A topological optimization biax decoupling tool servo device and a design method thereof

Abstract

The application discloses a topological optimization biaxial decoupling cutter servo device and a design method thereof, which comprises a compliant mechanism platform, a piezoelectric stack one, a piezoelectric stack two, a diamond cutter, a measuring baffle, a capacitive displacement sensor one, a capacitive displacement sensor two and an upper cover plate, the piezoelectric stack one and the piezoelectric stack two are pre-tightened to the compliant mechanism platform, the diamond cutter is installed on a cutter seat platform, the compliant mechanism platform further comprises a topological compliant mechanism, an input guide mechanism one, an input guide mechanism two and an output guide mechanism, the output guide mechanism is located at the front end of the compliant mechanism platform, and the rear end of the topological compliant mechanism is connected with the front ends of the input guide mechanism one and the input guide mechanism two. The topological optimization method is adopted to design the compliant mechanism, the optimal mechanism configuration-parameter design can be sought under the premise of meeting a series of constraint conditions in the case of given design domains and specified input and output actions, and therefore the mechanism performance is optimal.

Description

Technical Field

[0001] The present invention relates to the fields of elastic mechanics and ultra-precision metal cutting technology, and specifically to a topologically optimized dual-axis decoupled tool servo device and a design method thereof, as well as applications in ultra-precision machining equipment, micro-electromechanical systems, and other related fields. Background Art

[0002] Diamond turning methods based on a fast tool servo (FTS) system have become an important technology in the ultra-precision manufacturing of microstructured functional surfaces. This method achieves ultra-precision surface machining by precisely controlling material removal at the micro- and nanoscale by adjusting the tool position in real time during the turning process.

[0003] The core of this approach lies in the design of the compliant mechanism, which influences the FTS system's large travel range, high bandwidth, and nanometer-level motion precision. However, regardless of the drive method used in the FTS system, the travel range and operating bandwidth are mutually constrained. Therefore, further improving the balance between the mechanism's travel range and operating bandwidth has become a key goal in compliant mechanism design.

[0004] Because compliant mechanisms transmit motion through the elastic deformation of their materials, when they are subjected to multiple loads, these loads interfere with each other. This can lead to a decrease in the compliant mechanism's positioning accuracy, or even inability to complete the positioning function. This ultimately increases the mechanism's control difficulty. Therefore, considering how to design compliant mechanisms and improve their positioning accuracy is a key issue in reducing the control difficulty of compliant mechanisms.

[0005] At the same time, to ensure the reliability of compliant mechanisms during effective operation, stress distribution must be fully considered during their design. The movement of the mechanism may result in higher stress concentrations in localized areas, which can cause material fatigue, deformation, or cracking. To avoid this, designers need to ensure that the stresses in the mechanism remain within a controllable range throughout the entire movement process, not exceeding the allowable stress limit of the material. Therefore, considering stress control is a key aspect of ensuring the reliability of compliant mechanisms.

[0006] Based on the above analysis, traditional design solutions often lack scientific methods to select the best performance of the mechanism. Summary of the Invention

[0007] The purpose of the present invention is to provide a topology optimized dual-axis decoupling tool servo device and a design method thereof.

[0008] The technical solution adopted by the present invention is: a topology optimized dual-axis decoupled tool servo device, including a flexible mechanism platform, a piezoelectric stack 1, a piezoelectric stack 2, a diamond tool, a measuring baffle, a capacitive displacement sensor 1, a capacitive displacement sensor 2, and an upper cover plate.

[0009] The first piezoelectric stack and the second piezoelectric stack are pre-tightened on the compliance mechanism platform by wedge blocks 1 and 2, respectively. The driving directions of the first piezoelectric stack and the second piezoelectric stack are consistent. The first capacitive displacement sensor and the second capacitive displacement sensor are respectively installed in the first capacitive displacement sensor through hole 1 and the second capacitive displacement sensor through hole 2 of the upper cover plate. The measuring baffle is installed on the compliance mechanism platform and is located at the front end of the first capacitive displacement sensor and the second capacitive displacement sensor.

[0010] The front end of the compliant mechanism platform includes a tool holder platform, and the diamond tool is installed on the tool holder platform. The compliant mechanism platform also includes a topological compliant mechanism, an input guide mechanism 1, an input guide mechanism 2 and an output guide mechanism. The output guide mechanism is located at the front end of the compliant mechanism platform, and the rear end of the topological compliant mechanism is connected to the front ends of the input guide mechanism 1 and the input guide mechanism 2. The front end of the topological compliant mechanism is connected to the output guide mechanism, the rear end of the input guide mechanism 1 contacts the front end of the piezoelectric stack 1, and the rear end of the input guide mechanism 2 contacts the front end of the piezoelectric stack 2. The input guide mechanism 1 and the input guide mechanism 2 are double parallelogram hinge structures, and the double parallelogram hinge structure includes four straight-plate flexible hinges. The output end of the output guide mechanism is a symmetrical V-shaped flexible hinge.

