A modeling method considering non-ideal commutation electromechanical coupling of brushless direct current motor

Abstract

The application discloses a modeling method of considering non-ideal commutation electromechanical coupling of a brushless direct current motor, and the method comprises the following steps: step one, considering the electromagnetic torque fluctuation caused by the existence of inductance and non-rational commutation when the brushless direct current motor is controlled by using a six-step commutation method; step two, considering the time-varying meshing stiffness, meshing error, meshing damping, torsional stiffness and torsional damping of a gear, and using the lumped parameter method, a four-degree-of-freedom gear torsional vibration model is established; step three, according to the torque fluctuation and the four-degree-of-freedom gear torsional vibration model, the coupling variable-electromagnetic torque T e The application establishes the connection between the motor model and the forced vibration model of the mechanical system-gear, and obtains an electromechanical coupling dynamics model. The application has the beneficial effect that the establishment of the accurate electromechanical coupling mathematical model provides a solid model foundation and numerical analysis for subsequent high-precision control.

Description

Technical Field

[0001] This invention relates to the field of motor technology, and in particular to a modeling method for non-ideal commutation electromechanical coupling of brushless DC motors. Background Technology

[0002] A servo drive system is a complex electromechanical system composed of a transmission system, a motor, and a control system. It exhibits various forms of coupling, including electromechanical coupling, fluid-structure interaction, rigid-elastic coupling, and thermo-elastic coupling. Electromechanical coupling is a classic problem, characterized by the conversion of mechanical energy into electromagnetic energy. In typical servo systems, this manifests primarily as direct electromagnetic torque coupling, direct harmonic torque coupling, infinitesimal control loop coupling, and back-and-forth coupling between multiple transmission subsystems. Due to the high degree of coupling between mechanical and electromagnetic parameters, establishing an accurate electromechanical coupling model has always been a major challenge.

[0003] Currently, most scholars conduct research on motors and transmission systems separately. One group simplifies the transmission system, ignoring the effects of gear meshing stiffness and drive shaft torsional stiffness, and constructs a two-mass spring oscillator torsional vibration model directly applied to the motor rotor to study the motor's electromagnetic characteristics. This approach is relatively simple in structure and calculation, but it neglects the influence of corresponding mechanical parameters. Another group of scholars focuses on the transmission system as the primary research object, assuming the motor's electromagnetic torque is a known condition, and ignoring the fluctuations in electromagnetic torque caused by electromagnetic field disturbances due to mechanical parameters.

[0004] With the increasing demands on servo drive systems, constructing accurate electromechanical coupling models is crucial for improving the accuracy and response characteristics of these systems. Previous modeling methods failed to comprehensively consider the coupling effects of mechanical and electromagnetic parameters. In particular, for brushless DC motors, the models are often simplified to brushed DC motor models, resulting in relatively coarse models that no longer meet the needs of the evolving servo drive system landscape. Therefore, conducting in-depth electromechanical coupling model analysis is of profound significance. Summary of the Invention

[0005] This invention discloses a modeling method for electromechanical coupling considering non-ideal commutation of brushless DC motors. It establishes a dynamic mathematical model of the gear system and brushless DC motor using the lumped parameter method and the equivalent circuit method, and fully considers the fluctuations caused by the non-ideal commutation due to the presence of inductance. The electromechanical coupling model is constructed through the coupling variable - electromagnetic torque, providing theoretical guidance and model for the realization of its high-performance control, thereby effectively solving the technical problems involved in the background art.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A modeling method for non-ideal commutation electromechanical coupling of brushless DC motors, comprising the following steps:

[0008] Step 1: Consider the electromagnetic torque fluctuations caused by inductance and irrational commutation when using the six-step commutation method to control a brushless DC motor. The brushless DC motor is a three-phase motor, including phases A, B, and C. The electromagnetic torque's function over time within one commutation cycle is as follows:

[0009]

[0010] Where E is the back electromotive force and the time constant. L is the equivalent inductance of each phase of the motor, and R is the equivalent resistance of each phase of the motor. Let t1 be the back electromotive force constant, t1 be the moment when the current in phase A drops to 0 in the first stage, and I0 be the initial current. I1 represents the current in phase B and phase C at time t1, considering only the resistance.

