A rectangular planar voice coil motor optimization method for active-passive vibration isolation platform

Abstract

This invention provides an optimization method for a rectangular flat-plate voice coil motor for active and passive vibration isolation platforms, comprising: establishing a model of the voice coil motor; selecting parameters for optimization based on the model; obtaining optimization objectives for the motor, including peak thrust, coil density, and coil inductance; analyzing the sensitivity relationship between the motor parameters and the optimization objectives, and establishing a response surface based on an optimal prognostic surrogate model; and performing multi-objective optimization based on the EA algorithm based on the analysis results of the sensitivity relationship and the constraint conditions. After applying the method of this invention, the resonance peak near the natural frequency of the system is significantly reduced after inductance optimization, and the transmissibility decreases by approximately 30 dB compared to before optimization, effectively suppressing resonance amplification. Simultaneously, the mid-to-high frequency curves are smoother, and vibration transmission is further reduced, indicating that inductance optimization improves the velocity feedback damping injection capability and overall vibration isolation performance.

Description

Technical Field

[0001] This invention relates to the field of motor optimization, specifically to an optimization method for a rectangular flat-plate voice coil motor for active and passive vibration isolation platforms. Background Technology

[0002] Active and passive vibration isolation platforms are key fundamental components in precision manufacturing, optical measurement, and microelectronic equipment, and their performance directly affects the positioning accuracy and operational stability of high-end equipment. In recent years, with the increasing demands on vibration environments from ultra-precision machining and testing technologies, the application of active vibration isolation systems in high-performance equipment has been continuously expanding, and their dynamic response speed, output accuracy, and stability are also facing higher requirements.

[0003] As the core direct-drive actuator of the active vibration isolation system, the linearity of the output force, response bandwidth and thermal stability of the voice coil motor directly affect the vibration isolation performance of the system.

[0004] However, when targeting the specific application of active vibration isolation, rectangular voice coil motors still require comprehensive optimization in terms of high linearity output, low thermal drift, lightweight structure, and high rigidity support to simultaneously achieve high-frequency response, high precision, and high reliability in vibration isolation operation. However, there is currently no effective method for motor optimization. Summary of the Invention

[0005] The objective of this invention is achieved through the following technical solutions.

[0006] This invention proposes an optimization method for rectangular flat-plate voice coil motors for active and passive vibration isolation platforms. To this end, this invention will focus on the actual requirements of active and passive vibration isolation platforms for actuators, conducting multi-physics collaborative design and optimization research on rectangular voice coil motors to improve their overall performance and provide key component support for the development of high-performance active vibration isolation systems.

[0007] Specifically, this invention provides an optimization method for a rectangular flat-plate voice coil motor for active and passive vibration isolation platforms, comprising: A model of the voice coil motor is established; parameters for motor optimization are selected based on the model; the optimization objectives of the motor are obtained, including peak thrust, coil current density, and coil inductance; the sensitivity relationship between the motor parameters and the optimization objectives is analyzed, and a response surface is established based on the optimal prognostic surrogate model; based on the analysis results of the sensitivity relationship and the constraints, multi-objective optimization based on the EA algorithm is performed.

[0008] The advantages of this invention are: After applying the method of this invention, the resonance peak near the natural frequency of the system after inductor optimization is significantly reduced, and the transmissibility decreases by about 30 dB compared to before optimization, effectively suppressing the resonance amplification phenomenon. At the same time, the mid-to-high frequency curves are smoother, and vibration transmission is further reduced, indicating that inductor optimization improves the velocity feedback damping injection capability and overall vibration isolation performance. Attached Figure Description

[0009] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 A mesh partition diagram of a voice coil motor model according to an embodiment of the present invention is shown.

[0010] Figure 2 A magnetic flux density cloud diagram of a voice coil motor model according to an embodiment of the present invention is shown.

[0011] Figure 3 The diagram shows the vibration isolation effect of an inductor in an active vibration isolation system.

[0012] Figure 4 A schematic diagram of the parameterization of a voice coil motor according to an embodiment of the present invention is shown.

[0013] Figure 5 A schematic diagram illustrating the total impact of seven design parameters on three output objectives is shown.

[0014] Figure 6 A three-dimensional diagram illustrating the relationship between thrust and design variables is shown.

[0015] Figure 7 A three-dimensional diagram illustrating the relationship between inductance and design variables is shown.