[0011] Furthermore, the first piezoelectric stack and the second piezoelectric stack are fixed to the compliant mechanism platform by means of a first wedge block pre-tightening screw and a second wedge block pre-tightening screw, respectively.

[0012] Furthermore, the capacitive displacement sensor 1 and the capacitive displacement sensor 2 are fixed to the upper cover plate by the capacitive displacement sensor pre-tightening screw 1 and the capacitive displacement sensor pre-tightening screw 2, respectively.

[0013] Furthermore, the diamond tool is mounted on the tool holder platform by fastening screws.

[0014] The design method of the dual-axis decoupling tool servo device according to the above topology optimization includes the following steps:

[0015] Step 1: Construct a spring model based on topology optimization of the compliant mechanism;

[0016] The spring model consists of a continuous design domain and a spring with known stiffness. The design domain is divided into three parts: the designable area Ω_d, the specified solid area Ω_s, and the specified empty material area Ω_v. By integrating the kinematic characteristics of the mechanism design and the elastic mechanical characteristics of the structural design, an optimized mathematical description form based on the structural characteristic system stiffness-decoupling-strength model is established to meet the requirements of input-output decoupling and high-frequency response performance of the compliant mechanism system. Combined with the improved SIMP method, the specific mathematical model is constructed as follows:

[0017]

[0018] Where, represents the set of design variables, n represents the total number of unit design variables, V represents the material usage volume, V * represents the upper limit of the material volume, U represents the global displacement matrix caused by the external load vector F of the node, Φ m is the mth order eigenvalue λ m The relevant eigenvector, m represents the number of degrees of freedom N corresponding to the structure dof All modes of and υ * denote the maximum allowable output and input coupling constraint indices, ζ * Express the maximum allowable output end rotation coupling constraint index, c * and u * They represent the input flexibility constraint and input displacement constraint indices, θ * Express the motion transfer factor constraint index, σ * represents the global maximum stress constraint index;

[0019] Step 2: Set the modal frequency as the objective function;

[0020] To ensure that the compliant mechanism has specific performance characteristics and to optimize it towards the preset performance direction, the first-order natural frequency of the compliant mechanism is set as the objective function for optimization. Based on the Rayleigh quotient principle, the eigenvalue of any order of the system motion equation can be expressed as:

[0021]

[0022] m takes the value of 1;

[0023] Step 3: Construct motion coupling constraints;

[0024] Considering that the given design domain needs to be topologically transformed into a compliant mechanism with complete motion decoupling, an appropriate input-output coupling suppression strategy is first constructed to guide the material distribution in the design domain to continuously evolve towards the expected performance.

[0025] When the input terminal O is located on the left side of the design domainin,k The piezoelectric actuator is excited to generate a load F in,k When acting in the x direction, k=1,2, driving the output terminal O out In F in,1 When it acts, it moves in the x direction and produces the corresponding desired output displacement u out,1 , drive output terminal O out In F in,2 When it acts, it moves in the y direction and produces the corresponding desired output displacement u out,2 , due to the internal structural connection of the mechanism, at the output end O out The corresponding parasitic motion is generated along the lateral direction l At the same time, a corresponding parasitic motion is also generated in the lateral direction of the input end.

[0026] Based on the principle of kinematic geometry, in order to suppress the coupling interference at the output end, the parasitic motion along the other k≠l direction must be eliminated. The output coupling constraint model is established, and its calculation expression is as follows:

[0027]

[0028] Where, represents the output coupling constraint index;

[0029] At the same time, in order to suppress the coupling interference at the input end, the parasitic motion along the other l≠k direction must be eliminated. Among them, it is necessary to consider both input and output displacement, undesirable parasitic motion Not only for the input displacement u in,k Generates interference and shifts the desired output u out,k It will also affect the positioning accuracy. Therefore, based on the minimum operator selection principle, an input coupling constraint model is established, and its calculation expression is as follows:

[0030]

[0031] Where, * represents the input coupling constraint index;

[0032] In the specified entity area Ω s Output O out and The motion displacement suppression function between the output terminals O out and The motion displacement deviation constraint between them is calculated as follows:

[0033]

[0034] Where, ζ *Represents the output end motion displacement deviation constraint index;

[0035] Step 4: Construct input and output flexibility constraints;

[0036] When the load acts on the input terminal O on the left side of the design domain in,k When k=1,2, input terminal O in,k and output terminal O out,k Both produce corresponding elastic deformation u in,k and u out,k According to the elastic beam theory, the input compliance characteristics of the mechanism are obtained by the following formula:

[0037]

[0038] Where k in,k =c in,k -1 Represents the input stiffness characteristics, which includes the preset input virtual spring stiffness value Introduce the input displacement constraint function u in,k ≥u * , where u * represents the input displacement constraint index,

