CN114374338A - Method for calculating torque and rotating speed characteristics of annular traveling wave ultrasonic motor based on stator tooth structure and dynamic friction force - Google Patents

Method for calculating torque and rotating speed characteristics of annular traveling wave ultrasonic motor based on stator tooth structure and dynamic friction force Download PDF

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CN114374338A
CN114374338A CN202111601316.2A CN202111601316A CN114374338A CN 114374338 A CN114374338 A CN 114374338A CN 202111601316 A CN202111601316 A CN 202111601316A CN 114374338 A CN114374338 A CN 114374338A
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stator
rotor
calculating
speed
torque
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蒋春容
赵子龙
张津杨
陆旦宏
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Nanjing Institute of Technology
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Nanjing Institute of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02N—ELECTRIC MACHINES NOT OTHERWISE PROVIDED FOR
    • H02N2/00—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction
    • H02N2/10—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing rotary motion, e.g. rotary motors
    • H02N2/14—Drive circuits; Control arrangements or methods
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02N—ELECTRIC MACHINES NOT OTHERWISE PROVIDED FOR
    • H02N2/00—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction
    • H02N2/0005—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing non-specific motion; Details common to machines covered by H02N2/02 - H02N2/16
    • H02N2/005—Mechanical details, e.g. housings
    • H02N2/0065—Friction interface
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02N—ELECTRIC MACHINES NOT OTHERWISE PROVIDED FOR
    • H02N2/00—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction
    • H02N2/0005—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing non-specific motion; Details common to machines covered by H02N2/02 - H02N2/16
    • H02N2/005—Mechanical details, e.g. housings
    • H02N2/0065—Friction interface
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02N—ELECTRIC MACHINES NOT OTHERWISE PROVIDED FOR
    • H02N2/00—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction
    • H02N2/10—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing rotary motion, e.g. rotary motors
    • H02N2/12—Constructional details
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02N—ELECTRIC MACHINES NOT OTHERWISE PROVIDED FOR
    • H02N2/00—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction
    • H02N2/10—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing rotary motion, e.g. rotary motors
    • H02N2/16—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing rotary motion, e.g. rotary motors using travelling waves, i.e. Rayleigh surface waves
    • H02N2/163—Motors with ring stator

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Abstract

The invention discloses a method for calculating the torque and rotation speed characteristics of an annular traveling wave ultrasonic motor based on a stator tooth structure and dynamic friction force, which comprises the following steps: obtaining basic parameters of the annular traveling wave type ultrasonic motor and structural parameters of the stator teeth; calculating a contact start time; based on basic parameters, contact start time and preset rotor speedNObtaining a dynamic friction stress equation of the stator and the rotor; calculating and rotor speedNCorresponding motor output torqueT L(ii) a Judging and rotor speedNCorresponding motor output torqueT LThe size of (a) is (b),T Lgreater than 0, resetting rotor speedNValue of (A) andcalculating and rotor speedNCorresponding motor output torqueT L；T LStopping the calculation when the value is less than or equal to 0; according to all rotor speedsNAnd corresponding motor output torqueT LAnd determining the torque and rotation speed characteristics of the annular traveling wave type ultrasonic motor. The invention can effectively calculate the torque and rotating speed characteristics of the motor in the design and analysis stage of the annular traveling wave ultrasonic motor.

Description

Method for calculating torque and rotating speed characteristics of annular traveling wave ultrasonic motor based on stator tooth structure and dynamic friction force
Technical Field
The invention relates to a method for calculating the torque and rotation speed characteristics of an annular traveling wave ultrasonic motor based on a stator tooth structure and dynamic friction force, and belongs to the technical field of ultrasonic motors.
Background
The ultrasonic motor converts high-frequency alternating current into ultrasonic vibration of the metal elastic body by using the inverse piezoelectric effect of piezoelectric ceramics, and then converts the ultrasonic vibration of the metal elastic body into rotation or linear motion of the rotor or the mover by contact friction. The ultrasonic motor has many advantages, such as low speed and large torque, power failure self-locking, quick dynamic response and the like. A traveling-wave ultrasonic motor of the annular type is one of the most common types of ultrasonic motors.
