Method and System for Calculating Back EMF of Multi-Element Windings in Hollow Cup Armature Brushed Motors
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HUIZHOU LONGDE TECH CO LTD
- Filing Date
- 2025-12-23
- Publication Date
- 2026-05-26
Smart Images
Figure CN122087233A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of motor control technology, specifically to a method and system for calculating the back electromotive force of a multi-element winding in a hollow cup armature brushed motor. Background Technology
[0002] Hollow cup armature permanent magnet DC brushed motors have good linearity in mechanical characteristics. Once the air gap magnetic flux density is designed, the torque, current, and speed characteristic curves of the motor can be calculated by calculating the resistance of the windings and the back electromotive force generated.
[0003] The existing methods for calculating the back electromotive force (EMF) generated by the windings of hollow-cup armature permanent magnet DC brushed motors are based on the ideal conditions that assume the permanent magnet completely covers the windings axially and the number of components is infinite. However, in actual products, due to the presence of the commutator, the permanent magnet cannot completely cover the coil windings axially, and the number of winding components cannot be infinite. Therefore, existing methods for calculating the back EMF often result in calculated values that are larger than the actual values, leading to deviations between the actual product and the initial design performance. Summary of the Invention
[0004] In view of the above problems, embodiments of the present invention provide a method and system for calculating the back electromotive force of a multi-element winding of a hollow cup armature brushed motor, which is used to solve the problem that in the prior art, the calculated value of the back electromotive force is often larger than the actual value, resulting in a deviation between the actual product and the initial design performance.
[0005] According to one aspect of the present invention, a method for calculating the back electromotive force of a multi-element winding of a hollow cup armature brushed motor is provided, the method comprising: Obtain the parameters of the parallel magnetized permanent magnet, and through the air gap length g Remanence of permanent magnets B r relative permeability u r Permanent magnet thickness H and the ratio of inner and outer diameters k Calculate the radial air gap magnetic flux density fundamental wave amplitude. B m ; Obtain the winding parameters and determine the winding type and total axial height of the coil. l and the height of the straight section of the coil l r Axial height of permanent magnet l m Winding radius r Calculate the flux linkage amplitude of a single-turn coil rotating in a magnetic field. Φ m ; Based on total number of turns W and number of components n and the angular velocity of coil rotation Calculate the back electromotive force amplitude of a unit element E sm Based on the electrical angle of the back electromotive force generated by each component, the back electromotive force generated by each component is vector-synthesized to obtain the magnitude of the synthesized back electromotive force of the entire coil winding. E c ; Based on the magnitude of the back electromotive force E c The average back EMF of the motor is obtained by integrating the waveform of the back EMF with respect to the number of commutations of the motor. E avg and the value of the back electromotive force constant of the motor k e .
[0006] In one alternative approach, the parameters of the parallel magnetized permanent magnet are obtained, and the air gap length is used as a reference. g Remanence of permanent magnets B r relative permeability u r Permanent magnet thickness H and the ratio of inner and outer diameters k Calculate the radial air gap magnetic flux density fundamental wave amplitude. B m ， Includes the following sub-steps: Obtain the parallel magnetization air gap length g Remanence of permanent magnets B r relative permeability u r Permanent magnet thickness H and the ratio of inner and outer diameters k； Calculate the radial component of magnetization based on the parallel magnetization model. Thickness in the radial direction of the permanent magnet And further calculate to obtain the magnetic potential and air gap permeability ; Using formula Calculate radial air gap magnetic flux density The radial air gap magnetic flux density fundamental wave amplitude was extracted by performing a Fourier series expansion. B m 。
[0007] In one alternative approach, the calculation of the radial component of magnetization... The calculation method is as follows ,in The vacuum permeability. The thickness of the permanent magnet in the radial direction. The calculation method is as follows: ; in, H It is the magnitude of the permanent magnet thickness. k It is the ratio of the inner diameter to the outer diameter of the permanent magnet.
[0008] In one alternative approach, the magnetic potential The calculation method is as follows: ; and / or Air gap permeability The calculation method is as follows: .
[0009] In one alternative approach, the radial air gap magnetic flux density fundamental wave amplitude B m The calculation method is as follows: .