[0039] At the same time, considering the motion transfer factor θ of the mechanism k is represented as:

[0040]

[0041] Where θ * represents the motion transfer factor constraint index;

[0042] Step 5: Construct global stress constraints;

[0043] In the static design of compliant mechanisms, equivalent stress is usually used to evaluate their reliability. Therefore, equivalent stress is introduced into the topology optimization of compliant mechanisms as a way to measure stress. In the case of plane stress, the specific expression of equivalent stress is:

[0044]

[0045] Where σ i,x and σ i,y denote the principal stress of the ith element along the x and y directions, τ i,xy represents the shear stress of the i-th unit, V represents the auxiliary matrix, σ i The element stress vector representing the stress measurement point;

[0046] The P-norm stress measurement method is used to control the maximum stress. The P-norm stress measurement method is expressed as:

[0047]

[0048] Where, v i represents the material volume of the element, and P represents the stress norm parameter, which determines the closeness between the P-norm stress and the actual maximum stress;

[0049] In order to make the P-norm stress closer to the actual maximum stress, the adaptive constraint scaling method is used to improve the convergence and accuracy of the optimization algorithm, and further improve the closeness between the P-norm stress and the actual maximum stress. The corrected P-norm stress measurement is expressed as:

[0050]

[0051] Where c κ is the coefficient of the adaptive constraint scaling method;

[0052] On the left side of the design domain, input terminal O in,1 and O in,2 Mainly driven by the driving force F of the two piezoelectric actuators in,1 and F in,2 , and the stress generated along the x-axis direction at the two input ends is much smaller than the stress generated along the y-axis direction, so considering the two maximum loads and When the stress acts simultaneously, the stress constraint for topology optimization of the compliant mechanism is described as:

[0053]

[0054] Where σ s represents the yield strength of the material, α f Represents the safety factor of the material, α f >1,σ * Represents the global stress constraint index, that is, the allowable stress of the material;

[0055] Step 6: Modal frequency sensitivity analysis;

[0056] Perform relevant modal frequency sensitivity analysis on the objective function. In dynamics, the eigenvector {Φ m}For the mass matrix M, it has the normalization property {Φ m} T ·M·{Φ m}=1, so the objective function is designed for variables The first-order sensitivity solution of simplifies to:

[0057]

[0058] Step 7: Motion decoupling sensitivity analysis;

[0059] Perform motion decoupling sensitivity analysis on the objective function and output the coupling constraint function For design variables The sensitivity is expressed as:

[0060]

[0061] Input coupling constraint function υ k,l For design variables The sensitivity is expressed as:

[0062]

[0063] Output O out and The motion displacement deviation constraint ζ l For design variables The sensitivity is expressed as:

[0064]

[0065] Step 8: Input and output flexibility sensitivity analysis;

[0066] The relevant flexibility sensitivity analysis is performed on the objective function, and the static flexibility of the structure is defined as: From the equilibrium equation K·U k =F in,k , we can see that Λ=-U k , then the static flexibility of the structure c in,k The sensitivity expression is:

[0067]

[0068] Structural motion transfer factor θ k For design variables The sensitivity is expressed as:

[0069]

[0070] Step 9: Global stress sensitivity analysis;

[0071] Stress constraint σ max Sensitivity analysis of the design variables The sensitivity of is chain-derived to obtain:

[0072]

[0073] Step 10: Volume constraint sensitivity analysis;

[0074] Volume constraint V on design variables The sensitivity expression is:

[0075]

[0076] Finally, the above mathematical model is optimized and solved using the moving asymptote method. At the same time, the density filtering method is used to solve the numerical solution problem and numerical instability problem.

[0077] Compared with the existing technology, the present invention has the following advantages: it uses a two-piezoelectric stack drive, which has multiple advantages, including higher acceleration, fast response time, high output force density, high positioning accuracy, and sub-nanometer motion resolution. It also uses a topological approach to effectively solve the configuration-parameter integrated design, further improves the balance between stroke and working bandwidth, and simplifies the complexity of multi-performance design calculations.

[0078] The piezoelectric stack drive device adopts a compliant mechanism topology, which overcomes the difficulties of traditional multi-degree-of-freedom structural configuration design and further improves the structural performance from the perspective of conceptual design. Its advantages are novel structure and excellent flexibility, which makes it easy to achieve precision control of micro-displacement motion and easily control the motion trajectory of the tool motion platform in space. In terms of the guiding mechanism, the use of double parallel straight-plate flexible hinges and symmetrical V-shaped flexible hinges has the advantages of good flexibility and symmetrical distribution, which makes it easy to control the precision of micro-displacement motion and realizes the function and performance of virtual springs. The double parallel straight-plate flexible hinges can completely eliminate the coupling motion error of the mechanism, realize input decoupling, and behave as two ideal moving pairs during the motion process. The symmetrical V-shaped flexible hinge realizes not only motion in the x-axis direction, but also motion in the y-axis direction, which fully meets the function and performance requirements of the virtual spring stiffness, and the mutual motion coupling between the two axes is relatively small.

