WO2020134622A1 - 一种基于磁流变液的循环球式电液转向系统及其优化方法 - Google Patents

一种基于磁流变液的循环球式电液转向系统及其优化方法 Download PDF

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WO2020134622A1
WO2020134622A1 PCT/CN2019/116096 CN2019116096W WO2020134622A1 WO 2020134622 A1 WO2020134622 A1 WO 2020134622A1 CN 2019116096 W CN2019116096 W CN 2019116096W WO 2020134622 A1 WO2020134622 A1 WO 2020134622A1
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Prior art keywords
steering
magnetorheological fluid
electro
steering system
recirculating ball
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English (en)
French (fr)
Inventor
赵万忠
周小川
栾众楷
王春燕
张自宇
王一松
汪桉旭
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Nanjing Tianhang Institute Of Intelligent Equipment Co Ltd
Nanjing University of Aeronautics and Astronautics
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Nanjing Tianhang Institute Of Intelligent Equipment Co Ltd
Nanjing University of Aeronautics and Astronautics
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Priority claimed from CN201811622588.9A external-priority patent/CN109969255B/zh
Priority claimed from CN201822230759.5U external-priority patent/CN209617252U/zh
Application filed by Nanjing Tianhang Institute Of Intelligent Equipment Co Ltd, Nanjing University of Aeronautics and Astronautics filed Critical Nanjing Tianhang Institute Of Intelligent Equipment Co Ltd
Publication of WO2020134622A1 publication Critical patent/WO2020134622A1/zh
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
    • B62D—MOTOR VEHICLES; TRAILERS
    • B62D3/00—Steering gears
    • B62D3/02—Steering gears mechanical
    • B62D3/04—Steering gears mechanical of worm type
    • B62D3/06—Steering gears mechanical of worm type with screw and nut
    • B62D3/08—Steering gears mechanical of worm type with screw and nut using intermediate balls or the like
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
    • B62D—MOTOR VEHICLES; TRAILERS
    • B62D5/00—Power-assisted or power-driven steering
    • B62D5/06—Power-assisted or power-driven steering fluid, i.e. using a pressurised fluid for most or all the force required for steering a vehicle

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  • the invention belongs to the technical field of automobile steering systems, and in particular relates to a circulating ball type electro-hydraulic steering system based on magnetorheological fluid and a multi-objective optimization method.
  • Magnetorheological fluid is a new type of liquid material. When the magnetic field attached to the magnetorheological fluid changes, its apparent viscosity will change with the change of the magnetic field, so that the magnetorheological fluid can be used in fluids and solids. There is a reversible transformation between them, and it also has the advantages of good controllability, high magnetic permeability, no pollution, low energy consumption and so on. Because magnetorheological fluid can generate strong damping force in a short time according to the additional magnetic field, it can realize the function of transmitting torque and changing damping. It is currently widely used in automobile suspension systems, transmission systems, and braking systems.
  • the Chinese patent application number is CN201610913543.1
  • the patent name is “a vehicle steering control system”
  • an automobile steering control system uses magnetorheological fluids. Designing a new type of clutch to improve the safety and reliability when switching the driving mode of the car; the Chinese patent application number is CN201110185746.0, and the patent name is "Wire-controlled steering vehicle road sensor simulation execution device”.
  • the magneto-rheological fluid damper is used as the main
  • the road sensor simulates the actuator and controls the return speed through the magnetorheological fluid damper to ensure the stability of the steering wheel;
  • the Chinese patent application number is CN201420522322.8, and the patent name is "a composite steering tie rod".
  • the steering tie rod uses the physical characteristics of the magnetorheological fluid to control the viscosity of the magnetorheological fluid when the car punctures, thereby locking the tie rod and reducing the damage caused by the tyre puncture.
  • the electro-hydraulic power steering system is a relatively new type of power steering system. It combines the advantages of the electric power steering system and the electronically controlled hydraulic power steering system. It has low energy consumption, good economy, fast response, large assist torque, and high-speed road. Feel better and other advantages.
  • the existing electro-hydraulic steering system still uses the traditional hydraulic power assist mechanism. The entire system has high energy consumption and a complicated structure, which is not easy to install and maintain, and the manufacturing and maintenance costs have increased accordingly. The sense of road and sensitivity are not enough coordination.
  • the object of the present invention is to provide a circulating ball type electro-hydraulic steering system based on magnetorheological fluid and its optimization method, which solves the problem of large energy waste in the traditional steering system,
  • the invention utilizes the physical properties of the magnetorheological fluid to realize the boosting function, greatly simplifies the structure of the system, and at the same time improves the controllability of the steering feel at high speed.