[0011] Step 2: Considering the time-varying meshing stiffness, meshing error, meshing damping, torsional stiffness, and torsional damping of the gear, a four-degree-of-freedom gear torsional vibration model is established using the lumped coefficient method. This model is represented by the following dynamic equations:

[0012]

[0013] in, , , , These are gear 1, gear 2, the load, and the moment of inertia of the motor rotor. , For axial torsional stiffness, , For torsional damping, This is the load torque;

[0014] Step 3: Based on the torque fluctuation and four-degree-of-freedom gear torsional vibration model, through coupling variable - electromagnetic torque By establishing the connection between the motor model and the forced vibration model of the mechanical system-gear, an electromechanical coupled dynamic model is obtained, which is represented by the following equations:

[0015] .

[0016] As a preferred improvement of the present invention, in step one, the brushless DC motor is a three-phase motor, including phase A, phase B and phase C, and the drive circuit of the three-phase motor adopts a three-phase star connection.

[0017] As a preferred improvement of the present invention, in step one, the irrational reversal process includes two stages: a first stage and a second stage, specifically as follows:

[0018] Phase 1: From the disconnection of phase A until its phase current drops to 0, let the time be... At this time, the opposite electromotive forces are:

[0019]

[0020] Where E is the back electromotive force;

[0021] According to Kirchhoff's voltage and current laws:

[0022]

[0023] Considering time under normal circumstances Much smaller than the time constant To simplify, let the initial conditions be:

[0024]

[0025] Solving The relationship with time t is:

[0026]

[0027] when When the current in phase A drops to 0, at this time:

[0028]

[0029] exist At time t, the currents in phase B and phase C are:

[0030] ;

[0031] Second stage: Phase A current is 0, which is considered disconnected; phases B and C current continue to rise. According to Kirchhoff's voltage and current laws:

[0032]

[0033] The initial conditions are as follows:

[0034]

[0035] Solving With time The relationship is:

[0036]

[0037] make It can be known that To consider the current when only resistance is considered, then:

[0038]

[0039] when At this point, the current value is the initial condition in the first stage. ,but:

[0040]

[0041] when hour, ;

[0042] Based on the above analysis, the functional relationship of phase C current within one commutation cycle T is as follows: for:

[0043]

[0044] According to the law of conservation of energy, the relationship between electromagnetic torque and phase current is as follows: According to Kirchhoff's current law:

[0045]

[0046] again , Let be the back electromotive force constant, then It can be seen that the electromagnetic torque is related to the C-phase current. Proportional.

[0047] As a preferred improvement of the present invention, in step two, the angle of gear rotation... The relationship with time is as follows:

[0048]

[0049] in This refers to the elastic torsional angular displacement superimposed on the rigid body motion;

[0050] Meshing force between two gear teeth for:

[0051]

[0052] in The nonlinear total inter-tooth clearance is generally expressed using a piecewise function. Let the total inter-tooth clearance be... ,but:

[0053]

[0054] in To account for inter-tooth deformation due to meshing error, .

[0055] As a preferred improvement of the present invention, in step two, the time-varying meshing stiffness is considered to be affected by the rotational speed and varies with time. The changing curve is as follows:

[0056]

[0057] in For average meshing stiffness, It is the difference between the maximum time-varying meshing stiffness and the average meshing stiffness;

[0058] meshing error Also affected by rotational speed, over time The changing curve is as follows:

[0059]

[0060] in For gear error constants, This represents the gear error amplitude.