[0079] Piezoelectric stacks 1 and 2 drive independent flexible hinges in the same direction without coupling, achieving high control accuracy for the flexible device. The motion trajectory can be adjusted by adjusting the parameters of the piezoelectric stack drive signal.

[0080] The present invention uses a typical PID controller with a feedforward compensator to effectively improve the tracking performance of the entire system. At the same time, by calculating the system error and adjusting the piezoelectric stack drive voltage signal accordingly, the piezoelectric drive system can effectively compensate for the system motion error caused by external disturbances.

[0081] The present invention realizes high-precision multi-degree-of-freedom motion control, improves the accuracy and stability of the turning process, and brings significant technological progress and application prospects to related fields.

[0082] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 This is a partial design domain diagram of the dual-axis fully decoupled tool servo turning compliant mechanism of the present invention.

[0084] Figure 2 It is a plan view of the design of the dual-axis fully decoupled tool servo turning compliant mechanism of the present invention.

[0085] Figure 3 It is an internal top view of the dual-axis fully decoupled tool servo turning device of the present invention.

[0086] Figure 4 It is an overall schematic diagram of the dual-axis fully decoupled tool servo turning device of the present invention.

[0087] Figure 5 This is the global control block diagram of the dual-axis fully decoupled tool servo turning system of the present invention. DETAILED DESCRIPTION

[0088] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0089] Combine Figure 1-5 A topology optimized dual-axis decoupling tool servo device includes a compliant mechanism platform 6, a piezoelectric stack 1 9, a piezoelectric stack 2 11, a diamond tool 3, a measuring baffle 2, a capacitive displacement sensor 14, a capacitive displacement sensor 2 15, and an upper cover 16.

[0090] Piezoelectric stack 1 9 and piezoelectric stack 2 11 are pre-tightened to the compliance mechanism platform 6 via wedge block 1 8 and wedge block 2 10, respectively. The driving directions of piezoelectric stack 1 9 and piezoelectric stack 2 11 are consistent. Capacitive displacement sensor 1 14 and capacitive displacement sensor 2 15 are respectively installed in capacitive displacement sensor through hole 1 and capacitive displacement sensor through hole 2 of the upper cover 16. The measuring baffle 2 is installed on the compliance mechanism platform 6 and is located at the front end of capacitive displacement sensor 1 14 and capacitive displacement sensor 2 15.

[0091] The front end of the compliant mechanism platform 6 includes a tool holder platform 13, on which the diamond tool 3 is mounted.

[0092] The compliant mechanism platform 6 also includes a topological compliant mechanism 1, an input guide mechanism 1 7, an input guide mechanism 2 12 and an output guide mechanism 5. The topological compliant mechanism 1 is realized by setting an objective function and a constraint function. The output guide mechanism 5 is located at the front end of the compliant mechanism platform 6. The rear end of the topological compliant mechanism 1 is connected to the front end of the input guide mechanism 1 7 and the input guide mechanism 2 12. The front end of the topological compliant mechanism 1 is connected to the output guide mechanism 5. The rear end of the input guide mechanism 1 7 contacts the front end of the piezoelectric stack 1 9. The rear end of the input guide mechanism 2 12 contacts the front end of the piezoelectric stack 2 11. The input guide mechanism 1 7 and the input guide mechanism 2 12 are double parallelogram hinge structures. The double parallelogram hinge structure includes four straight-plate flexible hinges. The output end of the output guide mechanism 5 is a symmetrical V-shaped flexible hinge.

[0093] Furthermore, the piezoelectric stack 1 9 and the piezoelectric stack 2 11 are fixed to the compliance mechanism platform 6 by the wedge block pre-tightening screw 1 and the wedge block pre-tightening screw 2 respectively.

[0094] Furthermore, the capacitive displacement sensor 1 14 and the capacitive displacement sensor 2 15 are fixed to the upper cover plate 16 by means of the capacitive displacement sensor pre-tightening screw 1 and the capacitive displacement sensor pre-tightening screw 2, respectively.

[0095] Furthermore, the diamond tool 3 is mounted on the tool holder platform 13 via a fastening screw 4 .

[0096] In addition, see Figure 5 As shown, the patent of this invention applies a typical PID controller with a feedforward compensator to a dual-axis fully decoupled tool servo turning device, effectively improving the tracking, positioning and other performances of the precision motion of the overall system.