  • a circulating ball type electro-hydraulic steering system based on magnetorheological fluid of the present invention includes: a mechanical transmission module, an electric booster module, a magnetorheological fluid booster module and a booster control module;
  • the mechanical transmission module includes steering wheel, steering shaft, recirculating ball steering gear, steering rocker arm, steering straight tie rod, steering tie rod, left knuckle arm, left trapezoidal arm, left knuckle and left wheel, right knuckle arm , Right trapezoidal arm, right knuckle, right wheel;
  • the upper end of the steering shaft is connected to the steering wheel, and the lower end is connected to the input end of the recirculating ball diverter;
  • the recirculating ball diverter includes a steering screw, a steering nut rack, a recirculating ball diverter housing, a gear fan, and a recirculating steel ball, wherein The recirculating steel ball is placed in the closed pipeline between the steering nut rack and the steering screw;
  • the output end of the recirculating ball diverter is connected to one end of the steering rocker arm through the gear fan, and the other end of the steering rocker arm is passed through the steering straight rod and left
  • the knuckle arm is connected to drive the left knuckle and the left wheel to deflect;
  • the left knuckle arm is connected to one end of the steering tie rod via the left trapezoidal arm;
  • the other end of the steering tie rod is connected to the right trapezoidal arm, and the right trapezoidal arm is via the right knuckle
  • the arm is connected to the right
  • the electric booster module includes a booster motor and a booster motor deceleration mechanism, the input end of the booster motor deceleration mechanism is connected to the booster motor, and the output end of the booster motor deceleration mechanism is connected to the steering shaft;
  • the magnetorheological fluid boosting module includes a magnetorheological fluid cavity, a magnetorheological fluid material, an excitation coil, and an electrode plate;
  • the magnetorheological fluid material is placed in the magnetorheological fluid cavity in the circulating ball diverter; the exciting coil is placed outside the casing of the circulating ball diverter, and the direction of the magnetic field generated when the exciting coil is energized is energized with the electrode plate
  • the directions of the formed electric fields are perpendicular to each other;
  • the input end of the assist control module is connected to a torque sensor, a vehicle speed sensor, a steering wheel angular displacement sensor, and a displacement sensor, and the output end is connected to an assist motor, an excitation coil, and an electrode plate, respectively.
  • the torque sensor is installed on the steering shaft, and the torque input by the driver is acquired through the steering shaft and the torque signal is transmitted to the power assist control module;
  • the vehicle speed sensor is installed on the vehicle for Obtain the vehicle speed signal;
  • the steering wheel angular displacement sensor is installed on the steering wheel to obtain the steering wheel angle signal input by the driver when the car is turning;
  • the displacement sensor is installed on the steering tie rod to obtain the output of the steering tie rod Displacement signal.
  • the recirculating ball diverter is a rectangular parallelepiped; wherein, two ends of the steering nut rack are provided with a sealed and insulated magnetorheological fluid cavity, and the two magnetorheological fluid cavity are filled with magnetorheological fluid material , And communicate with each other through the catheter.
  • the number of the electrode plates is two, which are respectively placed at the front and back ends of the recirculating ball diverter housing in the radial direction, and the outside of the electrode plates is provided with an insulating layer, which is generated between the two electrode plates when energized electric field.
  • the excitation coils are rectangular in cross-section and are two identical pairs.
  • the two pairs of excitation coils are installed symmetrically on both sides of the exterior of the recirculating ball diverter housing in the axial direction.
  • Each pair of excitation coils is placed radially At the upper and lower ends of the outer part of the recirculating ball steering gear housing, the current direction in the excitation coil is consistent and the excitation coil installation plane is perpendicular to the electrode plate installation plane.
  • the upper and lower excitation coils on the same side are separated by an insulating material.
  • the torque input by the driver sequentially turns the steering wheel and the steering shaft during steering;
  • the power assist control module (ECU) outputs a power assist motor control signal to control the power assist motor according to the signals collected by the sensors, and the power assist motor outputs
  • the electromagnetic torque acts on the steering shaft through the assist motor deceleration mechanism to achieve the first level of steering assistance;
  • the steering shaft drives the steering screw of the recirculating ball steering gear.
  • the steering screw pushes the steering nut rack along the axial direction, and the steering nut rack
  • the steering rocker arm is driven to reciprocate and shake;
  • the power control module changes the current in the excitation coil by adjusting the excitation coil output signal, adjusts the size of the generated magnetic field, and then controls the characteristics of the magnetorheological fluid material, changing its excitation coil and electrode plate
  • the magnitude of the Lorentz force received in the mutually perpendicular electric fields is formed, and the Lorentz force is exerted on the steering nut rack to achieve the second-stage assist effect.
