Standing wave ultrasonic motor output performance calculation method based on LuGre dynamic friction model

Abstract

The invention discloses a LuGre dynamic friction model-based standing wave ultrasonic motor output performance calculation method, which comprises the following steps of: firstly, determining structure parameters and material parameters of a standing wave motor, establishing a vibration model of a stator, and analyzing nonlinear contact friction characteristics between the stator and a rotor on the basis of a LuGre dynamic friction model, so as to calculate the output performance of the standing wave ultrasonic motor. And establishing a dynamic friction model between the stator and the rotor, and finally calculating the mechanical characteristics of the motor under different loads by combining the motion equation of the rotor. According to the method, the LuGre dynamic friction model is adopted, the nonlinear dynamic friction characteristic between the stator and the rotor can be accurately described, and therefore the output performance calculation precision of the standing wave ultrasonic motor is improved.

Description

Technical Field

[0001] The invention relates to a method for calculating the output performance of a standing wave ultrasonic motor based on a LuGre dynamic friction model, and belongs to the technical field of ultrasonic motors. Background Art

[0002] The standing wave ultrasonic motor is a micro drive device. Its working principle is based on the inverse piezoelectric effect of piezoelectric materials. It uses ultrasound to excite standing waves in the elastic body to form elliptical motion. The standing wave ultrasonic motor does not rely on traditional electromagnetic coils, but uses the high-frequency vibration of the piezoelectric vibrator to generate driving force on the contact surface to achieve high-precision position control and torque output. Its characteristics include compact structure, low operating noise, and sensitive response. Therefore, it has been widely used in many fields such as precision machinery, automation control, and biomedical engineering, and has become an important force in promoting the development of miniaturization and precision drive technology.

[0003] The rotational power of the standing wave ultrasonic motor rotor comes from the friction between the stator and the rotor. The research on friction analysis is mainly divided into two categories: static friction model and dynamic friction model. The static friction model focuses on analyzing the friction characteristics of an object at a relative standstill or at the moment of relative motion. The dynamic friction model not only covers the static characteristics of friction, but also describes the dynamic changes of friction in depth, thereby reflecting the friction behavior more comprehensively. At present, the friction analysis between the stator and rotor of a standing wave ultrasonic motor mainly relies on the static friction model. Although the static friction model is simple, it is difficult to fully capture the complex changes of friction in the dynamic process. In view of this, the present invention introduces a dynamic friction model and proposes a method for calculating the output performance of a standing wave ultrasonic motor based on the LuGre dynamic friction model. This method can accurately describe the friction phenomenon between the stator and the rotor, and effectively improve the calculation accuracy of the output performance of the standing wave ultrasonic motor rotor. Summary of the invention

[0004] The present invention aims to address the above deficiencies in the prior art and to provide a method for calculating the output performance of a standing wave ultrasonic motor based on a LuGre dynamic friction model.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is a method for calculating the output performance of a standing wave ultrasonic motor based on the LuGre dynamic friction model, comprising the following steps:

[0006] S1: Determine the structural parameters and material parameters of the standing wave motor and establish the vibration model of the stator;

[0007] S2: According to the LuGre dynamic friction model, the contact friction between the stator and the rotor is analyzed to obtain the friction force on the rotor from the stator along the tangential direction;

[0008] S3: Calculate the rotor speed of the ultrasonic motor according to the rotor's rotational motion equation.

[0009] Preferably, in step S1, the vibration model of the stator first performs transient dynamic analysis on the three-dimensional finite element model of the stator to obtain the radial vibration response curve of the particles on the outer surface of the stator under the excitation of the applied voltage, and the curve is fitted to obtain the fitting function F(t), so as to obtain the radial vibration displacement of the particles at the top of the stator under the excitation of the applied voltage, and the tangential linear velocity v of the particles is obtained by differentiating the displacement with respect to time. As , the specific expression is as follows:

[0010]

[0011] Where A is the steady-state value of the radial amplitude, α is the sum of the inclination angle of the push piece when installed and the bending angle caused by the vibration, β is the angle between the push piece and the radial direction of the desired particle, ω s Refers to the angular frequency of the stator vibration, t e Indicates the time it takes for radial vibration to enter a steady state.

[0012] Preferably, in step S2, the contact friction analysis steps between the stator and the rotor are as follows:

[0013] A-1: Calculate the Coulomb friction force F between the stator and the rotor c , whose expression is:

[0014]

[0015] In the formula, μ d is the coefficient of kinetic friction between the rotor and stator, F p Indicates the force that causes the push piece to bend and deform.

[0016] A-2: The Coulomb friction force F c Substituting into the expression of the function s(v) describing Coulomb friction and Stribeck effect, the specific formula is as follows:

[0017]

[0018] In the formula, F s is the static friction, v s is the Stribeck speed, v is the stator speed and v As The difference.

[0019] A-3: Based on the function s(v) describing the Coulomb friction and Stribeck effect, find the derivative of the average bristle deflection χ Its expression is:

[0020]

[0021] Where σ0 is the bristle stiffness.

