CN110866315A - Electric drive system multi-field coupling optimization method based on bond diagram modeling - Google Patents
Electric drive system multi-field coupling optimization method based on bond diagram modeling Download PDFInfo
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Abstract
The invention discloses a bonding diagram modeling-based multi-field coupling optimization method for an electric drive system, which comprises the following steps of: s1: establishing a permanent magnet motor bonding diagram model; s2: establishing a speed reducer bonding diagram model; s3: establishing a bonding diagram model of the electric drive system, and deducing a state equation of the bonding diagram model of the electric drive system; s4: and inputting simulation parameters and correcting the electric drive system bonding diagram model. By adopting the technical scheme, the energy transfer process of the electric drive system is clearly described, the dynamic characteristics of the electric drive system can be dynamically reflected in real time, and a theoretical basis is provided for the optimal design of the electric drive system.
Description
Technical Field
The invention relates to the technical field of optimization design of an electric drive system, in particular to a multi-field coupling optimization method of the electric drive system based on bonding diagram modeling.
Background
The electric drive system comprises mutual transmission and conversion among various energy flows of electricity, magnetism, machines, liquid, heat and the like, and only by establishing an integrated model of multi-field coupling, more accurate load characteristics, efficiency characteristics, amplitude-frequency characteristics and temperature field characteristics can be obtained, so that design basis is provided for design and development and parameter optimization of the integrated electric drive system.
In the modeling of the electric drive system, most of the modeling is carried out by adopting a traditional theoretical modeling method. The electric drive system is divided into a plurality of subsystems such as mechanical subsystem, electric subsystem and magnetic field subsystem, then a kinetic equation of the system is established by applying a plurality of laws, and finally a transfer function between the input and the output of the electric drive system is derived by carrying out pull type transformation on a differential equation and combining the coupling relation of each subsystem. The traditional theoretical modeling method is easy to understand, but when more accurate modeling is needed to be carried out deep into the whole electric drive system or the number of subsystems contained in the system is increased, the connection and constraint conditions among the subsystems become abnormally complex. The traditional theoretical modeling method is difficult to realize and is easy to make mistakes. The bond map theory has the advantage of unifying multiple energy and field fields to build a model, so that the bond map theory goes into the field of vision of researchers. Its advantages and features are: the established bonding diagram model can be simulated forwards and backwards; the system construction and related parameters thereof can be flexibly and conveniently changed; corresponding mathematical models can be conveniently written by the key map model; the internal connection and energy transfer of the physical model can be clearly and visually expressed.
Today, there are related researchers that use the bond map method to model an electric drive system. Although the existing researchers adopt a bonding diagram model in the optimization design of the electric drive system, the established models are simple and only can reflect the kinematics and the kinematics of the electric drive system, and the models cannot be modeled on the electromagnetic conversion layer and the gear meshing principle inside the motor system, so that the action size of the models on the integrated design of the electric drive system is limited.
Disclosure of Invention
In order to solve the technical problems, the invention provides a multi-field coupling optimization method of an electric drive system based on bonding diagram modeling.
The technical scheme is as follows:
a multi-field coupling optimization method of an electric drive system based on bonding diagram modeling is characterized by comprising the following steps:
s1: establishing a permanent magnet motor bonding diagram model, and deducing a state equation of the permanent magnet motor bonding diagram model;
s2: establishing a reducer bonding diagram model, and deducing a state equation of the reducer bonding diagram model;
s3: establishing a bonding diagram model of the electric drive system according to the bonding diagram model of the permanent magnet motor and the bonding diagram model of the speed reducer, and deducing a state equation of the bonding diagram model of the electric drive system;
s4: and inputting simulation parameters, carrying out simulation analysis on the state equation of the electric drive system bonding diagram model, and correcting the electric drive system bonding diagram model until the electric drive system bonding diagram model can accurately reflect the dynamic characteristics of the speed reducer.
Compared with the prior art, the invention has the beneficial effects that:
the electric drive system multi-field coupling optimization method based on the bonding diagram modeling by adopting the technical scheme has the following advantages:
1. the whole electric drive system containing various energy fields can be directly and integrally represented, and the state equation of the whole electric drive system is easy to derive;
2. the sub-components of the electric drive system can be modeled separately and then can be easily connected together, so that other components can be conveniently added;
3. the energy transfer process of the electric drive system is clearly described, the dynamic characteristics of the electric drive system can be dynamically reflected in real time, and a theoretical basis is provided for the optimal design of the electric drive system.
