CN110011585B - Permanent magnet semi-direct drive type transmission shafting torsional vibration control method caused by external excitation - Google Patents
Permanent magnet semi-direct drive type transmission shafting torsional vibration control method caused by external excitation Download PDFInfo
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- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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Abstract
A permanent magnet semi-direct drive type transmission shaft system torsional vibration control method caused by external excitation belongs to a transmission shaft system torsional vibration control method. The method comprises the following steps: s1, establishing an electromechanical coupling dynamic model of a half direct drive main transmission shaft driven by a high-power permanent magnet motor to acquire dynamic information of the system; s2, analyzing the model by using a multi-scale method to obtain the relation between the parameter change of the electromechanical coupling system and the torsional vibration of the system; s3, determining the stability of the system when the parameters are changed; s4, constructing a time-lag feedback controller; s5, adjusting various parameters in the electromechanical coupling system according to the simulation effect; and S6, finishing the design. The method has the advantages that the stability interval and the vibration minimum point of each parameter of the electromechanical coupling system are firstly determined, and then the time-lag feedback controller is designed according to the parameters, so that the resonance phenomenon between an external excitation and a transmission system is avoided, the vibration amplitude is reduced, the robustness of the PI closed-loop controller is improved, and the reliable application of the low-speed and high-torque permanent magnet synchronous motor on the cutting part of the coal mining machine is guaranteed.
Description
Technical Field
The invention relates to a control method for torsional vibration of a transmission shaft system, in particular to a control method for the torsional vibration of a permanent magnet semi-direct drive type transmission shaft system caused by external excitation.
Background
In recent years, with the continuous development of coal mine mechanization, higher requirements are made on high efficiency and high reliability of fully mechanized mining equipment. The shearer loader is an important component of fully-mechanized mining equipment, the cutting part of the shearer loader at the present stage mainly adopts a transmission mode of 'a three-phase asynchronous motor + three-level straight tooth speed reduction + a cutting drum', and the transmission mode is very easy to generate faults under severe working conditions due to the fact that a transmission chain of the cutting part is long, particularly the faults of a planetary gear reducer at the cutting drum directly influence the reliable operation time of the shearer.
By adopting a semi-direct driving system consisting of a high-power permanent magnet synchronous motor, a three-level straight-tooth speed reducer and a cutting drum, the failure rate of the cutting part of the coal mining machine can be effectively reduced, and the purposes of energy conservation and emission reduction can be achieved. Because coal-winning machine cutting units can cause torsional vibration to the transmission shaft under the combined action of electromagnetic torque and cylinder load moment of torsion, and the coal-winning machine cutting units main drive system after changing leads to the reduction ratio to reduce because of having got rid of the planetary gear reduction gear moreover, the electromagnetic torque that the shafting received, load moment, load fluctuation will show the grow in comparing in former system, so torsional vibration that the shafting received will be more violent, consequently to the novel half direct drive transmission system electromechanical coupling torsional vibration control of cutting units become the problem of treating urgently.
Disclosure of Invention
The invention aims to provide a method for controlling torsional vibration of a permanent magnet semi-direct drive type transmission shaft system caused by external excitation, and solves the problem of electromechanical coupling torsional vibration of a novel semi-direct drive transmission system of a cutting part.
