An optimization method and system for improving scanning angle of electrostatic MEMS micromirror

Abstract

The application discloses an optimization method and system for improving the scanning angle of an electrostatic MEMS (Micro Electro Mechanical System) mirror, which comprises the following steps: establishing a dynamic equation of the electrostatic MEMS mirror, obtaining a driving torque, and establishing a driving torque expression; establishing a finite element model of a driver with different comb-to-shaft distances, simulating the finite element model, obtaining the relationship between the capacitance of different drivers and the angle, fitting the obtained relationship between the capacitance of different drivers and the angle, and obtaining a driver capacitance expression; obtaining an expression of a resonance amplitude based on the obtained driver capacitance expression, the driving torque expression and the dynamic equation of the electrostatic MEMS mirror, and obtaining the resonance amplitude of the electrostatic MEMS mirror under different comb-to-shaft distances based on the expression of the resonance amplitude; and selecting the comb-to-shaft distance corresponding to the maximum value in all resonance amplitudes to optimize the driver of the MEMS mirror. The MEMS mirror can reach the maximum scanning angle, thereby meeting the demand of the electrostatic MEMS mirror in a large field of view application scenario.

Description

Technical Field

[0001] This invention belongs to the field of microelectromechanical technology and relates to an optimization method and system for improving the scanning angle of electrostatic MEMS micromirrors. Background Technology

[0002] Electrostatically driven MEMS micromirrors are miniature electromechanical systems whose motion is controlled by a feedback control system, enabling rapid beam orientation and scanning. Electrostatic MEMS micromirrors are characterized by miniaturization, high precision, high reliability, and strong integration, and are widely used in fields such as 3D imaging, optical communication, and projection displays.

[0003] However, existing electrostatically driven MEMS micromirrors have a small scanning angle and a small field of view, which cannot meet the requirements for a large field of view in applications such as dynamic structured light imaging and lidar. Summary of the Invention

[0004] The purpose of this invention is to solve the problem of small scanning angle of electrostatically driven MEMS micromirrors in the prior art, and to provide an optimization method and system for improving the scanning angle of electrostatically driven MEMS micromirrors, which helps electrostatically driven MEMS micromirrors obtain a larger scanning angle.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] An optimization method for improving the scanning angle of electrostatic MEMS micromirrors includes the following steps:

[0007] S1: Establish the dynamic equation of the electrostatic MEMS micromirror, obtain the driving torque, and establish the expression of the driving torque;

[0008] S2: Establish finite element models of electrostatic actuators with different distances from comb teeth to the shaft, simulate the finite element models, obtain the relationship between different actuator capacitance and angle, and fit the obtained relationship between different actuator capacitance and angle to obtain the expression of actuator capacitance.

[0009] S3: Based on the obtained driver capacitance expression, driving torque expression and dynamic equation of electrostatic MEMS micromirror, obtain the expression of resonance amplitude, and based on the expression of resonance amplitude, obtain the resonance amplitude of electrostatic MEMS micromirror under different comb tooth to shaft distances.

[0010] S4: Select the distance from the comb tooth to the shaft corresponding to the maximum value among all resonant amplitudes as the optimization parameter, and optimize the driver of the MEMS micromirror based on the selected maximum value.

[0011] A further improvement of the present invention is that:

[0012] Step S1 includes the following steps:

[0013] The dynamic equation of the electrostatic MEMS micromirror is established using formula (1):

[0014]

[0015] In the formula, J is the moment of inertia of the mirror; θ is the mirror rotation angle; c is the damping coefficient of the electrostatic MEMS micromirror system; k is the stiffness of the torsion beam; and M is the driving torque.

[0016] The driving torque M is expressed by formula (2):

[0017]

[0018] In the formula, U is the driving voltage, and C is the capacitance between the driving comb teeth and the stationary comb teeth.

[0019] The expression for the driving voltage U is:

[0020]

[0021] In the formula, U m ω is the high level; ω is the driving frequency.

[0022] Step S2 includes the following steps:

[0023] The expression for the driver capacitance is established using formula (4):

[0024]

[0025] In the formula, b0, b1, and b2 are fitting coefficients.

[0026] Step S4 includes the following steps:

[0027] Substituting the driver capacitance expression into the driving torque expression, and then substituting the driving torque expression into the dynamic equation of the electrostatic MEMS micromirror, we can obtain the expression for the resonant amplitude.

[0028] In step S4, substituting the driver capacitance expression into the driver torque expression yields:

[0029]

[0030] In the formula, U is the driving voltage; b0 and b1 are fitting coefficients.

[0031] In step S4, the expression for the resonant amplitude is established using formula (6):

[0032]

[0033] In the formula, J represents the moment of inertia of the mirror; c represents the overall damping coefficient; U m This indicates a high level.

