Dynamic analysis optimization method for high-speed stamping hybrid mechanism with lubricating gap considering impact load

Abstract

The invention relates to a dynamic analysis optimization method for a high-speed stamping hybrid mechanism with a lubricating gap and considering an impact load. The dynamic analysis optimization method comprises the following steps: S1, defining structural parameters and design parameters; s2, establishing a lubrication gap motion model, a contact force model and an oil film bearing force model; s3, introducing a flexible beam unit model; s4, the relative motion state of the bearing and the shaft at the revolute pair element is judged; s5, establishing a kinetic equation; s6, solving the kinetic equation; s7, optimizing and improving the structural parameters of the mechanism; and S8, circulating the above process, and carrying out iterative solution until the kinetic analysis and parameter optimization are completed. The established rigid-flexible coupling kinetic equation containing the lubricating gap can more accurately predict the mechanism dynamic response characteristics of the high-speed stamping hybrid mechanism when the high-speed stamping hybrid mechanism is subjected to the impact load in actual work and operation, and the modeling method is suitable for dynamic response characteristic analysis and optimization design of high-speed stamping mechanisms of other configurations. The method has the advantages of wide applicability and the like.

Description

Technical Field

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

[0002] As a "less cutting" efficient machine tool, multi-link ultra-precision servo press meets the requirements of clean and green production and is widely used in automobile manufacturing, aerospace and other fields. Under the forming condition of multi-link ultra-precision servo press, the punching pressure and inertia force will cause elastic vibration deformation of the transmission system, seriously damaging the dimensional accuracy of the closing height between the upper and lower molds, and affecting the forming processing accuracy of the stamped parts; at the same time, due to the clearance and wear effect of the kinematic pair of the mechanism, it is easy to cause the separation and collision of the kinematic pair elements, which can lead to chaos and uncertainty in the movement of the end-executing slider, significantly reducing the accuracy of the relative position of the mold and the plate in the stamping process, and sharply increasing the size and geometric error of the workpiece. 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, and analyze the influence law of the dynamic error of the multi-link mechanism, so as to realize the multi-objective optimization design of the clearance size of the mechanism and break through the technical bottleneck of multi-link ultra-precision. Summary of the invention

[0003] In view of 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, which solves the problem of multiple losses 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, and 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 lubrication gap considering impact loads, which comprises 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, and calculate the contact force and oil film bearing capacity at the gap of the rotating pair elements based on the contact force model between the rotating pair elements and the oil film bearing capacity model respectively;

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

[0008] S4. According to the lubrication clearance motion model, the relative motion state of the bearing and the shaft at the rotating pair element is determined, and a mechanical analysis is performed, which specifically includes 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, an oil film bearing capacity model is established, and the oil film bearing capacity at the rotational pair clearance is solved.

[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, a contact force model between the rotational pair elements is established, and the contact and collision force between the rotational pair elements is solved.

[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, the combined force of the oil film bearing capacity and the contact and collision force is solved, 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 the rigid-flexible coupling dynamic equation of the mechanism with lubrication clearance considering the impact load. 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. Repeat 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 contact force model between the revolving pair elements is established in step S2, which specifically includes the following steps:

[0021] S211. The Lancarani-Nikravesh model is used to calculate the normal collision force between the rotational pair elements, and its expression is:

[0022]

[0023] In the formula, represents 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] In the formula, R i Indicates the radius of curvature of the bearing at the collision contact point; R j Indicates the radius of curvature 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 elements of the revolving pair is calculated using the modified Coulomb friction model, and its expression is:

[0027]

[0028] In the formula, c f represents the coefficient of kinetic friction, c n represents the dynamic correction coefficient, v t represents the velocity 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] In the formula, 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 at the lubrication gap The normal oil film bearing capacity and tangential oil film bearing capacity between each rotational pair element are expressed as:

[0034]

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

[0036]

[0037] In the formula, L represents the bearing width, η represents the deflection angle, ε represents the eccentricity, represents the first-order derivative of the eccentricity ε with respect to time, represents the deflection angle, 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 value 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, the oil film bearing capacity can be obtained by introducing the correction coefficient m, and its expression is:

[0040]

