WO2020151174A1 - 一种基于永磁磁通切换直线电机的轨道交通牵引系统 - Google Patents

一种基于永磁磁通切换直线电机的轨道交通牵引系统 Download PDF

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WO2020151174A1
WO2020151174A1 PCT/CN2019/092470 CN2019092470W WO2020151174A1 WO 2020151174 A1 WO2020151174 A1 WO 2020151174A1 CN 2019092470 W CN2019092470 W CN 2019092470W WO 2020151174 A1 WO2020151174 A1 WO 2020151174A1
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permanent magnet
traction system
motor
flux switching
rail transit
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French (fr)
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曹瑞武
陆鸣航
苏恩超
沈丹妮
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
    • B60L13/00—Electric propulsion for monorail vehicles, suspension vehicles or rack railways; Magnetic suspension or levitation for vehicles
    • B60L13/03—Electric propulsion by linear motors
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
    • B60L2200/00—Type of vehicles
    • B60L2200/26—Rail vehicles
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/60—Other road transportation technologies with climate change mitigation effect
    • Y02T10/72—Electric energy management in electromobility

Definitions

  • the invention relates to a train system driven by a permanent magnetic flux switching linear motor, which belongs to the technical field of motor drive and control.
  • linear induction motors are widely used in rail transit at home and abroad.
  • the secondary of the linear induction motor is only composed of an induction plate and a magnetic conductive plate.
  • the primary is composed of an armature winding and an iron core. It has the advantages of simple structure, small size and low cost.
  • the linear induction motor has high eddy current loss, so the efficiency and power The factor is low, and the control of the linear induction motor is more complicated, so its long-term operating cost and system cost are higher.
  • the purpose of the present invention is to provide a rail transit traction system based on permanent magnetic flux switching linear motors.
  • the traction system can effectively reduce the train drive motor's cost by reasonably designing the spatial arrangement of the drive motors. Traction output harmonics, without reducing the average value of traction output, achieve the effect of significantly reducing traction fluctuations, thereby reducing noise during operation and improving system stability.
  • the present invention proposes a sub-system of an urban rail transit traction system based on permanent magnet flux switching linear motors, including a carriage 10, a track 11 and a DC power supply system 12;
  • the carriage 10 includes a carriage body 100, a bogie 101, i* 2p primary permanent magnet flux switching linear motors 102, and an inverter and a motor controller 103;
  • the track 11 includes a train guide rail 110 and a secondary 111 of a permanent magnetic flux switching linear motor.
  • the secondary 111 of the permanent magnetic flux switching linear motor includes a secondary tooth 1110 and a secondary yoke 1111.
  • the permanent magnets are sequentially numbered flux linear motor primary switch 102 belonging to the same subsystem, referred to as the motor between the motor M 1 to M i 2 p, the centerline of the motor M a * and the motor M b of the distance denoted Is ⁇ (a, b) ; the distance between the center lines of the adjacent secondary teeth 1110 is ⁇ s ;
  • Fourier decomposition is performed on the traction force of any one of the permanent magnetic flux-switching linear motors during operation to obtain the amplitude of each traction force, According to the amplitude of the harmonics of the p+q term before the traction force, the order of the harmonics is arranged and numbered, which is recorded as h 1 to h p+q ;
  • the distance between the primary (102) of the permanent magnetic flux switching linear motors belonging to the same subsystem meets the following conditions:
  • x is a positive integer
  • mod(a,b) represents the remainder of dividing a by b
  • t and k are arrays that satisfy the following conditions:
  • t is a non-negative integer and k is a positive integer
  • the primary 102 of the permanent magnet flux-switching linear motor of the same subsystem is moved by an integral multiple of ⁇ s , so as to realize the sequence exchange between different motors and form a new arrangement;
  • x is a positive integer
  • t and k are arrays satisfying the following conditions:
  • t is a non-negative integer and k is a positive integer
  • the values of h 1 to h p+q are adjusted according to the number of harmonics that need to be eliminated in priority to form a permanent magnet flux-switched linear motor based on the new h 1 to h p+q.