[0034] An optimization system for improving the scanning angle of electrostatic MEMS micromirrors includes a driving torque expression establishment module, a driver capacitance expression establishment module, a driver capacitance expression establishment module, and a resonant amplitude acquisition module.

[0035] The driving torque expression establishment module is used to establish the dynamic equation of the electrostatic MEMS micromirror, obtain the driving torque, and establish the driving torque expression.

[0036] The driver capacitance expression establishment module is used to establish finite element models of electrostatic drivers with different comb tooth to shaft distances, simulate the finite element models, obtain the relationship between different driver capacitances and angles, and fit the obtained different driver capacitances and angles to obtain the driver capacitance expression.

[0037] The resonant amplitude acquisition module is used to obtain the resonant amplitude expression based on the acquired driver capacitance expression, driving torque expression and the dynamic equation of the electrostatic MEMS micromirror, and to obtain the resonant amplitude of the electrostatic MEMS micromirror under different comb-to-rotation axis distances based on the resonant amplitude expression.

[0038] The optimization module is used to select the distance from the comb teeth to the shaft corresponding to the maximum value among all resonant amplitudes as the optimization parameter, and optimize the driver of the MEMS micromirror based on the selected maximum value.

[0039] A terminal device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of any of the methods described in this invention.

[0040] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the methods described in this invention.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] This invention discloses an optimization method for improving the scanning angle of an electrostatic MEMS micromirror. The method sequentially obtains the dynamic equation, driving torque expression, and driver capacitance expression of the electrostatic MEMS micromirror, and based on these three expressions, derives the expression for the resonant amplitude. Using this expression, the resonant amplitude of the electrostatic MEMS micromirror is calculated for different comb-to-axis distances, and the largest amplitude value is selected as the optimization parameter to optimize the comb-to-axis distance in the electrostatic MEMS micromirror. The method disclosed in this invention achieves the maximum resonant amplitude using the optimal comb-to-axis distance without changing other parameters, enabling the MEMS micromirror to reach the maximum scanning angle, improving monitoring capability and efficiency, and thus meeting the needs of electrostatic MEMS micromirrors in large field-of-view applications. Attached Figure Description

[0043] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a schematic diagram of the electrostatic MEMS micromirror of the present invention;

[0045] Figure 2 Here are the finite element models of different electrostatic drivers of the present invention (where a represents b). m =230μm finite element model; b represents b m Finite element model with a diameter of 130 μm; c represents b m Finite element model with a diameter of 100 μm; d represents b m =80μm finite element model; e represents b m Finite element model with a diameter of 50 μm; f represents b m Finite element model with a diameter of 25 μm; g represents b m =15μm finite element model);

[0046] Figure 3 The figure shows the finite element simulation results of the relationship between the driver capacitance C and the rotation angle θ for different distances from the comb teeth to the shaft according to the present invention.

[0047] Figure 4 The capacitance fitting result is for the distance from the comb teeth to the shaft of the present invention being 230 μm.

[0048] Figure 5 The resonant amplitude of electrostatic MEMS micromirrors with different comb tooth distances to the shaft. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0050] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0051] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0052] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0053] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0054] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0055] The present invention will now be described in further detail with reference to the accompanying drawings:

[0056] This invention discloses an optimization method for improving the scanning angle of electrostatic MEMS micromirrors, comprising the following steps:

[0057] Step 1: Establish the dynamic equation of the electrostatic MEMS micromirror, obtain the driving torque, and establish the expression for the driving torque;

[0058] See Figure 1 Based on the currently designed electrostatic MEMS micromirror, the dynamic equations of its lumped parameter model are established:

[0059]

[0060] In the formula, J is the moment of inertia of the mirror; θ is the mirror rotation angle; c is the damping coefficient of the electrostatic MEMS micromirror system; k is the stiffness of the torsion beam; and M is the driving torque.

[0061] The driving torque M is expressed by formula (2):

[0062]

[0063] In the formula, U is the driving voltage, which is usually a square wave with a 50% space ratio, and can be written as:

[0064]

[0065] In the formula, U m ω is the high level; ω is the driving frequency; C is the capacitance between the comb teeth of the driver.

[0066] Step 2: Establish finite element models of the actuators with different distances from the comb teeth to the shaft, simulate the finite element models, obtain the relationship between the capacitance and angle of different actuators, and fit the obtained relationship between the capacitance and angle of different actuators to obtain the expression of the actuator capacitance.

[0067] Due to the strong edge effect and inter-tooth capacitance of the driver, it is difficult to obtain an analytical expression for the relationship between capacitance and mirror rotation angle. Therefore, finite element method (FEM) simulation is used to obtain the relationship between capacitance and mirror rotation angle. The FEM method is used to simulate the driver capacitance for different distances from the comb tooth to the shaft, and a Gaussian function is used to fit the relationship between driver capacitance and rotation angle.