The purpose of the invention is realized as follows: the invention provides a method for controlling permanent magnet semi-direct drive type transmission shafting torsional vibration caused by external excitation, which comprises the following steps:
the method comprises the following specific steps:
s1, establishing an electromechanical coupling dynamic model of a half direct drive main transmission shaft driven by a high-power permanent magnet motor, and acquiring dynamic information of the system:
according to the Lagrange-Maxwell principle, performing overall electromechanical coupling dynamics analysis on the main transmission system to obtain an electromechanical coupling dynamics model of a semi-direct drive main transmission shaft driven by a high-power permanent magnet motor;
s2: analyzing the electromechanical coupling dynamic model by using a multi-scale method to obtain the relation between the parameter change of the electromechanical coupling system and the torsional vibration of the system:
performing dynamics analysis on the electromechanical coupling dynamics model without time lag by using a multi-scale method, obtaining a frequency response function in a system polar coordinate form under the condition of considering main resonance, and obtaining the influence of the axial stiffness coefficient and the damping coefficient of the electromechanical coupling transmission system of the permanent-magnet semi-direct-drive cutting part on system torsional vibration;
s3: determining the stability of the system when the parameters change:
determining the stiffness coefficient and the damping coefficient of the main transmission shaft, the ampere turns of the permanent magnet motor and the stable region of the thickness of the permanent magnet in the step S2, and obtaining the point where the stiffness coefficient and the damping coefficient of the main transmission shaft, the ampere turns of the permanent magnet motor and the thickness of the permanent magnet have the minimum influence on the torsional vibration of the system in the stable region;
s4: constructing a time-lag feedback controller:
constructing a time-lag feedback controller according to various parameters obtained in the step S3, and adjusting control signals of the low-speed large-torque permanent magnet synchronous motor;
s5: adjusting various parameters in the electromechanical coupling system according to the simulation effect:
constructing a semi-direct drive type transmission shafting simulation model driven by a low-speed large-torque permanent magnet synchronous motor in MATLAB/SIMULINK, and substituting design parameters in the simulation model to verify the effectiveness of the design; simultaneously, the time lag parameters, the electrical parameters and the mechanical parameters of the time lag feedback controller are adjusted in combination with the previous step;
s6: and finishing the design.
Step S1: analyzing an internal magnetic field of the high-power permanent magnet synchronous motor to obtain the electromagnetic torque of the permanent magnet synchronous motor; then according to Lagrange-Maxwell principle, carrying out overall electromechanical coupling dynamics analysis on the main transmission system to obtain an electromechanical coupling dynamics model of the semi-direct drive main transmission shaft driven by the high-power permanent magnet motor, and finally adding time lag feedback to form a final control system dynamics model:
wherein: j. the design is a square1、J2The rotary inertia of the permanent magnet synchronous motor and the cutting drum are respectively; K. c is the torsional rigidity and damping coefficient of the semi-direct drive main transmission shaft respectively; theta1、θ2Respectively indicating the rotation angle of the output shaft of the permanent magnet synchronous motor and the rotation angle of the cutting drum, CeRepresenting rotational damping inside the permanent magnet synchronous machine; a nonlinear coefficient expressed as torsional stiffness of the main drive shaft; k is a radical of1、k2、k3Respectively representing the coefficients of a primary term, a secondary term and a tertiary term of the output torque of the permanent magnet synchronous motor; F. omega is the amplitude and phase of the load respectively;
carrying out dimensionless transformation on the formula (1) to obtain a dimensionless kinetic equation of the main transmission system:
wherein the content of the first and second substances,
x1＝θ1，x2＝θ2the remaining parameters are derived from the parameters in equation (1)And (6) discharging.
Step S2: in order to facilitate the analysis of the influence of each parameter on the torsional vibration of the system, the solution of the equation is set as follows:
then, carrying out perturbation analysis on the kinetic equation to obtain a frequency response function under a polar coordinate system, and converting the frequency response function under a Cartesian coordinate system by using the formula (4):
wherein r is1、r2To balance the magnitude of the first order approximation of the solution,
in order to balance the phase of the first order approximation,
introducing a tuning parameter sigma1、σ2Expressing the internal resonance frequency and the external excitation frequency to obtain a frequency response function under a Cartesian coordinate system;
step S3: the frequency response function (5) comprises all parameters in the whole system, and the influence of the rigidity coefficient and the damping coefficient of a main transmission shaft in the electromechanical coupling transmission system and the physical quantity of a power factor angle and the ampere turn number in the permanent magnet synchronous motor on the torsional vibration of the system is obtained according to the frequency response function; obtaining a Jacobian matrix of the system through a frequency response equation of a main transmission system, and calculating a Hurwitz determinant; when the frequency response function is influenced by small disturbance Δ p, the relationship between the Jacobian matrix and the small disturbance is as follows:
[Δp′1,Δp′2,Δp′3,Δp′4]T＝[J][Δp1,Δp2,Δp3,Δp4] (6)
according to the Jacobian matrix, the characteristic equation corresponding to the balance solution can be expressed as:
λ4+1λ3+2λ2+3λ+4＝0 (7)
wherein the content of the first and second substances,1、2、3and4derived from Jacobian matrix; the stability condition of the system can be judged according to the Jacobian matrix and the Hurwitz determinant as follows:
1＞0,1 2-3＞0,3(1 2-3)-1 2 4＞0,4＞0 (8)
obtaining vibration amplitude and phase corresponding to each physical quantity, and judging the stability of the vibration amplitude and phase; obtaining the stable regions of mechanical and electrical parameters such as the rigidity coefficient and the damping coefficient of the main transmission shaft; obtaining a point with minimum system vibration in a stable domain of a certain parameter; and obtaining the design range of each parameter of the permanent magnet synchronous motor and the main transmission shaft.