The ultrasonic motor converts high-frequency alternating current into ultrasonic vibration of the metal elastic body by using the inverse piezoelectric effect of piezoelectric ceramics, and then converts the ultrasonic vibration of the metal elastic body into rotation or linear motion of the rotor or the mover by contact friction. The ultrasonic motor has many advantages, such as low-speed large torque, outage self-locking, fast dynamic response and the like, and has wide application prospects in the fields of discontinuous motion, precision control, intelligent robots and the like. A traveling-wave ultrasonic motor of the annular type is one of the most common types of ultrasonic motors.
The torque-rotation speed characteristic is one of the important performances of the ultrasonic motor. The torque-rotation speed characteristics of the ultrasonic motor are difficult to calculate due to complicated non-linear problems related to contact, friction, and the like. The stator of the annular traveling wave ultrasonic motor is generally provided with a stator tooth structure so as to amplify the tangential vibration of the stator. The stator tooth structure makes the contact and friction problem of stator and rotor more complicated, has increaseed the degree of difficulty of accurate calculation motor torque rotational speed characteristic. The simplification is to directly consider the surface of the stator as continuous without counting the structure of the stator teeth, but the simplification also tends to bring larger errors. How to consider the stator tooth structure and accurately calculate the torque and rotation speed characteristics of the motor in the design stage of the motor so as to analyze and optimize the performance of the motor, and the problem to be solved is urgently needed by the annular traveling wave ultrasonic motor.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a method for calculating the torque and rotation speed characteristics of the traveling-wave ultrasonic motor based on the structure of the stator teeth and dynamic friction force, and can accurately calculate the torque and rotation speed characteristics of the motor in the design and analysis stage of the traveling-wave ultrasonic motor by considering the structural parameters of the stator teeth. In order to achieve the purpose, the invention is realized by adopting the following technical scheme:
in a first aspect, the invention provides a method for calculating the torque and rotation speed characteristics of a traveling-wave ultrasonic motor based on a stator tooth structure and dynamic friction, comprising the following steps:
obtaining basic parameters of the annular traveling wave type ultrasonic motor and structural parameters of the stator teeth;
calculating contact start time based on the acquired basic parameters and structural parameters;
obtaining a dynamic friction stress equation of the stator and the rotor based on the obtained basic parameters, the calculated contact starting time and a preset value of the rotor rotating speed N;
calculating the output torque T of the motor corresponding to the rotor speed N according to the dynamic friction stress equation of the stator and the rotorL；
Judging the output torque T of the motor corresponding to the rotor speed NLSize of (c), if TLIf more than 0, resetting the value of the rotor speed N and calculating the output torque T of the motor corresponding to the rotor speed NL(ii) a If TLStopping the calculation when the value is less than or equal to 0;
according to all the rotor rotating speeds N and the corresponding motor output torque T in the calculation processLAnd determining the torque and rotation speed characteristics of the annular traveling wave type ultrasonic motor.
With reference to the first aspect, further, the basic parameters of the ring traveling wave type ultrasonic motor include: elastic modulus E of friction material, friction coefficient mu, stator amplitude A, stator vibration frequency F, wave crest number n of stator working mode, and pre-pressure F between stator and rotornStator and rotor average contactRadius r, stator and rotor radial contact width b, friction material thickness h, distance a from the surface of a stator tooth to a neutral surface, and unit area rigidity coefficient sigma of a stator and rotor contact interface.
With reference to the first aspect, further, the structural parameters of the stator teeth include: number n of stator teethtCircumferential angle theta occupied by single stator tootht。
With reference to the first aspect, further, the calculating the contact start time is calculated by the following formula:
Figure BDA0003431879040000031
in the formula (1), θtIs the circumferential angle occupied by a single stator tooth, r is the average contact radius of the stator and the rotor, ntIs the number of stator teeth, b is the radial contact width of the stator and the rotor, E is the elastic modulus of the friction material, A is the amplitude of the stator, F is the vibration frequency of the stator, h is the thickness of the friction material, FnFor pre-stressing between stator and rotor, t1Is a contact start time, and the contact start time t1Falling within the following ranges:
Figure BDA0003431879040000032
in the formula (2), f is the stator vibration frequency.