[0068] See Figure 2 Establish different distances b from the comb teeth to the axis of rotation. m The finite element model of the driver (b is established here respectively) m (Actuator models for 230μm, 130μm, 100μm, 80μm, 50μm, 25μm, and 15μm) were used to simulate the relationship between the actuator capacitance and the rotation angle during the rotation of an electrostatic MEMS micromirror using the finite element method.

[0069] See Figure 3 Simulation results were obtained to obtain the relationship between the driver capacitance and the rotation angle θ for different distances from the comb teeth to the shaft.

[0070] The relationship between the driver capacitance and the rotation angle obtained from finite element simulation is fitted using a Gaussian function to obtain the expression for the driver capacitance:

[0071]

[0072] Where b0, b1, and b2 are fitting coefficients.

[0073] Step 3: Based on the obtained driver capacitance expression, driving torque expression and dynamic equation of electrostatic MEMS micromirror, obtain the expression of resonance amplitude, and based on the expression of resonance amplitude, obtain the resonance amplitude of electrostatic MEMS micromirror under different comb tooth to shaft distances.

[0074] When b m The capacitance fitting results at 230μm are as follows: Figure 4 As shown. Fitting coefficients b0, b1, and b2 can be obtained through fitting. The driving torque is related to the rate of change of capacitance with rotation angle; therefore, b2 can be ignored here. Different b... m The capacitance fitting coefficients are shown in Table 1.

[0075]

[0076] Furthermore, substituting the fitted capacitance expression and driving voltage into the driving torque expression:

[0077]

[0078] Furthermore, by substituting the expression for the driving torque into the dynamic equation of the electrostatic MEMS micromirror, the expression for the resonant amplitude can be obtained:

[0079]

[0080] Using different comb tooth distances to the pivot point b m Simulating the driver capacitor yields the corresponding b0 and b1. These b0, b1, the mirror moment of inertia J, the system damping coefficient c, and the high-level U of the driving voltage are then used to... m Substituting into equation (6) yields the resonance amplitude of the electrostatic MEMS micromirror at the corresponding distance from the comb teeth to the shaft.

[0081] Specifically, the different b in Table 1 m Substituting the corresponding fitting parameters into equation (6) yields the resonance amplitude of the electrostatic MEMS micromirror under different distances from the comb teeth to the axis of rotation. The moment of inertia of the mirror surface is taken as J = 4.7 × 10⁻⁶. -13 kg·m2 The high level of the driving voltage U m =100V, damping coefficient c = 1.01 × 10 -11 N·m·s·rad -1 To obtain different b m For the resonant amplitude of the electrostatic MEMS micromirror, see [link / reference]. Figure 5 .

[0082] Step 4: Select the maximum value among all resonant amplitudes as the optimization parameter, and optimize the MEMS micromirror driver based on the selected maximum value.

[0083] from Figure 5 As can be seen, the resonant amplitude of the electrostatic MEMS micromirror has a maximum value when the distance from the comb teeth to the axis of rotation is 50 μm.

[0084] Select b m =50μm is considered the optimal comb-to-axis distance for an electrostatic MEMS micromirror actuator. With other parameters remaining constant, based on this... m Designing the actuator for an electrostatic MEMS micromirror can maximize the scanning angle of the electrostatic MEMS micromirror.

[0085] This invention addresses the distance b from the comb teeth to the shaft in an electrostatic MEMS micromirror actuator. m The invention enables electrostatic MEMS micromirrors to achieve maximum resonant amplitude using the optimal comb-to-axis distance without changing other parameters. This allows the MEMS micromirrors to reach the maximum scanning angle, thus meeting the needs of electrostatic MEMS micromirrors in large field-of-view applications.

[0086] This invention also discloses an optimization system for improving the scanning angle of electrostatic MEMS micromirrors, including a driving torque expression establishment module, a driver capacitance expression establishment module, a driver capacitance expression establishment module, and a resonance amplitude acquisition module;

[0087] The driving torque expression establishment module is used to establish the dynamic equation of the electrostatic MEMS micromirror, obtain the driving torque, and establish the driving torque expression.

[0088] The driver capacitance expression establishment module is used to establish finite element models of electrostatic drivers with different comb tooth to shaft distances, simulate the finite element models, obtain the relationship between different driver capacitances and angles, and fit the obtained different driver capacitances and angles to obtain the driver capacitance expression.

[0089] The resonant amplitude acquisition module is used to obtain the resonant amplitude expression based on the acquired driver capacitance expression, driving torque expression and the dynamic equation of the electrostatic MEMS micromirror, and to obtain the resonant amplitude of the electrostatic MEMS micromirror under different comb-to-rotation axis distances based on the resonant amplitude expression.