  • the present invention also proposes an optimization method for a circulating ball type electro-hydraulic steering system based on magnetorheological fluid. Based on the above system, it includes the following steps:
  • the niche multi-objective particle swarm optimization algorithm is used to optimize the optimization variables of the electro-hydraulic steering system, and the optimal solution is obtained according to the optimization algorithm.
  • the electro-hydraulic steering system model includes a steering wheel model, a recirculating ball steering gear model, an electric power assist module model, and a magnetorheological fluid assist power module model.
  • step (4) the specific steps of the niche multi-objective particle swarm optimization algorithm in step (4) are as follows:
  • V i (t+1) V i (t)+c 1 *r 1 *(P best (t)-X i (t))+c 2 *r 2 *(G best (t)-X i ( t)) (1)
  • V i (t) and V i (t+1) are the velocity of particles at time t and t+1 respectively, and X i (t) and X i (t+1) are respectively time t and t
  • the position of the particle at +1, c 1 and c 2 are learning factors, r 1 and r 2 are random numbers between 0 and 1;
  • F i is the fitness of the individual X i in the external set
  • N s is the number of individuals in the niche
  • S i is the sharing degree of the individual X i
  • f sh (d ij ) is the relationship between the individual X i and the individual X j Sharing function
  • ⁇ is the parameter that controls the shape of the sharing function
  • ⁇ share is the initially specified sharing distance
  • d ij represents the Euclidean distance between the individual X i and the individual X j .
  • the step (3) comprises: selecting a steering screw center distance r a, sector gear pitch radius r p, the steering column stiffness K, motor inertia J m, excitation coil turns N, the effective area A steering nut , The fan inertia J c as an optimization variable, then the vector space in the niche multi-objective particle swarm optimization algorithm is a seven-dimensional vector space, and in the initial m particle position vector and velocity vector group, the first i particle position X 'i and the speed vector V' i is expressed as follows:
  • the present invention uses a magnetorheological fluid power assist module, which greatly simplifies the system structure, solves the road feel and sensitivity problems in the traditional hydraulic power assist module, and uses magnetorheological fluid The physical characteristics effectively improve the controllability of the road feel.
  • the invention replaces the complicated hydraulic mechanism by using the combination of magnetorheological fluid, excitation coil and electrode plate, produces similar boosting effect and improves the reliability and controllability of the system.
  • the optimization method of the present invention considers the multi-object coupling of the electro-hydraulic steering system, adopts the niche multi-object particle swarm optimization algorithm, and optimizes the steering feel, steering sensitivity and energy consumption of the electro-hydraulic steering system at the same time, and can obtain better overall performance Optimization results.
  • 1 is a block diagram of the principle structure of the system of the present invention.
  • FIG. 2 is an A-A sectional view of the recirculating ball diverter of the present invention
  • a circulating ball type electro-hydraulic steering system based on magnetorheological fluid of the present invention includes: a mechanical transmission module, an electric power assist module, a magnetorheological fluid power assist module and a power assist control module (ECU ).
  • ECU power assist control module
  • the mechanical transmission module includes a steering wheel 1, a steering shaft 3, a recirculating ball steering device 7, a steering rocker arm 20, a steering straight tie rod 19, a steering tie rod 17, a left knuckle arm 15, a left trapezoid arm 16, and a left knuckle 14 And left wheel 13, right knuckle arm 35, right trapezoid arm 34, right knuckle 33, right wheel 32;
  • the upper end of the steering shaft 3 is connected to the steering wheel 1 and the lower end is connected to the input end of the recirculating ball diverter 7;
  • the recirculating ball diverter 7 includes a steering screw 10, a steering nut rack 11, a recirculating ball diverter housing 18, and teeth Fan 21 and circulating steel ball 23, wherein the circulating steel ball 23 is placed in a closed pipe between the steering nut rack 11 and the steering screw 10;
  • the output end of the circulating ball diverter 7 passes through the gear fan 21 and the steering rocker 20
  • One end is connected, and the other end of the steering rocker arm 20 is connected to the left knuckle arm 15 through the steering straight rod 19 and drives the left knuckle 14 and the left wheel 13 to deflect;
  • the left knuckle arm 15 passes through the left trapezoidal arm 16 and the steering tie rod 17
  • the other end of the tie rod 17 is connected to the right trapezoidal arm 34.
  • the right trapezoidal arm 34 is connected to the right knuckle 33 via
  • the recirculating ball diverter is a rectangular parallelepiped; wherein, two ends of the steering nut rack 11 are respectively provided with a sealed and insulated magnetorheological fluid cavity, and the two magnetorheological fluid cavity are filled with magnetorheological fluid material , And communicate with each other through the catheter 9.
