A modeling method for parallel axis transmission electromechanical brake

Abstract

The application relates to a modeling method for a parallel shaft transmission electromechanical brake, and belongs to the technical field of computer-aided design.The parallel shaft transmission electromechanical brake taking a permanent magnet synchronous motor, a parallel gear box, a ball screw and a brake caliper as a modeling object solves the technical problem of insufficient model precision of the existing electromechanical brake.The modeling method of the application respectively establishes a permanent magnet synchronous motor model, a parallel gear box model, a ball screw model, a brake caliper model and a system friction model for the parallel shaft transmission electromechanical brake; and a parallel shaft transmission electromechanical brake model is obtained from the models.

Description

Technical Field

[0001] This invention belongs to the field of computer-aided design technology, specifically relating to a modeling method for electromechanical brakes with parallel shaft transmission. Background Technology

[0002] As the modern automotive industry accelerates its evolution towards electrification and intelligentization, steer-by-wire chassis technology has gradually matured and become an important development direction for improving vehicle driving efficiency and safety. In automotive braking, steer-by-wire technology, with its advantages of high reliability, high efficiency, and high responsiveness, has become a core component of automotive active safety systems. Steer-by-wire braking is divided into electro-hydraulic braking and electromechanical braking. Electromechanical braking, as a fully electrified steer-by-wire solution, completely replaces the hydraulic components in traditional hydraulic braking systems with electrical signals. Compared to electro-hydraulic braking, electromechanical braking has a more compact structure, faster response speed, and more precise control, and is expected to become the ultimate form of future automotive braking systems.

[0003] For simulation analysis and control algorithm development of electromechanical brakes, a high-precision mathematical model characterizing their dynamic motion characteristics is crucial. However, electromechanical brakes are typically complex electromechanical devices composed of components such as torque motors, gear reduction mechanisms, motion conversion mechanisms, and brake calipers. During operation, they are affected by multiple physical fields (mechanical, electrical, and magnetic) and strong nonlinear characteristics. Therefore, the mathematical modeling of electromechanical brakes needs to consider the complex nonlinear excitations and multi-physics coupling effects between the components.

[0004] Although various types of electromechanical brakes exist on the market, existing modeling methods for electromechanical brakes still suffer from insufficient accuracy and difficulty in characterizing the dynamic response of the brakes. Specifically:

[0005] (1) For torque motor modeling, existing methods are usually directly based on d-q Using a rotating coordinate system to establish voltage and torque equations makes it difficult to characterize the internal magnetic circuit coupling, flux linkage, and other relationships within the motor. d-q Rotating coordinate system of axis α-β Two-phase stationary coordinate system and a-b-c Dynamic transformation relationship of three-phase stationary coordinate system.

[0006] (2) For modeling gear reduction mechanisms, existing methods usually simplify the input and output of torque and speed to a fixed proportional relationship, which cannot characterize the nonlinear dynamic excitation and torsional vibration characteristics under gear meshing during operation.

[0007] (3) For modeling motion conversion mechanisms, existing methods usually treat them as rigid elements, which cannot characterize the complex flexible characteristics of components in the transmission system under contact vibration.

[0008] Therefore, to address the issue of insufficient accuracy in existing electromechanical brake models, designing a high-precision electromechanical brake model with multi-physics coupling and strong nonlinearity can accelerate the development of control algorithms for electromechanical braking systems and facilitate the mass production and application of electromechanical brakes. Summary of the Invention

[0009] In view of the above problems, the present invention provides a modeling method for electromechanical brakes with parallel shaft transmission, which takes the electromechanical brake with parallel shaft transmission, consisting of a permanent magnet synchronous motor (torque motor), a parallel gearbox (gear reduction mechanism), a ball screw (motion conversion mechanism), and a brake caliper, as the modeling object, and solves the problem of insufficient accuracy of electromechanical brake models in the prior art.

[0010] This invention provides a modeling method for a parallel-axis drive electromechanical brake, which includes a permanent magnet synchronous motor 1, a parallel gearbox 2, a ball screw 3, and a brake caliper 4. The specific steps are as follows:

[0011] Step S1: Establish a permanent magnet synchronous motor model for the parallel shaft drive electromechanical brake;

[0012] The permanent magnet synchronous motor model includes voltage equations, flux linkage equations, mechanical motion equations, and electromagnetic torque equations.

[0013] Clarke and Park transforms are applied to the voltage equation, flux linkage equation, mechanical motion equation, and electromagnetic torque equation to realize the permanent magnet synchronous motor model. a-b-c Three-phase stationary coordinate system α-β Two-phase stationary coordinate system and d-q Dynamic transformation in the axis rotation coordinate system yields omnidirectional control parameters for the permanent magnet synchronous motor 1 model.