[0010] In one alternative approach, the winding parameters are obtained, and based on the winding type and coil axial height... l Axial height of permanent magnet l m Winding radius r Calculate the flux linkage amplitude of a single-turn coil rotating in a magnetic field. Φ m This includes the following sub-steps: The winding is decomposed into a superimposed combination of basic winding shapes according to the winding type; Based on the basic winding shape and coil axial height l Axial height of permanent magnet l m and winding radius r Establish the spatial relationship between the coil and the magnetic field during the rotation process, and derive the functional relationship of the coil boundary in the air gap magnetic field; Based on the sinusoidal distribution of air gap magnetic flux density, the magnetic flux density is integrated over the effective area of the coil to obtain the amplitude of the magnetic flux for each basic winding shape. ； The magnetic flux of each basic winding shape is added together to obtain the flux amplitude of a single-turn coil rotating in a magnetic field. m .
[0011] In one alternative approach, the basic winding shape includes a rhombic winding and a rectangular winding, and the rhombic and rectangular windings can be stacked to form a hexagonal winding, wherein... The amplitude of the air gap magnetic flux passing through a single-turn coil of the rhombic winding is: ; The magnitude of the air gap magnetic flux passing through a single-turn coil of a rectangular winding is: ; The amplitude of the air gap magnetic flux passing through a single-turn coil of a hexagonal winding is: .
[0012] In one alternative approach, the total number of turns is used. W and number of components n and the angular velocity of coil rotation Calculate the back electromotive force amplitude of a unit element E sm Based on the electrical angle of the back electromotive force generated by each component, a vector synthesis is performed to obtain the magnitude of the back electromotive force synthesized by the entire coil winding. E c This includes the following sub-steps: Get the total number of turns W and number of components n ; Based on the spatial distribution of the coils contained in a unit element, the maximum flux linkage is calculated, and the angular velocity of the coil rotation is obtained. The analytical expression for the change of magnetic flux linkage per unit element with time is calculated, and the amplitude of the back electromotive force generated per unit element is obtained by differentiating this expression with respect to time. E sm ; Based on the electrical angle of the back electromotive force generated by each component, the back electromotive force generated by each component is vector-synthesized to obtain the amplitude of the overall back electromotive force of the multi-component system. E c .
[0013] In one alternative approach, the average back electromotive force E avg The specific calculation method is as follows: .
[0014] According to another aspect of the present invention, a motor system is provided, including a control unit and a coreless motor controlled by the control unit; the control unit includes: a processor, a memory, a communication interface and a communication bus, wherein the processor, the memory and the communication interface communicate with each other through the communication bus; The memory is used to store at least one executable instruction that causes the processor to perform the operation of the method for calculating the back electromotive force of a multi-element winding of a hollow cup armature brushed motor as described above.
[0015] According to another aspect of the present invention, a computer-readable storage medium is provided, wherein at least one executable instruction is stored therein, which, when executed on a motor system, causes the motor system to perform the operation of the method for calculating the back electromotive force of a multi-element winding of a coreless armature brushed motor as described above.
[0016] In this embodiment of the invention, for motors with parallel magnetization of permanent magnets, the large difference between the inner and outer radii of the permanent magnets in micro motors is considered. By analyzing the magnetomotive force and air gap permeability, the analytical formula for calculating the radial air gap magnetic flux density and the fundamental amplitude value of the radial air gap magnetic flux density are obtained, ensuring the accuracy of the back electromotive force calculation.
[0017] This invention analyzes the influence of the number of winding elements and the relative axial position of the permanent magnet to the winding on the back electromotive force (EMF) of motors using rhombic and hexagonal windings, which are widely used in engineering applications, and derives an analytical formula for calculating the back EMF. The calculation approach proposed in this paper can also be extended to calculate the back EMF of motors using different winding types.
[0018] The above description is merely an overview of the technical solutions of the embodiments of the present invention. In order to better understand the technical means of the embodiments of the present invention and to implement them in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the embodiments of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description
[0019] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This invention illustrates a flowchart of an embodiment of the method for calculating the back electromotive force of a multi-element winding of a hollow cup armature brushed motor. Figure 2 A schematic diagram of parallel magnetization of a miniature hollow cup armature motor in an embodiment of the present invention is shown; Figure 3 The flowchart shows a sub-step of step 110 in the method for calculating the back electromotive force of a multi-element winding of a hollow cup armature brushed motor according to the present invention. Figure 4 The flowchart shows a sub-step of step 120 in the method for calculating the back electromotive force of a multi-element winding of a hollow cup armature brushed motor according to the present invention.
