Fatigue reliability topology optimization method for compliant mechanisms considering material uncertainty

Abstract

The present invention provides a topological optimization method for fatigue reliability of a compliant mechanism considering material uncertainty, including describing the relationship between unit elastic modulus and unit density, and filtering the unit density; discretizing the material random field, linearly combining the standard Gaussian random variable and the deterministic eigenmode, and analyzing and calculating the random response of the compliant mechanism; constructing the fatigue constraint of the compliant mechanism, and aggregating the fatigue constraint to construct the fatigue failure limit state function of the compliant mechanism; establishing a double-layer cyclic topological optimization model for fatigue reliability of the compliant mechanism considering material uncertainty; calculating the sensitivity of the limit state function to random variables; using a moving progressive algorithm to update the design variables, using a mixed mean method to find the minimum functional target point, and judging whether the iteration meets the convergence condition, if so, obtaining the topological configuration of the compliant mechanism that meets the fatigue reliability requirements. The present invention enables the obtained compliant mechanism to have better fatigue reliability.

Description

Technical Field

[0001] The present invention relates to the technical field related to the optimization design of compliant mechanisms, and in particular to a fatigue reliability topology optimization method for compliant mechanisms taking material uncertainty into consideration. Background Art

[0002] A compliant mechanism is a mechanism that achieves motion, force transmission and energy conversion through the elastic deformation of flexible components. Compared with traditional rigid connection mechanisms, compliant mechanisms have the advantages of no revolving pairs, no friction, small footprint, integrated processing and high working precision. Based on these advantages, compliant mechanisms are widely used in micro-nano manipulation, precision machining, micro-electromechanical systems and other fields.

[0003] In the existing technology, compliant mechanisms need to withstand reciprocating motion and are prone to fatigue failure. Therefore, the topological optimization design of compliant mechanisms needs to consider fatigue performance. In actual work, parameters such as load size, material properties, and geometric boundaries inevitably have errors and uncertainties, which makes the fatigue performance of compliant mechanisms affected by these uncertain factors. At present, most of the topological optimization design methods of compliant mechanisms considering fatigue performance are based on deterministic conditions, and uncertain factors are likely to cause fatigue failure of the mechanism. Summary of the invention

[0004] Based on this, the purpose of the present invention is to provide a fatigue reliability topology optimization method for a compliant mechanism taking material uncertainty into consideration, so as to solve the deficiencies in the above-mentioned prior art.

[0005] The present invention provides a method for topological optimization of fatigue reliability of a compliant mechanism taking into account material uncertainty, the method comprising:

[0006] Define the design conditions for compliant mechanisms;

[0007] An improved solid isotropic material penalty model is used to describe the relationship between the unit elastic modulus and the unit density in the design condition, and a mapping filtering technology is used to filter the unit density;

[0008] The material random field in the design condition is discretized by using the series optimal linear estimation method, the standard Gaussian random variable and the linear combination of the deterministic eigenmode are used, and the random response of the compliant mechanism is calculated by using the chaotic polynomial expansion method combined with the finite element analysis;

[0009] A modified Goodman fatigue criterion is used to construct fatigue constraints of the compliant mechanism, a Kieisselmeier-Steinhauser function is used to aggregate the fatigue constraints, and a fatigue failure limit state function of the compliant mechanism is constructed;

[0010] Taking the minimization of the volume of the compliant mechanism as the objective function and the fatigue failure probability and output displacement of the compliant mechanism as constraints, a double-layer cyclic topology optimization model of fatigue reliability of the compliant mechanism considering material uncertainty is established;

[0011] Based on the double-layer cyclic topology optimization model of fatigue reliability of the compliant mechanism considering material uncertainty, the sensitivity of the volume, output displacement and fatigue constraint of the compliant mechanism to the design variables is solved, and the sensitivity of the limit state function to the random variables is calculated;

[0012] The design variables are updated using a moving progressive algorithm, a mixed mean method is used to find the minimum functional target point, and it is determined whether the moving progressive algorithm meets the convergence condition. If so, a compliant mechanism topology configuration that meets the fatigue reliability requirements is obtained.