  • the present invention proposes a rail transit traction system based on permanent magnet flux-switching linear motors.
  • the topic is to rationally design the spatial arrangement of the drive motors to eliminate the specified number of harmonics in a targeted manner, thereby effectively reducing the overall traction of the train drive motor Output harmonics, without reducing the average traction output, achieve the effect of significantly reducing traction fluctuations, thereby reducing noise during operation and improving system stability.
  • FIG. 1 is a schematic structural diagram of a rail transit traction system based on permanent magnet flux switching linear motors in Embodiment 1;
  • Embodiment 2 is a track front view of a rail transit traction system based on permanent magnetic flux switching linear motors in Embodiment 1;
  • FIG. 3 is a schematic diagram of a driving motor structure of a rail transit traction system based on a permanent magnet flux switching linear motor in Embodiment 1;
  • Embodiment 4 is a traction waveform diagram of a rail transit traction system based on permanent magnet flux switching linear motors in Embodiment 1;
  • FIG. 5 is a schematic structural diagram of a rail transit traction system based on permanent magnet flux switching linear motors in Embodiment 2;
  • 10-car, 11-track, 12-DC power supply system 100-car body, 101-bogie, 102-primary of permanent magnetic flux switching linear motor, 103-inverter and motor controller, 110- Train guide rail, 111-secondary of permanent magnetic flux switching linear motor, 1110-secondary gear, 1111-secondary yoke.
  • the present invention provides a rail transit traction system based on permanent magnetic flux switching linear motors.
  • the present invention will be further described in detail with reference to the drawings and examples. It should be understood that the specific implementation described here is only used to explain the present invention, but not to limit the present invention.
  • the present invention proposes a sub-system of an urban rail transit traction system based on permanent magnetic flux switching linear motors, including a carriage 10, a track 11 and a DC power supply system 12;
  • the carriage 10 includes a carriage body 100, a bogie 101, i* 2p primary permanent magnet flux switching linear motors 102, and an inverter and a motor controller 103;
  • the track 11 includes a train guide rail 110 and a secondary 111 of a permanent magnetic flux switching linear motor.
  • the secondary 111 of the permanent magnetic flux switching linear motor includes a secondary tooth 1110 and a secondary yoke 1111.
  • the permanent magnets are sequentially numbered flux linear motor primary switch 102 belonging to the same subsystem, referred to as the motor between the motor M 1 to M i 2 p, the centerline of the motor M a * and the motor M b of the distance denoted Is ⁇ (a, b) ; the distance between the center lines of the adjacent secondary teeth 1110 is ⁇ s ;
  • Fourier decomposition is performed on the traction force of any one of the permanent magnet flux-switching linear motors during operation to obtain the amplitude of each traction force, According to the amplitude of the harmonics of the p+q term before the traction force, the order of the harmonics is arranged and numbered, which is recorded as h 1 to h p+q ;
  • the distance between the primary (102) of the permanent magnetic flux switching linear motors belonging to the same subsystem meets the following conditions:
  • x is a positive integer
  • mod(a,b) represents the remainder of dividing a by b
  • t and k are arrays that satisfy the following conditions:
  • t is a non-negative integer
  • k is a positive integer
  • the primary 102 of the permanent magnet flux-switching linear motor of the same subsystem is moved by an integral multiple of ⁇ s , so as to realize the sequence exchange between different motors and form a new arrangement;
  • x is a positive integer
  • t and k are arrays satisfying the following conditions:
  • t is a non-negative integer and k is a positive integer
  • the values of h 1 to h p+q are adjusted according to the number of harmonics that need to be eliminated in priority to form a permanent magnet flux-switched linear motor based on the new h 1 to h p+q.
  • Figure 1 is a rail transit traction system based on permanent magnet flux-switching linear motors of the present invention.
  • this embodiment there are 4 subsystems of urban rail transit traction system based on permanent magnet flux-switching linear motors. Since the motors in the subsystems are distributed in the same way, and the train subsystems are equally spaced, only the first two of them are shown in Figure 1.
  • FIG. 1 enlarges the carriage 10 and increases the distance between the rails 11. In actual situations, the two are in close contact with each other through the wheel and rail, as shown in FIG. 2.