With reference to the first aspect, further, the obtaining a dynamic friction stress equation of the stator and the rotor includes:
calculating coulomb friction stress based on the acquired basic parameters and the calculated contact starting time;
calculating the relative movement speed of the stator and the rotor based on the acquired basic parameters and the preset value of the rotor rotating speed N;
and obtaining a dynamic friction stress equation of the stator and the rotor based on the calculated coulomb friction stress and the relative motion speed of the stator and the rotor.
With reference to the first aspect, further, the calculating coulomb frictional stress is calculated by the following formula:
Figure BDA0003431879040000033
in the formula (3), mu is a friction coefficient, E is an elastic modulus of the friction material, A is a stator amplitude, f is a stator vibration frequency, h is a thickness of the friction material, t is a thickness of the friction material1T is time, and the value of t is [0, 1/f ]]Epsilon is a constant, and its value is not more than 1 x 10-6N/m2，fcCoulomb frictional stress.
With reference to the first aspect, further, the stator-rotor dynamic friction stress equation is expressed by the following formula:
Figure BDA0003431879040000041
in the formula (4), σ is a unit area stiffness coefficient of a contact interface between the stator and the rotor, and fcIs the coulomb friction stress, ffFor stator and rotor dynamic frictional stresses, sgn is a sign function expressed as:
Figure BDA0003431879040000042
in the formulae (4) and (5), vrelFor the relative movement speed of the stator and the rotor, the calculation is carried out by the following formula:
Figure BDA0003431879040000043
in the formula (6), A is the amplitude of the stator, f is the vibration frequency of the stator, a is the distance from the surface of the stator teeth to the neutral plane, n is the number of wave peaks of the working mode of the stator, r is the average contact radius of the stator and the rotor, t is time, and the value range is [0, 1/f ]]N is a predetermined rotor speed, vrelThe relative movement speed of the stator and the rotor is shown.
With reference to the first aspect, further, the calculating is related to rotor rotationMotor output torque T corresponding to speed NLCalculated by the following formula:
Figure BDA0003431879040000044
in the formula (7), θtIs the circumferential angle occupied by a single stator tooth, r is the average contact radius of the stator and the rotor, ntIs the number of stator teeth, b is the radial contact width of the stator and the rotor, f is the vibration frequency of the stator, ffThe dynamic friction stress of the stator and the rotor is obtained.
With reference to the first aspect, further, the resetting of the value of the rotor rotation speed N and the calculation of the motor output torque T corresponding to the rotor rotation speed N are performedLThe method comprises the following steps:
adding a stepping constant Q to the value of the rotor rotating speed N to obtain a value of the rotor rotating speed N after the rotor rotating speed N is reset;
calculating the output torque T of the motor corresponding to the rotor speed N after the reset according to the basic parameters of the annular traveling wave type ultrasonic motor, the structural parameters of the stator teeth and the value of the rotor speed N after the resetL。
With reference to the first aspect, optionally, the value range of the step constant Q is greater than 0 and less than or equal to 10.
In a second aspect, the present invention provides a system for calculating a torque and rotation speed characteristic of a traveling-ring wave ultrasonic motor based on a stator tooth structure and dynamic friction, including:
an acquisition module: the method is used for acquiring basic parameters of the annular traveling wave type ultrasonic motor and structural parameters of the stator teeth;
a first calculation module: the contact starting time is calculated based on the acquired basic parameters and the acquired structural parameters;
a second calculation module: the dynamic friction stress equation of the stator and the rotor is obtained based on the obtained basic parameters, the calculated contact starting time and the preset value of the rotor rotating speed N;
a third calculation module: used for calculating the output torque T of the motor corresponding to the rotor speed N according to the dynamic friction stress equation of the stator and the rotorL；
A judging module: for determining the output torque T of the motor corresponding to the rotor speed NLSize of (c), if TLIf more than 0, resetting the value of the rotor speed N and calculating the output torque T of the motor corresponding to the rotor speed NL(ii) a If TLStopping the calculation when the value is less than or equal to 0;
torque-rotational speed characteristic confirmation module: is used for calculating the rotating speed N of all the rotors and the corresponding output torque T of the motorLAnd determining the torque and rotation speed characteristics of the annular traveling wave type ultrasonic motor.