[0014] Step S2: Establish a parallel gearbox model for the parallel shaft drive electromechanical brake;

[0015] Among them, considering the dynamic excitation of the gear transmission components in the parallel gearbox 2, a gear torsional vibration dynamic model is established, and a lumped parameter model of the fixed-axis gear transmission system is established using Newton-Euler theory; the parallel gearbox model is obtained based on the lumped parameter model and the meshing force between the input gear 201 and the output gear of the parallel gearbox in the gear transmission components.

[0016] Step S3: Establish a ball screw model for the parallel shaft transmission electromechanical brake;

[0017] Among them, considering the flexibility of the screw 301 in the ball screw 3, the kinetic energy, potential energy and Rayleigh loss of the ball screw 3 are established by the Lagrange equation, and the ball screw model is built based on the kinetic energy, potential energy and Rayleigh loss.

[0018] Step S4: Establish a brake caliper model for the electromechanical brake oriented towards parallel shaft transmission;

[0019] Among them, a brake caliper model of an electromechanical brake is established to address the strong nonlinear relationship between the load braking clamping force in the brake caliper 4 and the displacement of the nut 302 in the ball screw 3.

[0020] Step S5: Establish a system friction model for the parallel gearbox 2 and ball screw 3 for the parallel shaft transmission electromechanical brake;

[0021] Step S6. The electromechanical brake model for parallel shaft transmission obtained from steps S1-S5.

[0022] Optionally, in step S2, the dynamic excitation of the gear transmission component includes stiffness, damping, and gear meshing error.

[0023] Optionally, in step S4, when establishing the brake caliper model of the electromechanical brake, colored noise from external disturbances during the operation of the test device and the electromechanical brake is considered.

[0024] Optionally, in step S1, build a-b-c The voltage equation for the permanent magnet synchronous motor model in the three-phase stationary coordinate system is expressed as follows:

[0025]

[0026] in, , , These are permanent magnet synchronous motor 1 a-b-c Voltages in each phase of the shaft; , , For permanent magnet synchronous motor 1 a-b-c Current in each phase of the shaft; The stator winding resistance of permanent magnet synchronous motor 1; , , For permanent magnet synchronous motor 1 a-b-c magnetic flux linkages in each phase of the shaft; t Indicates time t .

[0027] Optionally, in step S1, build a-b-c The flux linkage equation of the permanent magnet synchronous motor model in the three-phase stationary coordinate system is expressed as follows:

[0028]

[0029]

[0030]

[0031] in, , , For permanent magnet synchronous motor 1 a-b-c The self-inductance coefficient of each phase stator winding of the shaft, , , , , , For permanent magnet synchronous motor 1 a-b-c Mutual inductance coefficient of stator windings between phases of the shaft; The inductance component generated by the basic air gap in the permanent magnet synchronous motor 1; The rotor position of permanent magnet synchronous motor 1 depends on the inductive component generated by the magnetic flux. The rotor permanent magnet flux linkage of permanent magnet synchronous motor 1; For the rotor of permanent magnet synchronous motor 1 in space N poles and stators a The electrical angle between phase windings.

[0032] Optionally, the mechanical motion equations of the permanent magnet synchronous motor model are constructed to characterize the motion characteristics of the permanent magnet synchronous motor 1 in the electromechanical brake, and the expression is:

[0033]

[0034] in, This represents the output angular acceleration of permanent magnet synchronous motor 1; The equivalent moment of inertia of permanent magnet synchronous motor 1; The electromagnetic torque of permanent magnet synchronous motor 1; This is the equivalent external load torque of the permanent magnet synchronous motor 1; This refers to the friction torque of the electromechanical braking system.

[0035] Optionally, build a-b-c The electromagnetic torque equation of the permanent magnet synchronous motor model in the three-phase stationary coordinate system is expressed as follows:

[0036]

[0037]

[0038] in, The electromagnetic power of permanent magnet synchronous motor 1; , , For permanent magnet synchronous motor 1 a-b-c Induced electromotive force in the three-phase stator windings of the shaft; This indicates the angular velocity of permanent magnet synchronous motor 1.

[0039] Alternatively, the expression for the parallel gearbox model is:

[0040]

[0041] in, , , , , These are respectively defined as the generalized coordinate vector, generalized mass matrix, generalized damping coefficient matrix, generalized stiffness coefficient matrix, and generalized force matrix of the parallel gearbox model; , These represent the first and second derivatives of the generalized coordinate vector of the parallel gearbox model, respectively.

[0042] Optionally, the expression for the ball screw model is:

[0043]

[0044] in, , , These are defined as the generalized mass matrix, generalized damping coefficient matrix, and generalized stiffness coefficient matrix of the ball screw system, respectively. The generalized coordinate vector representing ball screw 3 The first derivative; The generalized coordinate vector representing ball screw 3 The second derivative; This represents the generalized force vector based on ball screw 3.