Step S4: repeating the step S3 to obtain a frequency response function containing time-lag parameters and the stability thereof, and obtaining the effective design range of the time-lag parameters according to the requirements of the frequency response function and the stability; constructing a time-lag feedback controller on the basis of the control of the original permanent magnet synchronous motor;
delaying the speed signal of the motor by tau time, and then delaying the original speed omega and the delayed speed omegaτMaking a difference value omega-omegaτMultiplying by a scaling factor k to obtain k (ω - ω)τ) The signal is input as an adjustment signal to the PI regulator together with the normal speed signal as a command signal.
Step S5: and when the output rotating speed of the motor in the simulation result is consistent with the result in the theoretical analysis and meets the requirement of system stability, namely the rotating speed of the permanent magnet synchronous motor tends to be gentle, outputting the design range of each parameter in the system.
The method has the advantages that by adopting the scheme, when the torsional vibration of the permanent magnet semi-direct drive type transmission shafting caused by external excitation is controlled, on the basis of the electromechanical coupling transmission model, from two angles of electromechanical coupling system parameters and a motor control method, firstly, the stable interval and the vibration minimum point of each parameter of the electromechanical coupling system are determined, then, the time-lag feedback controller is designed according to the parameters, the resonance phenomenon between the external excitation and the transmission system is avoided, the vibration amplitude is reduced, the robustness of the PI closed-loop controller is improved, and the reliable application of the low-speed and high-torque permanent magnet synchronous motor on the cutting part of the coal mining machine is guaranteed.
The problem of electromechanical coupling torsional vibration of a novel semi-direct drive transmission system of the cutting part is solved, and the purpose of the invention is achieved.
The advantages are that: from the view point of parameter setting of the electromechanical coupling transmission system and control of the permanent magnet synchronous motor, the torsional vibration of the transmission chain caused by external excitation is greatly reduced.
Drawings
FIG. 1 is a schematic diagram of the system of the present invention.
FIG. 2 is a design flow diagram of the present invention.
FIG. 3 is a schematic diagram of a skew feedback controller according to the present invention.
FIG. 4 is a diagram showing the control effect of the semi-direct drive transmission shaft of the coal mining machine of the present invention when chaos occurs.
FIG. 5 is a diagram showing the effect of controlling the torsional amplitude value by using the semi-direct drive transmission shaft system of the coal mining machine.
In fig. 1, a permanent magnet synchronous motor; 2. a clutch; 3. an elastic torque shaft; 4. gear transmission is carried out; 5. a cutting drum.