Compared with the prior art, the stator tooth structure and dynamic friction force annular traveling wave ultrasonic motor torque and rotation speed characteristic calculation method provided by the embodiment of the invention has the beneficial effects that:
the invention obtains basic parameters of the annular traveling wave type ultrasonic motor and structural parameters of the stator teeth; calculating contact start time based on the acquired basic parameters and structural parameters; obtaining a dynamic friction stress equation of the stator and the rotor based on the obtained basic parameters, the calculated contact starting time and a preset value of the rotor rotating speed N; calculating the output torque T of the motor corresponding to the rotor speed N according to the dynamic friction stress equation of the stator and the rotorL(ii) a The invention considers the stator tooth structure and the dynamic friction stress equation of the stator and the rotor, and can effectively calculate the torque and rotating speed characteristics of the annular traveling wave ultrasonic motor in the design and analysis stage of the motor;
the invention judges the output torque T of the motor corresponding to the rotor speed NLSize of (c), if TLIf more than 0, resetting the value of the rotor speed N and calculating the output torque T of the motor corresponding to the rotor speed NL(ii) a If TLStopping the calculation when the value is less than or equal to 0; according to all the rotor rotating speeds N and the corresponding motor output torque T in the calculation processLDetermining the torque and rotation speed characteristics of the annular traveling wave type ultrasonic motor; the method has strong adaptability, and can calculate the torque and rotation speed characteristics of the annular traveling wave ultrasonic motor with different sizes; the invention can be used for structural design and optimization analysis of the annular traveling wave ultrasonic motor at the same time so as to improve the torque and rotating speed performance of the motor.
Drawings
FIG. 1 is a flow chart of a method for calculating the torque and rotation speed characteristics of a traveling-ring wave ultrasonic motor based on the structure of stator teeth and dynamic friction force according to an embodiment of the present invention;
FIG. 2 shows the dynamic friction stress f of the stator/rotor at a speed N of 0r/min for an embodiment of a second embodiment of the present inventionfA graph of time t;
fig. 3 is a schematic diagram of a torque and rotation speed characteristic calculation curve of the traveling-ring wave ultrasonic motor based on the stator tooth structure and the dynamic friction force in the second embodiment of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
The first embodiment is as follows:
as shown in fig. 1, a method for calculating the torque and rotation speed characteristics of a traveling-wave ultrasonic motor in a ring shape considering the structure of stator teeth and dynamic friction comprises the following steps:
step 1: and acquiring basic parameters of the annular traveling wave type ultrasonic motor.
Basic parameters of the ring traveling wave type ultrasonic motor include: elastic modulus E of friction material, friction coefficient mu, stator amplitude A, stator vibration frequency F, wave crest number n of stator working mode, and pre-pressure F between stator and rotornThe stator and rotor contact surface structure comprises a stator and rotor average contact radius r, a stator and rotor radial contact width b, a friction material thickness h, a distance a from a stator tooth surface to a neutral surface, and a unit area rigidity coefficient sigma of a stator and rotor contact interface.
Step 2: and acquiring structural parameters of the stator teeth.
Structural parameters of the stator teeth comprise: number n of stator teethtCircumferential angle theta occupied by single stator tootht。
And step 3: the contact start time is calculated by the following formula:
Figure BDA0003431879040000071
in the formula (1), θtIs the circumferential angle occupied by a single stator tooth, r is the average contact radius of the stator and the rotor, ntIs the number of stator teeth, b is the radial contact width of the stator and the rotor, E is the elastic modulus of the friction material, A is the amplitude of the stator, F is the vibration frequency of the stator, h is the thickness of the friction material, FnFor pre-stressing between stator and rotor, t1Is a contact start time, and the contact start time t1Falling within the following ranges:
Figure BDA0003431879040000072
in the formula (2), f is the stator vibration frequency.
And 4, step 4: the initial value of the rotor speed N is set to 0.
