Normal Vibration Stability Control Method of Maglev Train Based on Transfer Function

Abstract

The present invention relates to a method for controlling the normal vibration stability of a maglev train based on a transfer function. The steps are as follows: Obtain the mechanical structure parameters and electromagnetic parameters of the linear induction motor for the maglev train, and establish a mathematical model of the normal force of the linear induction motor; Obtain the dynamic model of the medium and low-speed maglev train considering the normal force through the spring-damping coupling model of the medium and low-speed maglev train; Perform Laplace transform on both sides of the obtained dynamic model of the medium and low-speed maglev train considering the normal force; Obtain the transfer function of the normal vibration of the maglev train according to the dynamic model of the medium and low-speed maglev train considering the normal force obtained by the Laplace transform; Perform stability control on the operation of the maglev train according to the obtained transfer function. The present invention solves the problem that the existing dynamic model of the maglev train does not consider the fluctuation of the normal force of the linear induction motor when established, and cannot analyze the influence of the normal vibration of the linear induction motor on the stable operation of the maglev train.

Description

Technical Field

[0001] The present invention belongs to the technical field of motor vibration analysis, and particularly relates to a method for controlling the normal vibration stability of a medium and low speed maglev train based on a transfer function. Background Technique

[0002] Motor vibration analysis technology is of great value to the safe and stable operation of motors. The normal vibration of the linear induction motor used in maglev trains will cause the suspension air gap of the maglev train to change, resulting in vertical displacement of the maglev train, and thus causing the maglev train to operate unstably. Therefore, analyzing the normal vibration of the linear induction motor used in medium and low speed maglev trains is an effective way to analyze whether the maglev train operates stably.

[0003] Existing maglev train dynamic models all use spring damping to equivalent the elastic elements of the train and air springs, analyze the electromagnetic force exerted by the suspension control system on the suspension frame, etc., and analyze the operation stability of the maglev train through this maglev train dynamic model. Moreover, the vibration research on maglev trains is mostly focused on the vehicle-track coupling vibration research. To sum up, when establishing the existing maglev train dynamic models, the influence of the fluctuation of the normal force of the linear induction motor on the operation stability of the maglev train is not taken into account, only the external environment and suspension control force, etc. are considered, and it cannot analyze the influence of the normal vibration of the linear induction motor on the operation stability of the maglev train. Summary of the Invention

[0004] Object of the Invention: The present invention provides a method for controlling the normal vibration stability of a maglev train based on a transfer function, where the transfer function is obtained by considering the normal force of the linear induction motor, and its purpose is to solve the problem that when establishing the existing maglev train dynamic models, the fluctuation of the normal force of the linear induction motor is not considered, and it cannot analyze the influence of the normal vibration of the linear induction motor on the stable operation of the maglev train.

[0005] Technical Solution:

[0006] The present invention proposes a method for controlling the normal vibration stability of a maglev train based on a transfer function, and the steps are as follows:

[0007] Step (1): Obtain the mechanical structure parameters of the linear induction motor used in the maglev train and the electromagnetic parameters of the linear induction motor, and establish a mathematical model of the normal force of the linear induction motor;

[0008] Step (2): Obtain a dynamic model of the medium and low speed maglev train considering the normal force in step (1) through the spring-damping coupling model of the medium and low speed maglev train;

[0009] Step (3): Perform Laplace transform on both sides of the dynamic model of the medium and low speed maglev train considering the normal force obtained in step (2);

[0010] Step (4) obtains the transfer function of the normal vibration of the maglev train according to the dynamic model of the medium- and low-speed maglev train considering the normal force obtained by Laplace transform in step (3).

[0011] Step (5) performs stability control on the operation of the maglev train according to the transfer function obtained in step (4).

[0012] Further, in step (1), the mathematical model of the normal force of the linear induction motor in the secondary magnetic field-oriented coordinate system is:

[0013]

[0014] where F z is the normal force of the linear induction motor, P is the power, L r is the secondary inductance of the linear induction motor, L m is the mutual inductance, g is the air-gap width, i sm is the current on the M axis, ψ r is the secondary magnetic flux of the linear induction motor.