[0061] The beneficial effects of this invention are as follows: Taking into account the non-abrupt commutation of brushless DC motors caused by inductance, a mathematical model of brushless DC motors considering non-ideal commutation is established, yielding a piecewise curve of electromagnetic torque changing with time; simultaneously, a four-degree-of-freedom gear transmission model considering gear meshing stiffness, meshing error, torsional stiffness, and damping is constructed, and a precise electromechanical coupling mathematical model is established through the coupling variable—electromagnetic torque, revealing the intrinsic connection between the motor and transmission system, providing direction and ideas for the design and improvement of the motor and transmission system, and providing a precise mathematical model for the realization of high-precision control. Attached Figure Description

[0062] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein:

[0063] Figure 1 This is a schematic diagram of the three-phase brushless DC motor and drive circuit of the present invention;

[0064] Figure 2 The three-phase current variation and e within one commutation cycle of this invention a Schematic diagram;

[0065] Figure 3 This is the equivalent circuit diagram of the present invention from the start of commutation to when the current of phase A is 0;

[0066] Figure 4This is the equivalent circuit diagram of the present invention after the A-phase current is 0;

[0067] Figure 5 This is a diagram of the gear pair meshing force model of the present invention;

[0068] Figure 6 This is a diagram of the torsional vibration model of the present invention;

[0069] Figure 7 This is a diagram of the segmented electromechanical coupling model of the present invention. Detailed Implementation

[0070] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0071] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0072] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0073] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection or an electrical connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0074] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0075] This invention provides a modeling method for non-ideal commutation electromechanical coupling of brushless DC motors, the method comprising the following steps:

[0076] Step 1: Consider the electromagnetic torque fluctuations caused by the presence of inductance and irrational commutation when using the six-step commutation method to control a brushless DC motor.

[0077] See details Figure 1 As shown, the brushless DC motor is a three-phase motor, specifically including phase A, phase B and phase C, and its drive circuit adopts a three-phase star connection.

[0078] in , , Let R be the phase voltage, R be the equivalent resistance of each phase, and L be the equivalent inductance of each phase. , , It is the back electromotive force. For commutation tubes, It is a diode. The following assumptions are made regarding the motor:

[0079] 1. Three-phase symmetry, the back electromotive force is a trapezoidal wave with a flat top divided into 120 degrees; 2. Neglect the voltage drop of the switching transistor and the freewheeling diode; 3. Neglect the influence of armature reaction, cogging effect and magnetic circuit saturation; 4. The equivalent inductance of the phase winding is constant, and the rotational speed remains constant during commutation.

[0080] Initially, phases AB are conducting. When commutation begins, phase C remains conducting. The current in the phase B winding starts to rise from 0. Due to the inductance, the current in phase A cannot instantly drop to 0; instead, it decreases through freewheeling via diode VD4, which is connected in anti-parallel to V4. After a period t1, the current in phase A is 0, while the currents in phases B and C continue to increase. After a period t2, this commutation cycle ends, and the next commutation cycle begins. Specifically... Figure 2 The diagram shown illustrates the changes in three-phase currents within one commutation cycle.

[0081] The state angle corresponding to one commutation cycle is 60 degrees, and the corresponding commutation cycle is... p is the number of pole pairs, n is the motor speed (r / min), and time constant. The ratio of the commutation period to the time constant is Based on the above analysis, the reversal process can be divided into two stages.

[0082] The specific first stage is as follows: Figure 3 As shown, the time from when phase A is disconnected until its phase current drops to 0 is assumed to be 1. Based on the assumption, the opposite electromotive forces at this time are:

[0083]

[0084] Where E is the back electromotive force. According to Kirchhoff's voltage and current laws:

[0085]

[0086] Considering time under normal circumstances Much smaller than the time constant To simplify, let the initial conditions be:

[0087]

[0088] get The relationship with time t is:

[0089]

[0090] when When the current in phase A drops to 0, at this time:

[0091]

[0092] exist At time t, the currents in phase B and phase C are:

[0093]

[0094] The specific second phase is as follows: Figure 4 As shown: Phase A current is 0, indicating disconnection, while phases B and C current continue to rise.