[0097] according to Figure 1-Figure 5 , the device of the present invention has two working modes:

[0098] (1) When a drive signal is applied only to piezoelectric stack 11 and piezoelectric stack 19 is not receiving a drive signal, piezoelectric stack 19 will not operate, and only piezoelectric stack 11 will operate. This allows for decoupled motion along the x-axis. Similarly, when a drive signal is applied only to piezoelectric stack 19 and piezoelectric stack 11 is not receiving a drive signal, piezoelectric stack 11 will not operate, and only piezoelectric stack 19 will operate. This allows for decoupled motion along the y-axis. This operating mode is suitable for applications requiring relatively low positioning accuracy.

[0099] (2) When applying drive signals to the two piezoelectric stacks, a typical PID controller with a feedforward compensator is used, which effectively improves system stability and achieves high tracking accuracy. Therefore, this operating mode is suitable for applications with high precision requirements and large travel ranges.

[0100] Through the above two working modes, the device of the present invention can flexibly select the working mode according to the needs of the specific application scenario, realizing decoupled motion in different directions or high-precision linkage control. This makes the device widely applicable in various application fields, bringing significant technological progress and practical application possibilities to related fields.

[0101] According to the above-mentioned design method of the dual-axis fully decoupled tool servo device, the following steps are included:

[0102] Step 1: Construct a spring model based on topology optimization of the compliant mechanism;

[0103] The spring model consists of a continuous design domain and springs with known stiffness (added at the input and output ends). The design domain is divided into three parts: the designable area Ω_d, the specified solid area Ω_s (rigid area), and the specified empty material area Ω_v (non-design area). By integrating the kinematic characteristics of the mechanism design and the elastic mechanical characteristics of the structural design, an optimized mathematical description of the stiffness-decoupling-strength model of the system based on structural characteristics (eigenvalues ​​and eigenvectors) is established to meet the requirements of input-output decoupling and high-frequency response performance of the compliant mechanism system. Combined with the improved SIMP method, the specific mathematical model is constructed as follows:

[0104]

[0105] Where, represents the set of design variables, n represents the total number of unit design variables, V represents the material usage volume, V * represents the upper limit of the material volume, U represents the global displacement matrix caused by the external load vector F of the node, Φ m is the mth order eigenvalue λ m The relevant eigenvector, m represents the number of degrees of freedom N corresponding to the structure dof All modes of and υ * denote the maximum allowable output and input coupling constraint indices, ζ * Express the maximum allowable output end rotation coupling constraint index, c * and u * They represent the input flexibility constraint and input displacement constraint indices, θ * Express the motion transfer factor constraint index, σ * represents the global maximum stress constraint index;

[0106] Step 2: Set the modal frequency as the objective function;

[0107] To ensure that the compliant mechanism has specific performance characteristics and to optimize it towards the preset performance direction, the first-order natural frequency of the compliant mechanism is set as the objective function for optimization. Based on the Rayleigh quotient principle, the eigenvalue of any order of the system motion equation can be expressed as:

[0108]

[0109] m takes the value of 1;

[0110] Step 3: Construct motion coupling constraints;

[0111] Considering that the given design domain needs to be topologically transformed into a compliant mechanism with complete motion decoupling, an appropriate input-output coupling suppression strategy is first constructed to guide the material distribution in the design domain to continuously evolve towards the expected performance.

[0112] like Figure 1 As shown, when the input terminal O is located on the left side of the design domain in,k The piezoelectric actuator is excited to generate a load F in,k When acting in the x direction, k=1,2, driving the output terminal O out In F in,1 When it acts, it moves in the x direction and produces the corresponding desired output displacement u out,1 , drive output terminal O out In F in,2 When it acts, it moves in the y direction and produces the corresponding desired output displacement u out,2 , due to the internal structural connection of the mechanism, at the output end O out The corresponding parasitic motion is generated along the lateral direction l At the same time, a corresponding parasitic motion is also generated in the lateral direction of the input end.

[0113] Based on the principle of kinematic geometry, in order to suppress the coupling interference at the output end, the parasitic motion along the other k≠l direction must be eliminated. The output coupling constraint model is established, and its calculation expression is as follows:

[0114]

[0115] Where, represents the output coupling constraint index;

[0116] At the same time, in order to suppress the coupling interference at the input end, the parasitic motion along the other l≠k direction must be eliminated. Among them, it is necessary to consider both input and output displacement, undesirable parasitic motion Not only for the input displacement u in，k Generates interference and shifts the desired output u out,kIt will also affect the positioning accuracy. Therefore, based on the minimum operator selection principle, an input coupling constraint model is established, and its calculation expression is as follows:

[0117]

[0118] Where, * represents the input coupling constraint index;

[0119] In the specified entity area Ω s Output O out and The motion displacement suppression function between the output terminals O out and The motion displacement deviation constraint between them is calculated as follows:

[0120]

[0121] Where, ζ * Represents the output end motion displacement deviation constraint index;

[0122] Step 4: Construct input and output flexibility constraints;