  • the track 11 includes a train guide rail 110 and a secondary 111 of a permanent magnetic flux switching linear motor.
  • the secondary 111 of the permanent magnetic flux switching linear motor includes a secondary tooth 1110 and a secondary yoke 1111.
  • j*2 q 4 sub-systems of the urban rail transit traction system based on permanent magnet flux switching linear motors form a complete traction system. It is the number of the subsystem, denoted as S1, S2, S3, S4 from left to right; is the number of the motor in S1, denoted as M1, M2 from left to right.
  • the centerline distance For the primary of the permanent magnet flux switching linear motor in the same subsystem, the centerline distance meets the following conditions:
  • x is a positive integer
  • mod(a,b) represents the remainder of dividing a by b
  • t and k are arrays that satisfy the following conditions:
  • t is a non-negative integer and k is a positive integer
  • the permanent magnet flux switching linear motor selected in this embodiment is shown in FIG. 3, and the magnetizing direction of the permanent magnet is shown in the direction of the arrow in the figure.
  • the ⁇ (a, b) of the subsystem satisfies the following conditions:
  • x is a positive integer
  • t and k are arrays satisfying the following conditions:
  • t is a non-negative integer and k is a positive integer
  • Equation (4) shows that ⁇ (x, x+1) is an integral multiple of ⁇ s , that is, the centerline distances of the four subsystems of S1, S2, S3 and S4 are all integral multiples of ⁇ s ; k that satisfies equation (6) , T do not exist at the same time, so the formula (5) has no practical significance and is regarded as constant and does not further restrict the distribution of subsystems in space.
  • the traction force waveform of each motor in this embodiment is compared with the waveform after the traction system output traction force in this embodiment is divided by 16 (average to each motor). It can be seen from the figure that the traction force fluctuation of each motor is 1.27kN when running alone. After adopting the structure of the traction system in this embodiment, the average traction force fluctuation of each motor is only 0.29kN, which is significantly smaller than the former, thus achieving harmonic reduction , Improve traction fluctuation, reduce noise, and improve system stability.
  • the method of using spatial arrangement to offset linear motor traction harmonics proposed by the present invention is not only applicable to permanent magnet flux switching linear motors, and the method is also applicable to other types of linear motors.
  • ⁇ s is a stator or secondary of the motor. Basic structure cycle length.
  • Fig. 5 is a rail transit traction system based on permanent magnet flux switching linear motor of the present invention.
  • the difference between this embodiment and Embodiment 1 is that the number of motors is increased in this embodiment to achieve the purpose of reducing more traction harmonics. Since the motors in the subsystems are distributed in the same way, and the subsystems are equally spaced, only the first two subsystems are shown in Figure 5.
  • j*2 q 4 sub-systems of the urban rail transit traction system based on permanent magnet flux switching linear motors form a complete traction system. It is the number of the subsystem, which is denoted as S1, S2, S3, and S4 from left to right; it is the motor number in S1, which is denoted as M1, M2, M3, and M4 from left to right.
  • the centerline distance For the primary of the permanent magnet flux switching linear motor in the same subsystem, the centerline distance meets the following conditions:
  • x is a positive integer
  • mod(a,b) represents the remainder of dividing a by b
  • t and k are arrays that satisfy the following conditions:
  • t is a non-negative integer and k is a positive integer
  • h 1 and h 2 are the harmonic orders of traction force to be eliminated according to actual needs. That is, the relative positions of M1 and M2 and the secondary teeth are staggered by 1/2h 1 pitch, and the relative positions of M3 and M4 and the secondary teeth are staggered by 1/2h 1 pitch, that is, the relative positions of M1 and M3 and the secondary teeth. Stagger 1/2h by 2 pitches.
  • the ⁇ (a, b) of the subsystem satisfies the following conditions:
  • x is a positive integer
  • t and k are arrays satisfying the following conditions:
  • t is a non-negative integer and k is a positive integer
  • the feature of this embodiment is that compared with the embodiment, the traction harmonics are further reduced, and it has a good application prospect in rail transit occasions that require a greater number of drive motors.