[0020] Figure 5 The diagram shows the relative magnetic pole position of the coil in the method for calculating the back electromotive force of a multi-element winding of a hollow cup armature brushed motor according to the present invention.
[0021] Figure 6The diagram shows the relative magnetic flux density position of the rhomboid single-turn coil in the back electromotive force calculation method of the multi-element winding of the hollow cup armature brushed motor of the present invention.
[0022] Figure 7 The flowchart shows a sub-step of step 130 in the method for calculating the back electromotive force of a multi-element winding of a hollow cup armature brushed motor according to the present invention.
[0023] Figure 8 The diagram shows a schematic of the back electromotive force waveform of the motor in the method for calculating the back electromotive force of a multi-element winding of a hollow cup armature brushed motor according to the present invention.
[0024] Figure 9 The waveform diagram of the back electromotive force test of motor 1 in an embodiment of the present invention is shown.
[0025] Figure 10 The waveform diagram of the back electromotive force test of motor 2 in an embodiment of the present invention is shown.
[0026] Figure 11 This diagram illustrates the structure of an embodiment of a motor system according to the present invention. Detailed Implementation
[0027] Exemplary embodiments of the invention will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein.
[0028] Figure 1 A flowchart of the first embodiment of the method for calculating the back electromotive force (EMF) of a multi-element winding in a hollow-cup armature brushed motor according to the present invention is shown. This method is performed by a brushed motor system containing a hollow-cup armature. Hollow-cup armature permanent magnet DC brushed motors are generally small in size and typically use sintered NdFeB magnet rings in their design. These magnets require pre-orientation during processing. Due to technological limitations, these magnetic rings are usually magnetized in parallel, and this type of magnetic ring is less expensive than radially magnetized magnetic rings. Because of the small size of the magnetic ring and the large difference between its inner and outer diameters, the influence of the difference in the inner and outer diameters of the permanent magnet on the magnetomotive force needs to be considered when calculating the radial air gap magnetic flux density of the motor. This invention also analyzes this issue and proposes a calculation expression for the fundamental amplitude of the radial air gap magnetic flux density to ensure the accuracy of the motor's back EMF calculation.
[0029] like Figure 1 As shown, the method includes the following steps: Step 110: Obtain the parameters of the parallel magnetized permanent magnet, and use the air gap length... g Remanence of permanent magnets B r Relative permeability u r Permanent magnet thickness Hand the ratio of inner and outer diameters k Calculate the radial air gap magnetic flux density fundamental wave amplitude. B m .
[0030] Given a fixed winding condition, the magnitude of the motor's back electromotive force is directly related to the radial air gap magnetic flux density; therefore, the accuracy of the air gap magnetic flux density calculation is particularly important. Miniature hollow cup armature motors typically use parallel magnetized permanent magnets. Using parallel magnetization can improve the sinusoidal distribution of the air gap magnetic flux density and achieve a higher peak magnetic flux density.
[0031] In this embodiment, the permanent magnet is a cylindrical permanent magnet with an inner diameter r1 and an outer diameter r2. The ratio of its inner to outer diameter is calculated... k At that time, it can be used k = r 1 / r 2.
[0032] In order to accurately calculate the radial air gap magnetic flux density amplitude value B m This step is specifically designed for parallel magnetized permanent magnets commonly used in miniature hollow cup motors. For easier understanding, please refer to [link to relevant documentation]. Figure 2 , Figure 2 This illustration shows a parallel magnetization diagram of a miniature hollow cup armature motor in an embodiment of the present invention. This parallel magnetization method results in a non-radial uniform magnetization direction. Furthermore, due to its small size, the radial thickness of the permanent magnet varies significantly along the circumference; for example, the radial thickness of the permanent magnet near the axis will be greater than that further away from the axis. In this case, this embodiment utilizes a magnetomotive force-permeability model and Fourier analysis to analytically derive the radial air gap magnetic flux density fundamental wave amplitude. B m .
[0033] Step 110 accurately calculated the fundamental wave amplitude of the air gap magnetic flux density generated by the micro parallel magnetized permanent magnet, overcoming the errors of the traditional simplified model.
[0034] Step 120: Obtain winding parameters and determine the winding type and total axial height of the coil. l and the height of the straight section of the coil l r Axial height of permanent magnet l m Winding radius r Calculate the flux linkage amplitude of a single-turn coil rotating in a magnetic field. Φ m .