And 5: coulomb friction stress was calculated by the following formula:
Figure BDA0003431879040000073
in the formula (3), mu is a friction coefficient, E is an elastic modulus of the friction material, A is a stator amplitude, f is a stator vibration frequency, h is a thickness of the friction material, t is a thickness of the friction material1T is time, and the value of t is [0, 1/f ]]Epsilon is a constant, and its value is not more than 1 x 10-6N/m2，fcCoulomb frictional stress.
Step 6: calculating the relative movement velocity v of the stator and the rotorrelCalculated by the following formula:
Figure BDA0003431879040000081
in the formula (4), A is the amplitude of the stator, f is the vibration frequency of the stator, a is the distance from the surface of the stator teeth to the neutral plane, n is the number of wave peaks of the working mode of the stator, r is the average contact radius of the stator and the rotor, and t is the time which takes the value ofIn the range of [0, 1/f]N is a predetermined rotor speed, vrelThe relative movement speed of the stator and the rotor is shown.
And 7: solving a dynamic friction stress equation of the stator and the rotor, which is expressed by the following formula:
Figure BDA0003431879040000082
in the formula (5), σ is a unit area stiffness coefficient of a contact interface between the stator and the rotor, and fcIs the coulomb friction stress, ffFor stator and rotor dynamic frictional stresses, sgn is a sign function expressed as:
Figure BDA0003431879040000083
in the formulae (5) and (6), vrelIn order to determine the relative movement speed of the stator and the rotor,
and 8: calculating the output torque T of the motor corresponding to the rotor speed NLCalculated by the following formula:
Figure BDA0003431879040000084
in the formula (7), r is the average contact radius of the stator and the rotor, b is the radial contact width of the stator and the rotor, f is the vibration frequency of the stator, and ffThe dynamic friction stress of the stator and the rotor is obtained.
And step 9: judging the output torque T of the motor corresponding to the rotor speed NLThe size of (2).
If TLIf more than 0, resetting the value of the rotor speed N and calculating the output torque T of the motor corresponding to the rotor speed NL(ii) a If TLAnd (5) ending the calculation when the value is less than or equal to 0.
Resetting the value of the rotor speed N, comprising: and adding the stepping constant Q to the value of the rotor rotating speed N to obtain the value of the rotor rotating speed N after the resetting.
The value range of the stepping constant Q is more than 0 and less than or equal to 10. The smaller the value is, the more the number of points is calculated, and the higher the precision is. Preferably, Q has a value of 5.
Step 10: according to all the rotor rotating speeds N and the corresponding motor output torque T in the calculation processLAnd determining the torque and rotation speed characteristics of the annular traveling wave type ultrasonic motor.
Example two:
the present embodiment is based on a specific application scenario of the method for calculating the torque and rotation speed characteristics of the traveling-ring wave ultrasonic motor based on the stator tooth structure and the dynamic friction force provided in the first embodiment, and the following embodiments are only used to more clearly illustrate the technical solution of the present invention, and the protection scope of the present invention is not limited thereby.
The steps will be described in detail with reference to fig. 1 by taking an annular traveling wave type ultrasonic motor with a diameter of 60mm as an example.
Step 1: and acquiring basic parameters of the annular traveling wave type ultrasonic motor.
The basic parameters of the annular traveling wave type ultrasonic motor are as follows: elastic modulus E of friction material 6.67X 108N/m2The friction coefficient mu is 0.14, the stator amplitude A is 2 mu m, the stator vibration frequency F is 41kHz, the number of wave peaks n of the working mode of the stator is 9, and the pre-pressure F between the stator and the rotorn250N, 27mm of average contact radius r of stator and rotor, 2mm of radial contact width b of stator and rotor, 0.5mm of thickness h of friction material, 2.5mm of distance a between stator tooth surface and neutral surface, 2.86X 10 of unit area rigidity coefficient sigma of contact interface between stator and rotor12N/m3。
Step 2: and acquiring structural parameters of the stator teeth.
Number n of stator teeth t90, the circumferential angle theta occupied by a single stator tootht＝3°。
And step 3: calculating the contact start time t1Calculating to obtain t1＝5.7210×10-6s, fall in
Figure BDA0003431879040000101
Within the range.
And 4, step 4: the initial value of the rotor speed N is set to 0 r/min.