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Power Engineering (AREA)
  • Transportation (AREA)
  • Mechanical Engineering (AREA)
  • Linear Motors (AREA)
  • Electric Propulsion And Braking For Vehicles (AREA)

Abstract

本发明公开了一种基于永磁磁通切换直线电机的轨道交通牵引系统。基于永磁磁通切换直线电机的轨道交通牵引系统由若干子系统构成。基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统包括车厢、轨道和直流供电系统。车厢包括车厢主体、转向架、i*2 p个永磁磁通切换直线电机的初级、逆变器及电机控制器。轨道包括列车导轨以及永磁磁通切换直线电机的次级。j*2 q个基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统组成一个完整的牵引系统。本发明具有次级结构简单、系统效率高、系统功率因数高的特点，并且提出了牵引系统中永磁磁通切换直线电机初级空间距离的设定规则，可以有效降低系统牵引力的波动，进而降低列车运行时的噪声，提高稳定性。

Description

一种基于永磁磁通切换直线电机的轨道交通牵引系统 技术领域
本发明涉及的是一种基于永磁磁通切换直线电机驱动的列车系统，属于电机驱动与控制技术领域。
背景技术
在城市化进程中，轨道交通扮演着不可或缺的角色。由传统旋转电机驱动的列车需要依靠机械传动装置，将旋转力矩转换为黏着式牵引力，导致效率较低，并且输出牵引力受到轨道状况、摩擦系数等因素影响，因此爬坡能力与拐弯能力较差，路线规划不便，成本较高，其应用受到了一定的限制。与旋转电机相比，直线电机驱动系统直接产生电磁力，电磁力为非黏着牵引力，摆脱了轨道状况的影响，同时直线电机无需机械传动装置，因此体积小、功率密度高的优点，因此在轨道交通领域应用前景光明。
目前，直线感应电机在国内外轨道交通领域应用广泛。直线感应电机的次级仅由感应板与导磁板构成，初级由电枢绕组与铁心构成，具有结构简单，体积小，成本低的优点，但是直线感应电机涡流损耗较高，因此效率与功率因数较低，同时直线感应电机的控制较为复杂，因此其长期运营成本与系统成本较高。
传统永磁直线同步电机的效率、功率因数、功率密度均较高；然而该类电机的永磁体置于次级，沿轨道铺设，次级成本高昂，且定位力较大，同时，传统永磁电机的弱磁性能较差，难以实现高速下的恒功率控制，调速范围有限，这些缺点极大地限制了其在长行程领域的应用。
近年来，永磁磁通切换直线电机引起了国内外学者的广泛关注，该类电机次级结构简单，仅由导磁材料构成，成本较低、便于维护，同时具有功率密度高、功率因数高、效率高的显著优点。研究结果表明，其长期运营成本低于感应电机，并且对系统容量要求更低。但是，该类电机运用于轨道交通领域时牵引力波动较大，会造成明显的噪声，并且降低电机运行的可靠性，这限制了该类电机在轨道交通领域的应用。
发明内容
针对现有技术上存在的不足，本发明目的在于提供一种基于永磁磁通切换直线电机的轨道交通牵引系统，该牵引系统通过合理设计驱动电机的空间排列方式，可以有效降低列车驱动电机的牵引力输出谐波，在不降低牵引力输出平均值的情况下，达到明显降低牵引力波动的效果，进而减小运行时的噪声，并提高系统的稳定性。
本发明提出的一种基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统，包括 车厢10、轨道11和直流供电系统12；
所述车厢10包含车厢主体100、转向架101、i*2 p个永磁磁通切换直线电机的初级102、以及逆变器与电机控制器103；
所述轨道11包含列车导轨110以及永磁磁通切换直线电机的次级111，所述永磁磁通切换直线电机的次级111包含次级齿1110与次级轭部1111。
进一步地，对属于同一子系统的所述永磁磁通切换直线电机的初级102依次编号，记作电机M 1至电机M i*2 p，电机M a与电机M b的中心线间距离记为λ (a,b)；相邻次级齿1110中心线间距离为τ s；对任一所述永磁磁通切换直线电机运行时的牵引力进行傅利叶分解，得到各次牵引力的幅值，根据牵引力前p+q项谐波的幅值大小，对谐波次数进行排列编号，记作h 1至h p+q；