[0013] Compared with the prior art, the beneficial effects of the present invention are: by describing the relationship between the unit elastic modulus and the unit density, by calculating the random response of the compliant mechanism and constructing the fatigue failure limit state function of the compliant mechanism, and by using the fatigue failure probability and the output displacement as constraints, a double-layer cyclic topological optimization model of the fatigue reliability of the compliant mechanism considering material uncertainty is established, and by updating the design variables and judging whether the iteration meets the convergence conditions, the optimal topological configuration of the compliant mechanism can be obtained, and the compliant mechanism has better fatigue reliability.

[0014] Furthermore, the design conditions include design domain, constraint boundary conditions, load size, setting initial values ​​of design variables, virtual spring stiffness at the input end, virtual spring stiffness at the output end, elastic modulus of the material, Poisson's ratio of the material, tensile strength coefficient, fatigue strength coefficient, mean of the random field and standard deviation of the random field.

[0015] Furthermore, the step of using an improved solid isotropic material penalty model to describe the relationship between the unit elastic modulus and the unit density in the design condition, and using a mapping filtering technology to filter the unit density includes:

[0016] An improved solid isotropic material penalty model is used to describe the interpolation relationship between element elastic modulus and element density.

[0017] Based on the density filtering technology, the cell density field is filtered by calculating the weighted average of the densities of the adjacent cells;

[0018] The smooth Heaviside mapping function is used to correct the filtered cell density so that the cell density variables are concentrated at the preset two ends.

[0019] Furthermore, the step of using the series optimal linear estimation method to discretize the material random field in the design condition, linearly combining the standard Gaussian random variable and the deterministic eigenmode, and using the chaotic polynomial expansion method combined with finite element analysis to calculate the random response of the compliant mechanism includes:

[0020] Using the series optimal linear estimation method to discretize the unit nodes of the material random field in the design condition;

[0021] Performing dimensionality reduction on the truncated reduction random problem of the material random field and performing linear combinations of the standard Gaussian random variables and deterministic eigenmodes;

[0022] The random response of the compliant mechanism is calculated by combining the chaotic polynomial expansion method with the quasi-static analysis method.

[0023] Furthermore, the steps of constructing the fatigue constraint of the compliant mechanism by using the modified Goodman fatigue criterion, aggregating the fatigue constraint by using the Kieisselmeier-Steinhauser function, and constructing the fatigue failure limit state function of the compliant mechanism include:

[0024] Calculating a signed von Mises equivalent stress based on the random response and constructing several fatigue stress constraints of the compliant mechanism using a modified Goodman fatigue criterion;

[0025] A plurality of fatigue stress constraints are condensed using a Kieisselmeier-Steinhauser function to obtain a condensed stress constraint, and a fatigue constraint metric of the Kieisselmeier-Steinhauser function is modified;

[0026] A fatigue failure limit state function of the compliant mechanism is constructed based on the cohesive stress constraint, and a fatigue reliability index is calculated using a functional metric method.

[0027] Furthermore, the expression of the double-layer cycle topology optimization model for fatigue reliability of the compliant mechanism considering material uncertainty is:

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] ;

[0035] In the formula, Represents the optimized volume, represents the cell density vector array, represents the unit volume filled with material, represents a vector of standard Gaussian distributed random variables, represents the virtual unit load array, The nodal displacement array resulting from the virtual unit load array acting on the output end, represents the output displacement of the compliant mechanism, Indicates the minimum output displacement limit, represents the limit state function of the compliant mechanism, represents the fatigue failure probability of the compliant mechanism, represents the allowable fatigue failure probability of the compliant mechanism, represents the global stiffness matrix of the compliant mechanism, represents the maximum load array of sinusoidal loads, represents each cell in the design domain, represents the cell density, Represents the cell density after filtering.

[0036] Furthermore, the steps of solving the sensitivity of the volume, output displacement and fatigue constraint of the compliant mechanism to design variables based on the double-layer cyclic topology optimization model of fatigue reliability of the compliant mechanism considering material uncertainty, and calculating the sensitivity of the limit state function to random variables include:

[0037] The chain method is used to calculate the volume of the optimized target compliant mechanism and the sensitivity of the output displacement and fatigue reliability constraints to the design variables.

[0038] The sensitivity of the limit state function to the random variables is calculated based on the surrogate model of polynomial chaos expansion.