Step (ii) of5: calculating the Coulomb friction stress fcCalculated by the following formula:
Figure BDA0003431879040000102
in the formula (8), t is time, epsilon is a constant and the value thereof is not more than 1 x 10-6N/m2In this embodiment, epsilon is 1 × 10-6N/m2。
Step 6: calculating the relative movement speed of the stator and the rotor by the following formula:
Figure BDA0003431879040000103
when the rotating speed N of the rotor is equal to 0r/min, corresponding vrelThe expression of (a) is:
Figure BDA0003431879040000104
in the formulae (9) and (10), t is time.
And 7: solving a dynamic friction stress equation of the stator and the rotor, wherein the dynamic friction stress equation of the stator and the rotor is as follows:
Figure BDA0003431879040000105
the time t has a value range of [0, 2.439 × 10%-5s]The equation is solved by numerical solution of differential equation, and the solving step length is set to not more than 1.0 × 10-7s, the smaller the solving step length is, the longer the time required for solving is, and the more accurate the result of the solving is.
FIG. 2 shows the dynamic friction stress f of the stator and rotor obtained by solving the equation when the rotor speed N is equal to 0r/minfGraph plot over time t.
And 8: calculating the output torque T of the motor corresponding to the rotor speed NLCalculated by the following formula:
Figure BDA0003431879040000111
when the rotating speed N is equal to 0r/min, corresponding output torque T is calculatedL＝0.9358Nm。
And step 9: judging the output torque T of the motor corresponding to the rotor speed NLThe size of (2).
If TLIf more than 0, resetting the value of the rotor speed N and calculating the output torque T of the motor corresponding to the rotor speed NL(ii) a If TLAnd (5) ending the calculation when the value is less than or equal to 0.
Resetting the value of the rotor speed N, comprising: and adding the stepping constant Q to the value of the rotor rotating speed N to obtain the value of the rotor rotating speed N after the resetting. In this embodiment, the step constant Q is 5.0r/min, and the process returns to step 5.
Step 10: according to all the rotor rotating speeds N and the corresponding motor output torque T in the calculation processLAnd determining the torque and rotation speed characteristics of the annular traveling wave type ultrasonic motor.
As shown in fig. 3, a torque/rotation speed characteristic curve is formed by connecting the torque/rotation speed points of the traveling-wave ultrasonic motor obtained by the loop calculation. According to the embodiment of the invention, a MATLAB is adopted to write a calculation program, and basic parameters of the annular traveling wave ultrasonic motor are manually input, so that a corresponding torque and rotating speed characteristic curve can be quickly given.
According to the method for calculating the torque and rotation speed characteristics of the annular traveling wave ultrasonic motor based on the stator tooth structure and the dynamic friction force, the stator tooth structure, the coulomb friction stress and the dynamic friction stress of the stator and the rotor are considered, and the torque and rotation speed characteristics of the annular traveling wave ultrasonic motor can be accurately calculated in the design and analysis stage of the motor; the method has strong adaptability, and can calculate the torque and rotation speed characteristics of the annular traveling wave ultrasonic motor with different sizes; the invention can be used for structural design and optimization analysis of the annular traveling wave ultrasonic motor at the same time so as to improve the torque and rotating speed performance of the motor.
Example three:
the embodiment of the invention provides a system for calculating the torque and rotation speed characteristics of an annular traveling wave ultrasonic motor based on a stator tooth structure and dynamic friction force, which comprises:
an acquisition module: the method is used for acquiring basic parameters of the annular traveling wave type ultrasonic motor and structural parameters of the stator teeth;
a first calculation module: the contact starting time is calculated based on the acquired basic parameters and the acquired structural parameters;
a second calculation module: the dynamic friction stress equation of the stator and the rotor is obtained based on the obtained basic parameters, the calculated contact starting time and the preset value of the rotor rotating speed N;
a third calculation module: used for calculating the output torque T of the motor corresponding to the rotor speed N according to the dynamic friction stress equation of the stator and the rotorL；
A judging module: for determining the output torque T of the motor corresponding to the rotor speed NLSize of (c), if TLIf more than 0, resetting the value of the rotor speed N and calculating the output torque T of the motor corresponding to the rotor speed NL(ii) a If TLStopping the calculation when the value is less than or equal to 0;
torque-rotational speed characteristic confirmation module: is used for calculating the rotating speed N of all the rotors and the corresponding output torque T of the motorLAnd determining the torque and rotation speed characteristics of the annular traveling wave type ultrasonic motor.