Drawings
Fig. 1 is an equivalent circuit diagram of a permanent magnet motor;
FIG. 2 is a permanent magnet machine bonding diagram model;
FIG. 3 is a first stage gear pair mesh kinetic model;
FIG. 4 is a first stage gear pair bond map model;
FIG. 5 is a physical model of a retarder;
FIG. 6 is a retarder key map model;
FIG. 7 is a schematic diagram of an electric drive system;
FIG. 8 is a key map model of an electric drive system;
FIG. 9 is a graph of electric drive system torque versus time based on a simulation of a bond map model of the electric drive system;
FIG. 10 is a graph of the speed of the electric drive system as a function of time based on a bond map model simulation of the electric drive system.
Detailed Description
The present invention will be further described with reference to the following examples and the accompanying drawings.
As shown in fig. 1, a method for optimizing multi-field coupling of an electric drive system based on bond map modeling includes the following steps:
s1: and establishing a permanent magnet motor bonding diagram model, and deducing a state equation of the permanent magnet motor bonding diagram model.
The step S1 includes:
s11: and establishing a permanent magnet motor bonding diagram model according to the physical model of the permanent magnet motor.
Please refer to fig. 1, Ua、Ub、UcRespectively, the phase voltage input of the permanent magnet motor, ea、eb、ecIs the respective counter electromotive force, i, of the permanent magnet motora、ib、icThe currents of the windings of each phase of the permanent magnet motor are respectively.
Referring to fig. 2 (fig. 2, 4, 6 and 8 are the same as fig. 2), the symbols in the following figures belong to the common symbols in the theory of bonding diagram: 0 is an equipotential joint, 1 is an equivalent flow joint, I is an inertia element, R is a resistance element, C is a capacitance element, 10To represent 1 st0Keys, the Arabic numerals 2-102 indicate the 2 nd-102 th keys. The established bonding diagram model can be simulated forwards and backwards; the system construction and related parameters thereof can be flexibly and conveniently changed; corresponding mathematical models can be conveniently written by the key map model; the internal connection and energy transfer of the physical model can be clearly and visually expressed. In the context of figure 2, it is shown,MSea、MSeb、MSecrespectively representing three-phase voltage input, Ia、Ib、IcInductance, R, representing a three-phase windinga、Rb、RcIndicating the resistance of the three-phase armature winding, MGY being a variable gyrator, MSeTLRepresenting the load torque of the motor, fa(θ)、fb(θ)、fc(theta) is a shape function of magnetic induction, KEIs the back electromotive force coefficient, KTIs an electromagnetic torque constant, RfRepresenting the coefficient of friction damping, T, of the rotor and bearingLIs the load torque. The established bonding diagram model can be simulated forwards and backwards; the system construction and related parameters thereof can be flexibly and conveniently changed; corresponding mathematical models can be conveniently written by the key map model; the internal connection and energy transfer of the physical model can be clearly and visually expressed.
S12: deducing a state equation of the permanent magnet motor bonding diagram model according to the permanent magnet motor bonding diagram model, wherein the state equation of the permanent magnet motor bonding diagram model is as follows:
in the formula (1), e10、e8、e15Respectively, the phase voltage input of the permanent magnet motor, e23Is the load torque of the permanent magnet machine I3、I10、I17Respectively equal effective inductance, I, of the permanent magnet motor24Is the rotor moment of inertia, p, of a permanent magnet machine3、p10、p17Flux linkages, p, for the windings of each phase of the permanent magnet machine24Is the angular momentum of the rotor, R2、R9、R16Respectively the resistance of the windings of the respective phases of the permanent magnet machine, fa(θ)、fb(θ)、fc(theta) is a shape function of magnetic induction, KEIs the back electromotive force coefficient, KTIs an electromagnetic torque constant, RfIs the friction damping coefficient of the rotor and the bearing.
S2: and establishing a reducer bonding diagram model, and deducing a state equation of the reducer bonding diagram model.
The step S2 includes:
s21: and establishing a six-degree-of-freedom first-stage gear pair meshing dynamic model according to the physical model of the first-stage gear pair.
Referring to fig. 3, under the influence of the factors of the tooth surface friction, each gear has three degrees of freedom in the meshing process, namely, the x direction, the y direction and the rotation direction, so that the supporting rigidity and the damping of the transmission shaft, the bearing, the box body and the like can be equivalent to the values in the x and y directions by using the combined equivalent value kpx、kpy、kgx、kgyAnd cpx、cpy、cgx、cgyTo express, the combined equivalent value k for the meshing stiffness and dampingmAnd cmAnd (4) showing.
S22: and establishing a six-degree-of-freedom first-stage gear pair bonding diagram model according to the first-stage gear pair meshing dynamics model.
