, and τ represents the product of the generalized acceleration vector and the Jacobian matrix.

[0110] S6. Based on the Baumgarte default stability algorithm, the Runge-Kutta method is used to solve the dynamic equations of the mechanism and obtain the generalized coordinates, generalized velocity, and generalized acceleration;

[0111] S7. Optimize and improve the structural parameters of the high-speed stamping hybrid mechanism under impact load through genetic optimization algorithm;

[0112] S8. The above process is repeated and the solution is iterated until the final solution time is reached, thereby completing the dynamic optimization analysis of the high-speed stamping hybrid mechanism under impact load.

[0113] like Figure 2 As shown in the figure, the lubrication clearance motion model of the high-speed stamping hybrid mechanism is established. The relative position relationship between the rotating sub-axis and the bearing under lubrication state is shown in the figure. Figure 3 As shown in Figure 2. In the figure, i and j represent the bearing and pin of the rotating pair respectively, with lubricant between them.

[0114] The eccentric vector between the bearing and the pin is expressed as:

[0115] e=r i A -r j A

[0116] Where r i A Indicates the distance from the origin of the coordinate system to the center of the bearing, r j A Indicates the distance from the origin of the coordinate system to the center of the pin;

[0117] The eccentricity is the degree of center deviation between the bearing and the pin, and its expression is:

[0118]

[0119] In the formula, r represents the gap value, where r = R i -R j , R i 、R j Respectively represent the radius size of the bearing and shaft;

[0120] The offset angle is the angle between the eccentric vector and the positive direction of the x-axis, and its expression is:

[0121]

[0122] Where, e x represents the projection of the eccentric vector e on the x-axis, e y represents the projection of the eccentric vector e in the y-axis direction;

[0123] The unit vector n can be expressed as:

[0124]

[0125] The collision depth between the shaft and the bearing is expressed as:

[0126] δ=er

[0127] When δ≥0, the shaft and bearing contact and generate collision force. When δ<0, the shaft and bearing are in a separated state and no collision force is generated.

[0128] In a preferred embodiment, the contact force model between the revolving pair elements is established in step S2, which specifically includes the following steps:

[0129] S211. The Lancarani-Nikravesh model is used to calculate the normal collision force between the elements of each rotation pair. The expression is:

[0130]

[0131] Where, Indicates the relative contact speed between the rotating pairs, δ n represents the embedding depth between the shaft and the bearing, K represents the stiffness coefficient, and D represents the damping coefficient. Their expressions are:

[0132]

[0133]

[0134] Where R i Indicates the curvature radius of the bearing at the collision contact point; R j Indicates the curvature radius of the pin at the collision contact point; δ i represents the shear modulus of the bearing, δ j represents the shear modulus of the pin, v represents Poisson's ratio; E represents elastic modulus; represents the initial contact velocity; c δ represents the coefficient of restitution;

[0135] S212. The tangential friction force between rotating pair elements is calculated using the modified Coulomb friction model. Compared with the traditional friction model, this model adds a dynamic correction coefficient, which can more accurately describe the friction characteristics at low speeds and is more consistent with actual conditions. Its expression is:

[0136]

[0137] Where c f represents the coefficient of kinetic friction, cn represents the dynamic correction coefficient, v t Indicates the speed value at time t, F n Indicates positive pressure;

[0138] S213. Calculate the contact force between the elements of the revolving pair. The expression is:

[0139] F d =F n n+F t t

[0140] Where n represents the normal unit vector, and t represents the tangential unit vector;

[0141] In a preferred embodiment, the oil film bearing capacity model between the rotating pair elements is established in step S2, which specifically includes the following steps:

[0142] S221, Based on the Gümbel boundary condition, assuming the same fluid temperature, viscosity and density, when the radial velocity between the pin and the bearing in the lubrication gap is The normal oil film bearing capacity and tangential oil film bearing capacity between each rotating pair element are expressed as follows:

[0143]