[0123] When the load acts on the input terminal O on the left side of the design domain in,k When k=1,2, input terminal O in,k and output terminal O out,k Both produce corresponding elastic deformation u in,k and u out,k According to the elastic beam theory, the input compliance characteristics of the mechanism are obtained by the following formula:

[0124]

[0125] Where k in,k =c in,k -1 Represents the input stiffness characteristics, which includes the preset input virtual spring stiffness value Considering that if the mechanism has an input end displacement u in,k Very small, the input end stiffness k in,k will be very large, which may satisfy the constraints of the aforementioned objective function and motion coupling function. To avoid this, the input displacement constraint function u is introduced in,k ≥u * , where u * represents the input displacement constraint index,

[0126] At the same time, considering the motion transfer factor θ of the mechanism k is represented as:

[0127]

[0128] Where θ * represents the motion transfer factor constraint index;

[0129] Step 5: Construct global stress constraints;

[0130] In the static design of compliant mechanisms, equivalent stress is usually used to evaluate their reliability. Therefore, equivalent stress is introduced into the topology optimization of compliant mechanisms as a way to measure stress. In the case of plane stress, the specific expression of equivalent stress is:

[0131]

[0132] Where σ i,x and σ i,y denote the principal stress of the ith element along the x and y directions, τ i,xy represents the shear stress of the i-th unit, V represents the auxiliary matrix, σ i The element stress vector representing the stress measurement point;

[0133] The P-norm stress measurement method is used to control the maximum stress. The P-norm stress measurement method is expressed as:

[0134]

[0135] Where, v i represents the material volume of the element, and P represents the stress norm parameter, which determines the closeness between the P-norm stress and the actual maximum stress;

[0136] In order to make the P-norm stress closer to the actual maximum stress, the adaptive constraint scaling method is used to improve the convergence and accuracy of the optimization algorithm, and further improve the closeness between the P-norm stress and the actual maximum stress. The corrected P-norm stress measurement is expressed as:

[0137]

[0138] Where c κ is the coefficient of the adaptive constraint scaling method;

[0139] On the left side of the design domain, input terminal O in,1 and O in,2 Mainly driven by the driving force F of the two piezoelectric actuators in,1 and F in,2 , and the stress generated along the x-axis direction at the two input ends is much smaller than the stress generated along the y-axis direction, so considering the two maximum loads and When the stress acts simultaneously, the stress constraint for topology optimization of the compliant mechanism is described as:

[0140]

[0141] Where σ s represents the yield strength of the material, α f Represents the safety factor of the material, α f >1,σ * Represents the global stress constraint index, that is, the allowable stress of the material;

[0142] Step 6: Modal frequency sensitivity analysis;

[0143] Perform relevant modal frequency sensitivity analysis on the objective function. In dynamics, the eigenvector {Φ m}For the mass matrix M, it has the normalization property {Φ m} T ·M·{Φ m}=1, so the objective function is designed for variables The first-order sensitivity solution of simplifies to:

[0144]

[0145] Step 7: Motion decoupling sensitivity analysis;

[0146] Perform motion decoupling sensitivity analysis on the objective function and output the coupling constraint function For design variables The sensitivity is expressed as:

[0147]

[0148] Input coupling constraint function υ k,l For design variables The sensitivity is expressed as:

[0149]

[0150] Output O out and The motion displacement deviation constraint ζ l For design variables The sensitivity is expressed as:

[0151]

[0152] Step 8: Input and output flexibility sensitivity analysis;

[0153] The relevant flexibility sensitivity analysis is performed on the objective function, and the static flexibility of the structure is defined as: From the equilibrium equation K·U k =Fin,k , we can see that Λ=-U k , then the static flexibility of the structure c in,k The sensitivity expression is:

[0154]

[0155] Structural motion transfer factor θ k For design variables The sensitivity is expressed as:

[0156]

[0157] Step 9: Global stress sensitivity analysis;

[0158] Stress constraint σ max Sensitivity analysis of the design variables The sensitivity of is chain-derived to obtain:

[0159]

[0160] Step 10: Volume constraint sensitivity analysis;

[0161] Volume constraint V on design variables The sensitivity expression is:

[0162]

[0163] Finally, the moving asymptote method (MMA) algorithm is used to optimize and solve the above mathematical model. At the same time, the density filtering method is used to solve the numerical solution problem and numerical instability problem.

[0164] The present invention adopts the topology optimization method to design the compliant mechanism. Under the premise of satisfying a series of constraints, the optimal mechanism configuration-parameter design can be sought under a given design domain and specified input and output functions, so as to achieve the optimal mechanism performance.