[0090] The optimization module is used to select the distance from the comb teeth to the shaft corresponding to the maximum value among all resonant amplitudes as the optimization parameter, and optimize the driver of the MEMS micromirror based on the selected maximum value.

[0091] This invention provides a distance b from the comb teeth to the shaft in an electrostatic MEMS micromirror actuator. m This invention provides an optimized design method for electrostatic MEMS micromirrors. Without altering other parameters, the optimal comb-to-axis distance allows for maximum resonant amplitude, enabling the micromirrors to achieve larger scanning angles. This, in turn, allows MEMS structured light cameras and LiDAR devices to have a wider field of view, improving their monitoring capabilities and efficiency.

[0092] This invention uses theoretical formulas to determine the distance b from the comb teeth to the axis of rotation in an electrostatic MEMS micromirror actuator. m By optimizing the design, this method can enable electrostatic MEMS micromirrors to have a larger scanning angle while keeping the overall structure and natural frequency of the electrostatic MEMS micromirror almost unchanged.

[0093] A schematic diagram of a terminal device according to an embodiment of the present invention. The terminal device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the various method embodiments described above. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the various device embodiments described above.

[0094] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention.

[0095] The terminal device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0096] The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0097] The memory can be used to store the computer program and / or module. The processor implements various functions of the terminal device by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory.

[0098] If the modules / units integrated into the terminal device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0099] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An optimization method for improving the scanning angle of electrostatic MEMS micromirrors, characterized in that, Includes the following steps: S1: Establish the dynamic equation of the electrostatic MEMS micromirror, obtain the driving torque, and establish the expression of the driving torque; S2: Establish finite element models of electrostatic actuators with different distances from comb teeth to the shaft, simulate the finite element models, obtain the relationship between different actuator capacitance and angle, and fit the obtained relationship between different actuator capacitance and angle to obtain the expression of actuator capacitance. S3: Based on the obtained driver capacitance expression, driving torque expression and dynamic equation of electrostatic MEMS micromirror, obtain the expression of resonance amplitude, and based on the expression of resonance amplitude, obtain the resonance amplitude of electrostatic MEMS micromirror under different comb tooth to shaft distances. S4: Select the distance from the comb tooth to the shaft corresponding to the maximum value among all resonant amplitudes as the optimization parameter, and optimize the driver of the MEMS micromirror based on the selected maximum value; Step S1 includes the following steps: The dynamic equation of the electrostatic MEMS micromirror is established using formula (1): In the formula, J Let be the moment of inertia of the mirror. θ For mirrored corners; c The damping coefficient of the electrostatic MEMS micromirror system; k To ensure the stiffness of the torsional beam; M For driving torque; Among them, driving torque M The expression is given by formula (2): In the formula, U It is the driving voltage. C It is the capacitance between the driving comb teeth and the stationary comb teeth; The driving voltage U The expression is: In the formula, U m It is a high level; ω It is the driving frequency; Step S2 includes the following steps: The expression for the driver capacitance is established using formula (4): In the formula, b 0、 b 1. b 2 represents the fitting coefficient; Step S3 includes the following steps: Substitute the driver capacitance expression into the driver torque expression, and then substitute the driver torque expression into the dynamic equation of the electrostatic MEMS micromirror to obtain the expression for the resonant amplitude. In step S3, substituting the driver capacitance expression into the driver torque expression yields: In the formula, U It is the driving voltage; b 0 and b 1 represents the fitting coefficient; In step S3, the expression for the resonant amplitude is established using formula (6): In the formula, J Indicates the moment of inertia of the mirror. c Indicates the damping coefficient; U m This indicates a high level.

2. An optimization system for improving the scanning angle of an electrostatic MEMS micromirror, implementing the method of claim 1, characterized in that, This includes a driving torque expression establishment module, a driver capacitance expression establishment module, a driver capacitance expression establishment module, and a resonant amplitude acquisition module; The driving torque expression establishment module is used to establish the dynamic equation of the electrostatic MEMS micromirror, obtain the driving torque, and establish the driving torque expression. The driver capacitance expression establishment module is used to establish finite element models of electrostatic drivers with different comb tooth to shaft distances, simulate the finite element models, obtain the relationship between different driver capacitances and angles, and fit the obtained different driver capacitances and angles to obtain the driver capacitance expression. The resonant amplitude acquisition module is used to obtain the resonant amplitude expression based on the acquired driver capacitance expression, driving torque expression and the dynamic equation of the electrostatic MEMS micromirror, and to obtain the resonant amplitude of the electrostatic MEMS micromirror under different comb-to-rotation axis distances based on the resonant amplitude expression. The optimization module is used to select the distance from the comb teeth to the shaft corresponding to the maximum value among all resonant amplitudes as the optimization parameter, and optimize the driver of the MEMS micromirror based on the selected maximum value.

3. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in claim 1.

4. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in claim 1.

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