[0144] When the radial velocity between the pin and the bearing in the lubrication gap The normal oil film bearing capacity and tangential oil film bearing capacity between each rotating pair element are expressed as follows:

[0145]

[0146] Where L is the bearing width, η is the deflection angle, and ε is the eccentricity. represents the first-order derivative of the eccentricity ε with respect to time, represents the deflection angle, Indicates the deflection angle The first derivative with respect to time, μ l represents the dynamic viscosity of the lubricant, ω represents the relative angular velocity; r represents the clearance between the bearing and the pin, where r = R i -R j ; R q represents the radius of the pin; k represents the definition parameter, which can be expressed as

[0147]

[0148] S222. Determine whether the eccentricity ε between the bearing and the pin is close to zero. If the eccentricity ε between the bearing and the pin is close to zero, then the oil film bearing capacity can be obtained by introducing the correction coefficient m, which is expressed as follows:

[0149]

[0150] Where, ε0 represents the correction interval;

[0151] S223. Obtain the component of the oil film bearing capacity at the gap of each rotating pair element on each axis, and its expression is:

[0152]

[0153] When the oil film bearing capacity at the gap between the rotating pair elements is less than the force between the elements, the oil film formed by the lubricant will fail, and the rotating pair elements will be in a contact and collision state. For the transition between the dry friction state and the lubricated state, the eccentricity coefficient e0 is introduced to improve the force model at the gap between the rotating pair elements. Its expression is:

[0154]

[0155] Where, e represents the eccentricity between the bearing and the pin, and e0 represents the eccentricity coefficient.

[0156] like Figure 3 As shown, in step S3, a flexible beam unit model is established, which specifically includes the following steps:

[0157] S31. Define the generalized coordinates of the flexible beam, which are expressed as:

[0158]

[0159] Where, (r ax r ay )、(r bx r by ) represent the position vectors of nodes a and b respectively, denote the slope vectors of nodes a and b respectively;

[0160] S32. Establish the mass matrix of the flexible beam, which is expressed as:

[0161] M e =∫ V ρS T SdV

[0162] Where ρ and V represent the density and volume of the flexible beam, respectively, S is the shape function, and S T is the transposed matrix of the shape function, where the shape function expression is:

[0163] S=[S1I,S2I,S3I,S41I]

[0164] Where, in, l is the length of the flexible beam, x represents the mapping of the flexible beam in the x-axis direction, and I is the unit matrix;

[0165] S33. Calculate the total strain energy ψ of the flexible beam element e , whose expression is:

[0166] ψ e =ψ p +ψ q

[0167] Where, ψ p , ψ q are the bending strain energy and axial strain energy of the flexible beam element, respectively, and their expressions are:

[0168]

[0169] Where B e is the cross-sectional area of ​​the flexible beam element, E e and I e is the Young's modulus and section moment of inertia of the beam element, κ e is the curvature of the beam, ε e is the flexible beam element strain, and its expression is:

[0170]

[0171] During the operation of the mechanism, the deformation of the flexible beam is small, so the beam element strain can be simplified as:

[0172]

[0173] S34. Calculate the total elastic force F of the flexible beam e , whose expression is:

[0174] F e =F p +F q =K p q e +K q q e

[0175] Where, F p and F q are the bending elastic force and the axial tensile elastic force, respectively, and their expressions are:

[0176]

[0177] Where K p and K q are the bending stiffness and axial tensile stiffness of the flexible beam, respectively.

[0178] In a preferred embodiment, the generalized external force model is established in step S5, which specifically includes the following steps:

[0179] S51. Based on the element shape function of the flexible beam element and the principle of virtual work, the virtual work generated by the generalized distributed gravity is obtained, and its expression is:

[0180]

[0181] Where ρ represents the density of the flexible beam, g represents the acceleration of gravity, S represents the shape function, and q f represents the generalized coordinates of the beam element, l represents the length of the flexible beam, q e represents generalized coordinates;

[0182] S52. Calculate the generalized distributed gravity of the flexible beam element. The expression is:

[0183]