Detailed Description
The invention provides a method for controlling permanent magnet semi-direct drive type transmission shafting torsional vibration caused by external excitation, which comprises the following steps:
s1, establishing an electromechanical coupling dynamic model of a half direct drive main transmission shaft driven by a high-power permanent magnet motor, and acquiring dynamic information of the system:
according to the Lagrange-Maxwell principle, performing overall electromechanical coupling dynamics analysis on the main transmission system to obtain an electromechanical coupling dynamics model of a semi-direct drive main transmission shaft driven by a high-power permanent magnet motor;
s2: analyzing the electromechanical coupling dynamic model by using a multi-scale method to obtain the relation between the parameter change of the electromechanical coupling system and the torsional vibration of the system:
performing dynamics analysis on the electromechanical coupling dynamics model without time lag by using a multi-scale method, obtaining a frequency response function in a system polar coordinate form under the condition of considering main resonance, and obtaining the influence of the axial stiffness coefficient and the damping coefficient of the electromechanical coupling transmission system of the permanent-magnet semi-direct-drive cutting part on system torsional vibration;
s3: determining the stability of the system when the parameters change:
determining the stiffness coefficient and the damping coefficient of the main transmission shaft, the ampere turns of the permanent magnet motor and the stable region of the thickness of the permanent magnet in the step S2, and obtaining the point where the stiffness coefficient and the damping coefficient of the main transmission shaft, the ampere turns of the permanent magnet motor and the thickness of the permanent magnet have the minimum influence on the torsional vibration of the system in the stable region;
s4: constructing a time-lag feedback controller:
constructing a time-lag feedback controller according to various parameters obtained in the step S3, and adjusting control signals of the low-speed large-torque permanent magnet synchronous motor;
s5: adjusting various parameters in the electromechanical coupling system according to the simulation effect:
constructing a semi-direct drive type transmission shafting simulation model driven by a low-speed large-torque permanent magnet synchronous motor in MATLAB/SIMULINK, and substituting design parameters in the simulation model to verify the effectiveness of the design; simultaneously, the time lag parameters, the electrical parameters and the mechanical parameters of the time lag feedback controller are adjusted in combination with the previous step;
s6: and finishing the design.
Step S1: analyzing an internal magnetic field of the high-power permanent magnet synchronous motor to obtain the electromagnetic torque of the permanent magnet synchronous motor; then according to Lagrange-Maxwell principle, carrying out overall electromechanical coupling dynamics analysis on the main transmission system to obtain an electromechanical coupling dynamics model of the semi-direct drive main transmission shaft driven by the high-power permanent magnet motor, and finally adding time lag feedback to form a final control system dynamics model:
wherein: j. the design is a square1、J2The rotary inertia of the permanent magnet synchronous motor and the cutting drum are respectively; K. c is the torsional rigidity and damping coefficient of the semi-direct drive main transmission shaft respectively; theta1、θ2Respectively indicating the rotation angle of the output shaft of the permanent magnet synchronous motor and the rotation angle of the cutting drum, CeRepresenting rotational damping inside the permanent magnet synchronous machine; a nonlinear coefficient expressed as torsional stiffness of the main drive shaft; k is a radical of1、k2、k3Respectively representing the coefficients of a primary term, a secondary term and a tertiary term of the output torque of the permanent magnet synchronous motor; F. omega is the amplitude and phase of the load respectively;
carrying out dimensionless transformation on the formula (1) to obtain a dimensionless kinetic equation of the main transmission system:
wherein the content of the first and second substances,
x1＝θ1，x2＝θ2the remaining parameters are derived from the parameters in equation (1).
Step S2: in order to facilitate the analysis of the influence of each parameter on the torsional vibration of the system, the solution of the equation is set as follows:
then, carrying out perturbation analysis on the kinetic equation to obtain a frequency response function under a polar coordinate system, and converting the frequency response function under a Cartesian coordinate system by using the formula (4):
wherein r is1、r2To balance the magnitude of the first order approximation of the solution,
in order to balance the phase of the first order approximation,
introducing a tuning parameter sigma1、σ2Expressing the internal resonance frequency and the external excitation frequency to obtain a frequency response function under a Cartesian coordinate system;
step S3: the frequency response function (5) comprises all parameters in the whole system, and the influence of the rigidity coefficient and the damping coefficient of a main transmission shaft in the electromechanical coupling transmission system and the physical quantity of a power factor angle and the ampere turn number in the permanent magnet synchronous motor on the torsional vibration of the system is obtained according to the frequency response function; obtaining a Jacobian matrix of the system through a frequency response equation of a main transmission system, and calculating a Hurwitz determinant; when the frequency response function is influenced by small disturbance Δ p, the relationship between the Jacobian matrix and the small disturbance is as follows:
[Δp′1,Δp′2,Δp′3,Δp′4]T＝[J][Δp1,Δp2,Δp3,Δp4] (6)
according to the Jacobian matrix, the characteristic equation corresponding to the balance solution can be expressed as:
λ4+1λ3+2λ2+3λ+4＝0 (7)
wherein the content of the first and second substances,1、2、3and4derived from Jacobian matrix; the stability condition of the system can be judged according to the Jacobian matrix and the Hurwitz determinant as follows:
1＞0,1 2-3＞0,3(1 2-3)-1 2 4＞0,4＞0 (8)
obtaining vibration amplitude and phase corresponding to each physical quantity, and judging the stability of the vibration amplitude and phase; obtaining the stable regions of mechanical and electrical parameters such as the rigidity coefficient and the damping coefficient of the main transmission shaft; obtaining a point with minimum system vibration in a stable domain of a certain parameter; and obtaining the design range of each parameter of the permanent magnet synchronous motor and the main transmission shaft.
