Geometric parameters optimization on storage performance degradation of ultrasonic motor based on simulation analysis

The performance of ultrasonic motor will drift due to material degradation and other reasons during long-term storage, which will directly affect the working performance after storage. Aiming at the optimization design of geometric parameters for performance storage degradation, this paper takes the piezoelectric constant d31 of ceramic chip and the elastic modulus of colloid as the characterization parameters of product storage degradation, and takes the stator tooth spacing and the thickness of rubber layer as the analysis objects of product geometric parameters optimization, and proposes a simulation analysis method based on finite element model. Through the analysis of the simulation results, it is found that the increase of the stator tooth spacing will lead to the increase of the change rate of the 5-wave modal frequency with the degradation of the material properties, and the decrease of the overall change rate of the amplitude. However, properly reducing the thickness of the adhesive layer can effectively reduce the influence of the degradation of the piezoelectric properties of the ceramic chip and the hardening of the gel on the frequency response characteristics of the stator of the ultrasonic motor under long-term storage.


Introduction
Ultrasonic motor (USM) is a new pattern of electrical machinery.Its piezoelectric ceramics, based on the inverse piezoelectric effect, make the stator tooth surface produce special vibration under the driving of ultrasonic frequency band alternating voltage greater than 20 kHz, and then drive the rotor to rotate under the action of friction.Compared with the electromagnetic motor, the USM has the advantages of small size, light weight, large torque/weight ratio, power failure self-locking, and no electromagnetic interference.Therefore, it is more and more widely used in military and civilian fields such as aerospace, intelligent robots, optical precision instruments [1].The US "Opportunity" and "Curiosity" rovers, China's Chang'e 5 and Zhang Heng 1 probes have all applied ultrasonic motors.
At present, the optimization design of the USM mainly focuses on the friction materials and contact interface characteristics.For example, Childs et al. [2] found that the elastic modulus of the friction material directly determines the size of the contact area and thus affects the conversion efficiency between the contact interfaces by studying the effect of the friction material properties on the wear of the friction material in the contact area and the performance of the USM.Tskaaki Ishii et al. [3] will develop a plastic matrix with carbon fiber as the friction material, which improves the service performance of the USM and greatly increases its service life.Gong Wen [4] prepared a kind of the USM friction material with good wear resistance by adding aluminum nitride and copper oxide particles into UHMWPE matrix.Bao Diying et al. [5] found that the nonlinear vibration of the stator of the USM, the thickness of the friction material and the moisture content affect the reliability of the starting of the USM.The study of the The research on the Canon annular USM by Ueha S [6] shows that by adding a lower stiffness flange shaped spring in the direction of the thicker rotor, stable and reliable contact between the rotor and stator can be ensured.Dong Yinghui et al. [7][8][9] analyzes the influence of flexible deformation on the stress distribution of contact interface and thinks that flexible rotor can reduce the sliding wear between stator and rotor of the USM.Zhang Aihua et al. [10] used composite materials to modify the surface of the stator, optimized the wear state between the stator and rotor of the USM, effectively improved the wear resistance of the stator, and extended the service life of the motor.Yoon et al. [11] used surface treatment technology to improve the torque of ultrasonic motor, and further analyzed the effect of coating on interface wear rate and speed.In addition, Zhang Jiao [12] effectively reduces the energy loss caused by the radial sliding of the contact surface by chamfering the stator teeth of the motor.
However, with the continuous improvement of the service life and reliability requirements of various military and civilian products, there are more and more scenarios for long-term storage of ultrasonic motors.For example, the storage life of ultrasonic motors for a missile is required to be 18 years, while the Chang'e V with ultrasonic motors is stored on the ground for 3 years before launch.The USM is prone to performance drift and creep during long-term storage, such as the decrease of piezoelectric constant of piezoelectric ceramics [13], the decrease of preload, etc., which directly affects the working performance after storage.Therefore, reducing the impact of long-term storage is very important to improve the reliability of the USM.Based on the Workbench simulation software, this paper establishes a refined geometric model for the stator of the USM.Taking the stator tooth spacing and the thickness of the rubber layer as the optimization objects, it studies how to reduce the influence of the piezoelectric performance degradation of the ceramic chip and the gel hardening on the frequency response characteristics of the stator of the USM under long-term storage through the adjustment of the key geometric parameters, and provides a solution for the optimization design of the USM facing the degradation of performance storage.