Example four:
embodiments of the present invention also provide a computer readable storage medium storing one or more programs, the one or more programs comprising instructions, which when executed by a computing device, cause the computing device to perform the steps of the method according to embodiment one.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (10)

1. A method for calculating the torque and rotation speed characteristics of an annular traveling wave ultrasonic motor based on a stator tooth structure and dynamic friction force is characterized by comprising the following steps:
obtaining basic parameters of the annular traveling wave type ultrasonic motor and structural parameters of the stator teeth;
calculating contact start time based on the acquired basic parameters and structural parameters;
obtaining a dynamic friction stress equation of the stator and the rotor based on the obtained basic parameters, the calculated contact starting time and a preset value of the rotor rotating speed N;
calculating the output torque T of the motor corresponding to the rotor speed N according to the dynamic friction stress equation of the stator and the rotorL；
Judging the output torque T of the motor corresponding to the rotor speed NLSize of (c), if TLIf more than 0, resetting the value of the rotor speed N and calculating the output torque T of the motor corresponding to the rotor speed NL(ii) a If TLStopping the calculation when the value is less than or equal to 0;
according to all the rotor rotating speeds N and the corresponding motor output torque T in the calculation processLAnd determining the torque and rotation speed characteristics of the annular traveling wave type ultrasonic motor.
2. The method for calculating the torque and rotation speed characteristics of a traveling-ring wave ultrasonic motor based on a stator tooth structure and dynamic friction according to claim 1, wherein the basic parameters of the traveling-ring wave ultrasonic motor include: elastic modulus E of friction material, friction coefficient mu, stator amplitude A, stator vibration frequency F, wave crest number n of stator working mode, and pre-pressure F between stator and rotornThe stator and rotor contact surface structure comprises a stator and rotor average contact radius r, a stator and rotor radial contact width b, a friction material thickness h, a distance a from a stator tooth surface to a neutral surface, and a unit area rigidity coefficient sigma of a stator and rotor contact interface.
3. The method for calculating the torque and rotation speed characteristics of the traveling-ring wave ultrasonic motor based on the structure of the stator teeth and the dynamic friction force according to claim 1, wherein the structural parameters of the stator teeth comprise: number n of stator teethtSingle statorCircumferential angle theta occupied by teetht。
4. The method of claim 1, wherein the calculating the contact start time is performed by the following equation:
Figure FDA0003431879030000021
in the formula (1), θtIs the circumferential angle occupied by a single stator tooth, r is the average contact radius of the stator and the rotor, ntIs the number of stator teeth, b is the radial contact width of the stator and the rotor, E is the elastic modulus of the friction material, A is the amplitude of the stator, F is the vibration frequency of the stator, h is the thickness of the friction material, FnFor pre-stressing between stator and rotor, t1Is a contact start time, and the contact start time t1Falling within the following ranges:
Figure FDA0003431879030000022
in the formula (2), f is the stator vibration frequency.
5. The method for calculating the torque and rotation speed characteristics of the traveling-ring wave ultrasonic motor based on the stator tooth structure and the dynamic friction force according to claim 1, wherein the obtaining of the stator and rotor dynamic friction stress equation comprises:
calculating coulomb friction stress based on the acquired basic parameters and the calculated contact starting time;
calculating the relative movement speed of the stator and the rotor based on the acquired basic parameters and the preset value of the rotor rotating speed N;
and obtaining a dynamic friction stress equation of the stator and the rotor based on the calculated coulomb friction stress and the relative motion speed of the stator and the rotor.
6. The method for calculating the torque and rotation speed characteristics of the traveling-ring wave ultrasonic motor based on the stator tooth structure and the dynamic friction force according to claim 5, wherein the Coulomb friction stress is calculated by the following formula:
Figure FDA0003431879030000031
in the formula (3), mu is a friction coefficient, E is an elastic modulus of the friction material, A is a stator amplitude, f is a stator vibration frequency, h is a thickness of the friction material, t is a thickness of the friction material1T is time, and the value of t is [0, 1/f ]]Epsilon is a constant, and its value is not more than 1 x 10-6N/m2，fcCoulomb frictional stress.
