Double-shaft complete decoupling cutter servo device and design method thereof

Abstract

The invention discloses a biaxial complete decoupling cutter servo device and a design method thereof, and the biaxial complete decoupling cutter servo device comprises a compliant mechanism platform, a piezoelectric stack I, a piezoelectric stack II, a diamond cutter, a measuring baffle plate, a capacitive displacement sensor I, a capacitive displacement sensor II and an upper cover plate, the diamond cutter is installed on the cutter holder platform, the compliant mechanism platform further comprises a topology compliant mechanism, a first input guide mechanism, a second input guide mechanism 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 topology compliant mechanism is connected with the front end of the first input guide mechanism and the front end of the second input guide mechanism. According to the method, the compliant mechanism is designed by adopting a topological optimization method, and the optimal mechanism configuration-parameter design can be sought under the condition that a design domain and specified input and output effects are given and a series of constraint conditions are met, so that the mechanism performance is optimal.

Description

Technical Field

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

[0002] The diamond turning method based on the Fast Tool Servo (FTS) system has become an important technology in the field of ultra-precision manufacturing of microstructured functional surfaces. This method can accurately control the removal of materials at the micro-nano scale by adjusting the position of the tool in real time during the turning process, thereby achieving ultra-precision machining of the surface.

[0003] The core of this method lies in the design of its compliant mechanism, which affects the large stroke, high bandwidth and nanometer-level motion accuracy of the FTS system. However, no matter what kind of drive mode the FTS system uses, there is a mutual constraint between its motion stroke and working bandwidth. Therefore, further improving the balance between the motion stroke and working bandwidth of the mechanism has become an important goal of compliant mechanism design.

[0004] Since the compliant mechanism transmits motion through the elastic deformation of the material, this means that when the mechanism is subjected to multiple loads, these loads will interfere with each other, which may cause the motion positioning accuracy of the compliant mechanism to decrease, or even fail to complete the positioning function, which will eventually increase the control difficulty of the mechanism. Therefore, considering how to design the compliant mechanism and improve the positioning accuracy is the main issue in reducing the control difficulty of the compliant mechanism.

[0005] At the same time, in order to ensure the reliability of the compliant mechanism during effective operation, the stress distribution must be fully considered during its design stage. The movement process of the mechanism may cause higher stress concentration in local areas, which may cause problems such as material fatigue, deformation or cracking. To avoid this, designers need to ensure that the stress of the mechanism remains within a controllable range throughout the movement process and does not exceed the allowable stress limit of the material. Therefore, considering stress control is a key aspect to ensure the reliability of the compliant mechanism.

[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 dual-axis fully decoupled tool servo device and a design method thereof.

[0008] The technical solution adopted by the present invention is: a dual-axis fully decoupled tool servo device, including a compliant 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 piezoelectric stack 1 and the piezoelectric stack 2 are pre-tightened on the compliant mechanism platform through the wedge block 1 and the wedge block 2 respectively. The driving directions of the piezoelectric stack 1 and the piezoelectric stack 2 are consistent. The capacitive displacement sensor 1 and the capacitive displacement sensor 2 are respectively installed in the capacitive displacement sensor through hole 1 and the capacitive displacement sensor through hole 2 of the upper cover plate. The measuring baffle is installed on the compliant mechanism platform and is located at the front end of the capacitive displacement sensor 1 and the capacitive displacement sensor 2.

[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, 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, 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, the double parallelogram hinge structures include four straight plate type flexible hinges, and the output end of the output guide mechanism is a symmetrical V-shaped flexible hinge.

[0011] Furthermore, the piezoelectric stack 1 and the piezoelectric stack 2 are fixed to the compliant mechanism platform by means of the wedge block pre-tightening screw 1 and the wedge block pre-tightening screw 2 respectively.

[0012] Furthermore, the capacitive displacement sensor 1 and the capacitive displacement sensor 2 are fixed on the upper cover plate by means of 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 means of a fastening screw.

[0014] According to the above-mentioned design method of the dual-axis fully decoupled tool servo device, the following steps are included:

[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 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 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] In the formula, 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 * denote the maximum allowable output and input coupling constraint indices, ζ * Express the maximum permissible output end rotation coupling constraint index, c * and u * They represent the input flexibility constraint and input displacement constraint indices respectively, 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] In order to ensure that the compliant mechanism has specific performance characteristics and optimize it towards the preset performance direction, the first-order natural frequency of the compliant mechanism is set as the objective function of its 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 function, an appropriate input-output coupling suppression strategy is first constructed to guide the material distribution of the design domain to continuously evolve in the direction of expected performance.

