Nonlinear dynamic modeling, solving and control method of linear motor
By establishing a two-degree-of-freedom nonlinear dynamic model and current control strategy for LRA, the problems of inaccurate vibration response prediction and poor consistency of LRA were solved, achieving high-precision vibration control and improved consistency, thus improving the haptic feedback effect of smartphones.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-23
- Publication Date
- 2026-03-13
AI Technical Summary
Existing technologies for the dynamic modeling and vibration control of linear vibration motors (LRAs) suffer from insufficient accuracy, ineffective consideration of parameter uncertainties, and poor adaptability of vibration control strategies. This results in inaccurate vibration response prediction and poor consistency, making it difficult to meet the stringent requirements of high-end smartphones for vibration consistency.
A two-degree-of-freedom nonlinear mass-spring-damped system model was adopted. The spring stiffness was decomposed by finite element static analysis and least squares fitting, and the damping ratio was solved by half-power bandwidth method. The nonlinear dynamic equation was established, and a current control optimization strategy was designed to achieve consistent control of vibration response across the entire frequency band.
It achieves accurate prediction and consistent control of LRA vibration response, with a goodness of fit as high as 0.95, and the left deviation of the resonance peak is reduced to 1/2 of the original, thus improving the tactile feedback experience.
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Abstract
Description
Technical Field
[0001] This invention relates to the field of structural dynamics, and more particularly to a nonlinear dynamic modeling and related vibration control method for a linear motor system. Background Technology
[0002] With the widespread adoption of mobile smart devices, haptic feedback has become one of the core dimensions of human-computer interaction. Linear vibration motors (LRAs), as the core actuators for realizing haptic feedback in smartphones, directly determine the quality of the user experience through vibration consistency. Compared to traditional rotary vibration motors (ERMs), LRAs offer advantages such as faster response speeds and clearer vibration output, making them the preferred vibration drive solution for mainstream smartphones. x Axial vibration motors are increasingly used in the market due to their better fit for the thinner and lighter design requirements of mobile phones.
[0003] However, existing technologies have significant limitations in the dynamic modeling and vibration control of LRA, making it difficult to meet the stringent requirements of high-end smartphones for vibration consistency. These limitations are manifested in the following three aspects: Traditional linear models lack accuracy: Existing studies mostly use linear mass-spring-damping models to describe the dynamic characteristics of LRAs. However, in practical applications, due to structural design (such as beam springs) and working principle (interaction between alternating magnetic field and permanent magnet), LRAs exhibit significant stiffness nonlinearity (cubic nonlinearity of springs) and electromagnetic force nonlinearity (BL curve changes with relative displacement). Linear models cannot accurately capture these nonlinear characteristics, resulting in large deviations in vibration response prediction.
[0004] Parameter uncertainties are not effectively considered: Factors such as manufacturing process fluctuations, changes in the usage environment, and aging and wear can lead to uncertainties in the core parameters of LRA, such as linear stiffness, nonlinear stiffness, and damping ratio. Existing models do not fully incorporate the impact of these parameter fluctuations, further reducing the reliability of vibration characteristic prediction and control.
[0005] Poor adaptability of vibration control strategies: Existing LRA control methods (such as PID control) are mostly based on linear model design, which cannot adapt to vibration fluctuations caused by nonlinear characteristics and parameter uncertainties. This results in poor consistency of vibration response between different motors and under different operating conditions of the same motor. In particular, the vibration deviation is significant near the resonance peak, which seriously affects the uniformity of the user's tactile experience.
[0006] Therefore, it is urgent to establish a dynamic model that can accurately describe the nonlinear characteristics of LRA, and to develop efficient vibration control strategies based on the model, so as to solve the problems of inaccurate vibration response prediction and poor consistency control effect in the existing technology, and meet the needs of smartphones for high-quality haptic feedback. Summary of the Invention
[0007] Based on the above analysis, the present invention aims to provide a nonlinear modeling method for LRA and related control measures to solve the LRA vibration control problem in engineering practice.