Step S4: repeating the step S3 to obtain a frequency response function containing time-lag parameters and the stability thereof, and obtaining the effective design range of the time-lag parameters according to the requirements of the frequency response function and the stability; constructing a time-lag feedback controller on the basis of the control of the original permanent magnet synchronous motor;
delaying the speed signal of the motor by tau time, and then delaying the original speed omega and the delayed speed omegaτMaking a difference value omega-omegaτMultiplying by a scaling factor k to obtain k (ω - ω)τ) The signal is input as an adjustment signal to the PI regulator together with the normal speed signal as a command signal.
Step S5: and when the output rotating speed of the motor in the simulation result is consistent with the result in the theoretical analysis and meets the requirement of system stability, namely the rotating speed of the permanent magnet synchronous motor tends to be gentle, outputting the design range of each parameter in the system.
The invention will be further explained with reference to the drawings
Example 1: in fig. 1, in a practical system using the method of the invention, a low-speed high-torque permanent magnet synchronous motor 1 is connected to an elastic torque shaft 3 of the cutting part of a shearer loader via a clutch 2 and then to a cutting drum 5 via a gear transmission 4. Through the mode, the permanent magnet synchronous motor drives the cutting drum. And then, the stable operation of the semi-direct-drive cutting transmission system of the coal mining machine is realized by designing the mechanical parameters of the elastic torque shaft 2 and the electrical parameters of the permanent magnet synchronous motor 1 and combining a time-lag feedback controller.
As shown in fig. 2, the method for controlling the permanent magnet semi-direct drive type transmission shaft torsional vibration caused by external excitation of the present invention comprises the following steps:
and S1, establishing an electromechanical coupling dynamic model of the half direct drive main transmission shaft driven by the high-power permanent magnet motor, and acquiring dynamic information of the system.
And analyzing the internal magnetic field of the high-power permanent magnet synchronous motor to obtain the electromagnetic torque of the permanent magnet synchronous motor. Then according to Lagrange-Maxwell principle, carrying out overall electromechanical coupling dynamics analysis on the main transmission system to obtain an electromechanical coupling dynamics model of the semi-direct drive main transmission shaft driven by the high-power permanent magnet motor, and finally adding time lag feedback to form a final control system dynamics model:
wherein: j. the design is a square1、J2The rotary inertia of the permanent magnet synchronous motor and the cutting drum are respectively; K. c is the torsional rigidity and damping coefficient of the semi-direct drive main transmission shaft respectively; theta1、θ2Respectively indicating the rotation angle of the output shaft of the permanent magnet synchronous motor and the rotation angle of the cutting drum, CeRepresenting rotational damping inside the permanent magnet synchronous machine; a nonlinear coefficient expressed as torsional stiffness of the main drive shaft; k is a radical of1、k2、k3Respectively representing the coefficients of a primary term, a secondary term and a tertiary term of the output torque of the permanent magnet synchronous motor; F. ω is the amplitude and phase of the load, respectively.