  • the recirculating ball diverter housing 18 surrounds the steering screw 10, the steering nut rack 11, the circulating steel ball 23 and the gear fan 21.
  • the electric booster module includes a booster motor 6 and a booster motor reduction mechanism 5, the input end of the booster motor reduction mechanism 5 is connected to the booster motor 6, and the output end of the booster motor reduction mechanism 5 is connected to the steering shaft 3;
  • the magnetorheological fluid boosting module includes a magnetorheological fluid cavity 24, a magnetorheological fluid material 25, an excitation coil 8, and an electrode plate 12;
  • the magnetorheological fluid material 25 is placed in the magnetorheological fluid cavity 24 in the circulating ball diverter 7; the exciting coil 8 is placed outside the casing 18 of the circulating ball diverter.
  • the direction of the magnetic field is perpendicular to the direction of the electric field formed when the electrode plate 12 is energized;
  • the input end of the assisted control module is connected to the torque sensor 4, the vehicle speed sensor, the steering wheel angular displacement sensor 2, and the displacement sensor 22, and the output end is connected to the assisted motor 6, the excitation coil 8, and the electrode plate 12, respectively.
  • the torque sensor 4 is installed on the steering shaft 3, and the torque input by the driver is obtained through the steering shaft 3 and the torque signal 29 is transmitted to the assist control module;
  • the vehicle speed sensor is installed on the vehicle , Used to obtain the vehicle speed signal 31;
  • the steering wheel angular displacement sensor 2 is installed on the steering wheel 1 to obtain the steering wheel angle signal 30 input by the driver when the vehicle is turning;
  • the displacement sensor 22 is installed on the steering tie rod 17 , Used to obtain the displacement signal 26 output from the tie rod.
  • the number of the electrode plates is two, which are respectively placed in the radial direction at the front and rear ends of the recirculating ball diverter housing, and the outside of the electrode plates is provided with an insulating layer, and an electric field is generated between the two electrode plates when energized .
  • the cross section of the exciting coil is rectangular and is exactly the same two pairs, the two pairs of exciting coils are installed symmetrically along the axial direction on both sides of the exterior of the recirculating ball steering gear housing, and each pair of exciting coils is placed in the circulation in the radial direction
  • the current direction in the excitation coil is consistent and the excitation coil installation plane is perpendicular to the electrode plate installation plane.
  • the upper and lower excitation coils on the same side are separated by an insulating material.
  • the torque input by the driver sequentially turns the steering wheel and the steering shaft during steering;
  • the assist control module outputs the assist motor control signal 28 according to the signals collected by the sensors to control the assist motor to assist, and the electromagnetic output by the assist motor
  • the torque acts on the steering shaft through the assist motor deceleration mechanism to achieve the first-stage steering assist;
  • the steering shaft drives the steering screw of the recirculating ball steering gear.
  • the steering screw pushes the steering nut rack along the axial direction, and the steering nut rack passes through the teeth
  • the fan-driven steering rocker reciprocates; the assist control module changes the current in the excitation coil by adjusting the excitation coil control signal 27, adjusts the size of the generated magnetic field, and then controls the characteristics of the magnetorheological fluid material to change its formation in the excitation coil and electrode plate
  • the magnitude of the Lorentz force received in the mutually perpendicular electric field, the Lorentz force is exerted on the steering nut rack to achieve the second level of boosting effect.
  • the present invention also proposes an optimization method for a circulating ball type electro-hydraulic steering system based on magnetorheological fluid. Based on the above system, it includes the following steps:
  • the electro-hydraulic steering system model includes a steering wheel model, a circulating ball steering gear model, an electric power assist module model, and a magnetorheological fluid power assist module model;
  • the electro-hydraulic steering system model is:
  • ⁇ m , J m , B m and T m are the rotation angle, rotational inertia, damping coefficient and output assist torque of the assisted motor, respectively
  • L A1 U A1 , I A1 and R A1 are the inductance of the assisted motor armature factor, voltage, current, resistance, K T1, K a, ⁇ 1 were induced voltage coefficient assist motor, scale factor
  • the angular velocity J lg is the moment of inertia of the steering screw, ⁇ lg steering screw angle, B lg steering screw viscous damping coefficient
  • T S is the measured torque of the torque sensor value
  • F b is the axial screw turning work load
  • r a is the center distance of the screw force
  • x m is The displacement of the steering nut rack
  • B lm is the viscosity resistance coefficient of the steering nut rack
  • F lm is the axial force of the nut rack
  • T cs
  • the vehicle dynamics model is:
  • the tire model is:
  • I z is the moment of inertia of the mass of the car on the z-axis
  • ⁇ r is the yaw rate
  • ⁇ is the body roll angle
  • N r , N ⁇ , N ⁇ , and N ⁇ are the unit yaw rate and the center of mass side deviation, respectively
  • Angle, unit roll angle speed, unit front wheel angle to the z-axis moment, u is the longitudinal speed
  • m is the mass of the vehicle
  • I x is the inertia of the suspension mass to the x-axis
  • ⁇ is the lateral angle of the center of mass
  • ⁇ is the front wheel slip angle
  • ⁇ is the front wheel steering angle
  • d is the tread
  • G P is a screw gear ratio to the front wheels
  • h is the centroid of the suspension to the roll axis
  • the multi-objective optimization model of the electro-hydraulic steering system is:
  • f 1 (X) is the energy consumption of the steering system
  • f 2 (X) is the steering feel
  • g 1 (X) is the steering assist range
  • g 2 (X) is the steering sensitivity.