[0015] Further, in step (1), the mathematical model of the normal force of the linear induction motor in the T-type equivalent circuit diagram of the linear induction motor is:

[0016]

[0017] where F z is the normal force of the linear induction motor; F za is the gravitational force, F zr is the repulsive force; μ0 is the vacuum permeability; l0 is the longitudinal length of the linear induction motor, l δ is the stack thickness of the primary iron core of the linear induction motor; B x is the horizontal component of the air-gap magnetic field, B z is the vertical component of the air-gap magnetic field; F x is the effective thrust of the linear induction motor.

[0018] Further, the solution formula for the effective thrust F x of the linear induction motor is:

[0019]

[0020] where m1 is the number of motor phases; v s is the synchronous speed, v s = 2πf1, τ is the pole pitch of the motor, and f1 is the rated frequency.

[0021] Further, in step (2), the medium- and low-speed maglev train is equivalent to a spring-damper model, and the dynamic model of the medium- and low-speed maglev train considering the normal force is:

[0022]

[0023] Among them, z v represents the vertical displacement of the body of the medium and low speed maglev train, and k s is the equivalent stiffness of the spring-damping coupling model, and c s is the equivalent damping, and m v represents the mass of the body of the medium and low speed maglev train, and F z is the normal force of the linear induction motor.

[0024] Furthermore, the dynamic model of the medium and low speed maglev train considering the normal force obtained by the Laplace transform in step (3) is:

[0025] (m v s 2 +c s s + k s )Z(s) = F z (s)

[0026] Among them, Z(s) is the Laplace transform of z v , and F z (s) is the Laplace transform of F z .

[0027] Furthermore, the transfer function of the normal vibration of the maglev train in step (4) is:

[0028]

[0029] Among them, Z(s) is the Laplace transform of z v , and F z (s) is the Laplace transform of F z .

[0030] Beneficial effects:

[0031] The present invention considers the influence of the normal vibration of the motor on the dynamic characteristics of the maglev train, improves the existing dynamic model of the medium and low speed maglev train, reflects the influence of the fluctuation of the normal force, that is, the normal vibration of the linear induction motor on the running stability of the maglev train in the dynamic model of the maglev train. By analyzing the dynamic model of the maglev train considering the normal force of the linear induction motor, the influence of the motor vibration on the train stability can be obtained, so as to guide the design of the motor for the maglev train to reduce the normal force fluctuation. While reducing the normal force fluctuation of the motor, the workload of the levitation controller can be reduced and the energy consumption can be saved. Description of the drawings

[0032] Figure 1 is a flowchart of the method for obtaining the transfer function of the normal vibration of the medium and low speed maglev train considering the normal force of the linear induction motor;

[0033] Figure 2 It is a T - type equivalent circuit diagram of a linear induction motor considering end effects;

[0034] Figure 3 It is a spring - damping coupling model for medium - and low - speed maglev trains;

[0035] Figure 4 It is a schematic structural diagram of a linear induction motor;

[0036] Figure 5 It is a schematic diagram of the normal force of a linear induction motor varying with time;

[0037] Figure 6 It is a schematic diagram of the vibration characteristics of a mass - damping - spring system. Specific implementation manners

[0038] For a more specific description of the present invention, the present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0039] The present invention first establishes a dynamic model of a medium - and low - speed maglev train considering the normal force of a linear induction motor. The transfer function of the normal vibration is solved through the dynamic model, and the stability control of the maglev train is realized through the transfer function. Due to its own structural reasons, there is a normal force between the primary and secondary windings of a linear induction motor that is several times the magnitude of the horizontal thrust. The normal force of a linear induction motor is divided into two components: normal attractive force and normal repulsive force, and externally shows as a normal resultant force and a normal torque. Usually, the normal attractive force is the largest component of the normal force, which is generated between the primary and secondary yokes of the linear induction motor. The reason for its generation is the main magnetic flux passing through the air gap, and its magnitude is proportional to the square of the effective excitation current and the excitation inductance, that is, it depends on the energy stored in the air gap. The normal repulsive force is generated by the interaction between the primary current and the induced eddy current on the secondary induction plate. Since the normal force of a linear induction motor has periodic fluctuations, it affects the suspension stability and safe operation of the maglev train, and also increases the difficulty of the suspension control system. Establishing a dynamic model of the maglev train is an effective method for analyzing the running stability of the maglev train.