[0045] Optionally, the expression for the system friction model is:

[0046]

[0047] in, σ 0 and σ 1 represents the stiffness coefficient and damping coefficient of friction in an electromechanical braking system, respectively. σ 2 represents the viscous friction coefficient of the electromechanical brake. T 0 and T c These are the Coulomb friction torque and static friction torque of the electromechanical brake, respectively. z This represents the average deformation of the bristles in the LuGre model. wc Stribeck speed; This represents the average deformation rate of the bristles in the LuGre model.

[0048] Compared with the prior art, the present invention has at least the following beneficial effects:

[0049] (1) The modeling method for electromechanical brakes for parallel shaft transmission of the present invention constructs a strong nonlinear and high-precision mathematical model for an electromechanical brake composed of a permanent magnet synchronous motor, a parallel gearbox, a ball screw and a brake caliper. The friction of each component in the electromechanical brake is integrated and represented as the total friction at the system level for modeling. In view of the needs of electromechanical brake simulation analysis and its control algorithm development, a systematic and highly applicable modeling method is formed.

[0050] (2) The modeling method for electromechanical brakes with parallel shaft transmission of the present invention, taking into account the multi-physics coupling characteristics of electromechanical brakes (mechanical-electrical-magnetic fields), is designed for mathematical modeling of permanent magnet synchronous motors. It fully considers the electromagnetic characteristics of the motor and implements the permanent magnet synchronous motor model based on Clarke transform and Park transform. a-b-c Three-phase stationary coordinate system α-β Two-phase stationary coordinate system and d-q The dynamic transformation in the axis rotating coordinate system allows for the dynamic characterization of the omnidirectional control parameters of the permanent magnet synchronous motor.

[0051] (3) The modeling method of the present invention for parallel shaft transmission electromechanical brakes takes into account the nonlinear dynamic excitation influence and torsional vibration characteristics of the gear reduction mechanism during the operation of the electromechanical brake, and comprehensively considers the stiffness, damping and gear meshing error of the gear transmission components, and can accurately characterize the dynamic behavior of the gear transmission.

[0052] (4) The modeling method of the present invention for electromechanical brakes for parallel shaft transmission is based on the Lagrange equation to build a high-precision flexible dynamic model for the complex flexible characteristics of the transmission components under contact vibration in the motion conversion mechanism of the electromechanical brake. By introducing flexible modal parameters, dynamic response distortion under high frequency excitation is avoided. Attached Figure Description

[0053] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0054] Figure 1 This is a flowchart of the modeling method for electromechanical brakes for parallel shaft transmission according to the present invention.

[0055] Figure 2 This is a schematic diagram of the transmission of the parallel gearbox in the parallel shaft transmission electromechanical brake of the present invention.

[0056] Figure 3 This is a schematic diagram representing the dynamic model of the gear system meshing transmission system of the parallel gearbox of the parallel shaft transmission electromechanical brake in this invention.

[0057] Figure 4 This is a schematic diagram of the ball screw transmission of the parallel shaft transmission electromechanical brake in this invention.

[0058] Figure 5 This is a schematic diagram representing the flexible dynamic model of the ball screw in the parallel shaft transmission electromechanical brake of this invention.

[0059] Figure 6 This is a schematic curve showing the relationship between the load braking clamping force and the displacement of the ball screw nut in the brake caliper of the parallel shaft transmission electromechanical brake in this invention.

[0060] Figure label:

[0061] 1-Permanent magnet synchronous motor, 101-Motor output end, 2-Parallel gearbox, 201-Parallel gearbox input end gear, 202-Parallel gearbox output end gear, 203-Parallel gearbox input end bearing, 204-Parallel gearbox output end bearing, 3-Ball screw, 301-Screw, 302-Nut, 303-Screw support bearing, 304-Ball screw housing, 4-Brake caliper, 401-Brake piston, 402-Brake pad. Detailed Implementation

[0062] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0063] A specific embodiment of the present invention, such as Figures 1-6 A modeling method for electromechanical brakes with parallel shaft transmissions is disclosed, and the specific steps are as follows:

[0064] like Figure 2 and Figure 4 As shown, the parallel shaft drive electromechanical brake includes a permanent magnet synchronous motor 1 (torque motor), a parallel gearbox 2 (gear reduction mechanism), a ball screw 3 (motion conversion mechanism), and a brake caliper 4.