Carrying out dimensionless transformation on the formula (1) to obtain a dimensionless kinetic equation of the main transmission system:
wherein the content of the first and second substances,
x1＝θ1，x2＝θ2the remaining parameters are derived from the parameters in equation (1).
S2: analyzing the model (2) by using a multi-scale method to obtain the relation between the parameter change of the electromechanical coupling system and the torsional vibration of the system:
and carrying out dynamic analysis on the model without time lag by using a multi-scale method, obtaining a frequency response function in a system polar coordinate form under the condition of considering main resonance, and obtaining the influence relation of axial stiffness coefficient, damping coefficient and the like of the permanent magnet semi-direct-drive cutting part electromechanical coupling transmission system on system torsional vibration.
In order to facilitate the analysis of the influence of each parameter on the torsional vibration of the system, the solution of the equation is set as follows:
and then, carrying out perturbation analysis on the kinetic equation to obtain a frequency response function under a polar coordinate system, wherein the frequency response function equation is a transcendental equation and cannot be solved. It is transformed into a cartesian coordinate system using equation (4):
wherein r is1、r2To balance the magnitude of the first order approximation of the solution,
in order to balance the phase of the first order approximation,
introducing a tuning parameter sigma1、σ2The internal resonance frequency and the external excitation frequency are expressed, and a frequency response function under a Cartesian coordinate system is obtained.
S3: stability analysis of a System when parameters change
The frequency response function (5) comprises all parameters in the whole system, so that the influence of the rigidity coefficient, the damping coefficient and the like of a main transmission shaft in the electromechanical coupling transmission system and the influence of physical quantities such as a power factor angle, ampere turns and the like in the permanent magnet synchronous motor on system torsional vibration can be obtained according to the frequency response function. And acquiring a Jacobian matrix of the system through a frequency response equation of the main transmission system, and calculating a Hurwitz determinant. Assuming that the frequency response function is affected by small perturbation Δ p, the relationship between the Jacobian matrix and the small perturbation is:
[Δp′1,Δp′2,Δp′3,Δp′4]T＝[J][Δp1,Δp2,Δp3,Δp4] (6)
according to the Jacobian matrix, the characteristic equation corresponding to the balance solution can be expressed as:
λ4+1λ3+2λ2+3λ+4＝0 (7)
wherein the content of the first and second substances,1、2、3and4derived from the Jacobian matrix, since there are many parameters, it will not be expanded. The stability condition of the system can be judged according to the Jacobian matrix and the Hurwitz determinant as follows:
1＞0,1 2-3＞0,3(1 2-3)-1 2 4＞0,4＞0 (8)
therefore, the vibration amplitude and phase corresponding to each physical quantity can be obtained, and the stability can be judged. Through the two steps, the stable regions of mechanical and electrical parameters such as the rigidity coefficient and the damping coefficient of the main transmission shaft can be obtained, and the point of minimum system vibration in the stable region of a certain parameter can be obtained. And further the design range of each parameter of the permanent magnet synchronous motor and the main transmission shaft can be obtained.
S4: constructing a time-lag feedback controller:
repeating the steps can obtain a frequency response function containing time-lag parameters and the stability thereof, and obtain the effective design range of the time-lag parameters according to the requirements of the frequency response function and the stability. Because the time lag generator in the mechanical structure has larger volume and non-ideal effect, the time lag feedback controller is constructed on the basis of the control of the original permanent magnet synchronous motor.
Delaying the speed signal of the motor by tau time, and then delaying the original speed omega and the delayed speed omegaτMaking a difference value omega-omegaτMultiplying by a scaling factor k to obtain k (ω - ω)τ) As an adjustment signal, is input to the PI regulator as a command signal together with the normal speed signal, as shown in fig. 3.
S5: adjusting various parameters in the electromechanical coupling system according to the simulation effect:
and (3) constructing a semi-direct-drive transmission shafting simulation model driven by a low-speed large-torque permanent magnet synchronous motor in MATLAB/SIMULINK, and substituting design parameters in the simulation model to verify the effectiveness of the design. And simultaneously, the time-lag parameters, the electrical parameters and the mechanical parameters of the time-lag feedback controller are adjusted in combination with the previous step, and if the output rotating speed of the motor in the simulation result is consistent with the result in the theoretical analysis and meets the requirement of system stability, namely the rotating speed of the permanent magnet synchronous motor tends to be gentle, the design range of each parameter in the system is output.