[0039] Furthermore, after the step of determining whether the moving progressive algorithm satisfies the convergence condition, the method further includes:

[0040] If the moving asymptotic algorithm does not meet the convergence condition, the improved solid isotropic material penalty model is repeatedly used to describe the relationship between the unit elastic modulus and the unit density in the design condition, and the mapping filtering technology is used to filter the unit density; the series optimal linear estimation method is used to discretize the material random field in the design condition, and the linear combination of the standard Gaussian random variable and the deterministic eigenmode is used, and the random response of the compliant mechanism is calculated by combining the chaotic polynomial expansion method with the finite element analysis; the fatigue constraint of the compliant mechanism is constructed by the modified Goodman fatigue criterion, the fatigue constraint is aggregated by the Kieisselmeier-Steinhauser function, and the Fatigue failure limit state function of the compliant mechanism; taking the minimization of the volume of the compliant mechanism as the objective function, and the fatigue failure probability and output displacement of the compliant mechanism as constraints, a double-layer cyclic topology optimization model of fatigue reliability of the compliant mechanism considering material uncertainty is established; based on the double-layer cyclic topology optimization model of fatigue reliability of the compliant mechanism considering material uncertainty, the sensitivity of the volume, output displacement and the fatigue constraint of the compliant mechanism to the design variables is solved, and the sensitivity of the limit state function to the random variables is calculated; the design variables are updated by using the moving progressive algorithm, and the minimum functional target point is found by using the mixed mean method until the moving progressive algorithm meets the convergence conditions, and the topological configuration of the compliant mechanism that meets the fatigue reliability requirements is obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flow chart of a method for topological optimization of fatigue reliability of a compliant mechanism considering material uncertainty in an embodiment of the present invention;

[0042] Figure 2 The design domain, boundary conditions and load action schematic diagram of the clamp mechanism in the embodiment of the present invention;

[0043] Figure 3 Schematic diagram of the topological configuration of the flexible clamp in an embodiment of the present invention;

[0044] Figure 4 is a stress distribution diagram of the flexible clamp in an embodiment of the present invention;

[0045] Figure 5 is a schematic diagram of a constraint iteration curve of a flexible clamp in an embodiment of the present invention;

[0046] Figure 6 is a modified Goodman diagram of the flexible gripper in an embodiment of the present invention.

[0047] The following specific implementation manner will further illustrate the present invention in conjunction with the above-mentioned drawings. DETAILED DESCRIPTION

[0048] See also Figure 1 , which shows a method for topological optimization of fatigue reliability of a compliant mechanism considering material uncertainty in an embodiment of the present invention, the method comprises steps S1 to S7:

[0049] S1, defines the design conditions of the compliant mechanism;

[0050] It should be noted that, in this embodiment, the design conditions include the design domain, constraint boundary conditions, load size, setting the initial value of the design variable, the virtual spring stiffness of the input end, the virtual spring stiffness of the output end, the elastic modulus of the material, the Poisson's ratio of the material, the tensile strength coefficient, the fatigue strength coefficient, the mean of the random field and the standard deviation of the random field.

[0051] S2, using an improved solid isotropic material penalty model to describe the relationship between the unit elastic modulus and the unit density in the design condition, and using a mapping filtering technology to filter the unit density;

[0052] Specifically, the step S2 includes steps S21 to S22:

[0053] S21, an improved solid isotropic material penalty model is used to describe the interpolation relationship between the element elastic modulus and the element density;

[0054] It can be understood that, in this embodiment, the expression of the interpolation relationship between the unit elastic modulus and the unit density is:

[0055] ;

[0056] In the formula, , They represent the elastic modulus of the unit after interpolation and the elastic modulus of the solid material after interpolation. represents the cell density, Represents a very small positive number, which is used to eliminate the singularity problem of stiffness matrix in the finite element analysis process. = , is the penalty parameter, and its value is 3.

[0057] S22, filtering the cell density field based on density filtering technology and by calculating the weighted average of the adjacent cell densities;

[0058] It can be understood that for numerical instability problems such as intermediate density units, checkerboards, and grid dependence, density filtering technology is used to filter the unit density field by calculating the weighted average of the adjacent unit densities. The expression is:

[0059] ;

[0060] In the formula, is the cell density value obtained after filtering, is the unit centroid and the central unit e The distance of the centroid is less than the filter radius The unit collection of For unit j The volume of is the weight coefficient, defined as , Representation unit j The density of Representation unit The distance from the cell centroid.