[0035] This step involves calculating the maximum magnetic flux that a coil circuit composed of a single conductor can capture when rotating in the magnetic field determined in the first step. This establishes the correlation between the spatial magnetic field and circuit parameters.
[0036] Step 130: Based on the total number of turns W and the number of components n, and the coil rotational angular velocity Calculate the back electromotive force amplitude of a unit element E sm Based on the electrical angle of the back electromotive force generated by each component, the back electromotive force generated by each component is vector-synthesized to obtain the magnitude of the synthesized back electromotive force of the entire coil winding. E c .
[0037] Of which, total number of turns W The total number of turns in the unit motor winding and the number of components. n This refers to the number of winding elements, which is usually an odd number, such as 3, 5, 7, 9, etc. Understandably, the number of elements is the same as the number of commutator segments in the motor.
[0038] Consider a component occupying an electrical angle of 2π / 2π in space. n Calculate the maximum flux linkage that the component can achieve. ψ s When the armature has an angular velocity ω The flux linkage changes according to a cosine law during rotation; by differentiating it with respect to time, the amplitude of the back electromotive force of the component can be obtained. E sm for: E sm =d ψ s / d t All n elements are uniformly distributed in space, and their induced electromotive forces form a vector polygon. By vector synthesis, the total back electromotive force amplitude synthesized within the entire armature winding (before commutation) can be obtained. E c .
[0039] Steps 120 and 130 quantify the effects of winding shape, number of elements, and axial coverage length of permanent magnet on effective magnetic flux and induced electromotive force.
[0040] Step 140: Based on the magnitude of the back electromotive force E c The average value of the back electromotive force is obtained by integrating the waveform of the back electromotive force with respect to the number of commutations of the motor. E avg .
[0041] Due to the rectification effect of the commutator in a brushed motor, the output back electromotive force (EMF) at both ends of the motor is pulsating DC, and its average value needs to be calculated. Considering the commutation process, the waveform of the output back EMF is given by a frequency of 2π / n The waveform is a periodically repeating pulsating waveform. Over one electrical angle period π, this waveform is integrally averaged. Therefore, the back electromotive force amplitude can be determined. E c Derivation E avg .
[0042] Furthermore, the back electromotive force constant of the motor can be obtained. K e .
[0043] Finally, in step 140, an analytical solution for the average back electromotive force considering the actual commutation process was obtained through a rigorous model. This method is highly systematic, has clear physical meaning, and the calculation results are in high agreement with the measured values.
[0044] Figure 3 A flowchart of a sub-step in step 110 of the method for calculating the back electromotive force of a multi-element winding in a hollow cup armature brushed motor according to the present invention is shown. Figure 3 As shown, the method includes the following steps: Step 111: Obtain the length of the parallel magnetization air gap g Remanence of permanent magnets B r relative permeability u r Permanent magnet thickness H and the ratio of inner and outer diameters k .
[0045] Step 112: Calculate the radial component of magnetization based on the parallel magnetization model. Thickness in the radial direction of the permanent magnet And further calculate to obtain the magnetic potential and air gap permeability ; Wherein, the calculation of the radial component of magnetization The calculation method is as follows ,in is the vacuum permeability.
[0046] The thickness of the permanent magnet in the radial direction The calculation method is as follows: ; in, H It is the magnitude of the permanent magnet thickness. k It is the ratio of the inner diameter to the outer diameter of the permanent magnet.
[0047] magnetic potential The calculation method is as follows: .
[0048] Air gap permeability The calculation method is as follows: ,Depend on Figure 2 It can be seen that for a permanent magnet structure with concentric inner and outer circles, the air gap permeability should be a constant value in the circumferential direction. Therefore, the air gap permeability can be converted into... .
[0049] Step 113: Using the formula Calculate radial air gap magnetic flux density The radial air gap magnetic flux density fundamental wave amplitude was extracted by performing a Fourier series expansion. B m 。
[0050] Among them, radial air gap magnetic flux density: .
[0051] Expanding the above formula using Fourier series, we can obtain the expression for the fundamental wave of the radial air gap magnetic flux density as follows: ; By substituting the parameters, the radial air gap magnetic flux density fundamental wave amplitude value can be obtained. .