7. The method for calculating the torque and rotation speed characteristics of the traveling-ring wave ultrasonic motor based on the stator tooth structure and the dynamic friction force according to claim 5, wherein the equation of the dynamic friction stress of the stator and the rotor is expressed by the following formula:
Figure FDA0003431879030000032
in the formula (4), σ is a unit area stiffness coefficient of a contact interface between the stator and the rotor, and fcIs the coulomb friction stress, ffFor stator and rotor dynamic frictional stresses, sgn is a sign function expressed as:
Figure FDA0003431879030000033
in the formulae (4) and (5), vrelFor the relative movement speed of the stator and the rotor, the calculation is carried out by the following formula:
Figure FDA0003431879030000034
in the formula (6), A is the amplitude of the stator, f is the vibration frequency of the stator, a is the distance from the surface of the stator teeth to the neutral plane, n is the number of wave peaks of the working mode of the stator, r is the average contact radius of the stator and the rotor, t is time, and the value range is [0, 1/f ]]N is a predetermined rotor speed, vrelThe relative movement speed of the stator and the rotor is shown.
8. The method for calculating the torque and speed characteristics of a traveling-ring wave ultrasonic motor based on a stator tooth structure and a dynamic friction force according to claim 1, wherein the calculation of the motor output torque T corresponding to the rotor speed N is performedLCalculated by the following formula:
Figure FDA0003431879030000041
in the formula (7), θtIs the circumferential angle occupied by a single stator tooth, r is the average contact radius of the stator and the rotor, ntIs the number of stator teeth, b is the radial contact width of the stator and the rotor, f is the vibration frequency of the stator, ffThe dynamic friction stress of the stator and the rotor is obtained.
9. The method of claim 1, wherein the value of the rotor speed N is reset and the motor output torque T corresponding to the rotor speed N is calculatedLThe method comprises the following steps:
adding a stepping constant Q to the value of the rotor rotating speed N to obtain a value of the rotor rotating speed N after the rotor rotating speed N is reset;
calculating the output torque T of the motor corresponding to the rotor speed N after the reset according to the basic parameters of the annular traveling wave type ultrasonic motor, the structural parameters of the stator teeth and the value of the rotor speed N after the resetL。
10. A system for calculating torque and rotation speed characteristics of an annular traveling wave ultrasonic motor based on a stator tooth structure and dynamic friction force is characterized by comprising:
an acquisition module: the method is used for acquiring basic parameters of the annular traveling wave type ultrasonic motor and structural parameters of the stator teeth;
a first calculation module: the contact starting time is calculated based on the acquired basic parameters and the acquired structural parameters;
a second calculation module: the dynamic friction stress equation of the stator and the rotor is obtained based on the obtained basic parameters, the calculated contact starting time and the preset value of the rotor rotating speed N;
a third calculation module: used for calculating the output torque T of the motor corresponding to the rotor speed N according to the dynamic friction stress equation of the stator and the rotorL；
A judging module: for determining the output torque T of the motor corresponding to the rotor speed NLSize of (c), if TLIf more than 0, resetting the value of the rotor speed N and calculating the output torque T of the motor corresponding to the rotor speed NL(ii) a If TLStopping the calculation when the value is less than or equal to 0;
torque-rotational speed characteristic confirmation module: is used for calculating the rotating speed N of all the rotors and the corresponding output torque T of the motorLAnd determining the torque and rotation speed characteristics of the annular traveling wave type ultrasonic motor.
CN202111601316.2A 2021-12-24 2021-12-24 Method for calculating torque and rotating speed characteristics of annular traveling wave ultrasonic motor based on stator tooth structure and dynamic friction force Pending CN114374338A (en)

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CN112464400A (en) * 2020-11-20 2021-03-09 南京工程学院 Method for calculating torque and rotating speed characteristics of radial standing wave type ultrasonic motor based on coulomb friction and viscous friction
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