[0061] S23, using a smooth Heaviside mapping function to correct the filtered cell density so that the cell density variable is concentrated at the preset two ends;

[0062] It can be understood that in order to obtain a clearer topological structure, a smooth Heaviside mapping function is used to correct the filtered cell density, so that the cell density variable is concentrated at both ends of 0 and 1. The expression of the mapping projection filter is:

[0063] ;

[0064] In the formula, is the design variable after mapping, is the threshold density, the value is 0.5, Parameters that control the smooth mapping.

[0065] S3, using the series optimal linear estimation method to discretize the material random field in the design condition, linearly combining the standard Gaussian random variables and the deterministic eigenmodes, and using the chaotic polynomial expansion method combined with finite element analysis to calculate the random response of the compliant mechanism;

[0066] It can be understood that the random field is discretized by using the series optimal linear estimation method. The truncation reduces the dimension of the random problem and converts the standard Gaussian random variable and deterministic eigenmodes Linear combinations of

[0067] Specifically, the step S3 includes steps S31 to S33:

[0068] S31, discretizing the unit nodes of the material random field in the design condition by using a series optimal linear estimation method;

[0069] It is understandable that the series optimal linear estimation method is used to convert the random field Nodes Discretization, random fields It can be expressed as:

[0070]

[0071] in, In the formula, represents a set of independent standard Gaussian random variables that satisfy , . is the covariance matrix The characteristic vector of represents the corresponding eigenvalue, that is , represents a random variable, Represents the covariance matrix The characteristic vector of represents a subset of the entire sample space.

[0072] S32, performing dimensionality reduction on the truncated reduction random problem of the material random field, and performing a linear combination of the standard Gaussian random variable and the deterministic eigenmode;

[0073] It can be understood that the random material field is approximated as independent standard Gaussian random variables and deterministic eigenmodes In order to reduce the dimension of the random problem, the random field Can be truncated to

[0074] ;

[0075] in, represents the eigenmode of the EOLE expansion, represents a truncated random field.

[0076] S33, calculating the random response of the compliant mechanism by using a chaotic polynomial expansion method combined with a quasi-static analysis method;

[0077] It is understandable that the random response of a compliant mechanism is constructed by using the chaotic polynomial expansion method. The proxy model between the random variables is expressed as:

[0078]

[0079] in, Represents the proxy model, represents the polynomial expansion coefficient, represents the orthogonal polynomial basis functions, which satisfy the equation , represents the Kroenecker delta symbol, represents the expectation operator;

[0080] By Hermite polynomial Constructing orthogonal polynomial basis functions It is expressed as:

[0081] ;

[0082] in, Represents a random variable The polynomial order of represents the number of random variables, is the index tuple, represents the Hermite polynomial, represents a random variable, represents the first Hermite polynomial, represents the first random variable, represents orthogonal polynomial basis functions.

[0083] To facilitate numerical processing, the polynomial is truncated to the specified order, namely:

[0084] ;

[0085] Coefficients in polynomial chaos expansion It can be expressed as:

[0086] ;

[0087] In the formula, The analytical expression is obtained through the corresponding orthogonal polynomial basis functions, while the integral is calculated using a non-embedded method;

[0088] ;

[0089] in, Indicates the total points. represents the corresponding weight of the integration point, It represents the system response at a specific integration point. The explicit function of the compliant mechanism response to the random variable can be obtained by combining the above polynomial chaos expansion method with the quasi-static analysis method.

[0090] S4, constructing fatigue constraints of the compliant mechanism using a modified Goodman fatigue criterion, aggregating the fatigue constraints using a Kieisselmeier-Steinhauser function, and constructing a fatigue failure limit state function of the compliant mechanism;

[0091] Specifically, the step S4 includes steps S41 to S43:

[0092] S41, calculating a signed von Mises equivalent stress based on the random response, and constructing a plurality of fatigue stress constraints of the compliant mechanism using a modified Goodman fatigue criterion;

[0093] The improved Goodman criterion is used to construct fatigue strength constraints. The amplitude and mean of the von Mises equivalent stress with a unit sign must be constrained within the safety region described by the modified Goodman diagram. Therefore, the fatigue strength constraint of the compliant mechanism is converted into two stress constraints, and the static strength constraint is converted into two stress constraints:

[0094] ;

[0095] ;

[0096] ;

[0097] ;

[0098] in, is the stress amplitude stress, represents the mean stress, is an infinite loop count ( ) under the allowable critical stress amplitude, and are the tensile strength and yield strength of the t-phase material, respectively. , , , They represent the constraints of four fatigue performance transformations respectively;

[0099] Allowable critical stress amplitude Calculated by the Basquin equation: in, represents the fatigue strength coefficient, Represents fatigue strength index.