[0008] A nonlinear dynamic modeling method for an LRA system includes the following steps: S1: Simplify the LRA into a two-degree-of-freedom nonlinear mass-spring-damped system; S2: The displacement-force curve of the beam spring is obtained through finite element static analysis. The total stiffness of the spring is decomposed into linear stiffness using the least squares method. K With third nonlinear stiffness K nl ; S3: Obtain the magnetic field through simulation nBgleff ( BL The electromagnetic force of the system is obtained by using the electromagnetic force formula and the curve. S4: Obtain system damping parameters: Based on measured motor vibration acceleration data, the system damping ratio is solved using the half-power bandwidth method. ξ And further obtain the damping coefficient C ; S5: Based on Newton's second law, establish the control equations for the oscillator and the external frame respectively, and obtain the two-degree-of-freedom nonlinear dynamic equations.
[0009] Furthermore, in S1, the two-degree-of-freedom nonlinear mass-spring-damped system includes an oscillator and an external frame. The oscillator includes a permanent magnet and its fixed frame, while the external frame includes a shell, a coil, and a test fixture simulating the mass of a mobile phone. The mass of the oscillator is set to... M 1. The mass of the external frame is M 2.
[0010] Furthermore, in S2, the finite element static analysis is performed on the beam spring, and the stiffness force of the beam spring is obtained by fitting, expressed as: ; in, This represents the vibration displacement of the external frame section; This represents the vibration displacement of the oscillator section.
[0011] Furthermore, in S3, the magnetic field nBgleff The curve was obtained by simulating the change of the magnetic field acting on the coil when the oscillator moves relative to the external frame. The electromagnetic force exhibits nonlinear characteristics as the oscillator reciprocates.
[0012] Furthermore, for nB g l effFor discrete data, a fitting algorithm is needed to best reflect the inherent patterns of the data. nBgleff A smooth curve is obtained and substituted into the electromagnetic force calculation formula, which is expressed as: ; in, n This refers to the number of coil turns. B g The magnetic flux density of the permanent magnet; i The current is sinusoidal to the coil. l eff This represents the effective length of the coil.
[0013] Furthermore, in S4, the half-power bandwidth method specifically includes the following steps: S41: Obtain the peak value of the acceleration frequency response curve X max and corresponding natural frequency f 0, indicating the response is... X max Frequency point at / √2 f 1 and f 2. Thus, the damping ratio can be calculated. ξ The calculation formula is expressed as: ; S42: The obtained damping ratio ξ Substituting into the system damping matrix formula, we obtain the system damping matrix, which is expressed as: ; Where Cm is the system damping matrix; M is the mass matrix; and K is the stiffness matrix.
[0014] Furthermore, in S5, the governing equations of the oscillator include the balance relationships of the oscillator's inertial force, damping force, linear stiffness force, nonlinear stiffness force, and electromagnetic force. The governing equations of the external frame include the balance relationships of the external frame's inertial force, damping force, linear stiffness force, nonlinear stiffness force, and electromagnetic force. The two-degree-of-freedom nonlinear dynamic equations are expressed as follows: .
[0015] A method for solving nonlinear dynamic equations, specifically for solving two-degree-of-freedom nonlinear dynamic equations, includes the following steps: S1: Transform the two-degree-of-freedom nonlinear dynamic equations into the Runge-Kutta formulation, i.e. dy = f ( y ), and specify the variable as , is represented as: ; S2: Determine initial values for calculation y0 =[0,0,0,0], integration step size h =0.002, begin the integral iteration calculation, the integral iteration formula is expressed as: ; in, t For time, n For the number of iterations, It is known as the Runge-Kutta coefficient or slope increment.
[0016] An LRA vibration control method is proposed to control a two-degree-of-freedom nonlinear dynamic equation. Specifically, by designing a current control optimization strategy, the current amplitude of the input coil is adaptively adjusted for different frequency bands to achieve consistent control of vibration response across the entire frequency band.
[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention can calculate the natural frequency of the LRA system and the vibration response at different frequencies, which can accurately reflect the actual vibration response of the LRA and provide a basis for the analysis of the vibration mechanism and response characteristics of the LRA.
[0018] 2. This method comprehensively considers the effects of linear stiffness of LRA beam spring, cubic nonlinear stiffness, mass of motor oscillator and shell, system damping ratio, and electromagnetic force. Compared with the traditional finite element modeling method, it eliminates the structural modeling and simulation analysis process in the finite element method, saving time and increasing efficiency. Quantitative design can be carried out in the early stage of design, thus eliminating the blindness of design and guiding structural design to be more scientific and rigorous.