S6: end of design
In fig. 4, in a system without the parameter design method and the time-lag feedback controller of the present invention, chaotic motion sometimes occurs in the system under the external excitation effect, the motion of the system is chaotic, and the vibration is large. After applying the method of the invention, the control system is transformed into a regular periodic movement. The method can reduce the vibration amplitude of the system, and as shown in fig. 5, the system added with the method is obviously smaller in amplitude and more stable than the system without control.
Claims (6)
1. A permanent magnet semi-direct drive type transmission shafting torsional vibration control method caused by external excitation is characterized in that: the method for controlling the torsional vibration of the transmission shaft system comprises the following specific steps:
s1, establishing an electromechanical coupling dynamic model of a half direct drive main transmission shaft driven by a high-power permanent magnet motor, and acquiring dynamic information of the system:
according to the Lagrange-Maxwell principle, performing overall electromechanical coupling dynamics analysis on the main transmission system to obtain an electromechanical coupling dynamics model of a semi-direct drive main transmission shaft driven by a high-power permanent magnet motor;
s2: analyzing the electromechanical coupling dynamic model by using a multi-scale method to obtain the relation between the parameter change of the electromechanical coupling system and the torsional vibration of the system:
performing dynamics analysis on the electromechanical coupling dynamics model without time lag by using a multi-scale method, obtaining a frequency response function in a system polar coordinate form under the condition of considering main resonance, and obtaining the influence of the axial stiffness coefficient and the damping coefficient of the electromechanical coupling transmission system of the permanent-magnet semi-direct-drive cutting part on system torsional vibration;
s3: determining the stability of the system when the parameters change:
determining the stiffness coefficient and the damping coefficient of the main transmission shaft, the ampere turns of the permanent magnet motor and the stable region of the thickness of the permanent magnet in the step S2, and obtaining the point where the stiffness coefficient and the damping coefficient of the main transmission shaft, the ampere turns of the permanent magnet motor and the thickness of the permanent magnet have the minimum influence on the torsional vibration of the system in the stable region;
s4: constructing a time-lag feedback controller:
constructing a time-lag feedback controller according to various parameters obtained in the step S3, and adjusting control signals of the low-speed large-torque permanent magnet synchronous motor;
s5: adjusting various parameters in the electromechanical coupling system according to the simulation effect:
constructing a semi-direct drive type transmission shafting simulation model driven by a low-speed large-torque permanent magnet synchronous motor in MATLAB/SIMULINK, and substituting design parameters in the simulation model to verify the effectiveness of the design; simultaneously, the time lag parameters, the electrical parameters and the mechanical parameters of the time lag feedback controller are adjusted in combination with the previous step;
s6: and finishing the design.
2. The method for controlling the torsional vibration of the permanent magnet semi-direct drive transmission shaft system caused by the external excitation as claimed in claim 1, wherein: step S1: analyzing an internal magnetic field of the high-power permanent magnet synchronous motor to obtain the electromagnetic torque of the permanent magnet synchronous motor; then according to Lagrange-Maxwell principle, carrying out overall electromechanical coupling dynamics analysis on the main transmission system to obtain an electromechanical coupling dynamics model of the semi-direct drive main transmission shaft driven by the high-power permanent magnet motor, and finally adding time lag feedback to form a final control system dynamics model:
wherein: j. the design is a square1、J2The rotary inertia of the permanent magnet synchronous motor and the cutting drum are respectively; K. c is the torsional rigidity and damping coefficient of the semi-direct drive main transmission shaft respectively; theta1、θ2Respectively indicating the rotation angle of the output shaft of the permanent magnet synchronous motor and the rotation angle of the cutting drum, CeRepresenting rotational damping inside the permanent magnet synchronous machine; a nonlinear coefficient expressed as torsional stiffness of the main drive shaft; k is a radical of1、k2、k3Respectively representing the coefficients of a primary term, a secondary term and a tertiary term of the output torque of the permanent magnet synchronous motor; F. omega is the amplitude and phase of the load respectively;
carrying out dimensionless transformation on the formula (1) to obtain a dimensionless kinetic equation of the main transmission system:
wherein the content of the first and second substances,
x1＝θ1，x2＝θ2the remaining parameters are derived from the parameters in equation (1).