[0184] S53. Calculate the equivalent elastic force of the flexible beam element. The expression is:

[0185] F f =K p q e +K q q e

[0186] Where K p represents the bending stiffness of the flexible member, K q represents the axial tensile stiffness of the flexible rod;

[0187] S54, consider the impact load F on the end of the high-speed stamping hybrid mechanism i Therefore, the generalized force of the high-speed stamping hybrid mechanism with lubricated clearance considering the impact load is obtained, and its expression is:

[0188] ζ e =g e +F z -F f +F i

[0189] Where, F z It represents the generalized force generated at the clearance of the revolving pair, F i Indicates the impact load value received by the end effector during its stroke.

[0190] Example 1

[0191] Figure 4 shows a simplified diagram of a high-speed stamping seven-bar linkage with lubricated clearance, taking into account the elasticity of the rods. In this mechanism, L2 and L7 are driving rods, L3 and L5 are connecting rods, L4 is a triangular plate member, and S6 is the end slider. Considering the gap between the two revolute pairs (A and B), the end slider S6 is subject to impact loads. Furthermore, simulation analysis shows that during the operation of the mechanism, rods L3 and L5 are subject to significant forces due to factors such as the gap collision force and the impact load on the slider. Therefore, the elasticity of these two rods was taken into account to more realistically reflect the dynamic response characteristics of the mechanism.

[0192] The generalized coordinates of each component in the mechanism can be expressed as:

[0193] q lri =(x ri y ri θ ri ) T (i=2,…,7)

[0194] Because the calculation of the elasticity of the rod is more complicated, other rods are treated as rigid rods. The generalized coordinates of each rod can be expressed as follows:

[0195]

[0196] Therefore, the generalized coordinates of the high-speed stamping seven-bar linkage with lubrication clearance are:

[0197] q le =(q lr2 q le3 q lr4 q le5 q lr6 q lr7 ) T

[0198] The kinematic constraints of this mechanism can be established based on the generalized coordinates of each component. In this mechanism, two revolute pairs (A and B) with clearances are considered. Due to the presence of clearances, the constraints between the connecting rods must be replaced with contact force constraints between the shaft and the bearing. Furthermore, this two-degree-of-freedom mechanism requires two actuators to achieve defined motion. Therefore, the constraint equations for the rigid-flexible coupling mechanism with dual lubrication clearances are as follows:

[0199]

[0200] The velocity constraint equation can be obtained by taking the first-order derivative with respect to time and using the Jacobian matrix.

[0201]

[0202] Where, Φ q Represents the Jacobian matrix form of the constraint equation, represents the generalized velocity vector, Φ t represents the time partial derivative of the Jacobian matrix, and υ represents the right side of the velocity constraint equation.

[0203] The above Jacobian matrix can be used to obtain the acceleration constraint equation by taking the second-order derivative with respect to time.

[0204]

[0205] Where, represents the generalized acceleration vector, and τ represents the right side of the acceleration constraint equation.

[0206] Introducing Lagrange multipliers in solving constraint equations can simplify the solution process. The formula is as follows:

[0207]

[0208] Where M le represents the mass matrix, λ represents the Lagrange multiplier, ζ le represents the generalized external force matrix.

[0209] During operation, the mechanism is subject to gravity, forces acting on the lubrication gap of the revolving pair, elastic forces generated by the flexible beam, and impact loads on the end slider. In this study, the impact load values ​​were measured using a high-precision pressure sensor.

[0210] Therefore, the generalized force of the rigid-flexible coupling dynamic model of the rotating pair lubrication clearance mechanism considering the impact load is:

[0211] ζ le =g e +F r -F e +F li

[0212] Where g e is the gravity acting on the mechanism, F r is the force generated by the lubrication gap, F e is the elastic force generated by the flexible rod, F li It is the impact load force on the end slider, measured by a high-precision pressure sensor test.