[0040] As Figure 1 shown, a method for controlling the normal vibration stability of a medium - and low - speed maglev train based on a transfer function according to the present invention includes the following steps:

[0041] Step (1): Obtain the mechanical structure parameters of the linear induction motor for the maglev train and the electromagnetic parameters of the linear induction motor, and establish a mathematical model of the normal force of the linear induction motor;

[0042] The mathematical model of the normal force of the linear induction motor can be expressed by the following formula:

[0043]

[0044] Among them, F Z is the normal force; μ0 is the magnetic permeability of vacuum; B z is the vertical component of the air-gap magnetic field; B x is the horizontal component of the air-gap magnetic field; This mathematical model of the normal force is derived based on the Maxwell stress theory, which can not only consider the influence of the vertical component of the air-gap magnetic field on the normal force, but also consider the influence of the horizontal component of the air-gap magnetic field on the normal force;

[0045] In the present invention, the mathematical model of the normal force of the linear induction motor is preferably obtained in two ways. One way is to obtain it in the secondary magnetic field oriented coordinate system, and the other way is to calculate the effective thrust based on the T-type equivalent circuit diagram of the linear induction motor in combination with the synchronous power calculation method, and then calculate the normal force of the linear induction motor considering the end effect.

[0046] The first way: In the secondary magnetic field oriented coordinate system, the normal force F of a single linear induction motor z can be expressed by the following formula:

[0047]

[0048] Among them, F z is the normal force of the linear induction motor, P is the power, L r is the secondary inductance of the linear induction motor, L m is the mutual inductance, g is the air-gap width, i sm is the current on the M axis, ψ r is the secondary magnetic flux of the linear induction motor.

[0049] Compared with the method of deriving the mathematical model of the normal force of the linear induction motor from the electromagnetic field theory by analyzing the primary structure of the linear induction motor, referring to the electromagnetic field analysis of the rotary induction motor, and using the Maxwell magnetic stress tensor, this mathematical model of the normal force has the advantages of fewer motor structure parameters and related coefficients to be measured, and this mathematical model of the normal force is similar to the traction force formula in structure, which is convenient for theoretical analysis and calculation.

[0050] The second way:

[0051] The step (1) can also obtain the mathematical model of the normal force of the linear induction motor considering the end effect by the method based on the equivalent circuit in combination with the synchronous power calculation method, which can be expressed by the following formula:

[0052]

[0053] Among them, F za is the gravitational force, F zr is the repulsive force; μ0 is the magnetic permeability of vacuum; l0, l δare the total longitudinal length of the motor and the stack thickness of the primary iron core; B x and B z are the horizontal and vertical components of the air-gap magnetic field respectively; F x is the effective thrust.

[0054] As Figure 2 shown, the equivalent circuit diagram of the linear induction motor considering the end effect. In the equivalent circuit, U1 and E1 are the rated phase voltage and the induced electromotive force respectively; I1, I0, I e and I2 are the primary current, the exciting current, the end effect current and the secondary reduced current respectively; r1 and r2' are the primary resistance and the secondary resistance respectively; x1, x'2 and x0 are the primary leakage reactance, the secondary leakage reactance and the exciting reactance respectively; Red is the equivalent resistance of the end effect; s is the slip frequency. Based on the equivalent circuit diagram of the linear induction motor and combined with the synchronous power calculation method, the effective thrust of the motor can be obtained and can be expressed by the following formula:

[0055]

[0056] where, m1 is the number of phases of the motor; v s is the synchronous speed, v s = 2πf1, τ is the pole pitch of the motor, and f1 is the rated frequency.

[0057] Since both the normal force and the thrust are the component forces of the electromagnetic force of the linear induction motor and there is a coupling relationship between them, first, based on the equivalent circuit diagram and combined with the synchronous power calculation method, the effective thrust is obtained, and then the normal force of the linear induction motor is calculated. At this time, the mathematical model of the normal force of the linear induction motor obtained is more accurate.