[0100] S42, using a Kieisselmeier-Steinhauser function to condense a plurality of the fatigue stress constraints to obtain a condensed stress constraint, and modifying a fatigue constraint metric of the Kieisselmeier-Steinhauser function;

[0101] It can be understood that the Kieisselmeier-Steinhauser (KS) function is used to condense the four stress constraints into one constraint, that is, the cohesion constraint, which is expressed as:

[0102] ;

[0103] in, represents the constraints after condensation, represents the fatigue performance constraint, represents an aggregation constraint, represents the number of stress constraints. Considering The limitation of Constrain it, the expression is:

[0104] ;

[0105] In the formula, represents the constraints after condensation, represents the modified constraint;

[0106] In order to improve the computational efficiency, the improved P norm method is used to condense the four different element stress constraints into four global stress constraints. The aggregate constraints are rewritten as:

[0107] ;

[0108] In order to make the P norm stress closer to the maximum value of the stress constraint , the P norm stress constraint is corrected by using adaptive constraint scaling technology, which can be expressed as:

[0109] ;

[0110] in, represents the adaptive constraint scaling factor, represents the P-norm stress.

[0111] S43, constructing a fatigue failure limit state function of the compliant mechanism based on the cohesive stress constraint, and calculating a fatigue reliability index using a functional metric method;

[0112] The fatigue failure limit state function of the compliant mechanism is constructed using the condensed constraints, and its definition is:

[0113] ;

[0114] in, is a Gaussian distributed random variable, represents an aggregation constraint, represents the fatigue failure limit state function.

[0115] The fatigue reliability index is calculated by the functional measurement method. The expression of the satisfactory relationship between the target reliability index and the allowable fatigue failure probability is:

[0116] ;

[0117] in, As the reliability index used by X, is the overall normal cumulative distribution function, It represents the relationship between the target reliability index and the allowable fatigue failure probability.

[0118] S5, taking the minimization of the volume of the compliant mechanism as the objective function and the fatigue failure probability and output displacement of the compliant mechanism as constraints, a double-layer cyclic topology optimization model of fatigue reliability of the compliant mechanism considering material uncertainty is established;

[0119] The expression of the double-layer cyclic topology optimization model for fatigue reliability of compliant mechanisms considering material uncertainty is:

[0120] ;

[0121] ;

[0122] ;

[0123] ;

[0124] ;

[0125] ;

[0126] ;

[0127] In the formula, Represents the optimized volume, represents the cell density vector array, represents the unit volume filled with material, represents a vector of standard Gaussian distributed random variables, represents the virtual unit load array, The nodal displacement array resulting from the virtual unit load array acting on the output end, represents the output displacement of the compliant mechanism, Indicates the minimum output displacement limit, represents the limit state function of the compliant mechanism, represents the fatigue failure probability of the compliant mechanism, represents the allowable fatigue failure probability of the compliant mechanism, represents the global stiffness matrix of the compliant mechanism, represents the maximum load array of sinusoidal loads, represents each cell in the design domain, represents the cell density, Represents the cell density after filtering.

[0128] S6, solving the sensitivity of the volume, output displacement and fatigue constraint of the compliant mechanism to the design variables based on the double-layer cyclic topology optimization model of fatigue reliability of the compliant mechanism considering material uncertainty, and calculating the sensitivity of the limit state function to the random variables;

[0129] Specifically, the step S6 includes step S61 to step S62:

[0130] S61, the chain method is used to calculate the volume of the optimized target compliant mechanism and the sensitivity of the output displacement and fatigue reliability constraints to the design variables;

[0131] It can be understood that the chain method is used to calculate the volume of the compliant mechanism and the sensitivity of the output displacement and fatigue reliability constraints to the design variables;

[0132] The sensitivity of the objective function and constraint function to the design variables is:

[0133] ;

[0134] in, represents the symbol of partial derivative, Representation unit The density of Representation unit , represents the set of all units, Represents the smooth Heaviside mapping function correcting the filtered unit The density of Represents the unit after density filtering The density of represents the constraint function or objective function, and It can be obtained by density filtering and Heaviside projection function derivation;

[0135] The sensitivity of the output displacement constraint to the design variables is:

[0136] ;

[0137] represents the transpose of the output displacement of the compliant mechanism. During the finite element analysis, the external load at the input end is independent of the design variables, and the finite element equilibrium equation is and Can be rewritten as:

[0138] ;

[0139] Through the limit state function, the derivative of the constraint function with respect to the design variable is obtained as follows:

[0140] ;

[0141] represents the aggregation constant, any stress constraint The sensitivity to the unit design variables is:

[0142] ;

[0143] Adjoint method is used to introduce adjoint matrix , so that:

[0144] ;

[0145] Partial derivatives of each stress constraint with respect to the element design variables It can be expressed as:

[0146] ;

[0147] ;

[0148] In the formula, Indicates The p-norm of the fatigue performance constraints, represents the von Mises stress amplitude of the element, represents the mean von Mises stress of the element, represents the element stress amplitude, represents the mean element stress, represents the mean coefficient, represents the element stress;

[0149] The partial derivative of each stress constraint with respect to the displacement of the element node It can be expressed as:

[0150] ;

[0151] ;

[0152] In the formula, represents the displacement of the desired e, represents the adaptive scaling factor corresponding to the second fatigue constraint;

[0153] The partial derivative of the P-norm global stress constraint with respect to the local stress constraint is:

[0154] ;

[0155] According to the surrogate model of polynomial chaos expansion, the sensitivity of random response to design variables is solved as follows:

[0156] ;

[0157] In the formula, represents the random response after PCE calculation, represents the weight function corresponding to the integral point, represents the integral point in the probability space, Indicates the total number of integral points;

[0158] Derivative of the limit state function with respect to a random variable It can be obtained by directly deriving the PCE proxy model.

[0159] S62, calculate the sensitivity of the limit state function to the random variable based on the proxy model of the polynomial chaos expansion.

[0160] S7, using a moving progressive algorithm to update the design variables, using a mixed mean method to find the minimum functional target point, and judging whether the iteration meets the convergence condition, if so, obtaining a compliant mechanism topology configuration that meets the fatigue reliability requirements;

[0161] It is worth noting that the step S7 also includes step S71:

[0162] S71, if the iteration does not meet the convergence condition, then repeatedly execute the improved solid isotropic material penalty model to describe the relationship between the unit elastic modulus and the unit density in the design condition, and use the mapping filtering technology to filter the unit density; use the series optimal linear estimation method to discretize the material random field in the design condition, linearly combine the standard Gaussian random variables and the deterministic eigenmode, and use the chaotic polynomial expansion method combined with the finite element analysis to calculate the random response of the compliant mechanism; use the modified Goodman fatigue criterion to construct the fatigue constraint of the compliant mechanism, use the Kieisselmeier-Steinhauser function to aggregate the fatigue constraint, and construct The fatigue failure limit state function of the compliant mechanism is obtained; taking the minimization of the volume of the compliant mechanism as the objective function, and taking the fatigue failure probability and output displacement of the compliant mechanism as constraints, a double-layer cyclic topology optimization model for fatigue reliability of the compliant mechanism considering material uncertainty is established; based on the double-layer cyclic topology optimization model for fatigue reliability of the compliant mechanism considering material uncertainty, the sensitivity of the volume, output displacement and fatigue constraints of the compliant mechanism to the design variables is solved, and the sensitivity of the limit state function to random variables is calculated; the design variables are updated using the moving progressive algorithm, and the minimum functional target point is found using the mixed mean method until the iteration meets the convergence conditions, so as to obtain the topological configuration of the compliant mechanism that meets the fatigue reliability requirements.

[0163] It needs to be explained that the outer layer sequence is deterministic topology optimization, which uses the moving asymptotic optimization algorithm to change the design variables; the inner layer loop is reliability analysis, which uses the mixed mean method to find the minimum functional target point; it is judged whether the convergence conditions of the optimization algorithm are met. If so, the topological configuration of the flexible mechanism that meets the fatigue reliability requirements is obtained.

[0164] In order to further verify the effectiveness of the fatigue reliability topology optimization method of a compliant mechanism considering material uncertainty of the present invention, this embodiment takes a flexible clamp as an example to explain the present invention.