[0165] The foregoing description is merely an advantageous embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that the present invention is susceptible to various modifications and variations. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A topology optimized dual-axis decoupling tool servo device, characterized in that: It includes a compliant mechanism platform (6), a piezoelectric stack 1 (9), a piezoelectric stack 2 (11), a diamond tool (3), a measuring baffle (2), a capacitive displacement sensor 1 (14), a capacitive displacement sensor 2 (15), and an upper cover plate (16). The piezoelectric stack 1 (9) and the piezoelectric stack 2 (11) are pre-tightened on the compliant mechanism platform (6) through the wedge block 1 (8) and the wedge block 2 (10), respectively. The driving directions of the piezoelectric stack 1 (9) and the piezoelectric stack 2 (11) are consistent. The capacitive displacement sensor 1 (14) and the capacitive displacement sensor 2 (15) are respectively installed in the capacitive displacement sensor through hole 1 and the capacitive displacement sensor through hole 2 of the upper cover (16). The measuring baffle (2) is installed on the compliant mechanism platform (6) and is located at the front end of the capacitive displacement sensor 1 (14) and the capacitive displacement sensor 2 (15). The front end of the compliance mechanism platform (6) includes a tool seat platform (13), and the diamond tool (3) is installed on the tool seat platform (13). The compliance mechanism platform (6) also includes a topological compliance mechanism (1), an input guide mechanism (7), an input guide mechanism (2) (12) and an output guide mechanism (5). The output guide mechanism (5) is located at the front end of the compliance mechanism platform (6), and the rear end of the topological compliance mechanism (1) is connected to the front ends of the input guide mechanism (7) and the input guide mechanism (2) (12). The front end of the topological compliance mechanism (1) is connected to the output guide mechanism (5), the rear end of the input guide mechanism (7) contacts the front end of the piezoelectric stack (9), and the rear end of the input guide mechanism (12) contacts the front end of the piezoelectric stack (11). The input guide mechanism (7) and the input guide mechanism (12) are double parallelogram hinge structures, and the double parallelogram hinge structure includes four straight plate type flexible hinges. The output end of the output guide mechanism (5) is a symmetrical V-shaped flexible hinge.

2. The topology optimized dual-axis decoupling tool servo device according to claim 1, characterized in that: The piezoelectric stack 1 (9) and the piezoelectric stack 2 (11) are fixed to the compliant mechanism platform (6) via the wedge block pre-tightening screw 1 and the wedge block pre-tightening screw 2 respectively.

3. The topology optimized dual-axis decoupling tool servo device according to claim 1, characterized in that: Capacitive displacement sensor 1 (14) and capacitive displacement sensor 2 (15) are fixed on the upper cover plate (16) by capacitive displacement sensor pre-tightening screw 1 and capacitive displacement sensor pre-tightening screw 2, respectively.

4. The topology optimized dual-axis decoupling tool servo device according to claim 1, characterized in that: The diamond tool (3) is mounted on the tool holder platform (13) via a fastening screw 4.