[0213] Therefore, the dynamic equation of the mechanism can be expressed as:

[0214]

[0215] During the solution process, the violation of constraint conditions may lead to numerical instability in the system. Here, the violation stabilization algorithm proposed by Baumgarte is introduced, and the violation parameters (γ, η) are introduced into the above equations. In summary, the dynamic equations of the mechanism are as follows:

[0216]

[0217] Where, Φ q Represents the Jacobian matrix form of the constraint equation, represents the generalized acceleration vector, τ represents the right side of the acceleration constraint equation, M le represents the mass matrix, λ represents the Lagrange multiplier, ζ le represents the generalized external force matrix, γ and η represent the default parameters, and τ represents the product of the generalized acceleration vector and the Jacobian matrix.

[0218] The geometric parameters of the high-speed stamping seven-bar linkage with lubricated clearance are shown in Table 1.

[0219] Table 1 Component parameters of each component of the mechanism

[0220]

[0221] The design parameters of the high-speed stamping seven-bar linkage with lubrication clearance are shown in Table 2.

[0222] Table 2 Design parameters of the mechanism

[0223]

[0224]

[0225] The simulation parameters of the high-speed stamping seven-bar linkage with lubricated clearance considering the elasticity of the rods are shown in Table 3.

[0226] Table 3. Simulation parameters of rods considering elasticity

[0227]

[0228] The pressure test peak values ​​of the seven-bar linkage with lubrication clearance under different conditions are shown in Table 4.

[0229] Table 4 Pressure test peak values ​​under different conditions

[0230]

[0231] In Table 4, the case conditions are that the gap value is 0.2 mm, the driving speed is 2πrad / s, and the impact position is 40 mm from the bottom dead center.

[0232] The simulation parameters of the lubrication clearance of the high-speed stamping seven-bar linkage with lubrication clearance are shown in Table 5.

[0233] Table 5 Lubrication gap simulation parameters

[0234]

[0235] This embodiment takes into account the elasticity of the two rods L3 and L5, the existence of the same clearance at the revolute pair A and B, and lubrication. The clearance value parameter is selected as 0.2mm, the drive speed is set to 2πrad / s, the dynamic viscosity of the lubricant is set to 100mPa·s, and the impact load is set to occur at a position 40mm from the bottom dead center of the slider. At this time, the impact load value is 284.0N. Figure 5 As shown in , when the end effector is subjected to impact load, the displacement response curves are basically consistent; Figure 6 As shown in the figure, the speed response curve shows a large fluctuation between 0.357s and 0.384s, with the maximum fluctuation value being 1.419m / s. Figure 7 As shown in the graph, the acceleration response of the end effector fluctuates greatly between 0.354s and 0.388s, and the maximum acceleration is 4202.050m / s 2 , and gradually converged in the following period of time.

[0236] like Figure 8a ), for the force response between the elements at the revolute pair A, the comparison results have roughly the same trend. However, after the impact load, the force response has a large fluctuation, with the maximum value being 97.293N. Figure 8b ), for the force response between the elements at the rotating pair B, the comparison results have the same trend. However, after the impact load, the force response has a large fluctuation, and its maximum value is 292.219N. Figure 9a )and Figure 9b ), the degree of chaos for the axial motion trajectories of kinematic pairs A and B is not significantly different. In summary, while impact loads have little effect on the displacement response of the mechanism, they can cause abrupt changes in the velocity and acceleration responses within a short period of time, increasing the instability of the mechanism's dynamic response. Impact loads can also exacerbate collisions between elements of revolving pairs containing clearances, increasing the instability of the mechanism's operation.