[0019] 3. Goodness of fit of the present invention to the vibration response of LRA R nl All values are greater than 0.95, which can accurately predict vibration characteristics. Moreover, the control strategy can reduce the left deviation of the resonance peak to at least half of the original value, effectively improving the vibration consistency of LRA and enhancing the tactile feedback experience. Attached Figure Description
[0020] Figure 1 This is a schematic diagram of the method flow of the present invention.
[0021] Figure 2 This is a schematic diagram, or actual diagram, of the LRA dynamic model of the present invention.
[0022] Figure 3 This is a schematic diagram of the movement process of the linear motor oscillator in this invention.
[0023] Figure 4 This is the BL curve obtained using the polynomial fitting method in this invention.
[0024] Figure 5This is a comparison chart of theoretical prediction results and actual vibration results for an example of this invention.
[0025] Figure 6 This invention demonstrates the theoretical control current applied to an example.
[0026] Figure 7 This is a comparison of the actual control effect of the present invention with the effect before control. Detailed Implementation
[0027] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings. The drawings constitute a part of this application and, together with the examples of the present invention, are used to illustrate the principles of the invention, but are not intended to limit the scope of the invention.
[0028] A specific embodiment of the present invention discloses a method for calculating the vibration response of an LRA nonlinear system, such as... Figure 1 As shown, the method includes the following steps: Step 1: The current signal, as the driving signal of the LRA model, needs to be measured and acquired. Based on the LRA's rated operating voltage and natural frequency design range, a variable frequency voltage with a constant amplitude is applied to the LRA, and the variable frequency current flowing through the LRA coil and the vibration response curve of the casing are collected.
[0029] Specifically, an LRA can be considered a single-phase AC motor, and the variable frequency current flowing through the LRA coil is collected using a current sensor.
[0030] Step 2: Establish the dynamic model of the LRA based on the mechanical structure and stress analysis results.
[0031] Specifically, the LRA system can be divided into two parts: the oscillator and the external frame. Its structural diagram and stress analysis results are shown in... Figure 2 The oscillator includes a permanent magnet and its fixed frame; the outer frame includes a shell, coils, and testing fixtures (used to simulate the mass of a mobile phone). The mass of the motor oscillator is set to... M 1. The mass of the external frame is M 2. The two are connected by a beam spring. Preliminary tests show that the nonlinear stiffness of the beam spring cannot be ignored under severe vibration. The stiffness parameters of the beam spring are obtained through finite element static analysis. The displacement-force curve of the beam spring is obtained through simulation, and then the total stiffness of the spring is decomposed into a combination of linear stiffness and cubic nonlinear stiffness using least squares fitting. Here, it is assumed... K For the linear stiffness of the beam spring, K nl This refers to the nonlinear stiffness of the beam spring. The system's forces can be mainly divided into three parts: firstly, the electromagnetic force generated when current flows through the coil. F Secondly, the stiffness force provided by the beam spring.K ( x 2- x 1)+ K nl ( x 2- x 1) 3 Thirdly, there is the damping force that hinders the relative motion between the oscillator and the external frame. x 1, x 2 represents the vibration displacement of the external frame and the motor oscillator. C This is the damping coefficient experienced by the motor system.
[0032] The dynamic equation of LRA is: (1) Step 3: Combine the static analysis results of the beam spring with the least squares method to obtain the linear stiffness of the beam spring. K and third nonlinear stiffness K nl .
[0033] Since the nonlinear characteristics of beam springs cannot be ignored, the linear stiffness of beam springs can be obtained by establishing a physical model of the beam spring and performing finite element static analysis and least squares fitting. K and third nonlinear stiffness K nl .
[0034] Step 4: Measurements based on the different relative displacements between the motor oscillator and the housing nB g l eff The simulation results of discrete data points were obtained, and a polynomial fitting method was used to obtain... nB g l eff By fitting the curve, the electromagnetic force can be obtained from the current. F .