[0065] The parallel gearbox 2 is equipped with a gear transmission component, which includes an input gear 201, an output gear 202, an input bearing 203, and an output bearing 204. The input gear 201 and the output gear 202 mesh. The input bearing 203 is located inside the input gear 201 and is connected to the motor output 101. The permanent magnet synchronous motor 1 includes a motor output end... 101; The ball screw 3 includes a screw support bearing 303, a screw 301, and a ball screw housing 304. The screw support bearing 303 and the screw 301 are disposed inside the ball screw housing 304. The screw support bearing 303 is disposed at one end of the screw 301. The parallel gearbox output gear 202 is disposed at the outermost end of the screw 301 where the screw support bearing 303 is disposed. The nut 302 is sleeved on the other end of the screw 301; The brake caliper 4 includes a brake piston 401 and a brake pad 402.

[0066] Step S1: Establish a permanent magnet synchronous motor model for the parallel shaft drive electromechanical brake.

[0067] Step S1-1: Based on the multi-physics coupling characteristics of the electromechanical brake and the electromagnetic characteristics of the permanent magnet synchronous motor 1, a system is built... a-b-c A model of a permanent magnet synchronous motor in a three-phase stationary coordinate system. The permanent magnet synchronous motor model includes voltage equations, flux linkage equations, mechanical motion equations, and electromagnetic torque equations.

[0068] Understandable, a-b-c The three-phase stationary coordinate system consists of three spatially stationary coordinates that differ from each other by 120° electrical degrees. a-b-c The system consists of three coordinate axes, each representing a phase voltage or current, and all of them are sinusoidal alternating quantities.

[0069] (1) Building a-b-c The voltage equation for the permanent magnet synchronous motor model in the three-phase stationary coordinate system is expressed as follows:

[0070] (1)

[0071] in, , , These are permanent magnet synchronous motor 1 a-b-c Voltages in each phase of the shaft; , , For permanent magnet synchronous motor 1 a-b-c Current in each phase of the shaft; The stator winding resistance of permanent magnet synchronous motor 1 is given. , , For permanent magnet synchronous motor 1 a-b-c magnetic flux linkages in each phase of the shaft; t Indicates time t .

[0072] (2) Building a-b-c The flux linkage equations for a permanent magnet synchronous motor model in a three-phase stationary coordinate system are as follows:

[0073] (2)

[0074] (3)

[0075] (4)

[0076] in, , , For permanent magnet synchronous motor 1 a-b-c The self-inductance coefficient of each phase stator winding of the shaft, , , , , , For permanent magnet synchronous motor 1 a-b-c Mutual inductance coefficient of stator windings between phases of the shaft; The inductance component generated by the basic air gap in the permanent magnet synchronous motor 1; The rotor position of permanent magnet synchronous motor 1 depends on the inductive component generated by the magnetic flux. The rotor permanent magnet flux linkage of permanent magnet synchronous motor 1; For the rotor of permanent magnet synchronous motor 1 in space N poles and stators a The electrical angle of the phase winding (abbreviated as the motor electrical angle).

[0077] (3) Construct the mechanical motion equations of the permanent magnet synchronous motor model to characterize the motion characteristics of the permanent magnet synchronous motor 1 in the electromechanical brake. The expression is:

[0078] (5)

[0079] in, This represents the output angular acceleration of permanent magnet synchronous motor 1; The equivalent moment of inertia of permanent magnet synchronous motor 1; The electromagnetic torque of permanent magnet synchronous motor 1; This is the equivalent external load torque of the permanent magnet synchronous motor 1; This refers to the friction torque of the electromechanical braking system.

[0080] (4) Buildinga-b-c The electromagnetic torque equation of the permanent magnet synchronous motor model in the three-phase stationary coordinate system is expressed as follows:

[0081] (6)

[0082] (7)

[0083] in, The electromagnetic power of permanent magnet synchronous motor 1; , , For permanent magnet synchronous motor 1 a-b-c Induced electromotive force in the three-phase stator windings of the shaft; This indicates the angular velocity of permanent magnet synchronous motor 1.

[0084] Step S1-2: Based on the Clarke transform and Park transform, realize the permanent magnet synchronous motor model in... α-β Two-phase stationary coordinate system and d-q Dynamic transformation in the axis rotation coordinate system is used to obtain the permanent magnet synchronous motor 1 in... α-β Two-phase stationary coordinate system and d-q Omnidirectional control parameters of a permanent magnet synchronous motor model in a rotating coordinate system.

[0085] Understandable, α-β A two-phase stationary coordinate system consists of two spatially orthogonal coordinates, differing by 90° electrical degrees, and both are stationary. α-β It consists of two coordinate axes, in which α shaft and a-b-c In the three-phase stationary coordinate system of the axis a Axis coincidence, β Axis ahead α Electrical angle of 90° axis α and β The component remains a sinusoidal alternating quantity; d-q The axis-rotating coordinate system consists of two orthogonal axes that rotate synchronously with the motor rotor. d-q The two coordinate axes form a single coordinate system. d and q Components are converted to DC.