[0165] The design domain, boundary conditions and load effects of the gripper mechanism are as follows: Figure 2 As shown, the gripper design domain size is 80μm×80μm, and the sinusoidal load Acting on the left midpoint, =150μN, = -60μN. Input spring stiffness and output spring rate are 10μN / μm respectively. Since the design domain of the gripper is symmetrical in the upper and lower parts, in order to improve the calculation efficiency, the upper half of the design domain is used for calculation, and the design domain is discretized into 6400 plane quadrilateral elements. In the numerical example, the elastic modulus E0 of the material is 203GPa, and the Poisson's ratio is 0.3, tensile strength 300MPa, fatigue strength coefficient is 300MPa, and the fatigue strength index b is .

[0166] Figure 3 , Figure 4 , Figure 5 and Figure 6 The topological configuration, stress distribution diagram, constraint iteration curve and modified Goodman diagram of the flexible gripper obtained by the fatigue reliability topological optimization design method of the compliant mechanism considering material uncertainty. Figure 5 and Figure 6 It can be seen that the compliant mechanism obtained by the fatigue reliability topology optimization of the compliant mechanism considering material uncertainty can meet the fatigue reliability requirements.

[0167] In summary, the fatigue reliability topology optimization method of the compliant mechanism considering material uncertainty in the above-mentioned embodiments of the present invention describes the relationship between the unit elastic modulus and the unit density, calculates the random response of the compliant mechanism and constructs the fatigue failure limit state function of the compliant mechanism, and establishes a double-layer cyclic topology optimization model of the fatigue reliability of the compliant mechanism considering material uncertainty by taking fatigue failure probability and output displacement as constraints. By updating the design variables and judging whether the iteration meets the convergence conditions, the optimal topological configuration of the compliant mechanism can be obtained, and the compliant mechanism can have better fatigue reliability.

[0168] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A fatigue reliability topology optimization method for compliant mechanisms considering material uncertainty, characterized in that: The method comprises: Define the design conditions for compliant mechanisms; An improved solid isotropic material penalty model is used to describe the relationship between the unit elastic modulus and the unit density in the design condition, and a mapping filtering technology is used to filter the unit density; The material random field in the design condition is discretized by using the series optimal linear estimation method, the material random field is expressed as a linear combination of a standard Gaussian random variable and a deterministic eigenmode, and the random response of the compliant mechanism is calculated by using a chaotic polynomial expansion method combined with finite element analysis; A modified Goodman fatigue criterion is used to construct fatigue constraints of the compliant mechanism, a Kieisselmeier-Steinhauser function is used to aggregate the fatigue constraints, and a fatigue failure limit state function of the compliant mechanism is constructed; The steps of constructing the fatigue constraint of the compliant mechanism by adopting the modified Goodman fatigue criterion, aggregating the fatigue constraint by using the Kieisselmeier-Steinhauser function, and constructing the fatigue failure limit state function of the compliant mechanism include: Calculating a signed von Mises equivalent stress based on the random response and constructing several fatigue stress constraints of the compliant mechanism using a modified Goodman fatigue criterion; A plurality of fatigue stress constraints are condensed using a Kieisselmeier-Steinhauser function to obtain a condensed stress constraint, and a fatigue constraint metric of the Kieisselmeier-Steinhauser function is modified; constructing a fatigue failure limit state function of the compliant mechanism based on the cohesive stress constraint, and calculating a fatigue reliability index using a functional metric method; Taking the minimization of the volume of the compliant mechanism as the objective function and the fatigue failure probability and output displacement of the compliant mechanism as constraints, a double-layer cyclic topology optimization model of fatigue reliability of the compliant mechanism considering material uncertainty is established; The expression of the double-layer cyclic topology optimization model for fatigue reliability of compliant mechanisms considering material uncertainty is: ； ； ； ； ； ； ； In the formula, Represents the optimized volume, represents the cell density vector array, represents the unit volume filled with material, represents a vector of standard Gaussian distributed random variables, represents the virtual unit load array, The nodal displacement array resulting from the virtual unit load array acting on the output end, represents the output displacement of the compliant mechanism, Indicates the minimum output displacement limit, represents the limit state function of the compliant mechanism, represents the fatigue failure probability of the compliant mechanism, represents the global stiffness matrix of the compliant mechanism, represents the maximum load array of sinusoidal loads, represents each cell in the design domain, represents the cell density, represents the cell density after filtering, represents the global stiffness matrix of the structure, represents the node displacement array, represents the number of finite element elements in the design domain, represents the allowable fatigue failure probability of the compliant mechanism; Based on the double-layer cyclic topology optimization model of fatigue reliability of the compliant mechanism considering material uncertainty, the sensitivity of the volume, output displacement and fatigue constraint of the compliant mechanism to the design variables is solved, and the sensitivity of the limit state function to the random variables is calculated; The design variables are updated using a moving progressive algorithm, the minimum functional target point is found using a mixed mean method, and it is determined whether the iteration meets the convergence condition. If so, a compliant mechanism topology configuration that meets the fatigue reliability requirements is obtained.