[0052] Figure 4 The flowchart illustrates a sub-step of step 120 in the method for calculating the back electromotive force of a multi-element winding in a hollow cup armature brushed motor according to the present invention. For example... Figure 4 As shown, the method includes the following steps: Step 121: Decompose the winding into basic winding shapes and combine them according to the winding type.
[0053] The basic winding shapes include rhomboid windings, rectangular windings, etc. For some common winding shapes, they can be decomposed according to their characteristics. For example, a common hexagonal winding can be decomposed into a superposition of rhomboid and rectangular windings. This allows for more accurate magnetic flux calculation.
[0054] Step 122: Based on the basic winding shape and the total axial height of the coil... l and the height of the straight section of the coil l r Axial height of permanent magnet l m and winding radius r Establish the spatial relationship between the coil and the magnetic field during the rotation process, and derive the functional relationship of the coil boundary in the air gap magnetic field.
[0055] In this embodiment, a single-turn rhombic coil is analyzed. The model of the coil's relative magnetic flux density position is established according to its different regions, and the magnetic flux amplitude of different regions is calculated and then added together. Figure 5 and Figure 6 As shown, the coil rotates uniformly around its axis relative to the permanent magnet, with its two endpoints coinciding with the magnetic pole boundary line as the initial state. At this point, the magnetic flux through the coil is at its maximum. By unfolding the coil's position relative to the magnetic poles in a plane, the relationship between the air gap magnetic flux density and the coil can be obtained.
[0056] Finally, we obtain the following in region (I):
[0057] In region (II),
[0058] Step 123: Based on the sinusoidal distribution of air gap magnetic flux density, integrate the magnetic flux density over the effective area of the coil to obtain the amplitude of the magnetic flux for each basic winding shape. ； Continuing with the example of the rhombic coil, the magnetic flux through the coil is the integral of the air gap magnetic flux density over the area, combined with the attached... Figure 6 ,have, ; ; ; in, Φ Let d be the magnetic flux through the coil. A The derivative of the coil area, B m This represents the amplitude of the air gap magnetic flux density. Integrating the above three equations, we obtain... .
[0059] Based on the relationship between the air gap magnetic flux density and the coil in different regions, and considering that region (II) is symmetrical to region (I), the amplitude of the total magnetic flux of a single-turn coil of the rhombic winding can be obtained. Φ t : .
[0060] Similarly, using the above method, the amplitude of the air gap magnetic flux passing through a single-turn coil of a rectangular winding can be obtained: .
[0061] Step 124: Sum the magnetic flux of each basic winding shape to obtain the flux amplitude linked when a single-turn coil rotates in a magnetic field. m .
[0062] In this embodiment, the hexagonal winding single-turn coil can be regarded as a superposition of a rhombic winding and a rectangular winding. Therefore, the amplitude of the air gap magnetic flux passing through it is: .
[0063] Figure 7 The flowchart illustrates a sub-step of step 130 in the method for calculating the back electromotive force of a multi-element winding in a hollow cup armature brushed motor according to the present invention. For example... Figure 3 As shown, the method includes the following steps: Step 131: Obtain the total number of turns W and number of components n and the angular velocity of coil rotation .
[0064] Step 132: Calculate the maximum flux linkage based on the spatial distribution of the coils contained in the unit element.
[0065] The magnetic flux passing through the coil varies at different angles relative to the permanent magnet, and its distribution roughly follows a trigonometric function cos(β). By calculating the integral over the number of turns of the coil, the maximum flux linkage per unit element can be obtained, which, after simplification, yields the following formula: .
[0066] Step 133: Obtain the angular velocity of coil rotation The analytical expression for the change of magnetic flux per unit element with time is calculated, and the amplitude of the back electromotive force is obtained by differentiating the expression with respect to time. E sm .
[0067] Based on the steps above, when the coil rotates uniformly around its axis at an angular velocity ω, the flux linkage changes according to a cosine law. Taking the derivative with respect to time, we can obtain the magnitude of the back electromotive force it generates. e s for: ; This leads to the magnitude of the back electromotive force generated by a unit element. .
[0068] Step 134: Based on the electrical angle of the back EMF generated by each component, perform vector synthesis of the back EMF generated by each component to obtain the amplitude of the overall back EMF synthesized by the multiple components. E c .
[0069] Specifically: .