[0237] Since the motor directly drives rods L2 and L7 to operate the mechanism, and the revolving clearances A and B are located between rods L2 and L3 and between rods L7 and L4, respectively, the collision force at the clearances directly affects rods L2 and L7. Slider S6, as the end effector, directly affects the kinematic characteristics of the entire mechanism. Therefore, the structural parameters of rods L2, L7, and S6 were optimized. The dynamic viscosity of the lubricant in the revolving clearances was also optimized. Figure 10 The figure shows the functional relationship between the number of iterations and the fitness value during the optimization process using the genetic optimization algorithm. The mass and moment of inertia of the component are important factors in determining the mass distribution of the component. Therefore, the mass and moment of inertia of rods L2 and L7, the mass of the slider, and the dynamic viscosity of the lubricating oil are used as the optimization design variables. The design variables are expressed as follows:

[0238] X c =(m2,J2,m7,J7,m6,μ) T

[0239] =(x (1) ,x (2) ,x (3) ,x (4) ,x (5) ,x (6) ,x (7) ) T

[0240] When the seven-link press mechanism with lubricating clearance has both revolving pair clearance A and revolving pair clearance B, the constraints of the dynamic optimization model can be expressed as

[0241]

[0242] Where, and are the upper and lower bounds for the optimization design variables.

[0243] and The value range of is shown in the table. The lower limit of the component mass is half of the initial mass, and the upper limit of the component mass is twice the initial mass. The lower limit of the moment of inertia assumes that the axis of rotation passes through the center of mass of the rod, and the upper limit of the moment of inertia assumes that the axis of rotation passes through the end point of the rod.

[0244] Table 6 and The value range of

[0245]

[0246] The slider is the end effector of the press mechanism, and its kinematic characteristics are of great research significance. Acceleration is the bridge connecting the kinematics and dynamics of the mechanism and is closely related to the force of the system. At the same time, the peak value of the slider acceleration increases due to the gap, and the vibration is intensified. Therefore, optimizing the slider acceleration is of great practical significance. Taking the minimum maximum value of the end effector slider acceleration as the objective function of the optimization design, the specific expression can be expressed as

[0247] F o =||a H || ∞

[0248] Where a H is the slider acceleration.

[0249] Ultimately, after several iterations of the genetic optimization algorithm, the optimal solution for structural parameter optimization was obtained: m2 = 0.1412, J2 = 0.0002073, m7 = 0.1596, J7 = 0.0001886, m6 = 0.19039, and μ = 0.21535. The optimal value of the objective function was 1.1047. This structural parameter optimization improved the mechanism's operating accuracy and its ability to withstand external impact loads.

[0250] The present invention provides a method for dynamic analysis and optimization of a high-speed stamping hybrid mechanism with a lubricated gap that takes into account impact loads. The rigid-flexible coupling dynamic model with a lubricated gap that takes into account impact loads, the lubricated gap of the rotating pair, and the flexible rod is established to accurately predict the dynamic response characteristics of the high-speed stamping hybrid mechanism in actual working operation. According to Example 1, since the drive shaft is the component that the motor directly drives the mechanism to operate, and the end effector is the component that directly bears the external impact load during the operation of the mechanism, optimizing the structural parameters of the two through a genetic optimization algorithm can effectively reduce the adverse effects of the gap effect of the mechanism during high-speed stamping operation, improve the dynamic performance and dynamic accuracy of the mechanism, and improve the design accuracy of the parameters of the entire machine. Considering the impact of impact loads in the design stage can make the high-speed stamping hybrid mechanism more reliable and extend the life of the mechanism. The modeling method and structural parameter optimization method of this dynamic model are applicable to the dynamic response characteristic analysis and optimization design of high-speed stamping mechanisms of other configurations.