5. The design method of a topology optimized dual-axis decoupling tool servo device according to any one of claims 1 to 4, characterized in that: The following steps are involved: Step 1: Construct a spring model based on topology optimization of the compliant mechanism; The spring model consists of a continuous design domain and a spring with known stiffness. The design domain is divided into three parts: the designable region Ω d , the specified entity area Ω s and the specified empty material area Ω v By integrating the kinematic characteristics of the mechanism design and the elastic mechanical characteristics of the structure design, an optimized mathematical description form of the stiffness-decoupling-strength model based on the structural characteristic system is established to meet the requirements of the compliant mechanism system with input-output decoupling and high-frequency response performance. Combined with the improved SIMP method, the specific mathematical model is constructed as follows: Where, represents the set of design variables, n represents the total number of unit design variables, V represents the material usage volume, V * represents the upper limit of the material volume, U represents the global displacement matrix caused by the external load vector F of the node, Φ m is the mth order eigenvalue λ m The relevant eigenvector, m represents the number of degrees of freedom N corresponding to the structure dof All modes of and v * denote the maximum allowable output and input coupling constraint indices, ζ * Express the maximum allowable output end rotation coupling constraint index, c * and u * They represent the input flexibility constraint and input displacement constraint indices, θ * Express the motion transfer factor constraint index, σ * represents the global maximum stress constraint index; Step 2: Set the modal frequency as the objective function; To ensure that the compliant mechanism has specific performance characteristics and to optimize it towards the preset performance direction, the first-order natural frequency of the compliant mechanism is set as the objective function for optimization. Based on the Rayleigh quotient principle, the eigenvalue of any order of the system motion equation can be expressed as: In the formula, m is 1; Step 3: Construct motion coupling constraints; Considering that the given design domain needs to be topologically transformed into a compliant mechanism with complete motion decoupling, an appropriate input-output coupling suppression strategy is first constructed to guide the material distribution in the design domain to continuously evolve towards the expected performance. When the input terminal O is located on the left side of the design domain in,k The piezoelectric actuator is excited to generate a load F in,k When acting in the x direction, k=1,2, driving the output terminal O out In F in,1 When it acts, it moves in the x direction and produces the corresponding desired output displacement u out,1 , drive output terminal O out In F in,2 When it acts, it moves in the y direction and produces the corresponding desired output displacement u out,2 , due to the internal structural connection of the mechanism, at the output end O out The corresponding parasitic motion is generated along the lateral direction l At the same time, a corresponding parasitic motion is also generated in the lateral direction of the input end. Based on the principle of kinematic geometry, in order to suppress the coupling interference at the output end, the parasitic motion along the other k≠l direction must be eliminated. The output coupling constraint model is established, and its calculation expression is as follows: Where, represents the output coupling constraint index; At the same time, in order to suppress the coupling interference at the input end, the parasitic motion along the other l≠k direction must be eliminated. Among them, it is necessary to consider both input and output displacement, undesirable parasitic motion Not only for the input displacement u out,k Generates interference and shifts the desired output u out,k It will also affect the positioning accuracy. Therefore, based on the minimum operator selection principle, an input coupling constraint model is established, and its calculation expression is as follows: Where, v * represents the input coupling constraint index; In the specified entity area Ω s Output O out and The motion displacement suppression function between the output terminals O out and The motion displacement deviation constraint between them is calculated as follows: Where, ζ * Represents the output end motion displacement deviation constraint index; Step 4: Construct input and output flexibility constraints; When the load acts on the input terminal O on the left side of the design domain in,k When k=1,2, input terminal O in,k and output terminal O out,k Both produce corresponding elastic deformation u in,k and u out,k According to the elastic beam theory, the input compliance characteristics of the mechanism are obtained by the following formula: Where k in,k =c in,k -1 Represents the input stiffness characteristics, which includes the preset input virtual spring stiffness value Introduce the input displacement constraint function u in,k ≥u * , where u * represents the input displacement constraint index, At the same time, considering the motion transfer factor θ of the mechanism k is represented as: Where θ * represents the motion transfer factor constraint index; Step 5: Construct global stress constraints; In the static design of compliant mechanisms, equivalent stress is usually used to evaluate their reliability. Therefore, equivalent stress is introduced into the topology optimization of compliant mechanisms as a way to measure stress. In the case of plane stress, the specific expression of equivalent stress is: Where σ i,x and σ i,y denote the principal stress of the ith element along the x and y directions, τ i,xy represents the shear stress of the i-th unit, V represents the auxiliary matrix, σ i The element stress vector representing the stress measurement point; The P-norm stress measurement method is used to control the maximum stress. The P-norm stress measurement method is expressed as: Where, v i represents the material volume of the element, and P represents the stress norm parameter, which determines the closeness between the P-norm stress and the actual maximum stress; In order to make the P-norm stress closer to the actual maximum stress, the adaptive constraint scaling method is used to improve the convergence and accuracy of the optimization algorithm, and further improve the closeness between the P-norm stress and the actual maximum stress. The corrected P-norm stress measurement is expressed as: Where c κ is the coefficient of the adaptive constraint scaling method; On the left side of the design domain, input terminal O in,1 and O in,2 Mainly driven by the driving force F of the two piezoelectric actuators in,1 and F in,2 , and the stress generated along the x-axis direction at the two input ends is much smaller than the stress generated along the y-axis direction, so considering the two maximum loads and When the stress acts simultaneously, the stress constraint for topology optimization of the compliant mechanism is described as: Where σ s represents the yield strength of the material, α f Represents the safety factor of the material, α f >1,σ * Represents the global stress constraint index, that is, the allowable stress of the material; Step 6: Modal frequency sensitivity analysis; Perform relevant modal frequency sensitivity analysis on the objective function. In dynamics, the eigenvector Φ m For the mass matrix M with normalized properties {Φ m } T ·M·{Φ m }=1, so the objective function is designed for variables The first-order sensitivity solution of simplifies to: Step 7: Motion decoupling sensitivity analysis; Perform motion decoupling sensitivity analysis on the objective function and output the coupling constraint function For design variables The sensitivity is expressed as: Input coupling constraint function υ k,l For design variables The sensitivity is expressed as: Output O out and The motion displacement deviation constraint ζ l For design variables The sensitivity is expressed as: Step 8: Input and output flexibility sensitivity analysis; The relevant flexibility sensitivity analysis is performed on the objective function, and the static flexibility of the structure is defined as: From the equilibrium equation K·U k =F in,k , we can see that Λ=-U k , then the static flexibility of the structure c in,k The sensitivity expression is: Structural motion transfer factor θ k For design variables The sensitivity is expressed as: Step 9: Global stress sensitivity analysis; Stress constraint σ max Sensitivity analysis of the design variables The sensitivity of is chain-derived to obtain: Step 10: Volume constraint sensitivity analysis; Volume constraint V on design variables The sensitivity expression is: Finally, the above mathematical model is optimized and solved using the moving asymptote method. At the same time, the density filtering method is used to solve the numerical solution problem and numerical instability problem.

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