[0070] Furthermore, with different numbers of components, the number of commutations per revolution of the coil is 2.n Second-rate. Figure 8 The waveform of the back electromotive force generated by the entire armature after commutation (taking a 3-element example) can be analyzed to obtain the average value of the back electromotive force generated by the winding under different numbers of elements. E avg for, ; Will Substituting into the above equation and rearranging, we get: ; .
[0071] Therefore, the back electromotive force constant of the motor can be obtained. k e for, .
[0072] To further illustrate the technical effects of this invention, two motors are used as examples for calculation and actual measurement comparison. Below, one hollow cup armature permanent magnet DC brushed motor with rhomboid and one with hexagonal windings are taken as research objects. The accuracy of the calculation method proposed in this paper is verified by comparing the back electromotive force calculated using the analytical formula of this invention with the test results of the actual samples.
[0073] The key parameters of a hollow cup armature permanent magnet DC brushed motor with a diamond winding are shown in Table 1 below, and the hexagonal winding is shown in Table 2 below.
[0074] Table 1 Design parameters of rhomboid hollow cup armature permanent magnet DC brushed motor
[0075] Table 2 Design parameters of hexagonal hollow cup armature permanent magnet DC brushed motor
[0076] The back electromotive force of the prototype was calculated and tested using a rotational speed of 3000 r / min as the benchmark. The calculation results for the radial air gap magnetic flux density and back electromotive force are summarized in Table 3 below. Table 3. Calculated back electromotive force values for two hollow cup armature permanent magnet DC brushed motors
[0077] The back EMF waveforms and results for motors 1 and 2 at a test speed of 3000 r / min are shown below. Figure 9 and Figure 10 As shown, the calculated and measured back EMF values of two motors with different winding shapes were compared, with error ratios of 1.32% and 4.98% respectively, demonstrating the accuracy of the analytical formula for calculating the back EMF of the motor given in this paper.
[0078] Figure 11 The diagram shows a structural schematic of an embodiment of a motor system according to the present invention. The specific embodiments of the present invention do not limit the specific implementation of the motor system.
[0079] like Figure 11 As shown, the motor system includes a control unit and a coreless motor controlled by the control unit. Specifically, the coreless motor is a coreless armature brushed motor with multi-element windings. The control unit may include: a processor 401, a communications interface 402, a memory 403, and a communication bus 404.
[0080] The processor 401, communication interface 402, and memory 403 communicate with each other via communication bus 404. Communication interface 402 is used to communicate with other network elements, such as clients or other servers. Processor 401 executes program 405, specifically performing the relevant steps described in the embodiment of the method for calculating the back electromotive force of multi-element windings in a coreless armature brushed motor.
[0081] Specifically, program 405 may include program code, which includes computer-executable instructions.
[0082] Processor 401 may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement embodiments of the present invention. The motor system includes one or more processors, which may be processors of the same type, such as one or more CPUs; or processors of different types, such as one or more CPUs and one or more ASICs.
[0083] Memory 403 is used to store program 405. Memory 403 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.
[0084] Specifically, program 405 can be called by processor 401 to cause the motor system to perform the following operations: Obtain the parameters of the parallel magnetized permanent magnet, and through the air gap length g Remanence of permanent magnets B r Relative permeability u r Permanent magnet thickness H and the ratio of inner and outer diametersk Calculate the radial air gap magnetic flux density fundamental wave amplitude. B m ; Obtain the winding parameters and determine the winding type and total axial height of the coil. l and the height of the straight section of the coil l r Axial height of permanent magnet l m Winding radius r Calculate the flux linkage amplitude of a single-turn coil rotating in a magnetic field. Φ m ; Based on total number of turns W and number of components n and the angular velocity of coil rotation Calculate the back electromotive force amplitude of a unit element E sm Based on the electrical angle of the back electromotive force generated by each component, the back electromotive force generated by each component is vector-synthesized to obtain the magnitude of the synthesized back electromotive force of the entire coil winding. E c ; Based on the magnitude of the back electromotive force E c The average back EMF of the motor is obtained by integrating the waveform of the back EMF with respect to the number of commutations of the motor. E avg and the value of the back electromotive force constant of the motor k e .
[0085] In this embodiment of the invention, for motors with parallel magnetization of permanent magnets, the large difference between the inner and outer radii of the permanent magnets in micro motors is considered. By analyzing the magnetomotive force and air gap permeability, the analytical formula for calculating the radial air gap magnetic flux density and the fundamental amplitude value of the radial air gap magnetic flux density are obtained, ensuring the accuracy of the back electromotive force calculation.