属于同一子系统的所述永磁磁通切换直线电机的初级(102)间距离，满足如下条件：
Figure PCTCN2019092470-appb-000001
其中，x为正整数，mod(a,b)表示a除以b的余数，t、k为满足如下条件的数组：
t·2 k+2 k-1+1≤2 p  (3)
其中t为非负整数，k为正整数；
当不存在使(1)具有实际意义的x时，(1)视为恒成立；当不存在满足(3)的t、k数组时，(2)式视为恒成立；
作为一种优选，对同一子系统的所述永磁磁通切换直线电机的初级102移动τ s的整倍数距离，以实现不同电机间的顺序调换，形成新的排列方式；
进一步地，j*2 q个基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统组成一个完整的牵引系统；
对子系统依次编号，记作子系统S 1至子系统S j*2 q，子系统S a与子系统S b的中心线间距离记为Λ (a,b)；子系统间的Λ (a,b)满足如下条件：
Figure PCTCN2019092470-appb-000002
其中，x为正整数，t、k为满足如下条件的数组：
t·2 k+2 k-1+1≤2 q  (6)
其中t为非负整数，k为正整数；
当不存在使(4)具有实际意义的x时，(4)视为恒成立；当不存在满足(6)的t、k数组时，(5)式视为恒成立；
作为一种优选，对不同子系统移动τ s的整倍数距离，以实现不同子系统间的顺序调换，形成新的排列方式；
作为一种优选，根据优先需要消除的谐波次数，对h 1至h p+q的值进行调整，形成基于新的h 1至h p+q构成的一种基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统及其构成的牵引系统。
本发明电机主要存在如下优点：
本发明提出的一种基于永磁磁通切换直线电机的轨道交通牵引系统，课题通过合理设计驱动电机的空间排列方式，针对性的消除指定次数的谐波，进而有效降低列车驱动电机的整体牵引力输出谐波，在不降低平均牵引力输出的前提下，达到明显降低牵引力波动的效果，进而减小运行时的噪声，并提高系统的稳定性。
附图说明
下面结合附图和实施例对本发明进一步说明：
图1是实施例1中一种基于永磁磁通切换直线电机的轨道交通牵引系统的结构示意图；
图2是实施例1中一种基于永磁磁通切换直线电机的轨道交通牵引系统的轨道正视图；
图3是实施例1中一种基于永磁磁通切换直线电机的轨道交通牵引系统的驱动电机结构示意图；
图4是实施例1中一种基于永磁磁通切换直线电机的轨道交通牵引系统的牵引力波形图；
图5是实施例2中一种基于永磁磁通切换直线电机的轨道交通牵引系统的结构示意图；
其中，10-车厢，11-轨道，12-直流供电系统，100-车厢主体，101-转向架，102-永磁磁通切换直线电机的初级，103-逆变器与电机控制器，110-列车导轨，111-永磁磁通切换直线电机的次级，1110-次级齿，1111-次级轭部。
具体实施方式
本发明提供一种基于永磁磁通切换直线电机的轨道交通牵引系统，为使本发明的目的，技术方案及效果更加清楚，明确，以及参照附图并举实例对本发明进一步详细说明。应当理解，此处所描述的具体实施仅用以解释本发明，并不用于限定本发明。
本发明提出的一种基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统，包括车厢10、轨道11和直流供电系统12；
所述车厢10包含车厢主体100、转向架101、i*2 p个永磁磁通切换直线电机的初级102、以及逆变器与电机控制器103；
所述轨道11包含列车导轨110以及永磁磁通切换直线电机的次级111，所述永磁磁通切换直线电机的次级111包含次级齿1110与次级轭部1111。
进一步地，对属于同一子系统的所述永磁磁通切换直线电机的初级102依次编号，记作电机M 1至电机M i*2 p，电机M a与电机M b的中心线间距离记为λ (a,b)；相邻次级齿1110中心线间距离为τ s；对任一所述永磁磁通切换直线电机运行时的牵引力进行傅利叶分解，得到各次牵引力的幅值，根据牵引力前p+q项谐波的幅值大小，对谐波次数进行排列编号，记作h 1至h p+q；