[0025] When the input port 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 along the x direction to produce the corresponding expected output displacement u out,1 , drive output terminal O out In F in,2 When it acts, it moves in the y direction to produce the corresponding expected 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 l direction 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] In the formula, 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 displacements, undesirable parasitic motion Not only for the input displacement u in,k produces 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] In the formula, υ * 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] In the formula, 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 port 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 The corresponding elastic deformation u in,k and u out,k According to the elastic beam theory, the input flexibility characteristics of the mechanism are obtained by the following formula:

[0037]

[0038] In the formula, 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] In the formula, 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 topological 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] In the formula, 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 ith element, 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] In the formula, v i represents the material volume of the unit, 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] In the formula, 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 two piezoelectric actuators F 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 of the topology optimization of the compliant mechanism is described as:

[0053]

[0054] In the formula, 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, therefore, the objective function is used to design the variables The first-order sensitivity solution of simplifies to:

[0057]

[0058] Step 7: Motion decoupling sensitivity analysis;

[0059] Perform relevant 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 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 know 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 algorithm. At the same time, the density filtering method is used to solve the numerical solution problem and numerical instability problem.

[0077] Compared with the prior art, the present invention has the following beneficial effects: the present invention adopts two piezoelectric stack drives, has multiple advantages, including higher acceleration, fast response time, high output force density, high positioning accuracy and sub-nanometer motion resolution, adopts topological method 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 calculation;

[0078] The piezoelectric stack drive device adopts a compliant mechanism topology structure, 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, excellent flexibility, easy to achieve precision control of micro-displacement motion, and easy to control the motion trajectory of the tool motion platform in space. In terms of the guiding mechanism, the use of double parallel straight plate type flexible hinges and symmetrical V-shaped flexible hinges has the advantages of good flexibility and symmetrical distribution, which are easy to control the precision of micro-displacement motion and realize the function and performance of virtual springs. The double parallel straight plate type flexible hinge 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 can not only realize motion in the x-axis direction, but also realize 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] The piezoelectric stack 1 and the piezoelectric stack 2 drive independent flexible hinges in the same direction without coupling with each other, thus achieving high control accuracy of the flexible device. Meanwhile, the motion trajectory can be achieved by adjusting the parameters of the piezoelectric stack driving signal.

[0080] The present invention adopts 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 driving 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 technical progress and application prospects to related fields.

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

[0083] Figure 1 It 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 It is a global control block diagram of the dual-axis fully decoupled tool servo turning system of the present invention. DETAILED DESCRIPTION

[0088] The specific implementation modes of the present invention are described in detail below with reference to the accompanying drawings.

[0089] Combination Figure 1-5 A dual-axis fully decoupled 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 1 14, a capacitive displacement sensor 2 15, and an upper cover 16.

[0090] 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 plate 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.

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

[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 ends 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 structures include four straight plate type 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 compliant mechanism platform 6 by means of a wedge block pre-tightening screw 1 and a wedge block pre-tightening screw 2, respectively.

[0094] Furthermore, the capacitive displacement sensor 1 14 and the capacitive displacement sensor 2 15 are fixed on 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 by means of a fastening screw 4 .

[0096] In addition, see Figure 5 As shown, the patent of the present 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 only the driving signal is applied to the piezoelectric stack 11 and the piezoelectric stack 19 is not driven by the driving signal, the piezoelectric stack 19 will not work, and only the piezoelectric stack 11 will work. In this way, decoupled motion along the x-axis direction can be achieved. Similarly, when only the driving signal is applied to the piezoelectric stack 19 and the piezoelectric stack 11 is not driven by the driving signal, the piezoelectric stack 11 will not work, and only the piezoelectric stack 19 will work. In this way, decoupled motion along the y-axis direction can be achieved. This working method is suitable for application scenarios with relatively general positioning accuracy requirements.

[0099] (2) When the driving signal is applied to the two piezoelectric stacks, a typical PID controller with a feedforward compensator is used at the same time, which can effectively improve the stability of the system and have higher tracking accuracy. Therefore, this working mode is suitable for applications with high precision requirements and large travel.