[0058] The normal force generated by the linear induction motor is usually a resistance. The existence of the normal force causes the vehicle to have an additional weight and increases the burden and power consumption of the suspension system. When the normal force fluctuates, it will interfere with or even cause the failure of the suspension system. And the normal force is also affected by the end effect of the linear induction motor. The above mathematical model of the normal force not only considers the influence of the horizontal component of the air-gap magnetic field on the normal force, but also takes into account the influence of the end effect of the linear induction motor on the normal force, making the analysis result more accurate and more in line with the actual situation.

[0059] In practical applications, the normal force F of the linear induction motor can be obtained by selecting the above two mathematical models of the normal force of the linear induction motor according to actual needs z for subsequent method steps.

[0060] Step (2) obtains the dynamic model of the maglev train considering the normal force in step (1) through the suspension frame spring-damping coupling model;

[0061] As Figure 3As shown, for the spring-damping coupling model of the maglev train, the entire vertical dynamic system of the maglev train is equivalent to a spring-damping coupling system. The equivalent stiffness is k s , and the equivalent damping is c s ;

[0062] The dynamic model of the maglev train considering the normal force can be expressed by the following formula:

[0063]

[0064] where z v represents the vertical displacement of the car body, k s is the equivalent stiffness of the spring-damping coupling model, c s is the equivalent damping, m v represents the mass of the car body, F z is the normal force of the linear induction motor; in the present invention, the influence of the normal force of the linear induction motor is considered in the dynamic model of the maglev train. When the normal force F z changes, the vertical displacement z v of the maglev train car body can be calculated. Thus, it can be seen that the present invention can describe the influence of the fluctuation of the normal force of the linear induction motor on the running stability of the maglev train, that is, the influence on the levitation air gap of the maglev train. The levitation control system can pre-adjust the levitation air gap according to the influence of the normal force fluctuation on the levitation air gap, which can not only increase the efficiency of the levitation control system but also reduce the power consumption of the levitation control system; and the fluctuation of the normal force can be reduced through motor design, thereby reducing the fluctuation of the levitation air gap of the maglev train.

[0065] This formula combines the dynamic model of the maglev train and the mathematical model of the normal force of its linear induction drive motor, and the influence of the normal force of the linear induction motor on the vertical vibration of the maglev train can be obtained.

[0066] In step (3), the Laplace transform is performed on both sides of the dynamic model of the maglev train considering the normal force obtained in step (2); the following formula is obtained:

[0067] (m v s 2 +c s s + k s )Z(s) = F z (s)

[0068] where Z(s) is the Laplace transform of z v , and F z (s) is the Laplace transform of f z ;

[0069] Step (4) obtains the transfer function of the normal vibration of the maglev train based on the maglev train dynamics model considering the normal force obtained by Laplace transform in step (3), and the calculation can be expressed by the following formula:

[0070]

[0071] Step (5) performs stability control on the operation of the maglev train according to the transfer function obtained in step (4).

[0072] Taking the 25-slot flat-type three-phase double-layer winding linear induction motor as an example in the present invention, the structure diagram of the motor is as Figure 4 shown; by establishing a 3D model of the linear induction motor for medium and low-speed maglev trains through Maxwell, a more practical graph of the normal force of the linear induction motor changing with time can be obtained, making the analysis results more accurate.

[0073] Taking the 25-slot flat-type three-phase double-layer winding linear induction motor as an example in the present invention to calculate the distribution of its normal force over time, as Figure 5 shown, the fluctuation of the normal force of the linear induction motor is very large in the first 50 ms, and the fluctuation trend of the normal force is relatively stable and gradually approaches a sine type after 50 ms.

[0074] In the present invention, the dynamics model is equivalent to a second-order mass-damping spring system, and its vibration characteristics are as Figure 6 shown. It can be seen from its vibration graph that the adjustment range in the previous stage is relatively large and tends to be stable in the later stage, which is consistent with the change law of the normal force.