属于同一子系统的所述永磁磁通切换直线电机的初级(102)间距离，满足如下条件：
Figure PCTCN2019092470-appb-000003
其中，x为正整数，mod(a,b)表示a除以b的余数，t、k为满足如下条件的数组：
t·2 k+2 k-1+1≤2 p  (3)
其中，t为非负整数，k为正整数；
当不存在使(1)具有实际意义的x时，(1)视为恒成立；当不存在满足(3)的t、k数组时，(2)式视为恒成立；
作为一种优选，对同一子系统的所述永磁磁通切换直线电机的初级102移动τ s的整倍数距离，以实现不同电机间的顺序调换，形成新的排列方式；
进一步地，j*2 q个基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统组成一个完整的牵引系统；
对子系统依次编号，记作子系统S 1至子系统S j*2 q，子系统S a与子系统S b的中心线间距离记为Λ (a,b)；子系统间的Λ (a,b)满足如下条件：
Figure PCTCN2019092470-appb-000004
其中，x为正整数，t、k为满足如下条件的数组：
t·2 k+2 k-1+1≤2 q  (6)
其中t为非负整数，k为正整数；
当不存在使(4)具有实际意义的x时，(4)视为恒成立；当不存在满足(6)的t、k数组时，(5)式视为恒成立；
作为一种优选，对不同子系统移动τ s的整倍数距离，以实现不同子系统间的顺序调换， 形成新的排列方式；
作为一种优选，根据优先需要消除的谐波次数，对h 1至h p+q的值进行调整，形成基于新的h 1至h p+q构成的一种基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统及其构成的牵引系统。
实施例1
参见图1，图1为本发明的一种基于永磁磁通切换直线电机的轨道交通牵引系统，本实施例中共4个基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统，由于各子系统中电机空间分布方式相同，且列车各子系统在空间中等距分布，故图1中仅展示了其中前两个。为了更清晰的展示本实施例中各部分，图1放大了车厢10增加了轨道11之间的距离，实际情况中，两者通过轮轨紧密接触，如图2所示。
本实施例中，i＝1，p＝1，j＝4，q＝0。本实施例中，基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统，包括车厢10、轨道11和直流供电系统12；车厢10包含车厢主体100、转向架101、i*2 p＝2个永磁磁通切换直线电机的初级102、以及逆变器与电机控制器103。轨道11包含列车导轨110以及永磁磁通切换直线电机的次级111，所述永磁磁通切换直线电机的次级111包含次级齿1110与次级轭部1111。j*2 q＝4个基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统组成一个完整的牵引系统。为子系统编号，自左向右分别记作S1,S2,S3,S4；为S1中的电机编号，自左向右分别记作M1,M2。
对于同一子系统内的永磁磁通切换直线电机初级，中心线距离满足如下条件：
Figure PCTCN2019092470-appb-000005
其中，x为正整数，mod(a,b)表示a除以b的余数，t、k为满足如下条件的数组：
t·2 k+2 k-1+1≤2 p  (3)
其中t为非负整数，k为正整数；
当不存在使(1)具有实际意义的x时，(1)视为恒成立；当不存在满足(3)的t、k数组时，(2)式视为恒成立；
代入i＝1，p＝1，j＝4，q＝0。(1)式表明λ (x,x+2)为τ s的整倍数，由于每节车厢仅有2台电机，因此(1)式视为恒成立；满足(3)式的k、t有：k＝1，t＝0；因此(2)式表明M1与M2的中心线距离λ (1，2)为τ s的整数加1/2h 1倍。
本实施例选取的永磁磁通切换直线电机参见图3，其永磁体充磁方向如图中箭头方向所示。有限元仿真表明，该电机额定情况下，牵引力含有大量二次谐波，因此选取h 1＝2；结合 (2)式结论，即M1与M2与次级齿的相对位置错开1/4个齿距。