Proposed workflow
Under long-term storage, the performance of ceramic, colloid and other materials of ultrasonic motor will deteriorate with time, which will lead to the shift of key performance parameters of the motor and affect the performance and reliability of the product.From the perspective of optimization design, the traditional development process is the iterative process of design, processing, test and redesign, which leads to long development cycle and large investment.Using simulation modeling and analysis technology can quickly get the degradation trend of product performance characteristics, greatly reduce the investment of time and funds, and provide a more intuitive way to optimize the design.
In this paper, firstly, the stator geometry model is established, and parameterization is carried out after selecting the structural geometry parameters as the optimization objective and characterizing the storage degradation material parameters of the product.Then, the simulation analysis matrix of geometric parameters and material parameters is established according to the material degradation trend.According to the simulation analysis matrix, the harmonic response is analyzed after the simple harmonic voltage excitation of the input piezoelectric characteristics.Finally, obtain and compare the simulation results of the dynamic response parameters of the stator tooth surface, and complete the optimization design analysis of the geometric parameters for performance storage degradation.The specific method flow is shown in Figure 1.

Simulation modelling and setting
The stator of the ultrasonic motor studied in this paper is comb tooth structure, and its geometric model is shown in Figure 2. The smile shaped hole of the stator is filled with epoxy resin for insulation.Table 1 shows the material parameters of stator and smile shaped hole.As shown in Figure 3, the piezoelectric ceramic sheet is pasted on the stator through epoxy adhesive in a ring, and then polarized and configured with electrodes, where "(A) z+", "(A) z -", "(B) z+" and "(B) z -" respectively represent the positive and negative polarization zone of the two zones of A and B, and the group represents the non-polarized zone.The piezoelectric characteristics of piezoelectric ceramic material (PZT-8) have a direct impact on the output of ultrasonic motor.The piezoelectric constitutive equation is: in Formula (1), , S, T, d, E stand for the compliance coefficient matrix, strain tensor, stress tensor, the piezoelectric coefficient matrix, and the electric field strength tensor, respectively.
The matrix form of the constitutive equation is:     Table 2 shows the main performance parameters of piezoelectric ceramic material PZT-8.However, after long-term storage, the piezoelectric constant of piezoelectric ceramics will deteriorate, especially the key parameter d 31 will decline.In addition, the epoxy adhesive material will gradually age and harden during long-term storage, and its elastic modulus will increase.Its stiffness characteristics will also have a great impact on the output characteristics of the ultrasonic motor.Therefore, in this paper, the piezoelectric constant d 31 of ceramic chip and the elastic modulus E of colloid are selected as the characterization parameters of product storage degradation, and the stator tooth spacing and the thickness of adhesive layer are selected as the optimization objects of product geometric parameters.
Then, the simulation analysis matrix of the stator tooth spacing, the thickness of the adhesive layer, the piezoelectric constant of the ceramic chip and the elastic modulus of the gel is established.In order to make the difference between the simulation results more obvious, the tooth spacing and the thickness of the adhesive layer were expanded to 0.0003m, 0.0007m, 2.00E-05m and 6.00E-05m respectively on the basis of the original design values of 0.0005m and 4.00E-05m.The piezoelectric E s constant and colloidal elastic modulus of the ceramic chip are set according to the degradation trend of the material at -3.08 1010/m V −, 5.78E+09Pa and -2.28 1010/m V −, 7.78E+09Pa.See Table 3 for the simulation analysis matrix of optimization of stator geometric parameters of ultrasonic motor for performance storage degradation.Before the analysis, parameters of the stator assembly are assigned according to Table 1 -Table 3, the mesh is divided, and the displacement constraint is applied to the holes uniformly distributed in the circumferential direction at the bottom of the stator.The grid division result of the stator assembly model is shown in Figure 4, with a total of 15000 grid units.Then, carry out simulation calculation step by step according to Table 3.

Calculation results and analysis
According to the characteristics of the 5-wave motor, the operating frequency is generally selected near the natural frequency when the stator assembly presents the 5-wave mode.As shown in Figure 5, the working mode shape diagram of the original design structure of the stator (tooth spacing 0.0003m, rubber layer thickness 4.00E05m) before storage is shown, and the modal frequency is 32575Hz.Therefore, in the frequency response analysis, the analysis frequency range is set as 23kHz~43kHz, and the analysis results are shown in Figure 6.