[0251] The above embodiments are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A dynamic analysis and optimization method for a high-speed stamping hybrid mechanism with a lubricated gap considering impact loads, characterized in that: It includes the following steps: S1. Define the structural parameters and design parameters of the high-speed stamping hybrid mechanism; S2. Establish a lubrication clearance motion model for the high-speed stamping hybrid mechanism, and calculate the contact force and oil film bearing capacity at the clearance of the rotating pair elements respectively based on the contact force model between the rotating pair elements and the oil film bearing capacity model; S3. Introduce a flexible beam element model into the system using the absolute coordinate point method; S4. According to the lubrication clearance motion model, judge the relative motion state between the bearing and the shaft at the rotating pair elements, and conduct a mechanical analysis, which specifically includes the following steps: S41. When e < r, the bearing and the pin shaft are not in contact, and the acting force is the oil film bearing capacity. Then establish an oil film bearing capacity model and solve the oil film bearing capacity at the clearance of the rotating pair; S42. When e > r + e0, the bearing and the pin shaft are in a dry friction contact and collision state, and the acting force is the contact collision force. Then establish a contact force model between the rotating pair elements and solve the contact collision force between the rotating pair elements; S43. When r < e < r + e0, the bearing and the pin shaft are in a transition state, and the acting force is a combined force of the oil film bearing capacity and the contact collision force. Then solve the combined force of the oil film bearing capacity and the contact collision force, and its expression is: Where, F l Represents the contact collision force, F d represents the oil film bearing capacity, e represents the eccentricity of the pin relative to the bearing, r represents the clearance between the bearing and the pin, and e0 represents the eccentricity coefficient; S5. Calculate the mass matrix, Jacobian matrix and generalized external force matrix of the system, and establish a rigid-flexible coupling dynamic equation of the mechanism with lubrication clearance considering the impact load, and its expression is; Where, Φ q Represents the Jacobian matrix form of the constraint equation, represents the generalized acceleration vector, τ represents the right side of the acceleration constraint equation, M le represents the mass matrix, λ represents the Lagrange multiplier, ζ le represents the generalized external force matrix, γ and η represent the default parameters, and τ represents the product of the generalized acceleration vector and the Jacobian matrix; S6. Based on the Baumgarte constraint stabilization algorithm, use the Runge-Kutta method to solve the dynamic equation of the mechanism, and obtain the generalized coordinates, generalized velocities and generalized accelerations; S7. Through the genetic optimization algorithm, optimize and improve the structural parameters of the high-speed stamping hybrid mechanism under the impact load; S8. Cycle the above process and perform iterative solution until the final solution time is reached. Thus, the dynamic optimization analysis of the high-speed stamping hybrid mechanism under the impact load is completed.

2. The dynamic analysis and optimization method of a high-speed stamping hybrid mechanism with lubrication clearance considering impact load according to claim 1 is characterized in that: In step S2, establishing the contact force model between the rotating pair elements specifically includes the following steps: S211. Use the Lancarani-Nikravesh model to calculate the normal collision force between each rotating pair element, and its expression is: Where, Indicates the relative contact speed between the rotating pairs, δ n represents the embedding depth between the shaft and the bearing, K represents the stiffness coefficient, and D represents the damping coefficient. Their expressions are: Where R i Indicates the curvature radius of the bearing at the collision contact point; R j Indicates the curvature radius of the pin at the collision contact point; δ i represents the shear modulus of the bearing, δ j represents the shear modulus of the pin, v represents Poisson's ratio; E represents elastic modulus; represents the initial contact velocity; c δ represents the coefficient of restitution; S212. Use the modified Coulomb friction model to calculate the tangential friction force between the rotating pair elements, and its expression is: Where c f represents the coefficient of kinetic friction, c n represents the dynamic correction coefficient, v t Indicates the speed value at time t, F n Indicates positive pressure; S213. Calculate the contact resultant force between the rotating pair elements, and its expression is: F d =F n n+F t t In the formula, n represents the normal unit vector, and t represents the tangential unit vector.