子系统的Λ (a,b)满足如下条件：
Figure PCTCN2019092470-appb-000006
其中，x为正整数，t、k为满足如下条件的数组：
t·2 k+2 k-1+1≤2 q  (6)
其中t为非负整数，k为正整数；
当不存在使(4)具有实际意义的x时，(4)视为恒成立；当不存在满足(6)的t、k数组时，(5)式视为恒成立；
代入i＝1，p＝1，j＝4，q＝0。(4)式表明Λ (x,x+1)为τ s的整倍数，即S1、S2、S3与S4四个子系统的中心线距离均为τ s的整倍数；满足(6)式的k、t不同时存在，因此(5)式不具有实际意义，视为恒成立，不进一步限制子系统在空间的分布。
参见图4，经过有限元仿真后，将本实施例中的每台电机单独运行的牵引力波形，以及采用本实施例中牵引系统输出牵引力除以16(平均至每台电机)后波形进行对比。由图可知，每台电机单独运行时的牵引力波动为1.27kN，采用本实施例中牵引系统结构之后，平均到每台电机的牵引力波动仅为0.29kN，明显小于前者，因此达到了削减谐波，改善牵引力波动，减小噪声，提高系统稳定性的作用。
值得注意的是，本发明提出的利用空间排布以抵消直线电机牵引力谐波的方法不仅仅适用于永磁磁通切换直线电机，该方法同样适用于其他类型的直线电机。对于某一给定的直线牵引电机，只需求得该电机的推力波动谐波分布情况，即可通过本发明提出的方法减小其推力波动，此时τ s为该电机定子或次级的一个基本结构周期长度。
实施例2
参见图5，图5为本发明的一种基于永磁磁通切换直线电机的轨道交通牵引系统。本实施例与实施例1的区别在于，本实施例增加了电机数量，以达到削减更多次数牵引力谐波的目的。由于各子系统中电机空间分布方式相同，且各子系统在空间中等距分布，故图5中仅展示了其中前两个子系统。
本实施例中，i＝1，p＝2，j＝2，q＝1。即每个车厢10包含车厢主体100、转向架101、i*2 p＝4个永磁磁通切换直线电机的初级102。j*2 q＝4个基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统组成一个完整的牵引系统。为子系统编号，自左向右分别记作S1,S2,S3,S4；为S1中的电机编号，自左向右分别记作M1,M2,M3,M4。
对于同一子系统内的永磁磁通切换直线电机初级，中心线距离满足如下条件：
Figure PCTCN2019092470-appb-000007
其中，x为正整数，mod(a,b)表示a除以b的余数，t、k为满足如下条件的数组：
t·2 k+2 k-1+1≤2 p   (3)
其中t为非负整数，k为正整数；
当不存在使(1)具有实际意义的x时，(1)视为恒成立；当不存在满足(3)的t、k数组时，(2)式视为恒成立；
代入i＝1，p＝2，j＝2，q＝1。(1)式表明λ (x,x+2)为τ s的整倍数，即M1与M3，M2与M4的中心线距离为τ s的整倍数；满足(3)式的k、t组合有：(k＝1，t＝0)、(k＝1，t＝1)以及(k＝2，t＝0)；(2)式表明λ (1，2)与λ (3，4)为τ s的整数加1/2h 1倍，λ (1，3)为τ s的整数加1/2h 2倍。其中，h 1与h 2为根据实际需要，决定消除的牵引力谐波次数。即M1与M2和次级齿的相对位置错开1/2h 1个齿距，M3与M4和次级齿的相对位置错开1/2h 1个齿距，即M1与M3和次级齿的相对位置错开1/2h 2个齿距。
子系统的Λ (a,b)满足如下条件：
Figure PCTCN2019092470-appb-000008
其中，x为正整数，t、k为满足如下条件的数组：
t·2 k+2 k-1+1≤2 q   (6)
其中t为非负整数，k为正整数；
当不存在使(4)具有实际意义的x时，(4)视为恒成立；当不存在满足(6)的t、k数组时，(5)式视为恒成立；
代入i＝1，p＝2，j＝2，q＝1。(1)式表明Λ (x,x+2)为τ s的整倍数，即S1与S3，S2与S4的中心线距离均为τ s的整倍数；式的k、t组合有：k＝1，t＝0；(6)式表明Λ (1，2)为τ s的整数加1/2h 3倍。其中，h 3为根据实际需要，决定消除的牵引力谐波次数。
本实施例的特点在于，与实施例相比，进一步削减了牵引力谐波，在对驱动电机数量需求更大的轨道交通场合具有良好应用前景。