[0095] Similarly, according to Kirchhoff's voltage and current laws:

[0096]

[0097] The initial conditions are as follows:

[0098]

[0099] Solving With time The relationship is:

[0100]

[0101] make It can be known that To consider the current when only resistance is considered, then:

[0102]

[0103] when At this point, the current value is the initial condition in the first stage. ,but:

[0104]

[0105] when hour, .

[0106] Based on the above analysis, the functional relationship of phase C current within one commutation cycle T is as follows: for:

[0107]

[0108] According to the law of conservation of energy, the relationship between electromagnetic torque and phase current is as follows: According to Kirchhoff's current law:

[0109]

[0110] again , Let be the back electromotive force constant, then It can be seen that the electromagnetic torque is related to the C-phase current. Proportional. (Based on the above) The current function relationship and the electromagnetic torque function relationship over time within one commutation cycle are as follows:

[0111]

[0112] Where E is the back electromotive force and the time constant. L is the equivalent inductance of each phase of the motor, and R is the equivalent resistance of each phase of the motor. Let I be the back electromotive force constant, and I0 be the initial current. I1 represents the current in phase B and phase C at time t1, considering only the resistance.

[0113] Step 2: Considering the time-varying meshing stiffness, meshing error, meshing damping, torsional stiffness, and torsional damping of the gear, a four-degree-of-freedom gear torsional vibration model is established using the lumped coefficient method.

[0114] Specifically, such as Figure 5 The figure shows a pure torsional dynamics model of a pair of fixed-axis gears meshing.

[0115] in For time-varying meshing stiffness of gear pairs, For meshing damping, To account for meshing error, It is a gear i The rotational angular velocity. The angle of rotation of the gear. The relationship with time is as follows:

[0116]

[0117] in This represents the elastic torsional angular displacement superimposed on the rigid body's motion. The meshing force between the two gear teeth. for:

[0118]

[0119] in The nonlinear total inter-tooth clearance is generally expressed using a piecewise function. Let the total inter-tooth clearance be... ,but:

[0120]

[0121] in To account for inter-tooth deformation due to meshing error, .

[0122] The main reason for time-varying meshing stiffness is the alternating single and double tooth meshing of gear teeth. When the single-tooth meshing region alternates with the double-tooth meshing region, it causes a sudden change in meshing stiffness. Therefore, time-varying meshing stiffness is considered to be affected by rotational speed and varies with time. A changing curve.

[0123]

[0124] in For average meshing stiffness, It is the difference between the maximum time-varying meshing stiffness and the average meshing stiffness.

[0125] meshing error Also affected by rotational speed, over time Changing curve:

[0126]

[0127] in For gear error constants, This represents the gear error amplitude.

[0128] Specific examples Figure 6 As shown, based on the gear pair meshing force model, the influence of bearing support stiffness and damping is ignored, and the lumped coefficient method is used to establish a four-degree-of-freedom gear torsional vibration model.

[0129] in: , , , Gear 1, Gear 2, Load, and Motor rotor moment of inertia. , For axial torsional stiffness, , For torsional damping, This represents the load torque.

[0130] According to Newton's second law, its dynamic equation can be expressed as:

[0131] .

[0132] in, , , , These are gear 1, gear 2, the load, and the moment of inertia of the motor rotor. , For axial torsional stiffness, , For torsional damping, This is the load torque;

[0133] Step 3: Based on the torque fluctuation and four-degree-of-freedom gear torsional vibration model, through coupling variable - electromagnetic torque By establishing the connection between the motor model and the forced vibration model of the mechanical system-gear, an electromechanical coupled dynamic model is obtained. The establishment process can be found in [reference needed]. Figure 7 As shown, the model is represented by the following equation:

[0134] .

[0135] The beneficial effects of this invention are as follows: Taking into account the non-abrupt commutation of brushless DC motors due to inductance, a mathematical model of the brushless DC motor considering non-ideal commutation is established, yielding a piecewise curve of electromagnetic torque changing with time. Simultaneously, a four-degree-of-freedom gear transmission model considering gear meshing stiffness, meshing error, torsional stiffness, and damping is constructed. Through the coupling variable—electromagnetic torque—a precise electromechanical coupling mathematical model is established, providing a solid model foundation and numerical analysis for subsequent high-precision control.