Referring to fig. 4, MSe is a variable potential source, TF is a transformer, and MTF is a variable transformer.
S23: and deducing a state equation of the first-stage gear pair bonding diagram model according to the first-stage gear pair bonding diagram model.
The state equation of the first-stage gear pair bonding diagram model is as follows:
in the formula (2), e26、e38、e60Input torque, friction and load torque, p, of the first gear pair, respectively27Is the angular momentum, p, of the first stage drive gear33And p40The translational momentum, p, of the first-stage driving gear in the x-direction and the y-direction respectively47And p54The translational momentum p in the x direction and the y direction of the first-stage driven gear respectively61Angular momentum of the first stage driven gear, q34、q41、q44、q48、q55Corresponding displacements, I, on keys 34, 41, 44, 48, 55, respectively27、I61The rotational inertia of the first-stage driving gear and the first-stage driven gear respectively, I33、I40、I47、I54The corresponding masses, C, on the 33 th, 40 th, 47 th, 54 th keys, respectively34、C41Compliance in x-and y-directions, C, respectively, of the first stage drive gear44Indicating the compliance of the first gear set, C48、C55Compliance, R, in the y-and x-directions, respectively, of the first stage driven gear35、R42、R45、R49、R56、R62、R63Damping corresponding to keys 35, 42, 45, 49, 56, 62, 63, respectively, Rp、RgRespectively, the radius of the first-stage driving gear and the first-stage driven gear, β is the meshing angle of the first-stage driving gear and the first-stage driven gear, H is the distance between the meshing point and the node of the first-stage driving gear and the first-stage driven gear, and lambda is1、λ2The directions of the friction force acting on the first-stage driving gear and the first-stage driven gear are respectively.
S24: and establishing a reducer bonding diagram model according to the physical model of the reducer and based on the physical model of the reducer and the first-stage gear pair bonding diagram model (see fig. 6). The gear pair bonding diagram model and the reducer bonding diagram model can accurately analyze the characteristics of the reducer and other characteristics of a gear transmission mechanism, and provide a theoretical basis for the optimization design of the reducer and other gear transmission systems.
Referring to fig. 5, the speed reducer includes a speed reducer input shaft for inputting power, a speed reducer intermediate shaft for transmitting power, and a speed reducer output shaft for outputting power, the speed reducer input shaft and the speed reducer intermediate shaft are driven by a first stage gear pair, the speed reducer intermediate shaft and the speed reducer output shaft are driven by a second stage gear pair, the first stage gear pair includes a first stage driving gear fixedly sleeved on the speed reducer input shaft and a first stage driven gear fixedly sleeved on the speed reducer intermediate shaft, the first stage driving gear is engaged with the first stage driven gear, the second stage gear pair includes a second stage driving gear fixedly sleeved on the speed reducer intermediate shaft and a second stage driven gear fixedly sleeved on the speed reducer output shaft, and the second stage driving gear is engaged with the second stage driven gear.
S25: and deducing a state equation of the reducer bonding diagram model according to the reducer bonding diagram model.
The state equation of the speed reducer bonding diagram model is as follows:
in the formula (3), e64、e76、e98Input torque, friction and load torque, p, of the second gear pair, respectively65Is the angular momentum, p, of the second stage drive gear71And p78The translational momentum, p, of the second-stage driving gear in the x-direction and the y-direction respectively85And p92The translational momentum p in the x direction and the y direction of the second-stage driven gear respectively99Angular momentum of the driven gear of the second stage, q72、q79、q82、q86、q93Corresponding displacements at the 72 th, 79 th, 82 th, 86 th, 93 th keys, I65、I99The rotational inertia of the second driving gear and the second driven gear respectively, I71、I78、I85、I92The corresponding masses, C, on the 71 th, 78 th, 85 th, 92 th keys, respectively72、C79Compliance in the x-and y-directions, C, respectively, of the second stage drive gear82Indicating the compliance of the second gear set, C86、C93Compliance in the y-and x-directions, R, respectively, of the second stage driven gear73、R80、R83、R87、R94、R100、R101Corresponding damping at keys 73, 80, 83, 87, 94, 100, 101, q102For angular displacement on the intermediate shaft of the speed reducer, C102Indicating the compliance of the intermediate shaft of the reducer, Rp’、Rg' radii of the second driving gear and the second driven gear, β ' an engagement angle between the second driving gear and the second driven gear, H ' a distance between an engagement point of the second driving gear and the second driven gear and a node, and lambda1’、λ2' directions in which frictional force acts on the second stage driving gear and the second stage driven gear, respectively.