[0086] (1) Implementation based on Clarke transform a-b-c Three-phase stationary coordinate system to α-β Transformation of two-phase stationary coordinate systems.

[0087] Furthermore, the expression for the Clarke transform is:

[0088] (8)

[0089] (9)

[0090] in, , , and , As the conversion factor, Here is the Clarke transformation matrix. N These are the Clarke transform coefficients, where the motor vector control uses the constant amplitude transform. N Pick During equal power conversion N Pick .

[0091] Based on equations (8) and (9), we obtain , , and , , Obtained through Clarke transform α-β Voltage in a two-phase stationary coordinate system , and current , The expression is:

[0092] (10)

[0093] (11)

[0094] Based on the inversion of equations (10) and (11), the following is obtained: α-β Voltage in a two-phase stationary coordinate system , to , , and current , To current , The transformation relationship is the inverse Clarke transform.

[0095] (2) Implementation based on Park transformation α-β Two-phase stationary coordinate system to d-q Transformation of the axis-rotating coordinate system.

[0096] Furthermore, the expression for the Park transform is:

[0097] (12)

[0098] (13)

[0099] in, , As the conversion factor, This is the Park transformation matrix.

[0100] Based on equations (12) and (13), we obtain α-β Voltage in a two-phase stationary coordinate system , and current , Obtained through Park transformation d-q Voltage in a rotating coordinate system , and current , The expression is:

[0101]

[0102] Based on the inversion of equations (10) and (11), the following is obtained: d-q Voltage in a rotating coordinate system , to u α , u β and d-q Current in a rotating coordinate system , to i α , i β The transformation relationship is the inverse Park transformation.

[0103] Step S2: Establish a parallel gearbox model for the parallel shaft drive electromechanical brake.

[0104] See Figure 3 Taking into account the dynamic excitations such as stiffness, damping, and gear meshing error of the gear transmission components in parallel gearbox 2, a dynamic analysis of gear torsional vibration is performed on parallel gearbox 2. A lumped parameter model of parallel gearbox 2 is established using Newton-Euler theory, and the expression is as follows:

[0105] (16)

[0106] in, , , , These are the equivalent moments of inertia of the permanent magnet synchronous motor 1, the ball screw 301, the input gear 201 of the parallel gearbox, and the output gear 202 of the parallel gearbox. , , , These refer to the rotation angles of the permanent magnet synchronous motor 1, the ball screw 301, the input gear 201 of the parallel gearbox, and the output gear 202 of the parallel gearbox; , This refers to the torsional stiffness coefficient between the motor output terminal 101 and the lead screw 301. , The torsional damping coefficient between the motor output terminal 101 and the lead screw 301; , The radius of the motor output end 101 and the lead screw 301 at the gear connection end; The meshing force between the input gear 201 and the output gear 202 of the parallel gearbox; The equivalent external load torque of the ball screw 301 in ball screw 3; This indicates the angular velocity of the input gear 201 of the parallel gearbox; This indicates the angular velocity of gear 202 at the output end of the parallel gearbox; This indicates the angular velocity of permanent magnet synchronous motor 1; This indicates the angular velocity of the screw 301 in the ball screw 3; This represents the angular acceleration of permanent magnet synchronous motor 1; This represents the angular acceleration of the input gear 201 of the parallel gearbox; This represents the angular acceleration of the output gear 202 of the parallel gearbox; This indicates the angular velocity acceleration of the lead screw 301 in the ball screw 3.

[0107] Furthermore, the meshing force between the input gear 201 and the output gear 202 of the parallel gearbox... The expression is as follows:

[0108] (17)

[0109] in, , The meshing stiffness coefficient and meshing damping coefficient are the input gear 201 and output gear 202 of the parallel gearbox. This refers to the combined meshing error of gear teeth caused by manufacturing and assembly errors; This indicates the change in the overall meshing error of gear teeth caused by manufacturing and assembly errors over time.

[0110] Arrange equations (16) and (17) to obtain the matrix form of the parallel gearbox model, which is expressed as:

[0111] (18)

[0112] in, , , , , These are respectively defined as the generalized coordinate vector, generalized mass matrix, generalized damping coefficient matrix, generalized stiffness coefficient matrix, and generalized force matrix of the parallel gearbox model; , These represent the first and second derivatives of the generalized coordinate vector of the parallel gearbox model, respectively.

[0113] Furthermore, , , , , The expression is as follows:

[0114] (19)

[0115] (20)

[0116] (twenty one)

[0117] (twenty two)

[0118] (twenty three).

[0119] Step S3: Establish a ball screw model for the parallel shaft transmission electromechanical brake.

[0120] like Figure 3 and Figure 5 As shown, this invention comprehensively considers the flexibility of the screw 301 in the ball screw 3, characterizes the kinetic energy, potential energy and Rayleigh loss of the ball screw 3 through the Lagrange equation, and builds a flexible dynamic model of the ball screw based on this.