以上显示和描述了本发明的基本原理和主要特征和本发明的优点。本行业的技术人员应该了解，本发明不受上述实施例的限制，上述实施例和说明书中描述的只是说明本发明的原 理，在不脱离本发明精神和范围的前提下，本发明还会有各种变化和改进，这些变化和改进都落入要求保护的本发明范围内。本发明要求保护范围由所附的权利要求书及其等效物界定。

Claims (6)

  1. 一种基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统，包括车厢(10)、轨道(11)和直流供电系统(12)，其特征在于，
    所述车厢(10)包含车厢主体(100)、转向架(101)、i*2 p个永磁磁通切换直线电机的初级(102)、以及逆变器与电机控制器(103)；
    所述轨道(11)包含列车导轨(110)以及永磁磁通切换直线电机的次级(111)，所述永磁磁通切换直线电机的次级(111)包含次级齿(1110)与次级轭部(1111)。
  2. 根据权利要求1所述的一种基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统，其特征在于，
    对属于同一子系统的所述永磁磁通切换直线电机的初级(102)依次编号，记作电机M 1至电机M i*2 p，电机M a与电机M b的中心线间距离记为λ (a,b)；相邻次级齿(1110)中心线间距离为τ s；对任一所述永磁磁通切换直线电机运行时的牵引力进行傅利叶分解，得到各次牵引力的幅值，根据牵引力前p+q项谐波的幅值大小，对谐波次数进行排列编号，记作h 1至h p+q；
    属于同一子系统的所述永磁磁通切换直线电机的初级(102)间距离，满足如下条件：
    Figure PCTCN2019092470-appb-100001
    其中，x为正整数，mod(a,b)表示a除以b的余数，t、k为满足如下条件的数组：
    t·2 k+2 k-1+1≤2 p  (3)
    其中t为非负整数，k为正整数；
    当不存在使(1)具有实际意义的x时，(1)视为恒成立；当不存在满足(3)的t、k数组时，(2)式视为恒成立。
  3. 根据权利要求2所述的一种基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统，其特征在于，对同一子系统的所述永磁磁通切换直线电机的初级(102)移动τ s的整倍数距离，以实现不同电机间的顺序调换，形成新的排列方式。
  4. 根据权利要求1至3任一项所述的一种基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统构成的完整牵引系统，其特征在于，
    j*2 q个基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统组成一个完整的牵引系统；
    对子系统依次编号，记作子系统S 1至子系统S j*2 q，子系统S a与子系统S b的中心线间距离记为Λ (a,b)；子系统间的Λ (a,b)满足如下条件：
    Figure PCTCN2019092470-appb-100002
    其中，x为正整数，t、k为满足如下条件的数组：
    t·2 k+2 k-1+1≤2 q  (6)
    其中t为非负整数，k为正整数；
    当不存在使(4)具有实际意义的x时，(4)视为恒成立；当不存在满足(6)的t、k数组时，(5)式视为恒成立。
  5. 根据权利要求4所述的一种基于永磁磁通切换直线电机的轨道交通牵引系统，其特征在于，对不同子系统移动τ s的整倍数距离，以实现不同子系统间的顺序调换，形成新的排列方式。
  6. 根据权利要求1至5任一项所述的一种基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统及其构成的牵引系统，其特征在于，根据优先需要消除的谐波次数，对h 1至h p+q的值进行调整，形成基于新的h 1至h p+q构成的一种基于永磁磁通切换直线电机的城市轨道交通牵引系统的子系统及其构成的牵引系统。
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