[0022] A-4: According to the LuGre dynamic friction model, the tangential friction force F exerted on the rotor by the stator top particle is obtained. t , the specific formula is as follows:

[0023]

[0024] Where σ1 is the bristle damping coefficient and σ2 is the viscous friction coefficient related to the macroscopic displacement.

[0025] Preferably, in step S3, the rotational motion equation of the rotor is specifically expressed as:

[0026]

[0027] Where J is the moment of inertia, ω r is the rotor speed, T load is the load torque; T is the torque generated by friction, according to the tangential friction force F of the rotor on the top particle of the stator t The specific expression is:

[0028] T=F t nr

[0029] Where n is the number of push plates fixed on the stator of the ultrasonic motor, and r is the radius length of the rotor.

[0030] Beneficial technical effects:

[0031] The present invention discloses a method for calculating the output performance of a standing wave ultrasonic motor based on a LuGre dynamic friction model. First, the structural parameters and material parameters of the standing wave motor are determined, and a vibration model of the stator is established. The radial vibration displacement of the stator is obtained according to transient dynamic analysis, and the tangential linear velocity of the stator is obtained. Then, based on the LuGre dynamic friction model, the nonlinear contact friction characteristics between the stator and the rotor are analyzed, and a dynamic friction model between the stator and the rotor is established. Finally, the mechanical characteristics of the motor under different loads are calculated in combination with the motion equation of the rotor. The present invention adopts the LuGre dynamic friction model, which can accurately describe the nonlinear dynamic friction characteristics between the stator and the rotor, thereby improving the calculation accuracy of the output performance of the standing wave ultrasonic motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a flow chart for calculating the output performance of a standing wave ultrasonic motor based on the LuGre dynamic friction model.

[0033] Figure 2 It is a comparison chart of the calculated results and experimental results of the mechanical properties under different loads of a specific embodiment of the present invention. DETAILED DESCRIPTION

[0034] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0035] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0036] The present invention discloses a method for calculating the output performance of a standing wave ultrasonic motor based on a LuGre dynamic friction model. The calculation process is as follows: Figure 1 As shown, the following steps are included:

[0037] S1: Determine the structural parameters and material parameters of the standing wave motor and establish the vibration model of the stator;

[0038] S2: According to the LuGre dynamic friction model, the contact friction between the stator and the rotor is analyzed to obtain the friction force on the rotor from the stator along the tangential direction;

[0039] S3: Calculate the angular velocity of the ultrasonic motor rotor according to the rotor's rotational motion equation.

[0040] In step S1, the stator vibration model is established by first performing transient dynamic analysis on the three-dimensional finite element model of the stator to obtain the radial vibration response curve of the particles on the outer surface of the stator under the excitation of the external voltage, and fitting the curve to obtain the fitting function F(t), thereby obtaining the radial vibration displacement of the particles at the top of the stator under the excitation of the external voltage, and the tangential linear velocity v of the particles is obtained by taking the derivative of the displacement with respect to time. As , the specific expression is as follows:

[0041]

[0042] Where A is the steady-state value of the radial amplitude, α is the sum of the inclination angle of the push piece when installed and the bending angle caused by the vibration, β is the angle between the push piece and the radial direction of the desired particle, ω s Refers to the angular frequency of the stator vibration, t e Indicates the time it takes for radial vibration to enter a steady state.

[0043] In step S2, the contact friction analysis steps between the stator and the rotor are as follows:

[0044] A-1: Calculate the Coulomb friction force F between the stator and the rotor c , whose expression is:

[0045]

[0046] In the formula, μ d is the coefficient of kinetic friction between the rotor and stator, F pIndicates the force that causes the push piece to bend and deform.

[0047] A-2: The Coulomb friction force F c Substituting into the expression of the function s(v) describing Coulomb friction and Stribeck effect, the specific formula is as follows:

[0048]

[0049] In the formula, F s is the static friction, v s is the Stribeck speed, v is the stator speed and v As The difference.

[0050] A-3: Based on the function s(v) describing the Coulomb friction and Stribeck effect, find the derivative of the average bristle deflection χ Its expression is:

[0051]

[0052] Where σ0 is the bristle stiffness.

[0053] A-4: According to the LuGre dynamic friction model, the tangential friction force F exerted on the rotor by the stator top particle is obtained. t , the specific formula is as follows:

[0054]

[0055] Where σ1 is the bristle damping coefficient and σ2 is the viscous friction coefficient related to the macroscopic displacement.

[0056] In step S3, the rotational motion equation of the rotor is specifically expressed as:

[0057]

[0058] Where J is the moment of inertia, ω r is the rotor speed, T load is the load torque; T is the torque generated by friction, according to the tangential friction force F of the rotor on the top particle of the stator t The specific expression is:

[0059] T=F t nr

[0060] Where n is the number of push plates fixed on the stator of the ultrasonic motor, and r is the radius length of the rotor.

[0061] In a specific embodiment, a piezoelectric ceramic ring with an inner diameter of 5 mm, an outer diameter of 10 mm, a thickness of 5 mm and 8 pushers is used as an example. In step S1, the tangential linear velocity v of the thin sheet isAs In the calculation formula, the installation angle of the thin film is 45°, the steady-state value A of the radial amplitude is 0.65μm through simulation, F(t) is obtained by least squares fitting, and the resonant frequency of the piezoelectric ceramic is 76.464kHz through simulation.