[0035] Specifically, when alternating current is applied to the LRA, the coil generates an alternating magnetic field. This alternating magnetic field interacts with the magnetic field of the permanent magnet, causing the oscillator block, the housing, and the tooling to vibrate unidirectionally, such as... Figure 3 As shown, when the oscillator block reciprocates continuously, because the permanent magnet is mounted on the oscillator block, the coil experiences a change in the magnetic field of the permanent magnet as the oscillator block moves. This electromagnetic force can be expressed as: (2) in, Electromagnetic force, measured in N; This refers to the number of coil turns. B gThe magnetic flux density of the permanent magnet is expressed in tons (T). The sinusoidal current flowing through the coil is expressed in amperes (A). l eff This represents the effective length of the coil.
[0036] To solve for the electromagnetic force, a simulation model of the permanent magnet was established, and the results were obtained. nB g l eff Discrete data concerning the relative displacement of the oscillator and the outer shell. For among them... nB g l eff For discrete data, a polynomial fitting method is further used to obtain the fitted curve, such as in... Figure 4 As shown.
[0037] Step 5: Based on the measured linear motor vibration acceleration data, the damping ratio of the motor system is obtained using the half-power bandwidth method, and then the system damping matrix is obtained.
[0038] The damping of the LRA system is affected by the external environment and can only be calculated through experimental methods.
[0039] Specifically, based on the LRA vibration acceleration data measured in the experiment, the damping ratio of the system is obtained using the half-power bandwidth method, and then the damping matrix C to be determined is calculated. m .
[0040] The expression for the dynamic amplification factor of the system response is: (3) in, The ratio of the excitation frequency to the natural frequency; when the frequency ratio approaches 1, the system resonates. At the resonance location, the maximum peak value is: (4) Find the frequency corresponding to half power, that is: (5) We can obtain: (6) If the range is specified under small damping conditions, then the frequency ratio can be approximated as: (7) The subtraction and addition of the two frequencies are as follows: (8) Further, we can obtain: (9) Therefore, the damping ratio can be calculated from the two frequencies at half power. This allows us to obtain the system damping matrix.
[0041] Specifically, the peak value of the experimentally measured acceleration frequency response curve is first obtained. Then, the frequency corresponding to half power, that is, 0.707 times the vibration amplitude, is calculated. The damping ratio of the motor system is calculated according to formula (9), and then the system damping matrix is obtained.
[0042] (10) At this point, a complete LRA nonlinear dynamic model has been built.
[0043] Step 6: Input the current as the excitation signal into the LRA nonlinear dynamic model, and use the fourth-order Runge-Kutta method to obtain the vibration response of the LRA, and compare it with the measured data.
[0044] Specifically, the fourth-order Runge-Kutta method is often used to solve the nonlinear dynamic equations of LRA with measured current as the input signal.
[0045] First, we further transform equation (1) into the Rungekuta form, that is... dy = f ( y ), and specify the variables, where the variable is . ,Right now: (11) Determine the initial state of the system y 0 =[0,0,0,0], Integral step size h =0.002, begin the integral iteration calculation, the integral iteration formula is as follows: (12) in, t For time, n For the number of iterations, These are known as Runge-Kutta coefficients or slope increments. This allows for the solution of the vibration response of a motor system in the time domain.
[0046] Compare the solution results with the measured results, such as Figure 5 As shown. Figure 5 For the comparison results of the LRA example of the present invention, the input is a sinusoidal current with a peak value of 0.25A. The results show that the goodness of fit of the LRA example model is greater than 0.95, which verifies the accuracy of the model.
[0047] Step 7: Design the required vibration response curve and import it as the excitation signal into the LRA nonlinear dynamic model. The theoretical current signal result can then be derived. Apply the theoretical current signal as the excitation condition to the actual LRA and collect the actual vibration effect.
[0048] The control method is based on a complete LRA nonlinear dynamic model. The model was validated in step six, so the input current of the LRA can be inferred from the designed vibration response results. Furthermore, the control current is applied to the actual LRA system, and the actual vibration effect of the LRA is observed. Figure 6 The theoretical control current applied to an LRA instance is shown. Figure 7 The comparison of vibration response before and after applying the control current is shown. In the LRA example, this control strategy can reduce the left deviation of the resonance peak to at least half of the original value, effectively improving the vibration consistency of the LRA and enhancing the tactile feedback experience.
[0049] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.