[0016] Figure 8 A three-dimensional diagram illustrating the relationship between electrical density and design variables is shown.

[0017] Figure 9 A schematic diagram of a 3D Pareto front according to an embodiment of the present invention is shown.

[0018] Figure 10 A schematic diagram of the optimal solution of motor optimization design parameters according to an embodiment of the present invention is shown.

[0019] Figure 11 A schematic diagram of the response results of optimized design parameters according to an embodiment of the present invention is shown.

[0020] Figure 12 The time-domain plot of the vibration signal after the addition of active control is shown.

[0021] Figure 13 A schematic diagram of a 3D Pareto front according to an embodiment of the present invention is shown. Detailed Implementation

[0022] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0023] In this invention, the voice coil motor has two layers of permanent magnet arrays, forming a symmetrical layout along both the x and y axes. To ensure sufficient ease of installation, the motor has mounting plates at both the top and bottom. The motor body, from top to bottom, consists of a yoke, permanent magnet array, coil, and bracket. The yoke enhances the magnetic flux path, and the energized coil is fixed to the upper mounting plate by the bracket. This achieves a zero-stiffness design for the voice coil motor, eliminating the mechanical connection between the permanent magnet array and the bracket.

[0024] 1. Problem Analysis 1.1 Air gap magnetic field of motor A 3D model of the unoptimized motor was created. Motor dimensional parameters were set in ANSYS / MAXWELL software. The magnet material was NdFe-35, with a remanence Br of 1.3T and coercivity Hc of 899000 A / m. The yoke material was DT4C with a magnetic saturation of 2.07T. The voice coil motor model was as follows: Figure 1 As shown, mesh generation is required before solving the finite element analysis.

[0025] After the mesh is generated, the solution is performed. For example... Figure 2 The image shown is a magnetic density cloud map.

[0026] Examining the magnetic field strength curve, the magnetic flux density waveform in the air gap exhibits a double-peak shape, approaching zero near the permanent magnet connection point. The coil needs to be positioned within the effective peak region of the magnetic flux density to effectively utilize the air gap flux density. Furthermore, the peak value of the air gap flux density is 0.32T, indicating that the air gap magnetic field of the voice coil motor prototype requires further optimization.

[0027] 1.2 Coil Inductance There is an active vibration isolation dynamic model: in: Voice coil motor coil resistance (Ω); : Voice coil motor coil inductance (H); : Force constant of voice coil motor (N / A); : Back electromotive force coefficient (V·s / m); The equivalent mass of the upper plate and its load on the vibration isolation platform; Laplace complex variable; and The equivalent stiffness and damping for passive vibration isolation.

[0028] X(s): Output displacement signal (Laplace transform of the mass block displacement). That is, the absolute displacement of the vibration isolation platform relative to the ground.

[0029] Y(s): Input displacement signal (Laplace transform of base disturbance). That is, the external vibration or base movement input to the vibration isolation system.

[0030] U(s): Control voltage signal (Laplace transform of the controller's input voltage). That is, the drive voltage applied to the voice coil motor actuator.

[0031] The vibration isolation effect of different inductors in an active vibration isolation system is analyzed using MATLAB / Simulink software.

[0032] Figure 3 As can be seen, increasing the inductance raises the resonance peak near the natural frequency by about 6dB, limiting the injection of velocity feedback damping; at the same time, the vibration isolation initiation frequency is pushed up, and low-frequency vibration isolation deteriorates. Therefore, it is necessary to optimize the inductance to suppress the peak and enter the vibration isolation zone earlier.

[0033] Optimized design of 2 voice coil motors 2.1 Optimize parameters The voice coil motor structure proposed in this invention is still based on the Lorentz force principle. The two main factors generating the Lorentz force are a magnetic field and current. As mentioned earlier, this voice coil motor structure is a moving coil type, and the stator already generates a uniform air gap magnetic field. Now, a current perpendicular to the magnetic field needs to be passed through the coil to generate the Lorentz force. The dimensions of the voice coil motor actuator are as follows... Figure 4 As shown in Table 1, the meaning and values ​​of the parameters are as follows.

[0034] Considering the mutual constraints and influences between input and output parameters, the variables for motor optimization are set to seven: yoke. Magnet height Coil width Coil height Coil current Number of coil turns Motor depth .