[0121] Furthermore, the kinetic energy of ball screw 3 The expression is:

[0122] (twenty four)

[0123] in, , , The mass of the screw support bearing 303, screw 301 and nut 302 in ball screw 3; This represents the equivalent moment of inertia of the lead screw 301; This indicates the angular velocity of the lead screw 301; This indicates the moving speed of the leadscrew 301; This indicates the moving speed of the lead screw support bearing 303; This indicates the speed of nut 302.

[0124] Furthermore, the potential energy of ball screw 3 The expression is:

[0125] (25)

[0126] in, , , The equivalent axial stiffness of the screw support bearing 303, the equivalent axial stiffness of the screw 301, and the equivalent contact stiffness of the nut in the ball screw 3 are given. The transmission ratio of ball screw 3 ( , (for ball screw lead). , , This indicates the displacement of the lead screw 301, lead screw support bearing 303, and nut 302 in the ball screw 3; This indicates the rotation angle of the lead screw 301.

[0127] Furthermore, the Rayleigh loss of ball screw 3 The expression is:

[0128] (26)

[0129] in, , , The equivalent axial damping of the ball screw support bearing 303, the equivalent axial damping of the ball screw 301, and the equivalent contact damping of the nut 302 are given. This indicates the moving speed of the leadscrew 301; This indicates the moving speed of the lead screw support bearing 303; Indicates the speed of nut 302; This indicates the angular velocity of the lead screw 301.

[0130] Furthermore, the generalized coordinate vector of ball screw 3 is defined. and generalized force vector The expression is:

[0131] (27)

[0132] (28)

[0133] in, The torque transmitted from the parallel gearbox 2 to the ball screw 3, The load braking clamping force of brake caliper 4.

[0134] Furthermore, the Lagrange quantity is defined in ball screw 3. Considering the Rayleigh loss of ball screw 3 The generalized coordinate vector based on ball screw 3 is obtained. and generalized force vector The Lagrange equation is expressed as:

[0135] (29)

[0136] in, The generalized coordinate vector representing ball screw 3 The first derivative;

[0137] Furthermore, substituting equations (24) to (28) into equation (29) and rearranging them into matrix form, we can obtain the ball screw model, expressed as:

[0138] (30)

[0139] in, , , These are defined as the generalized mass matrix, generalized damping coefficient matrix, and generalized stiffness coefficient matrix of the ball screw system, respectively. The generalized coordinate vector representing ball screw 3 The second derivative of .

[0140] Furthermore, , , The expression is as follows:

[0141]

[0142] (33)

[0143] Step S4: Establish a brake caliper model for the electromechanical brake oriented towards parallel shaft transmission.

[0144] As the load mechanism of the electromechanical brake, the brake caliper 4 requires a model (i.e., a load braking clamping force estimation model) that characterizes the relationship between the load braking clamping force and the displacement of the nut in the ball screw, thereby describing the braking clamping force experienced by the brake disc during braking in real time. To address the strongly nonlinear relationship between the load braking clamping force and the displacement of the nut in the ball screw, the augmented least squares method is used to solve the load braking clamping force estimation model based on test data from the experimental bench. This effectively avoids interference from sensor measurement noise and external disturbances during the operation of the electromechanical brake on the estimation of the load braking clamping force during bench testing.

[0145] Specifically, considering the strong nonlinear relationship between the load braking clamping force in the brake caliper 4 and the displacement of the nut 302 in the ball screw 3, and taking into account colored noise such as sensor measurement noise during bench testing and external disturbances during the operation of the electromechanical brake, a brake caliper model of the electromechanical brake is established, namely, the load braking clamping force in the brake caliper 4. Displacement of nut 302 in ball screw 3 x n ( t The nonlinear relationship curve of ) is expressed as:

[0146] (34)

[0147] in, for t The measured value of the load braking clamping force during the test bench test; to The parameters of the brake caliper model to be estimated; x ( t )for t Displacement after removing the braking gap at all times x ( t ) =x n ( t ) S gap , S gap This is the initial braking gap. for t Displacement measurement value of nut 302 in ball screw 3 during time bench test; The brake caliper model has colored noise and follows a first-order autoregressive model.

[0148] Furthermore, the brake caliper model exhibits colored noise and follows a first-order autoregressive model. The representation is:

[0149] (35)

[0150] in, for The mean 0 and variance σ at time points 2 White noise; express The white noise value at any given time; The colored noise parameter to be estimated is denoted as .

[0151] Furthermore, the brake caliper model parameters to be estimated and the colored noise parameters are combined into an augmented parameter vector. A ,as follows:

[0152] (36)

[0153] Furthermore, the displacement polynomial and noise posterior residual estimates of nut 302 are... The estimated value is defined as the augmented regression vector. The expression is:

[0154] (37).