3. The dynamic analysis and optimization method of a high-speed stamping hybrid mechanism with lubrication clearance considering impact load according to claim 2 is characterized in that: In step S2, establishing the oil film bearing capacity model between the rotating pair elements specifically includes the following steps: S221, Based on the Gümbel boundary condition, assuming the same fluid temperature, viscosity and density, when the radial velocity between the pin and the bearing in the lubrication gap is The normal oil film bearing capacity and tangential oil film bearing capacity between each rotating pair element are expressed as follows: When the radial velocity between the pin and the bearing in the lubrication gap The normal oil film bearing capacity and tangential oil film bearing capacity between each rotating pair element are expressed as follows: Where L is the bearing width, η is the deflection angle, and ε is the eccentricity. represents the first-order derivative of the eccentricity ε with respect to time, represents the deflection angle, Indicates the deflection angle The first derivative with respect to time, μ l represents the dynamic viscosity of the lubricant, ω represents the relative angular velocity; r represents the clearance between the bearing and the pin, where r = R i -R j ; R q represents the radius of the pin; k represents the definition parameter, where S222. Judge whether the eccentricity ε between the bearing and the pin shaft tends to zero. If the eccentricity ε between the bearing and the pin shaft tends to zero, then introduce a correction coefficient m to obtain the oil film bearing capacity, and its expression is: In the formula, ε0 represents the correction interval; S223. Obtain the components of the oil film bearing capacity at the clearance of each rotating pair element on each axis, and its expression is: When the bearing capacity of the oil film at the gap between the rotating pair elements is less than the force between the elements, the oil film formed by the lubricant will fail, and the rotating pair elements are in a contact collision state. For the transition between the dry friction state and the lubricated state, the eccentricity coefficient e0 is introduced to improve the force model at the gap between the rotating pair elements, and its expression is: Where, e represents the eccentricity between the bearing and the pin, and e0 represents the eccentricity coefficient.

4. The dynamic analysis and optimization method of a high-speed stamping hybrid mechanism with lubrication clearance considering impact load according to claim 1 is characterized in that: The flexible beam unit model is established in step S3, which specifically includes the following steps: S31. Define the generalized coordinates of the flexible beam, which are expressed as: Where, (r ax r ay )、(r bx r by ) represent the position vectors of nodes a and b respectively, denote the slope vectors of nodes a and b respectively; S32. Establish the mass matrix of the flexible beam, which is expressed as: M e =∫ V ρS T SDV Where ρ and V represent the density and volume of the flexible beam, respectively, S is the shape function, and S T is the transposed matrix of the shape function, where the shape function expression is: S=[S1I,S2I,S3I,S41I] Where, in, l is the length of the flexible beam, x represents the mapping of the flexible beam in the x-axis direction, and I is the unit matrix; S33. Calculate the total strain energy ψ of the flexible beam element e , whose expression is: ψ e =ψ p +ψ q Where, ψ p , ψ q are the bending strain energy and axial strain energy of the flexible beam element, respectively, and their expressions are: Where B e is the cross-sectional area of ​​the flexible beam element, E e and I e is the Young's modulus and section moment of inertia of the beam element, κ e is the curvature of the beam, ε e is the flexible beam element strain; S34. Calculate the total elastic force F of the flexible beam e , whose expression is: F e =F p +F q =K p q e +K q q e Where, F p and F q are the bending elastic force and the axial tensile elastic force, respectively, and their expressions are: Where K p and K q are the bending stiffness and axial tensile stiffness of the flexible beam, respectively.

5. The dynamic analysis and optimization method of a high-speed stamping hybrid mechanism with lubrication clearance considering impact load according to claim 1 is characterized in that: The generalized external force model is established in step S5, which specifically includes the following steps: S51. Based on the element shape function of the flexible beam element and the principle of virtual work, the virtual work generated by the generalized distributed gravity is obtained, and its expression is: Where ρ represents the density of the flexible beam, g represents the acceleration of gravity, S represents the shape function, and q f represents the generalized coordinates of the beam element, l represents the length of the flexible beam, q e represents generalized coordinates; S52. Calculate the generalized distributed gravity of the flexible beam element. The expression is: S53. Calculate the equivalent elastic force of the flexible beam element. The expression is: F f =K p q e +K q q e Where K p represents the bending stiffness of the flexible member, K q represents the axial tensile stiffness of the flexible rod; S54, consider the impact load F on the end of the high-speed stamping hybrid mechanism i Therefore, the generalized force of the high-speed stamping hybrid mechanism with lubricated clearance considering the impact load is obtained, and its expression is: ζ e =g e +F z -F f +F i Where, F z It represents the generalized force generated at the clearance of the revolving pair, F i Indicates the impact load value received by the end effector during its stroke.

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