[0136] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. Other modifications can be easily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A modeling method for non-ideal commutation electromechanical coupling of brushless DC motors, characterized in that, The method includes the following steps: Step 1: Consider the electromagnetic torque fluctuations caused by inductance and irrational commutation when using the six-step commutation method to control a brushless DC motor. The brushless DC motor is a three-phase motor, including phases A, B, and C. The electromagnetic torque's function over time within one commutation cycle is as follows: Where E is the back electromotive force and the time constant. L is the equivalent inductance of each phase of the motor, and R is the equivalent resistance of each phase of the motor. Let t1 be the back electromotive force constant, t1 be the moment when the current in phase A drops to 0 in the first stage, and I0 be the initial current. I1 represents the current in phase B and phase C at time t1, considering only the resistance. Step 2: Considering the time-varying meshing stiffness, meshing error, meshing damping, torsional stiffness, and torsional damping of the gear, a four-degree-of-freedom gear torsional vibration model is established using the lumped coefficient method. This model is represented by the following dynamic equations: in, , , , These are gear 1, gear 2, the load, and the moment of inertia of the motor rotor. , For axial torsional stiffness, , For torsional damping, This is the load torque; Step 3: Based on the torque fluctuation and four-degree-of-freedom gear torsional vibration model, through coupling variable - electromagnetic torque By establishing the connection between the motor model and the forced vibration model of the mechanical system-gear, an electromechanical coupled dynamic model is obtained, which is represented by the following equations: 。 2. The modeling method for non-ideal commutation electromechanical coupling of a brushless DC motor according to claim 1, characterized in that: In step one, the drive circuit of the brushless DC motor adopts a three-phase star connection.

3. The modeling method for non-ideal commutation electromechanical coupling of a brushless DC motor according to claim 2, characterized in that: In step one, the irrational reversal process includes two stages: the first stage and the second stage, specifically: Phase 1: From the disconnection of phase A until its phase current drops to 0, let the time be... At this time, the opposite electromotive forces are: Where E is the back electromotive force; According to Kirchhoff's voltage and current laws: Considering time under normal circumstances Much smaller than the time constant To simplify, let the initial conditions be: Solving The relationship with time t is: when When the current in phase A drops to 0, at this time: exist At time t, the currents in phase B and phase C are: ； Second stage: Phase A current is 0, which is considered disconnected; phases B and C current continue to rise. According to Kirchhoff's voltage and current laws: The initial conditions are as follows: Solving With time The relationship is: make It can be known that To consider the current when only resistance is considered, then: when At this point, the current value is the initial condition in the first stage. ,but: when hour, ; Based on the above analysis, the functional relationship of phase C current within one commutation cycle T is as follows: for: According to the law of conservation of energy, the relationship between electromagnetic torque and phase current is as follows: According to Kirchhoff's current law: again , Let be the back electromotive force constant, then It can be seen that the electromagnetic torque is related to the C-phase current. Proportional.

4. The modeling method for non-ideal commutation electromechanical coupling of a brushless DC motor according to claim 1, characterized in that: In step two, the angle of gear rotation The relationship with time is as follows: in This refers to the elastic torsional angular displacement superimposed on the rigid body motion; Meshing force between two gear teeth for: in The nonlinear total inter-tooth clearance is generally expressed using a piecewise function. Let the total inter-tooth clearance be... ,but: in To account for inter-tooth deformation due to meshing error, .

5. The modeling method for non-ideal commutation electromechanical coupling of a brushless DC motor according to claim 1, characterized in that: In step two, the time-varying meshing stiffness is considered to be affected by the rotational speed, and varies with time. The changing curve is as follows: in For average meshing stiffness, It is the difference between the maximum time-varying meshing stiffness and the average meshing stiffness; meshing error Also affected by rotational speed, over time The changing curve is as follows: in For gear error constants, This represents the gear error amplitude.

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