[0155] Furthermore, based on equations (34) to (37), the augmented least squares method is adopted, combining each time step... t ( t =1, 2, 3, ... n The measured value of the load braking clamping force in the test bench F cl ( t ) and load braking clamping force Displacement of nut 302 in ball screw 3 x n ( t The augmented parameter vector is solved recursively. A The specific steps for obtaining each value are as follows:

[0156] Step (1): Perform augmented least squares parameter initialization and define the estimated value of the augmented parameter vector at the initial time. Parameter estimation covariance matrix P (0), the initial noise posterior residual estimate And the forgetting factor λ, expressed as:

[0157] (38)

[0158] Where δ represents the initial covariance matrix parameter, and the forgetting factor λ is usually between 0.95 and 1.

[0159] Step (2), based on t Augmented parameter vector estimate at time 1 ,calculate tTime-prior colored noise residual The expression is:

[0160] (39)

[0161] Step (3), based on t Parameter estimation covariance moments at time 1 P ( t 1) Calculate t Time gain vector The expression is:

[0162] (40)

[0163] Step (4), based on t Augmented parameter vector estimate at time 1 And obtained from equations (39) and (40) t Time-prior colored noise residual and gain vector ,renew t Augmented parameter vector estimate at time step The expression is:

[0164] (41)

[0165] Step (5), Update t Time parameter estimation covariance matrix P ( t ) and noise posterior residual estimates ( t The expression is:

[0166] (42)

[0167] Step (6): Determine the estimated value of the augmented parameter vector. Â ( t The convergence of ) is expressed as:

[0168] (43)

[0169] in, τ For the augmented parameter vector estimate threshold, which is greater than 0, t m Indicates the allowed number of iterations. λ min ( P ( t )) represents a matrix P ( tThe smallest eigenvalue of ) λ m express P ( t Minimum feature value threshold.

[0170] When equation (43) is not satisfied, the result obtained based on equation (42) is... P ( t )and ( t Return to step (2), and when equation (43) is satisfied, output... t Augmented parameter vector estimate at time step  ( t )for A Therefore, it is possible to base this on equation (34) and the displacement of the nut in the ball screw at the current moment. x n Real-time acquisition of load braking clamping force F cl ,like Figure 5 As shown.

[0171] Step S5: Establish a system friction model for the parallel shaft transmission electromechanical brake.

[0172] During operation, friction occurs within the components of the electromechanical brake, in addition to the permanent magnet synchronous motor 1, including the parallel gearbox 2, ball screw 3, and brake caliper 4. A system friction model is established. To address the various frictional influences experienced by the parallel shaft drive electromechanical brake during braking, the LuGre model is used for system friction modeling.

[0173] To address the various frictional influences experienced by the electromechanical brake during braking, a system friction model is established using the LuGre model, with the following expression:

[0174] (44)

[0175] in, σ 0 and σ 1 represents the stiffness coefficient and damping coefficient of friction in an electromechanical braking system, respectively. σ 2 represents the viscous friction coefficient of the electromechanical brake. T 0 and T c These are the Coulomb friction torque and static friction torque of the electromechanical brake, respectively. z This represents the average deformation of the bristles in the LuGre model. w c Stribeck speed; This represents the average deformation rate of the bristles in the LuGre model.

[0176] Step S6. The electromechanical brake model for parallel shaft transmission obtained from steps S1-S5.

[0177] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A modeling method for electromechanical brakes with parallel shaft transmissions, characterized in that, The parallel shaft drive electromechanical brake includes a permanent magnet synchronous motor, a parallel gearbox, a ball screw, and a brake caliper. The specific steps are as follows: Step S1: Establish a permanent magnet synchronous motor model for the parallel shaft drive electromechanical brake; The permanent magnet synchronous motor model includes voltage equations, flux linkage equations, mechanical motion equations, and electromagnetic torque equations. Clarke and Park transforms are applied to the voltage equation, flux linkage equation, mechanical motion equation, and electromagnetic torque equation to realize the permanent magnet synchronous motor model. abc Three-phase stationary coordinate system α-β Two-phase stationary coordinate system and dq Dynamic transformation in the axis rotation coordinate system is used to obtain the omnidirectional control parameters of the permanent magnet synchronous motor model. Step S2: Establish a parallel gearbox model for the parallel shaft drive electromechanical brake; Among them, considering the dynamic excitation of the gear transmission components in the parallel gearbox, a gear torsional vibration dynamic model is established, and a lumped parameter model of the fixed-axis gear transmission system is established using Newton-Euler theory; the parallel gearbox model is obtained based on the lumped parameter model and the meshing force between the input gear and the output gear in the parallel gearbox. Step S3: Establish a ball screw model for the parallel shaft transmission electromechanical brake; Among them, considering the flexibility of the ball screw, the kinetic energy, potential energy and Rayleigh loss of the ball screw are established by the Lagrange equation, and a ball screw model is built based on the kinetic energy, potential energy and Rayleigh loss. Step S4: Establish a brake caliper model for the electromechanical brake oriented towards parallel shaft transmission; Among them, a brake caliper model of an electromechanical brake is established to address the strong nonlinear relationship between the load braking clamping force in the brake caliper and the displacement of the nut in the ball screw. Step S5: Establish a system friction model for the parallel gearbox and ball screw for the parallel shaft transmission electromechanical brake; Step S6. Obtain the electromechanical brake model for parallel shaft transmission from steps S1 to S5.