[0041] In the formula, 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 of 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 lubrication state, the eccentricity coefficient e0 is introduced to improve the force model at the gap of the rotating pair elements, and its expression is:

[0045]

[0046] In the formula, 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 is expressed as:

[0049]

[0050] In the formula, (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 S V

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

[0059]

[0060] In the formula, B e is the cross-sectional area of ​​the flexible beam unit, 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] In the formula, F p and F q are bending elastic force and axial tensile elastic force, respectively, and their expressions are:

[0064]

[0065]

[0066] In the formula, 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. According to 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] In the formula, ρ represents the density of the flexible beam, g represents the acceleration due to 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, and its expression is:

[0072]

[0073] S53. Calculate the equivalent elastic force of the flexible beam unit, and its expression is:

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

[0075] In the formula, 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 lubrication gap considering the impact load is obtained, and its expression is:

[0077] ζ e =g e +F z -F f +F i

[0078] In the formula, 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 dynamic analysis and optimization method of a high-speed stamping hybrid mechanism with a lubricated gap considering impact loads provided by the present invention can accurately predict the dynamic response characteristics of the high-speed stamping hybrid mechanism in actual working operation by establishing a rigid-flexible coupling dynamic model with a lubricated gap considering impact loads by considering impact loads, lubricated gaps of rotating pairs and flexible rods. At the same time, the structural parameters of the rods in the high-speed stamping hybrid mechanism are optimized by the dynamic optimization design method considering impact loads provided by the present invention, which 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 whole 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 the dynamic model are suitable for the dynamic response characteristic analysis and optimization design of high-speed stamping mechanisms of other configurations. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 It is a flow chart of the dynamic analysis and optimization method of the high-speed stamping hybrid mechanism with lubrication gap considering the impact load of the present invention;

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

[0083] Figure 3 is a schematic diagram of a 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 Embodiment 1 of the present invention;

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

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

[0088] Figure 6 is a speed dynamic response characteristic comparison diagram 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] Fig.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] In order to fully describe the technical content, structural features, objectives and effects of the present invention, the following will be described in detail 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 lubrication 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 transitional 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:

[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, looping the above process and solving iteratively until the final solution time is reached, thus 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 secondary center shaft and the bearing under lubrication state is shown in Figure 3 As shown. Among them, i and j represent the bearing and pin of the rotating pair respectively, and there is lubricant between the two.

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

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

[0116] In the formula, r i A Represents 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 the 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] In the formula, 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 rotational pair elements, and its expression is:

[0130]

[0131] In the formula, represents 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] In the formula, R i Indicates the radius of curvature of the bearing at the collision contact point; R j Indicates the radius of curvature 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 the 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 in line with the actual situation. Its expression is:

[0136]

[0137] In the formula, c f represents the coefficient of kinetic friction, cn represents the dynamic correction coefficient, v t represents the velocity 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] In the formula, 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 at the lubrication gap The normal oil film bearing capacity and tangential oil film bearing capacity between each rotational pair element are expressed as:

[0143]

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

[0145]

[0146] In the formula, L represents the bearing width, η represents the deflection angle, ε represents the eccentricity, represents the first-order derivative of the eccentricity ε with respect to time, represents the deflection angle, 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 value 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, the oil film bearing capacity can be obtained by introducing the correction coefficient m, and its expression is:

[0149]

[0150] In the formula, 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 of 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 lubrication state, the eccentricity coefficient e0 is introduced to improve the force model at the gap of the rotating pair elements, and its expression is:

[0154]

[0155] In the formula, 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 is expressed as:

[0158]

[0159] In the formula, (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 S V

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

[0168]

[0169] In the formula, B e is the cross-sectional area of ​​the flexible beam unit, 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 unit 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] In the formula, F p and F q are bending elastic force and axial tensile elastic force, respectively, and their expressions are:

[0176]

[0177] In the formula, 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. According to 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] In the formula, ρ represents the density of the flexible beam, g represents the acceleration due to 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, and its expression is:

[0183]

[0184] S53. Calculate the equivalent elastic force of the flexible beam unit, and its expression is:

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

[0186] In the formula, 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 lubrication gap considering the impact load is obtained, and its expression is:

[0188] ζ e =g e +F z -F f +F i

[0189] In the formula, 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] As shown in Figure 4, a schematic diagram of a high-speed stamping seven-bar linkage with lubricated clearance considering the elasticity of the rods is shown. In this mechanism, L2 and L7 are driving rods, L3 and L5 are connecting rods, L4 is a triangular plate component, and S6 is an end slider. Considering the gap between the two revolute pairs (A and B), the end slider S6 is subjected to an impact load. In addition, simulation analysis shows that during the operation of the mechanism, due to factors such as the gap collision force and the impact load suffered by the slider, the forces borne by the two rods L3 and L5 are relatively large. Therefore, the elasticity of the two rods is 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 motion constraint relationship of the mechanism can be established based on the generalized coordinates of each component. In this mechanism, two revolute pairs (A and B) with clearance are considered. Due to the existence of clearance, the constraint relationship between the connecting rods needs to be replaced by the contact force constraint between the shaft and the bearing. In addition, this two-degree-of-freedom mechanism requires two drives to obtain a certain motion. Therefore, the constraint equation of the rigid-flexible coupling mechanism with double lubrication clearance is 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] In the formula, Φ q The Jacobian matrix form of the constraint equation is represented by 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] In the formula, 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 the operation of the mechanism, the mechanism is subject to gravity, the force at the lubrication gap of the rotating pair, the elastic force generated by the flexible beam, and the end slider is subject to impact load. In this study, the impact load value is measured using a high-precision pressure sensor.

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

[0211] ζ le =g e +F r -F e +F li

[0212] In the formula, g e is the gravity 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] In the solution process, the violation of constraint conditions may lead to numerical instability in the system. Here, the violation stability algorithm proposed by Baumgarte is introduced, and the violation parameters (γ, η) are introduced into the above equation. In summary, the dynamic equation of the mechanism is as follows:

[0216]

[0217] In the formula, Φ q The Jacobian matrix form of the constraint equation is represented by 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 lubrication clearance are shown in Table 1.

[0219] Table 1 Component parameters of each part 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 rods of the high-speed stamping seven-bar linkage with lubrication gap considering elasticity 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 high-speed stamping 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 gap at the revolute pair A and B, and lubrication, and selects the gap value parameter as 0.2mm, sets the drive speed to 2πrad / s, the dynamic viscosity of the lubricant to 100m Pa·s, and sets the impact load occurrence position to 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, for the speed response curve, it can be seen that there is a large fluctuation between 0.357s and 0.384s, and the maximum fluctuation value is 1.419m / s; Figure 7 As shown in the figure, 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, but after the impact load, the force response has a large fluctuation, and its maximum value is 97.293N. Figure 8b ), for the force response between the elements at the rotating pair B, the comparison results have the same trend, but after the impact load, the force response has a large fluctuation, and its maximum value is 292.219N. Figure 9a )and Figure 9b ), for the axis motion trajectories of kinematic pair A and kinematic pair B, the degree of chaos is not much different. In summary, the impact load has little effect on the displacement response of the mechanism, but it will cause a sudden change in the velocity and acceleration response in a short period of time, increasing the instability of the mechanism's dynamic response. The impact load will intensify the collision between the elements of the revolving pair with clearance, increasing the instability of the mechanism's operation.

[0237] Since the motor directly drives rod L2 and rod L7 to make the mechanism work, and the clearances A and B of the rotating pair are located between rod L2 and rod L3 and between rod L7 and rod L4 respectively, the collision force at the clearance directly affects rod L2 and rod L7. Slider S6, as the end effector, directly affects the motion characteristics of the entire mechanism. Therefore, the structural parameters of rod L2, rod L7 and S6 are optimized. In addition, the dynamic viscosity of the lubricating oil in the clearance of the rotating pair is optimized. Fig.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 that determine 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 lubrication clearance has both revolving clearance A and revolving clearance B, the constraints of the dynamic optimization model can be expressed as

[0241]

[0242] In the formula, and The upper and lower bounds of 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 rotation axis passes through the center of mass of the rod, and the upper limit of the moment of inertia assumes that the rotation axis passes through the end point of the rod.

[0244] Table 6 and The value range of

[0245]

[0246] As the end effector of the press mechanism, the kinematic characteristics of the slider are of great research significance. Acceleration is the bridge between 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 sharply due to the gap, and the vibration intensifies. Therefore, it is of great practical significance to optimize the acceleration of the slider. Taking the 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] In the formula, a H is the slider acceleration.