[0062] In a specific embodiment, in step S2, the Coulomb friction force F c The calculation formula of dynamic friction coefficient μ d Take 0.32; in the expression of the function s(v) describing the Coulomb friction and Stribeck effect, the static friction F s Take 4.5N, Stribeck speed v s Take 0.005m / s; in the calculation formula of the derivative of the average bristle deflection χ, the bristle stiffness σ0 is taken as 2.86×10 9 ; In the calculation formula of the tangential friction force F acting on the rotor, the bristle damping coefficient σ1 is 0.9 and the viscous friction coefficient σ2 is 0.03.

[0063] In a specific embodiment, the moment of inertia J in the rotor rotation motion equation in step S3 is 3.38×10 -5 kg*m 2 .

[0064] Specific embodiment Substitute the above data into Figure 1 The calculation is performed based on the LuGre dynamic friction model based on the standing wave ultrasonic motor output performance calculation flow chart shown in the figure. Figure 2 The torque-speed characteristic curve of the standing wave ultrasonic motor obtained after calculation. The calculation results of the torque-speed characteristic of the standing wave ultrasonic motor in this embodiment are as follows: Figure 2 As shown, the calculation method of the present invention is close to the experimental value, which indicates that the calculation method of the present invention has high accuracy.

[0065] In the specific implementation process, the present invention obtains the tangential friction force exerted on the rotor based on the LuGre dynamic friction model, thereby calculating the rotor speed, accurately describing the friction phenomenon between the stator and the rotor, and improving the calculation accuracy of the standing wave ultrasonic motor rotor output performance.

[0066] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A method for calculating the output performance of a standing wave ultrasonic motor based on the LuGre dynamic friction model, characterized in that: The following steps are involved: S1: Determine the structural parameters and material parameters of the standing wave motor and establish the vibration model of the stator; S2: According to the LuGre dynamic friction model, the contact friction between the stator and the rotor is analyzed to obtain the friction force on the rotor from the stator along the tangential direction; S3: Calculate the rotor speed of the ultrasonic motor according to the rotor's rotational motion equation.

2. The method for calculating the output performance of a standing wave ultrasonic motor based on the LuGre dynamic friction model according to claim 1, characterized in that: In step S1, the stator vibration model is established by first performing transient dynamic analysis on the three-dimensional finite element model of the stator to obtain the radial vibration response curve of the particles on the outer surface of the stator under the excitation of the external voltage, and fitting the curve to obtain the fitting function F(t), thereby obtaining the radial vibration displacement of the particles at the top of the stator under the excitation of the external voltage, and the tangential linear velocity v of the particles is obtained by taking the derivative of the displacement with respect to time. As , the specific expression is as follows: Where A is the steady-state value of the radial amplitude, α is the sum of the inclination angle of the push piece when installed and the bending angle caused by the vibration, β is the angle between the push piece and the radial direction of the desired particle, ω s Refers to the angular frequency of the stator vibration, t e Indicates the time it takes for radial vibration to enter a steady state.

3. The method for calculating the output performance of a standing wave ultrasonic motor based on the LuGre dynamic friction model according to claim 1, characterized in that: In step S2, the contact friction between the stator and the rotor is analyzed to obtain the Coulomb friction force F between the stator and the rotor. c , whose expression is: In the formula, μ d is the coefficient of kinetic friction between the rotor and stator, F p Indicates the force that causes the push piece to bend and deform.

4. The method for calculating the output performance of a standing wave ultrasonic motor based on the LuGre dynamic friction model according to claim 1, characterized in that: In step S2, the obtained Coulomb friction force F c Substituting into the expression of the function s(v) describing Coulomb friction and Stribeck effect, the specific formula is as follows: In the formula, F s is the static friction, v s is the Stribeck speed, v is the stator speed and v As The difference.

5. The method for calculating the output performance of a standing wave ultrasonic motor based on the LuGre dynamic friction model according to claim 1, characterized in that: In step S2, the derivative of the average bristle deflection χ is obtained. Its expression is: Where σ0 is the bristle stiffness.

6. The method for calculating the output performance of a standing wave ultrasonic motor based on the LuGre dynamic friction model according to claim 1, characterized in that: According to the LuGre dynamic friction model, the tangential friction force F on the rotor acting on the stator top particle is obtained: t , the specific formula is as follows: Where σ1 is the bristle damping coefficient and σ2 is the viscous friction coefficient related to the macroscopic displacement.

7. The method for calculating the output performance of a standing wave ultrasonic motor based on the LuGre dynamic friction model according to claim 1, characterized in that: In step S3, the rotational motion equation of the rotor is specifically expressed as: Where J is the moment of inertia, ω r is the angular velocity of the rotor, T load is the load torque; T is the torque generated by friction, according to the tangential friction force F of the rotor on the top particle of the stator t The specific expression is: T=F t nr Where n is the number of push plates fixed on the stator of the ultrasonic motor, and r is the radius length of the rotor.

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