[0035] Table 1 Initial values ​​of optimization variables 2.2 Optimization Objectives 2.2.1 Motor thrust To address the active vibration control requirements of precision vibration isolation platforms, the upper plate of the vibration isolation platform and its load are equivalent to a single-degree-of-freedom mass block. The base position is moved to The displacement of the upper plate is The dynamic equation of an active vibration isolation system can be written as follows: in This is the output force of the voice coil motor. The equivalent disturbance force of the machine itself. and The equivalent stiffness and damping for passive vibration isolation.

[0036] Ground vibration is transmitted to the active vibration isolation platform through its base; this ground vibration can be considered as a motion excitation of the base. When the ground vibrates, even without considering the machine's own disturbance, the upper plate and its load on the active vibration isolation platform will experience relative motion due to inertia. To suppress this interference between the active and passive vibration isolation platforms caused by ground vibration, the voice coil motor needs to output a compensating force. This invention utilizes the ground vibration velocity amplitude envelope. To characterize the ground excitation intensity. At a frequency of Under sinusoidal vibration conditions, ground velocity amplitude With the corresponding acceleration amplitude Satisfies a sine relationship: This acceleration can be understood as the base's frequency... The equivalent motion excitation applied to the platform. When the goal of active control is to minimize the acceleration and displacement response of the upper plate, the main function of the output force required by the voice coil motor is to counteract the inertial effect caused by the base. Therefore, in the thrust demand estimation stage, this invention adopts a conservative approximation dominated by the inertial effect, that is, assuming that the voice coil motor is mainly used to counteract the platform's inertial response caused by ground vibration.

[0037] in: The equivalent mass of the upper plate and its load on the vibration isolation platform; : The required compensation thrust amplitude for the voice coil motor; : Acceleration amplitude; The frequency of ground vibration; : The velocity amplitude of ground vibration at a given frequency.

[0038] After testing, the peak ground vibration velocity in the laboratory was 45. .

[0039] 2.2.2 Motor Response In actual operating conditions, voice coil motors are not always in a stable state; they mostly operate in a state of acceleration, constant speed, and deceleration. The dynamic response time of a voice coil motor is affected by the coil inductance L. The voltage balance equation for a voice coil motor is: in: Drive voltage (V) Coil current (A) Coil resistance (Ω) : Coil inductance (H) Back electromotive force coefficient (V·s / m) Speed ​​of movement (m / s) Ignoring the back electromotive force term, the current response can be expressed as: in τ is the electrical time constant, which determines the rise of the motor current to its steady-state value. In the design of voice coil motors, optimizing τ is a key parameter for improving dynamic response performance. τ is related to both inductance L and resistance R. Reducing the coil inductance L or increasing the resistance R requires coordinated design to avoid conflicts during optimization. However, increasing the resistance R will inevitably lead to increased heat in the coil, so reducing the inductance L is the primary goal in the optimization design.

[0040] Due to the size limitations of the active and passive vibration isolation platform, the width of the voice coil motor is limited to less than 60mm, the height to less than 30mm, and the depth to less than 70mm. The main design parameters for the voice coil motor of this invention are peak thrust F, coil current density J, and coil inductance L. The design objectives can be expressed as follows.

[0041] 3. Motor parameter sensitivity analysis Sensitivity analysis is a method for studying and analyzing how sensitive changes in the state or output of a model are to changes in system parameters or surrounding conditions. Sensitivity analysis can determine which parameters have a significant impact on the system or model. In this section, sensitivity analysis helps to visually demonstrate the magnitude of the influence of the input motor parameters on the output results. (Regarding the yoke thickness...) Magnet height Coil width Coil height Coil current Number of coil turns Motor depth The sensitivity relationship between the target and the optimization objective is analyzed.

[0042] Figure 5 The study reveals the total impact of seven design parameters on three output targets, with color depth representing the degree of influence. For inductors, the number of coil turns contributes 96.2% of the impact, consistent with physical principles. Motor thrust is primarily determined by yoke thickness, current, and the number of coil turns. Yoke thickness contributes 14.3%, while current and the number of coil turns contribute 34.7% and 48.3%, respectively. Figure 5 The absence of numbers in the medium grayscale area indicates that the optimized parameters have a relatively small impact on the target output parameters, so parameters with a small contribution can be ignored when performing the next optimization step.