[0249] Finally, after several iterations of the genetic optimization algorithm, the best solution for structural parameter optimization was obtained: m2 is 0.1412, J2 is 0.0002073, m7 is 0.1596, J7 is 0.0001886, m6 is 0.19039, and μ is 0.21535. The optimal value of the objective function is 1.1047. Structural parameter optimization improves the working accuracy of the mechanism 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 rods can accurately predict the dynamic response characteristics of the high-speed stamping hybrid mechanism in actual operation. According to Example 1, since the drive shaft is a component that the motor directly drives the mechanism to operate, and the end effector is a 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 whole machine. Considering the impact of the impact load at 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 suitable for the dynamic response characteristic analysis and optimization design of high-speed stamping mechanisms of other configurations.

[0251] The above embodiments are only descriptions of the preferred implementation modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design 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 all fall within the protection scope determined by the claims of the present invention.

Claims

1. A dynamic analysis and optimization method for a high-speed stamping hybrid mechanism with lubrication clearance 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 element, and conduct a mechanical analysis, which specifically includes the following steps: S41. When e < r, the bearing and the pin shaft do not 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 rotating pair clearance; 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 transitional 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: In the formula, 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; In the formula, Φ q The Jacobian matrix form of the constraint equation is represented by 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 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; S7. Through the genetic optimization algorithm, optimize and improve the structural parameters of the high-speed stamping hybrid mechanism under the impact load; S8. Loop the above process, iterate and solve 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 method for dynamic analysis and optimization of a high-speed stamping hybrid mechanism with lubrication clearance considering impact load according to claim 1 is characterized in that: The specific steps for establishing the contact force model between the rotating pair elements in step S2 are as follows: S211. Use the Lancarani-Nikravesh model to calculate the normal collision force between each rotating pair element, and its expression is: In the formula, represents 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: In the formula, R i Indicates the radius of curvature of the bearing at the collision contact point; R j Indicates the radius of curvature 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: In the formula, c f represents the coefficient of kinetic friction, c n represents the dynamic correction coefficient, v t represents the velocity value at time t, F n Indicates positive pressure; S213. Calculate the resultant contact 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 method for dynamic analysis and optimization of a high-speed stamping hybrid mechanism with lubrication clearance considering impact load according to claim 2 is characterized in that: The specific steps for establishing the oil film bearing capacity model between the rotating pair elements in step S2 are as follows: 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 at the lubrication gap The normal oil film bearing capacity and tangential oil film bearing capacity between each rotational pair element are expressed as: When the radial velocity between the pin and the bearing at the lubrication gap The normal oil film bearing capacity and tangential oil film bearing capacity between each rotational pair element are expressed as: In the formula, L represents the bearing width, η represents the deflection angle, ε represents the eccentricity, represents the first-order derivative of the eccentricity ε with respect to time, represents the deflection angle, 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 value 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 oil film bearing capacity at the gap of 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 lubrication state, the eccentricity coefficient e0 is introduced to improve the force model at the gap of the rotating pair elements, and its expression is: In the formula, e represents the eccentricity between the bearing and the pin, and e0 represents the eccentricity coefficient.

4. The method for dynamic analysis and optimization 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 is expressed as: In the formula, (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] In the formula, 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 In the formula, ψ p , q are the bending strain energy and axial strain energy of the flexible beam element, respectively, and their expressions are: In the formula, B e is the cross-sectional area of ​​the flexible beam unit, 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 In the formula, F p and F q are the bending elastic force and the axial tensile elastic force, respectively, and their expressions are: In the formula, K p and K q are the bending stiffness and axial tensile stiffness of the flexible beam, respectively.

5. The method for dynamic analysis and optimization 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. According to 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: In the formula, ρ represents the density of the flexible beam, g represents the acceleration due to 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, and its expression is: S53. Calculate the equivalent elastic force of the flexible beam unit, and its expression is: F f =K p q e +K q q e In the formula, 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 lubrication gap considering the impact load is obtained, and its expression is: ζ e =g e +F z -F f +F i In the formula, 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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