[0086] This invention also provides a computer-readable storage medium storing at least one executable instruction that, when executed on a motor system, causes the motor system to perform the method for calculating the back electromotive force of a multi-element winding of a hollow cup armature brushed motor as described in any of the above method embodiments.
[0087] Specifically, the executable instructions can be used to cause the motor system to perform the following operations: Obtain the parameters of the parallel magnetized permanent magnet, and through the air gap length g Remanence of permanent magnets B r Relative permeability u r Permanent magnet thickness H and the ratio of inner and outer diameters kCalculate the radial air gap magnetic flux density fundamental wave amplitude. B m ; Obtain the winding parameters and determine the winding type and total axial height of the coil. l and the height of the straight section of the coil l r Axial height of permanent magnet l m Winding radius r Calculate the flux linkage amplitude of a single-turn coil rotating in a magnetic field. Φ m ; Based on total number of turns W and number of components n and the angular velocity of coil rotation Calculate the back electromotive force amplitude of a unit element E sm Based on the electrical angle of the back electromotive force generated by each component, the back electromotive force generated by each component is vector-synthesized to obtain the magnitude of the synthesized back electromotive force of the entire coil winding. E c ; Based on the magnitude of the back electromotive force E c The average back EMF of the motor is obtained by integrating the waveform of the back EMF with respect to the number of commutations of the motor. E avg and the value of the back electromotive force constant of the motor k e .
[0088] The algorithms or displays provided herein are not inherently related to any particular computer, virtual system, or other device. Furthermore, the embodiments of this invention are not directed to any particular programming language.
[0089] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. Similarly, for the sake of brevity and to aid in understanding one or more aspects of the invention, in the description of exemplary embodiments of the invention above, various features of the embodiments are sometimes grouped together in a single embodiment, figure, or description thereof. The claims, which follow the detailed description, are hereby expressly incorporated into that detailed description, wherein each claim itself is a separate embodiment of the invention.
[0090] Those skilled in the art will understand that the modules in the device of the embodiment can be adaptively changed and placed in one or more devices different from that embodiment. Modules, units, or components in the embodiment can be combined into a single module, unit, or component, and further, they can be divided into multiple sub-modules, sub-units, or sub-components, except that at least some of such features and / or processes or units are mutually exclusive.
[0091] It should be noted that the above embodiments are illustrative of the invention and not restrictive, and that those skilled in the art can devise alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses should not be construed as limiting the claims. The word "comprising" does not exclude the presence of elements or steps not listed in the claims. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The invention can be implemented by means of hardware comprising several different elements and by means of a suitably programmed computer. In the unit claims enumerating several means, several of these means may be embodied by the same item of hardware. The use of the words first, second, and third, etc., does not indicate any order. These words can be interpreted as names. The steps in the above embodiments, unless otherwise specified, should not be construed as limiting the order of execution.
Claims
1. A method for calculating the back electromotive force of a multi-element winding in a hollow cup armature brushed motor, characterized in that, The method includes: Obtain the parameters of the parallel magnetized permanent magnet, and through the air gap length g Remanence of permanent magnets B r Relative permeability u r Permanent magnet thickness H and the ratio of inner and outer diameters k Calculate the radial air gap magnetic flux density fundamental wave amplitude. B m ; Obtain the winding parameters and determine the winding type and total axial height of the coil. l and the height of the straight section of the coil l r Axial height of permanent magnet l m Winding radius r Calculate the flux linkage amplitude of a single-turn coil rotating in a magnetic field. Φ m ; Based on total number of turns W and number of components n and the angular velocity of coil rotation Calculate the back electromotive force amplitude of a unit element E sm Based on the electrical angle of the back electromotive force generated by each component, the back electromotive force generated by each component is vector-synthesized to obtain the magnitude of the synthesized back electromotive force of the entire coil winding. E c ; Based on the magnitude of the back electromotive force E c The average back EMF of the motor is obtained by integrating the waveform of the back EMF with respect to the number of commutations of the motor. E avg and the value of the back electromotive force constant of the motor k e .