S3: and establishing a bonding diagram model of the electric drive system according to the bonding diagram model of the permanent magnet motor and the bonding diagram model of the speed reducer, and deducing a state equation of the bonding diagram model of the electric drive system.
Referring to fig. 7 and 8, the electric drive system includes a permanent magnet motor and a speed reducer, which are driven by a connecting shaft.
In step S3, the equation of state of the electric drive system bond map model:
in the formula (4), q25Is the deformation of the output shaft of the motor.
S4: and inputting simulation parameters, carrying out simulation analysis on the state equation of the electric drive system bonding diagram model, and correcting the electric drive system bonding diagram model until the electric drive system bonding diagram model can accurately reflect the dynamic characteristics of the speed reducer.
The simulation parameters are as follows: input torque Tin12Nm, load torque ToutThe stiffness of the middle shaft was 8 × 108Nm/rad, 20Nm, and the other main parameters are shown in table 1:
table 1 simulation principal parameters
It is noted that the stiffness described in table 1 is reciprocal to the compliance described in this example.
The load is 0 at the beginning of the simulation, and the load is added at the time of 0.4s, and the simulation result is as follows:
fig. 8 and 9 show output torque and output speed, respectively, at the output of the electric drive system. After the load is added at 0.4s, the torque ripple of its output increases as a result of the abrupt stiffness change due to the gear contact ratio not being an integer. When the load is added within 0.4s, the output speed of the electric drive system is reduced and then reaches a stable value again, which is caused by the speed regulation of the motor.
Finally, during operation of the electric drive system, the outputs of the entire system are mutually influenced and coupled by the subsystems. The integrated modeling of the electric drive system can obtain integral information, thereby providing a research basis for integrated design research and further optimizing the performance of the whole electric drive system.
Finally, it should be noted that the above-mentioned description is only a preferred embodiment of the present invention, and those skilled in the art can make various similar representations without departing from the spirit and scope of the present invention.
Claims (8)
1. A multi-field coupling optimization method of an electric drive system based on bonding diagram modeling is characterized by comprising the following steps:
s1: establishing a permanent magnet motor bonding diagram model, and deducing a state equation of the permanent magnet motor bonding diagram model;
s2: establishing a reducer bonding diagram model, and deducing a state equation of the reducer bonding diagram model;
s3: establishing a bonding diagram model of the electric drive system according to the bonding diagram model of the permanent magnet motor and the bonding diagram model of the speed reducer, and deducing a state equation of the bonding diagram model of the electric drive system;
s4: and inputting simulation parameters, carrying out simulation analysis on the state equation of the electric drive system bonding diagram model, and correcting the electric drive system bonding diagram model until the electric drive system bonding diagram model can accurately reflect the dynamic characteristics of the speed reducer.
2. The method for optimizing multi-field coupling of an electric drive system based on bond map modeling as set forth in claim 1, wherein said step S1 comprises:
s11: establishing a permanent magnet motor bonding diagram model according to a physical model of the permanent magnet motor;
s12: and deducing a state equation of the permanent magnet motor bonding diagram model according to the permanent magnet motor bonding diagram model.
3. The bonding diagram modeling-based electric drive system multi-field coupling optimization method of claim 2, wherein the state equation of the permanent magnet motor bonding diagram model is as follows:
in the formula (1), e10、e8、e15Respectively, the phase voltage input of the permanent magnet motor, e23Is the load torque of the permanent magnet machine I3、I10、I17Respectively equal effective inductance, I, of the permanent magnet motor24Is the rotor moment of inertia, p, of a permanent magnet machine3、p10、p17Flux linkages, p, for the windings of each phase of the permanent magnet machine24Is the angular momentum of the rotor, R2、R9、R16Respectively the resistance of the windings of the respective phases of the permanent magnet machine, fa(θ)、fb(θ)、fc(theta) is a shape function of magnetic induction, KEIs the back electromotive force coefficient, KTIs an electromagnetic torque constant, RfIs the friction damping coefficient of the rotor and the bearing.
4. The method for optimizing multi-field coupling of an electric drive system based on bond map modeling as set forth in claim 1, wherein said step S2 comprises:
s21: establishing a six-degree-of-freedom first-stage gear pair meshing dynamic model according to the physical model of the first-stage gear pair;
s22: establishing a six-degree-of-freedom first-stage gear pair bonding diagram model according to the first-stage gear pair meshing dynamics model;
s23: deducing a state equation of the first-stage gear pair bonding diagram model according to the first-stage gear pair bonding diagram model;
s24: establishing a reducer bonding diagram model according to a physical model of the reducer and based on the physical model of the reducer and the first-stage gear pair bonding diagram model;
s25: and deducing a state equation of the reducer bonding diagram model according to the reducer bonding diagram model.