[0043] 4. Establishing a response surface based on the optimal prognostic surrogate model (MOP) Compared to traditional response surface methodology (RSM) fitting, MOP handles nonlinear and overfitting problems better. After sensitivity analysis, examining the MOP module results reveals a clear relationship between the optimization objective and the optimization variables through the response surface model. Figure 6 In the figures (a), (b), and (c), the three-dimensional relationship between thrust and design variables is shown.

[0044] The coil current and the number of coil turns have a significant impact on the motor output, consistent with the sensitivity analysis above, where current and number of turns account for 34.7% and 48.3%, respectively. The thrust F increases with increasing coil current and number of coil turns; for Figure 6 Analysis in (a) shows that the yoke thickness has a relatively small effect on the thrust F, but a certain relationship exists; the thrust F increases slowly with increasing yoke thickness. Figure 6 The analysis in (c) shows that the thickness of the magnet and the thickness of the yoke have the same sensitivity relationship with the thrust F as 4.7% and 14.3% in the sensitivity analysis. As the thickness of the magnet and the thickness of the yoke increase, the thrust F increases slowly.

[0045] Figure 7 In the figures (a), (b), and (c), the three-dimensional relationship between inductance and design variables is shown.

[0046] analyze Figure 7 It can be seen that the inductance of a coil is absolutely positively correlated with the number of turns, which conforms to the laws of physics. Furthermore, it has little to do with the thickness of the yoke. Due to the secondary effects of edge magnetic flux and local saturation in the magnetic circuit, changes in the yoke thickness will lead to changes in magnetic reluctance. The process is as follows, based on Ohm's law for magnetic circuits: In the formula: :magnetic flux; Magnetomotive force; Total magnetic reluctance; According to the definition of inductance: After decomposing the total magnetic reluctance, we obtain: In the formula: Air gap magnetic reluctance; : Magnetic core reluctance; : Magnetic yoke reluctance; Wherein the magnetic reluctance of the yoke: In the formula: : Average magnetic path length of the yoke; : Permeability; : yoke width; : Magnetic yoke thickness; When the thickness of the magnetic yoke increases: The change in inductance can be obtained as follows: As can be seen from the above derivation, increasing the thickness of the yoke will affect the inductance. Although the effect is small, it still needs to be considered in the design to minimize the yoke thickness in the optimized result.

[0047] Figure 8 In the figure, (a), (b), and (c) represent the three-dimensional relationship between electrical density and design variables, respectively.

[0048] Depend on Figure 8The electrical density response surface reveals the relationship between electrical density and various design variables. Since electrical density is a comprehensive consideration in motor design, it influences almost all design variables. Therefore, a clear correspondence between motor electrical density and design variables cannot be observed solely from the 3D response surface. However, it can help us find the optimal solution more quickly in the subsequent algorithm optimization.

[0049] The purpose of optimizing the coil current density of a motor is mainly twofold. First, excessive copper losses in the motor will lead to reduced motor efficiency. Second, and most importantly, due to the working environment of actively vibration-isolated voice coil motors, the uncertainty of ground and equipment vibrations necessitates multiple peak thrusts per unit time to achieve vibration control. In this case, the heat dissipation capacity and demagnetization risk of the voice coil motor need to be considered. Based on motor design experience, the coil current density should be maintained at 10A / mm². 2 Furthermore, a smaller coil cross-sectional area was selected to reduce the weight of the mover.

[0050] 5. Multi-objective optimization based on EA algorithm Based on the sensitivity analysis and constraints of the voice coil motor design parameters obtained in the previous chapter, the EA multi-objective optimization algorithm was set and written using Optislang software to minimize the inductance and thrust. Using the objective function, the maximum sample size was set to 5000, the maximum number of iterations to 250, and the stopping generation to 21 in the optislang software to avoid invalid iterations. The initial population was 20, with a crossover probability of 0.8 (high crossover rate enhances global exploration capability), and a mutation probability of 0.1. Subsequently, based on the MOP model optimization, 5000 designs were computed in 30 minutes. Of these, 4686 designs met the constraints, achieving a compliance rate of 93.4%.

[0051] By examining the 3D Pareto front, we can gain a more intuitive understanding of the constraints and influences among the three objective functions in this optimization.