2. The method according to claim 1, characterized in that, The parameters of the parallel magnetized permanent magnet are obtained, and the air gap length is used to determine these parameters. g Remanence of permanent magnets B r Relative permeability u r Permanent magnet thickness H and the ratio of inner and outer diameters k Calculate the radial air gap magnetic flux density fundamental wave amplitude. B m ， Includes the following sub-steps: Obtain the parallel magnetization air gap length g Remanence of permanent magnets B r Relative permeability u r Permanent magnet thickness H and the ratio of inner and outer diameters k； Calculate the radial component of magnetization based on the parallel magnetization model. Thickness in the radial direction of the permanent magnet And further calculate to obtain the magnetic potential and air gap permeability ; Using formula Calculate radial air gap magnetic flux density The radial air gap magnetic flux density fundamental wave amplitude was extracted by performing a Fourier series expansion. B m .
3. The method according to claim 2, characterized in that, The calculation of the radial component of magnetization The calculation method is as follows ,in The vacuum permeability. The thickness of the permanent magnet in the radial direction. The calculation method is as follows: ； in, H It is the magnitude of the permanent magnet thickness. k It is the ratio of the inner diameter to the outer diameter of the permanent magnet.
4. The method according to claim 2, characterized in that, The magnetic potential The calculation method is as follows: Air gap magnetic permeability The calculation method is as follows: .
5. The method according to claim 4, characterized in that, Radial air gap magnetic flux density fundamental wave amplitude B m The calculation method is as follows: 。 6. The method according to claim 1, characterized in that, The winding parameters are obtained, and based on the winding type and the total axial height of the coil... l and the height of the straight section of the coil l r Axial height of permanent magnet l m Winding radius r Calculate the flux linkage amplitude of a single-turn coil rotating in a magnetic field. Φ m This includes the following sub-steps: The winding is decomposed into a superimposed combination of basic winding shapes according to the winding type; Based on the basic winding shape and coil axial height l Axial height of permanent magnet l m and winding radius r Establish the spatial relationship between the coil and the magnetic field during the rotation process, and derive the functional relationship of the coil boundary in the air gap magnetic field; Based on the sinusoidal distribution of air gap magnetic flux density, the magnetic flux density is integrated over the effective area of the coil to obtain the amplitude of the magnetic flux for each basic winding shape. ； The magnetic flux of each basic winding shape is added together to obtain the flux amplitude of a single-turn coil rotating in a magnetic field. m .
7. The method according to claim 6, characterized in that, The basic winding shapes include rhombic windings and rectangular windings, and rhombic and rectangular windings can be stacked to form a hexagonal winding. The amplitude of the air gap magnetic flux passing through a single-turn coil of the rhombic winding is: ； The magnitude of the air gap magnetic flux passing through a single-turn coil of a rectangular winding is: ； The amplitude of the air gap magnetic flux passing through a single-turn coil of a hexagonal winding is: 。 8. The method according to claim 1, characterized in that, The total number of turns W and number of components n and the angular velocity of coil rotation Calculate the back electromotive force amplitude of a unit element E sm Based on the electrical angle of the back electromotive force generated by each component, a vector synthesis is performed to obtain the magnitude of the back electromotive force synthesized by the entire coil winding. E c This includes the following sub-steps: Get the total number of turns W and number of components n ; The maximum flux linkage is calculated based on the spatial distribution of the coils contained in a unit element. Obtain the angular velocity of coil rotation The analytical expression for the change of magnetic flux linkage per unit element with time is calculated, and the amplitude of the back electromotive force E generated per unit element is obtained by differentiating this expression with respect to time. sm ; Based on the electrical angle of the back electromotive force generated by each component, the back electromotive force generated by each component is vector-synthesized to obtain the amplitude of the overall back electromotive force of the multi-component system. E c .
9. The method according to claim 8, characterized in that, The average back electromotive force E avg The specific calculation method is as follows: 。 10. A motor system, characterized in that, It includes a control unit and a hollow cup motor controlled by the control unit; the control unit includes: a processor, a memory, a communication interface and a communication bus, and the processor, the memory and the communication interface communicate with each other through the communication bus; The memory is used to store at least one executable instruction that causes the processor to perform the operation of the method for calculating the back electromotive force of a multi-element winding of a hollow cup armature brushed motor as described in any one of claims 1-9.
11. A computer-readable storage medium, characterized in that, The storage medium stores at least one executable instruction, which, when executed on the motor system, causes the motor system to perform the operation of the method for calculating the back electromotive force of a multi-element winding of a hollow cup armature brushed motor as described in any one of claims 1-9.