Claims
1. A nonlinear dynamic modeling method for an LRA system, characterized in that, Includes the following steps: S1: Simplify the LRA into a two-degree-of-freedom nonlinear mass-spring-damped system; S2: The displacement-force curve of the beam spring is obtained through finite element static analysis. The total stiffness of the spring is decomposed into linear stiffness using the least squares method. K With third nonlinear stiffness K nl ; S3: Obtain the magnetic field through simulation nBgleff The curve is obtained, and the electromagnetic force of the system is obtained through the electromagnetic force formula; S4: Obtain system damping parameters: Based on measured motor vibration acceleration data, the system damping ratio is solved using the half-power bandwidth method. ξ And further obtain the damping coefficient C ; S5: Based on Newton's second law, establish the control equations for the oscillator and the external frame respectively, and obtain the two-degree-of-freedom nonlinear dynamic equations.
2. The nonlinear dynamic modeling method for the LRA system according to claim 1, characterized in that, In S1, the two-degree-of-freedom nonlinear mass-spring-damped system includes an oscillator and an external frame. The oscillator includes a permanent magnet and its fixed frame, and the external frame includes a shell, a coil, and a test fixture simulating the mass of a mobile phone. The mass of the oscillator is set to... M 1. The mass of the external frame is M 2.
3. The nonlinear dynamic modeling method for the LRA system according to claim 1, characterized in that, In S2, the finite element static analysis is performed on the beam spring, and the stiffness force of the beam spring is obtained by fitting, which is expressed as: ； in, This represents the vibration displacement of the external frame section; This represents the vibration displacement of the oscillator section.
4. The nonlinear dynamic modeling method for the LRA system according to claim 1, characterized in that, In S3, the magnetic field nB g l eff The curve was obtained by simulating the change of the magnetic field acting on the coil when the oscillator moves relative to the external frame. The electromagnetic force exhibits nonlinear characteristics as the oscillator reciprocates.
5. The nonlinear dynamic modeling method for the LRA system according to claim 3, characterized in that, for nB g l eff For discrete data, a fitting algorithm is needed to best reflect the inherent patterns of the data. nBgleff A smooth curve is obtained and substituted into the electromagnetic force calculation formula, which is expressed as: ； in, n This refers to the number of coil turns. B g The magnetic flux density of the permanent magnet; i The current is sinusoidal to the coil. l eff This represents the effective length of the coil.
6. The nonlinear dynamic modeling method for LRA systems according to claim 1, characterized in that, In step S4, the half-power bandwidth method specifically includes the following steps: S41: Obtain the peak value of the acceleration frequency response curve X max and corresponding natural frequency f 0, indicating the response is... X max Frequency point at / √2 f 1 and f 2. Thus, the damping ratio can be calculated. ξ The calculation formula is expressed as: ； S42: The obtained damping ratio ξ Substituting into the system damping matrix formula, we obtain the system damping matrix, which is expressed as: ； Where Cm is the system damping matrix; M is the mass matrix; and K is the stiffness matrix.
7. The nonlinear dynamic modeling method for LRA systems according to claim 1, characterized in that, In step S5, the governing equations of the oscillator include the balance relationships of the oscillator's inertial force, damping force, linear stiffness force, nonlinear stiffness force, and electromagnetic force. The governing equations of the external frame include the balance relationships of the external frame's inertial force, damping force, linear stiffness force, nonlinear stiffness force, and electromagnetic force. The two-degree-of-freedom nonlinear dynamic equations are expressed as follows: 。 8. A method for solving nonlinear dynamic equations, used to solve two-degree-of-freedom nonlinear dynamic equations as described in any one of claims 1-7, characterized in that, Includes the following steps: S1: Transform the two-degree-of-freedom nonlinear dynamic equations into the Runge-Kutta formulation, i.e. dy = f ( y ), and specify the variable as , is represented as: ； S2: Determine initial values for calculation y 0 =[0,0,0,0], integration step size h =0.002, begin the integral iteration calculation, the integral iteration formula is expressed as: ； in, t For time, n For the number of iterations, It is known as the Runge-Kutta coefficient or slope increment.
9. An LRA vibration control method for controlling the two-degree-of-freedom nonlinear dynamic equations as described in any one of claims 1-7, characterized in that, By designing a current control optimization strategy, the current amplitude of the input coil is adaptively adjusted for different frequency bands, thereby achieving consistent control of vibration response across the entire frequency band.