Simulation analysis of optimized design of stator tooth spacing
Figure 7 shows the change curve of the key characteristic frequency of the stator with the degradation of the piezoelectric constant d 31 of the ceramic chip and the elastic modulus of the colloid under the storage environment of the product at three tooth spacing levels.Figure 8 shows the change curve of stator key characteristic amplitude under different tooth spacing.Table 4 is the analysis table of the degradation amount of stator key characteristic parameters between degradation levels S 0 and S 2 under different tooth spacing.It can be found that the increase of the stator tooth spacing leads to the decrease of its 5-wave modal frequency and the increase of its amplitude.The geometric dimension of tooth spacing increases from 0.0003m to 0.0007m, and the change rate of 5-wave modal frequency increases by 1.15 ‰ with the degradation of material properties, while the change rate of amplitude degradation decreases by 3.36%.

Simulation analysis of optimized design of adhesive layer thickness
Figure 9 shows the change curve of the key characteristic frequency of the stator with the degradation of the piezoelectric constant d31 of the ceramic chip and the elastic modulus of the colloid under the storage environment of the product under three adhesive layer thicknesses.Figure 10 shows the change curve of stator key characteristic amplitude under different adhesive layer thickness.Table 5 is the analysis table of the degradation amount of the key characteristic parameters of the stator between the degradation levels S 0 and S 2 under different adhesive layer thicknesses.It can be found that the increase of the thickness of the stator rubber layer leads to the increase of its 5-wave modal frequency and the corresponding amplitude reduction.The thickness of the adhesive layer increased from 0.00002m to 0.00006m, the change rate of frequency degradation increased by 7.59 ‰, and the change rate of amplitude degradation increased by 0.8%, the change rate of amplitude reduction fluctuates slightly.

Frequency Hz
The level of material degradation 0.00002m 0.00004m 0.00006m

Conclusions
In this paper, for the stator of the USM, the piezoelectric constant d 31 of ceramic chip and the elastic modulus E of colloid are used as the characterization parameters of product storage degradation, and the stator tooth spacing and the thickness of rubber layer are used as the optimization analysis objects of product geometric parameters, Based on the simulation software, the modal and frequency response simulation calculations are carried out, and the simulation results are used to carry out the optimization design analysis of the geometric parameters of the ultrasonic motor for performance storage degradation.The main conclusions are as follows: 1.For the change of non-span scale, the change of tooth spacing has a greater impact on the 5-wave modal frequency and corresponding amplitude of the product stator than the thickness of the rubber layer.
2. After the stator tooth spacing increases, the change rate of 5-wave modal frequency increases with the degradation of material properties, and the overall change rate of amplitude decreases.
3. The smaller the thickness of the adhesive layer, the smaller the change rate of frequency degradation and amplitude degradation.Properly reducing the thickness of the adhesive layer can effectively reduce the influence of the degradation of the piezoelectric properties of the ceramic chip and the hardening of the gel on the frequency response characteristics of the stator of the USM under long-term storage.
In the research content of this paper, the degradation values of the piezoelectric constant and the elastic modulus of the colloid of the ceramic are assumed according to the reasonable trend.In the follow-up research work, storage test and performance degradation test will be carried out for relevant materials to obtain more accurate simulation results.

Amplitude m
The level of material degradation 0.00002m 0.00004m 0.00006m

Figure 1 .
Figure 1.Optimization design flow of stator geometric parameters of the USM for performance storage degradation.

Figure 5 .
Figure 5. Vibration mode diagram of initial working mode of stator.

Figure 6 .
Figure 6.Simulation results of stator frequency response curve.

Figure 7 .Figure 8 .
Figure 7. Variation curve of stator key characteristic frequency under different tooth spacing.

Figure 9 .
Figure 9. Variation curve of stator key characteristic frequency under different rubber layer thickness.

Figure 10 .
Figure 10.Variation curve of stator key characteristic amplitude under different rubber layer thickness.

Table 1 .
Material parameters in the model.

Table 3 .
Geometric and material parameter analysis matrix.

Table 4 .
Degradation analysis table of key characteristic parameters of stator under different tooth spacing.

Table 5 .
Degradation analysis table of key characteristic parameters of stator under different rubber layer thickness.