[0075] In summary, when analyzing the dynamic characteristics of the train in the present invention, considering the characteristics of the normal vibration of the linear induction motor, after analyzing the influence of the normal vibration of the linear induction motor on the running stability of the maglev train, the vertical vibration characteristics of the maglev train affected by the motor can be obtained according to the normal vibration characteristics of the linear induction motor. When the suspension control system adjusts and controls the suspension air gap, the power consumption of the suspension control system can be reduced; by obtaining the transfer function, the accuracy of analyzing the running stability of the train is improved. It can also be used to guide the motor design, reduce the normal vibration of the motor, thereby reducing the vertical vibration of the maglev train and increasing the running stability of the maglev train.

Claims

1. A normal vibration stability control method for maglev trains based on transfer functions, characterized in that: The steps are as follows: Step (1): Obtain the mechanical structure parameters and electromagnetic parameters of the linear induction motor for maglev trains, and establish a mathematical model of the normal force of the linear induction motor; Step (2): Obtain the dynamic model of the medium and low speed maglev train considering the normal force in step (1) through the spring-damping coupling model of the medium and low speed maglev train; Step (3): Perform Laplace transform on both sides of the dynamic model of the medium and low speed maglev train considering the normal force obtained in step (2); Step (4): Obtain the transfer function of the normal vibration of the maglev train according to the dynamic model of the medium and low speed maglev train considering the normal force obtained by the Laplace transform in step (3); Step (5): Perform stability control on the operation of the maglev train according to the transfer function obtained in step (4).

2. The method for controlling the normal vibration stability of a maglev train based on a transfer function according to claim 1, characterized in that: In step (1), the mathematical model of the normal force of the linear induction motor is as follows in the secondary magnetic field orientation coordinate system: Among them, F z is the normal force of the linear induction motor, P is the power, L r is the secondary inductance of the linear induction motor, L m is the mutual inductance, g is the air-gap width, i sm is the current on the M axis, ψ r is the secondary magnetic flux of the linear induction motor.

3. The method for controlling the normal vibration stability of a maglev train based on a transfer function according to claim 1, characterized in that: In step (1), the mathematical model of the normal force of the linear induction motor is as follows in the T-type equivalent circuit diagram of the linear induction motor: Among them, F z is the normal force of the linear induction motor; F za is the gravitational force, and F zr is the repulsive force; μ0 is the magnetic permeability of vacuum; l0 is the longitudinal length of the linear induction motor, and l δ is the stack thickness of the primary iron core of the linear induction motor; B x is the horizontal component of the air-gap magnetic field, and B z is the vertical component of the air-gap magnetic field; F x is the effective thrust of the linear induction motor.

4. The method for controlling the normal vibration stability of a maglev train based on a transfer function according to claim 3, characterized in that: The effective thrust F of the linear induction motor x The solution formula is as follows: where m1 is the number of phases of the motor; v s is the synchronous speed, v s = 2πf1, I2 is the secondary reduced current, r2' is the secondary resistance, and S is the slip frequency.

5. The method for controlling the normal vibration stability of a maglev train based on a transfer function according to claim 1, characterized in that: In step (2), the medium and low speed maglev train is equivalent to a spring-damping model, and the dynamic model of the medium and low speed maglev train considering the normal force is: Among them, z v represents the vertical displacement of the body of the medium and low speed maglev train, k s is the equivalent stiffness of the spring-damping coupling model, c s is the equivalent damping, m v represents the mass of the body of the medium and low speed maglev train, F z is the normal force of the linear induction motor.

6. The method for controlling the normal vibration stability of a maglev train based on a transfer function according to claim 1, characterized in that: The dynamic model of the medium and low speed maglev train considering the normal force obtained by the Laplace transform in step (3) is: (m v s 2 +c s s+k s )Z(s) = F z (s) Among them, Z(s) is the Laplace transform of z v , F z (s) is the Laplace transform of F z .

7. The method for controlling the normal vibration stability of a maglev train based on a transfer function according to claim 1, characterized in that: The transfer function of the normal vibration of the maglev train in step (4) is: Among them, Z(s) is the Laplace transform of z v , F z (s) is the Laplace transform of F z .

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