2. The modeling method according to claim 1, characterized in that, In step S2, the dynamic excitation of the gear transmission component includes stiffness, damping, and gear meshing error.

3. The modeling method according to claim 1, characterized in that, In step S4, when establishing the brake caliper model of the electromechanical brake, colored noise from external disturbances during the operation of the test device and the electromechanical brake is taken into account.

4. The modeling method according to claim 1, characterized in that, In step S1, build abc The voltage equation for the permanent magnet synchronous motor model in the three-phase stationary coordinate system is expressed as follows: in, , , These are permanent magnet synchronous motors. abc Voltages in each phase of the shaft; , , These are permanent magnet synchronous motors. abc Current in each phase of the shaft; This refers to the stator winding resistance of a permanent magnet synchronous motor. , , These are permanent magnet synchronous motors. abc magnetic flux linkages in each phase of the shaft; t Indicates time t .

5. The modeling method according to claim 4, characterized in that, In step S1, build abc The flux linkage equation of the permanent magnet synchronous motor model in the three-phase stationary coordinate system is expressed as follows: in, , , These are permanent magnet synchronous motors. abc The self-inductance coefficient of each phase stator winding of the shaft, , , , , , These are permanent magnet synchronous motors. abc Mutual inductance coefficient of stator windings between phases of the shaft; The inductive component generated by the basic air gap in the space of a permanent magnet synchronous motor; The rotor position of a permanent magnet synchronous motor depends on the inductive component generated by the magnetic flux. For permanent magnet rotor flux linkage of permanent magnet synchronous motor; For the rotor of a permanent magnet synchronous motor in space N poles and stators a The electrical angle between phase windings.

6. The modeling method according to claim 5, characterized in that, The mechanical motion equations of the permanent magnet synchronous motor model are constructed to characterize the motion characteristics of the permanent magnet synchronous motor in the electromechanical brake. The expression is as follows: in, This indicates the output angular acceleration of the permanent magnet synchronous motor; This is the equivalent moment of inertia of the permanent magnet synchronous motor; The electromagnetic torque of the permanent magnet synchronous motor; This is the equivalent external load torque of the permanent magnet synchronous motor; This refers to the friction torque of the electromechanical braking system.

7. The modeling method according to claim 6, characterized in that, Set up abc The electromagnetic torque equation of the permanent magnet synchronous motor model in the three-phase stationary coordinate system is expressed as follows: in, The electromagnetic power of the permanent magnet synchronous motor; , , For permanent magnet synchronous motors abc Induced electromotive force in the three-phase stator windings of the shaft; This indicates the angular velocity of the permanent magnet synchronous motor.

8. The modeling method according to claim 1, characterized in that, The expression for the parallel gearbox model is: in, , , , , These are respectively defined as the generalized coordinate vector, generalized mass matrix, generalized damping coefficient matrix, generalized stiffness coefficient matrix, and generalized force matrix of the parallel gearbox model; , These represent the first and second derivatives of the generalized coordinate vector of the parallel gearbox model, respectively.

9. The modeling method according to claim 1, characterized in that, The expression for the ball screw model is: in, , , These are defined as the generalized mass matrix, generalized damping coefficient matrix, and generalized stiffness coefficient matrix of the ball screw system, respectively. Generalized coordinate vector representing the ball screw The first derivative; Generalized coordinate vector representing the ball screw The second derivative; This represents the generalized force vector based on the ball screw.

10. The modeling method according to claim 7, characterized in that, The expression for the system friction model is: in, and These are the stiffness coefficient and damping coefficient of friction in an electromechanical braking system, respectively. The coefficient of viscous friction for electromechanical brakes. T 0 and T c These are the Coulomb friction torque and static friction torque of the electromechanical brake, respectively. z This represents the average deformation of the bristles in the LuGre model. w c Stribeck speed; This represents the average deformation rate of the bristles in the LuGre model; The characteristic function representing the transition from static friction to Coulomb friction.

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