5. The method for optimizing the multi-field coupling of the electric drive system based on the linkage diagram modeling as claimed in claim 4, wherein in step S23, the state equation of the first-stage gear pair linkage diagram model is:
in the formula (2), e26、e38、e60Input torque, friction and load torque, p, of the first gear pair, respectively27Is the angular momentum, p, of the first stage drive gear33And p40The translational momentum, p, of the first-stage driving gear in the x-direction and the y-direction respectively47And p54The translational momentum p in the x direction and the y direction of the first-stage driven gear respectively61Angular momentum of the first stage driven gear, q34、q41、q44、q48、q55Corresponding displacements, I, on keys 34, 41, 44, 48, 55, respectively27、I61The rotational inertia of the first-stage driving gear and the first-stage driven gear respectively, I33、I40、I47、I54The corresponding masses, C, on the 33 th, 40 th, 47 th, 54 th keys, respectively34、C41Compliance in x-and y-directions, C, respectively, of the first stage drive gear44Indicating the compliance of the first gear set, C48、C55Compliance, R, in the y-and x-directions, respectively, of the first stage driven gear35、R42、R45、R49、R56、R62、R63Damping corresponding to keys 35, 42, 45, 49, 56, 62, 63, respectively, Rp、RgRespectively, the radius of the first-stage driving gear and the first-stage driven gear, β is the meshing angle of the first-stage driving gear and the first-stage driven gear, H is the distance between the meshing point and the node of the first-stage driving gear and the first-stage driven gear, and lambda is1、λ2The directions of the friction force acting on the first-stage driving gear and the first-stage driven gear are respectively.
6. The bond map modeling based electric drive system multi-field coupling optimization method of claim 5, wherein: in step S24, the speed reducer includes a speed reducer input shaft for inputting power, a speed reducer intermediate shaft for transmitting power, and a speed reducer output shaft for outputting power, the speed reducer input shaft and the speed reducer intermediate shaft are driven by a first gear pair, the speed reducer intermediate shaft and the speed reducer output shaft are driven by a second gear pair, the first gear pair includes a first driving gear fixedly sleeved on the speed reducer input shaft and a first driven gear fixedly sleeved on the speed reducer intermediate shaft, the first driving gear is engaged with the first driven gear, the second gear pair includes a second driving gear fixedly sleeved on the speed reducer intermediate shaft and a second driven gear fixedly sleeved on the speed reducer output shaft, and the second driving gear is engaged with the second driven gear.
7. The method for optimizing the multi-field coupling of the electric drive system based on the bonding diagram modeling according to claim 6, wherein in step S25, the state equation of the reducer bonding diagram model is as follows:
in the formula (3), e64、e76、e98Input torque, friction and load torque, p, of the second gear pair, respectively65Is a second stage mainAngular momentum of moving gear, p71And p78The translational momentum, p, of the second-stage driving gear in the x-direction and the y-direction respectively85And p92The translational momentum p in the x direction and the y direction of the second-stage driven gear respectively99Angular momentum of the driven gear of the second stage, q72、q79、q82、q86、q93Corresponding displacements at the 72 th, 79 th, 82 th, 86 th, 93 th keys, I65、I99The rotational inertia of the second driving gear and the second driven gear respectively, I71、I78、I85、I92The corresponding masses, C, on the 71 th, 78 th, 85 th, 92 th keys, respectively72、C79Compliance in the x-and y-directions, C, respectively, of the second stage drive gear82Indicating the compliance of the second gear set, C86、C93Compliance in the y-and x-directions, R, respectively, of the second stage driven gear73、R80、R83、R87、R94、R100、R101Corresponding damping at keys 73, 80, 83, 87, 94, 100, 101, q102For angular displacement on the intermediate shaft of the speed reducer, C102Indicating the compliance of the intermediate shaft of the reducer, Rp’、Rg' radii of the second driving gear and the second driven gear, β ' an engagement angle between the second driving gear and the second driven gear, H ' a distance between an engagement point of the second driving gear and the second driven gear and a node, and lambda1’、λ2' directions in which frictional force acts on the second stage driving gear and the second stage driven gear, respectively.
8. The method for optimizing the multi-field coupling of the electric drive system based on the bond map modeling as claimed in claim 7, wherein in step S3, the equation of state of the bond map model of the electric drive system is:
in the formula (4), q25Is the deformation of the output shaft of the motor.
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