2. The method for topological optimization of fatigue reliability of compliant mechanisms considering material uncertainty according to claim 1 is characterized in that: The design conditions include design domain, constraint boundary conditions, load size, setting initial values ​​of design variables, virtual spring stiffness at the input end, virtual spring stiffness at the output end, elastic modulus of the material, Poisson's ratio of the material, tensile strength coefficient, fatigue strength coefficient, mean of the random field and standard deviation of the random field.

3. The method for topological optimization of fatigue reliability of compliant mechanisms considering material uncertainty according to claim 1, characterized in that: The step of using an improved solid isotropic material penalty model to describe the relationship between the unit elastic modulus and the unit density in the design condition, and using a mapping filtering technology to filter the unit density comprises: An improved solid isotropic material penalty model is used to describe the interpolation relationship between element elastic modulus and element density. Based on the density filtering technology, the cell density field is filtered by calculating the weighted average of the densities of the adjacent cells; The smooth Heaviside mapping function is used to correct the filtered cell density so that the cell density variables are concentrated at the preset two ends.

4. The method for topological optimization of fatigue reliability of compliant mechanisms considering material uncertainty according to claim 1, characterized in that: The steps of using the series optimal linear estimation method to discretize the material random field in the design condition, linearly combining the standard Gaussian random variable and the deterministic eigenmode, and using the chaotic polynomial expansion method combined with finite element analysis to calculate the random response of the compliant mechanism include: Using the series optimal linear estimation method to discretize the unit nodes of the material random field in the design condition; Performing dimensionality reduction on the truncated reduction random problem of the material random field and performing linear combinations of the standard Gaussian random variables and deterministic eigenmodes; The random response of the compliant mechanism is calculated by combining the chaotic polynomial expansion method with the quasi-static analysis method.

5. The method for topological optimization of fatigue reliability of compliant mechanisms considering material uncertainty according to claim 1, characterized in that: The steps of solving the sensitivity of the volume, output displacement and fatigue constraint of the compliant mechanism to design variables based on the double-layer cyclic topology optimization model of fatigue reliability of the compliant mechanism considering material uncertainty, and calculating the sensitivity of the limit state function to random variables include: The chain method is used to calculate the volume of the optimized target compliant mechanism and the sensitivity of the output displacement and fatigue reliability constraints to the design variables. The sensitivity of the limit state function to the random variables is calculated based on the surrogate model of polynomial chaos expansion.

6. The method for topological optimization of fatigue reliability of compliant mechanisms considering material uncertainty according to claim 1, characterized in that: After the step of determining whether the iteration satisfies the convergence condition, the method further comprises: If the iteration does not meet the convergence condition, the improved solid isotropic material penalty model is repeatedly used to describe the relationship between the unit elastic modulus and the unit density in the design condition, and the mapping filtering technology is used to filter the unit density; the series optimal linear estimation method is used to discretize the material random field in the design condition, and the linear combination of the standard Gaussian random variable and the deterministic eigenmode is used, and the random response of the compliant mechanism is calculated by combining the chaotic polynomial expansion method with the finite element analysis; the fatigue constraint of the compliant mechanism is constructed by the modified Goodman fatigue criterion, the fatigue constraint is aggregated by the Kieisselmeier-Steinhauser function, and the Fatigue failure limit state function of the compliant mechanism; taking the minimization of the volume of the compliant mechanism as the objective function, and the fatigue failure probability and output displacement of the compliant mechanism as constraints, a double-layer cyclic topology optimization model of fatigue reliability of the compliant mechanism considering material uncertainty is established; based on the double-layer cyclic topology optimization model of fatigue reliability of the compliant mechanism considering material uncertainty, the sensitivity of the volume, output displacement and the fatigue constraint of the compliant mechanism to the design variables is solved, and the sensitivity of the limit state function to the random variables is calculated; the design variables are updated using the moving progressive algorithm, and the minimum functional target point is found by the mixed mean method until the iteration meets the convergence conditions, and the topological configuration of the compliant mechanism that meets the fatigue reliability requirements is obtained.

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