[0100] Through the above two working modes, the device of the present invention can flexibly select the working mode according to the needs of specific application scenarios to achieve decoupled motion in different directions or high-precision linkage control. This makes the device widely applicable in various application fields and brings 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 a spring 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 structure design, an optimized mathematical description form 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] In the formula, 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 * denote the maximum allowable output and input coupling constraint indices, ζ * Express the maximum permissible output end rotation coupling constraint index, c * and u * They represent the input flexibility constraint and input displacement constraint indices respectively, 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] In order to ensure that the compliant mechanism has specific performance characteristics and optimize it towards the preset performance direction, the first-order natural frequency of the compliant mechanism is set as the objective function of its 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 function, an appropriate input-output coupling suppression strategy is first constructed to guide the material distribution of the design domain to continuously evolve in the direction of 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 along the x direction to produce the corresponding expected output displacement u out,1 , drive output terminal O out In F in,2 When it acts, it moves in the y direction to produce the corresponding expected 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 l direction 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] In the formula, 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 displacements, undesirable parasitic motion Not only for the input displacement u in,k produces 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] In the formula, υ * 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] In the formula, 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 port 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 The corresponding elastic deformation u in,k and u out,k According to the elastic beam theory, the input flexibility characteristics of the mechanism are obtained by the following formula:

[0124]

[0125] In the formula, 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 When the input stiffness k is very small, in,k will be very large, which may satisfy the constraints of the aforementioned objective function and motion coupling function. To avoid this situation, 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] In the formula, 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 topological 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] In the formula, 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 ith element, 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] In the formula, v i represents the material volume of the unit, 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] In the formula, 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 two piezoelectric actuators F 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 of the topology optimization of the compliant mechanism is described as:

[0140]

[0141] In the formula, 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, therefore, the objective function is used to design the variables The first-order sensitivity solution of simplifies to:

[0144]

[0145] Step 7: Motion decoupling sensitivity analysis;

[0146] Perform relevant 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 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 =F in,k , we know that Λ=-U k , then the static flexibility of the structure cin,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 a topological optimization method to design a compliant mechanism. Under the condition of a given design domain and specified input and output functions, and under the premise of satisfying a series of constraints, the best mechanism configuration-parameter design can be sought, thereby achieving optimal mechanism performance.

[0165] The above description is only an advantageous embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A dual-axis fully decoupled tool servo device, characterized in that: It comprises a compliant mechanism platform (6), a first piezoelectric stack (9), a second piezoelectric stack (11), a diamond tool (3), a measuring baffle (2), a first capacitive displacement sensor (14), a second capacitive displacement sensor (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 plate (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 holder platform (13), and the diamond tool (3) is installed on the tool holder platform (13). The compliance mechanism platform (6) also includes a topological compliance mechanism (1), an input guide mechanism 1 (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 1 (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) is in contact with the front end of the piezoelectric stack (9), and the rear end of the input guide mechanism (12) is in contact with 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 dual-axis fully decoupled 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) by means of a wedge block pre-tightening screw 1 and a wedge block pre-tightening screw 2 respectively.

3. The dual-axis fully decoupled 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 dual-axis fully decoupled 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 the dual-axis fully decoupled 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 area 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 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: In the formula, 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 * denote the maximum allowable output and input coupling constraint indices, ζ * Express the maximum permissible output end rotation coupling constraint index, c * and u * They represent the input flexibility constraint and input displacement constraint indices respectively, 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; In order to ensure that the compliant mechanism has specific performance characteristics and optimize it towards the preset performance direction, the first-order natural frequency of the compliant mechanism is set as the objective function of its 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 function, an appropriate input-output coupling suppression strategy is first constructed to guide the material distribution of the design domain to continuously evolve in the direction of 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 expected output displacement u out,1 , drive output terminal O out In F in,2 When it acts, it moves along the y direction to produce the corresponding expected 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 l direction 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: In the formula, 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 displacements, undesirable parasitic motion Not only for the input displacement u out,k produces 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: In the formula, υ * 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: In the formula, 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 port 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 The corresponding elastic deformation u in,k and u out,k According to the elastic beam theory, the input flexibility characteristics of the mechanism are obtained by the following formula: In the formula, 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: In the formula, 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 topological optimization of compliant mechanisms as a way to measure stress. In the case of plane stress, the specific expression of equivalent stress is: In the formula, 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 ith element, 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: In the formula, v i represents the material volume of the unit, 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: In the formula, 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 two piezoelectric actuators F 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 of the topology optimization of the compliant mechanism is described as: In the formula, σ s represents the yield strength of the material, α f Represents the safety factor of the material, α f >1,σ * It 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, it has the normalization property {Φ m } T ·M·{Φ m }=1, therefore, the objective function is used to design the variables The first-order sensitivity solution of simplifies to: Step 7: Motion decoupling sensitivity analysis; Perform relevant motion decoupling sensitivity analysis on the objective function and output 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 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 know 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 algorithm. At the same time, the density filtering method is used to solve the numerical solution problem and numerical instability problem.

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