3. The method for controlling the torsional vibration of the permanent magnet semi-direct drive transmission shaft system caused by the external excitation as claimed in claim 1, wherein: step S2: in order to facilitate the analysis of the influence of each parameter on the torsional vibration of the system, the solution of the equation is set as follows:
then, carrying out perturbation analysis on the kinetic equation to obtain a frequency response function under a polar coordinate system, and converting the frequency response function under a Cartesian coordinate system by using the formula (4):
wherein r is1、r2To balance the magnitude of the first order approximation of the solution,
in order to balance the phase of the first order approximation,
introducing a tuning parameter sigma1、σ2Expressing the internal resonance frequency and the external excitation frequency to obtain a frequency response function under a Cartesian coordinate system;
4. the method for controlling the torsional vibration of the permanent magnet semi-direct drive transmission shaft system caused by the external excitation as claimed in claim 3, wherein: the frequency response function (5) comprises all parameters in the whole system, and the influence of the rigidity coefficient and the damping coefficient of a main transmission shaft in the electromechanical coupling transmission system and the physical quantity of a power factor angle and an ampere turn number in the permanent magnet synchronous motor on the torsional vibration of the system is obtained according to the frequency response function; obtaining a Jacobian matrix of the system through a frequency response equation of a main transmission system, and calculating a Hurwitz determinant; when the frequency response function is influenced by small disturbance Δ p, the relationship between the Jacobian matrix and the small disturbance is as follows:
[Δp′1,Δp′2,Δp′3,Δp′4]T＝[J][Δp1,Δp2,Δp3,Δp4] (6)
according to the Jacobian matrix, the characteristic equation corresponding to the balance solution can be expressed as:
λ4+1λ3+2λ2+3λ+4＝0 (7)
wherein the content of the first and second substances,1、2、3and4derived from Jacobian matrix; the stability condition of the system can be judged according to the Jacobian matrix and the Hurwitz determinant as follows:
1＞0，1 2-3＞0，3(1 2-3)-1 2 4＞0，4＞0 (8)
obtaining vibration amplitude and phase corresponding to each physical quantity, and judging the stability of the vibration amplitude and phase; obtaining the stability regions of the mechanical and electrical parameters of the rigidity coefficient and the damping coefficient of the main transmission shaft; obtaining a point with minimum system vibration in a stable domain of a certain parameter; and obtaining the design range of each parameter of the permanent magnet synchronous motor and the main transmission shaft.
5. The method for controlling the torsional vibration of the permanent magnet semi-direct drive transmission shaft system caused by the external excitation as claimed in claim 1, wherein: step S4: repeating the step S3 to obtain a frequency response function containing time-lag parameters and the stability thereof, and obtaining the effective design range of the time-lag parameters according to the requirements of the frequency response function and the stability; constructing a time-lag feedback controller on the basis of a PI (proportional-integral) regulator of the permanent magnet synchronous motor;
delaying the speed signal of the motor by tau times and thenThe original speed omega and the delayed speed omega are comparedτMaking a difference value omega-omegaτMultiplying by a scaling factor k to obtain k (ω - ω)τ) The signal is input as an adjustment signal to the PI regulator together with the normal speed signal as a command signal.
6. The method for controlling the torsional vibration of the permanent magnet semi-direct drive transmission shaft system caused by the external excitation as claimed in claim 1, wherein: step S5: and when the output rotating speed of the motor in the simulation result is consistent with the result in the theoretical analysis and meets the requirement of system stability, namely the rotating speed of the permanent magnet synchronous motor tends to be gentle, outputting the design range of each parameter in the system.
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