[0052] Figure 9 As can be seen, there is a certain conflict between the objective functions. When the thrust is set to be large, the inductance will increase sharply, and the increase in thrust is often accompanied by an increase in the number of coil turns, so the increase in inductance needs to be considered. There is no situation where all three design objectives can be achieved optimally; therefore, a reasonable balance needs to be struck between the various objective parameters. The voice coil motor designed in this invention has high requirements for thrust and inductance, so these two objective parameters should be considered first. After achieving the target settings for thrust and inductance, a smaller inductance is selected. In addition, the processing cost should also be considered; the cross-sectional area of ​​the coil should be appropriate, and the thickness of the yoke should be considered to ensure strength. Considering the magnet thickness, under the same objective parameters, a smaller magnet thickness is selected to ensure sufficient space for installing the coil frame.

[0053] 6. Results of Multi-Objective Optimization from Figure 10 , Figure 11 The results show that the voice coil motor's thrust, coil current density, and coil inductance have all changed. Compared to the results before optimization, the thrust has increased to 8.9 N, while the current density remains at 9 A / m. 2 The values ​​are around 0.53 mH, consistent with normal values. The inductance is reduced to 0.79 mH. The optimized time constant τ is calculated to be 0.53 ms.

[0054] 7 Experimental Verification Vibration isolation principle The active vibration isolation system consists of an upper plate, an electromagnetic actuator, sensors, and a controller. When the actuator coil is energized, it generates a Lorentz force in the magnetic field, which is transmitted to the upper plate through the support to achieve active compensation. The sensors measure vibration in real time, and the controller calculates the compensation force and adjusts the current to form a closed-loop vibration suppression system.

[0055] Vibration isolation effect PID feedback is used, and active vibration control is added. Figure 12 The vibration signal in the time domain after active control is added.

[0056] Figure 13 The results show that the resonance peak near the natural frequency of the system is significantly reduced after inductor optimization, and the transmissibility decreases by about 30 dB compared to before optimization, effectively suppressing the resonance amplification phenomenon. At the same time, the mid-to-high frequency curves are smoother, and vibration transmission is further reduced, indicating that inductor optimization improves the velocity feedback damping injection capability and overall vibration isolation performance.

[0057] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. An optimization method for a rectangular flat-plate voice coil motor for active and passive vibration isolation platforms, characterized in that, include: Establish a model of the voice coil motor; Select the parameters for motor optimization based on the model; Obtain the optimization objectives of the motor, which include thrust amplitude, coil current density, and coil inductance; The sensitivity relationship between the motor's parameters and the optimization target is analyzed, and a response surface is established based on the optimal prognostic surrogate model. Based on the analysis results of the aforementioned sensitivity relationship and the constraints, multi-objective optimization based on the EA algorithm is performed.

2. The method according to claim 1, characterized in that, The process of establishing the model of the voice coil motor includes: Perform 3D modeling of the unoptimized motor; Establish an active vibration isolation dynamic model.

3. The method according to claim 2, characterized in that, The parameters include: magnetic yoke , magnetic steel height , coil width , coil height , coil current , coil turns , motor depth .

4. The method according to claim 2, characterized in that, The active vibration isolation dynamic model is as follows: in: Voice coil motor coil resistance (Ω); : Voice coil motor coil inductance (H); : Voice coil motor force constant (N / A); : Back electromotive force coefficient (V·s / m); : equivalent mass of the isolation platform top plate and its load; : Laplace complex variable; and For passive vibration isolation, the equivalent stiffness and damping are given. X(s): Output displacement signal, i.e., the absolute displacement of the vibration isolation platform relative to the ground; Y(s): Input displacement signal, i.e., external vibration or base movement input to the vibration isolation system; U(s): Control voltage signal, i.e., the driving voltage applied to the voice coil motor actuator.

5. The method according to claim 1, characterized in that, The multi-objective optimization based on the EA algorithm includes: To minimize electrical density and inductance, thrust The objective function is set to a maximum sample size of 5000, a maximum number of iterations of 250, and a stopping generation of 21 in the optislang software; the initial population is 20, the crossover probability is 0.8, and the mutation probability is 0.

1.

6. The method according to claim 1, characterized in that, The thrust amplitude The calculation method is as follows: in: : Equivalent mass of the isolation platform top plate and its load; : acceleration amplitude; : frequency of ground vibrations; : velocity amplitude of ground vibration at frequency f.

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