  • the niche multi-objective particle swarm optimization algorithm is used to optimize the optimization variables of the electro-hydraulic steering system, and the optimal solution is obtained according to the optimization algorithm;
  • V i (t+1) V i (t)+c 1 *r 1 *(P best (t)-X i (t))+c 2 *r 2 *(G best (t)-X i ( t)) (1)
  • V i (t) and V i (t+1) are the velocity of particles at time t and t+1 respectively, and X i (t) and X i (t+1) are respectively time t and t
  • the position of the particle at +1, c 1 and c 2 are learning factors, r 1 and r 2 are random numbers between 0 and 1;
  • step 4.3 uses the following formula:
  • F i is the fitness of the individual X i in the external set
  • N s is the number of individuals in the niche
  • S i is the sharing degree of the individual X i
  • f sh (d ij ) is the relationship between the individual X i and the individual X j Sharing function
  • ⁇ is the parameter that controls the shape of the sharing function
  • ⁇ share is the initially specified sharing distance
  • d ij represents the Euclidean distance between the individual X i and the individual X j .
  • step (3) comprises: selecting a steering screw center distance r a, sector gear pitch radius r p, the steering column stiffness K, motor inertia J m, excitation coil turns N, the steering nut effective area A, With the tooth fan rotational inertia J c as the optimization variable, the vector space in the niche multi-objective particle swarm optimization algorithm is a seven-dimensional vector space, and in the initial m particle position vector and velocity vector group, the i particles positions X 'i and the speed vector V' i is expressed as follows:
  • the vector global space corresponding to the optimization variable of the historical global optimal position of the particle represented by G best in steps 4.3 and 4.4 is:

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  • Chemical & Material Sciences (AREA)
  • Combustion & Propulsion (AREA)
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  • Mechanical Engineering (AREA)
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Abstract

一种基于磁流变液的循环球式电液转向系统及其优化方法，系统包括：机械传动模块、电动助力模块、磁流变液助力模块和助力控制模块（ECU）；磁流变液材料（25）置于循环球转向器（7）内的磁流变液空腔（24），励磁线圈（8）置于循环球转向器壳体（18）的外部，励磁线圈（8）通电产生的磁场方向与电极板（12）通电形成的电场方向相互垂直。通过建立电液转向系统优化模型，采用小生境多目标粒子群优化算法进行优化，简化了系统的结构，提高了转向路感的可控性。

Description

一种基于磁流变液的循环球式电液转向系统及其优化方法 技术领域
本发明属于汽车转向系统技术领域，具体涉及一种基于磁流变液的循环球式电液转向系统及其多目标优化方法。
背景技术
磁流变液是一种新型液体材料，当附加在磁流变液上的磁场发生变化时，其表观粘度将随着磁场的改变而改变，从而使得磁流变液可以在流体和类固体之间进行可逆的转变，同时其还具有可控性好、磁导率高、无污染、低能耗等优点。由于磁流变液能根据附加磁场在短时间内产生强大的阻尼力，可以实现传递力矩和改变阻尼的功能，目前在汽车悬架系统、传动系统、制动系统都得到了广泛应用。在汽车转向系统领域，磁流变液目前也有少量应用，例如中国专利申请号为CN201610913543.1，专利名称为“一种车辆转向控制系统”提出了一种汽车转向控制系统利用了磁流变液设计新型离合器，提升了汽车驾驶模式切换时的安全和可靠性；中国专利申请号为CN201110185746.0，专利名称为“线控转向汽车路感模拟执行装置”利用磁流变液阻尼器作为主要的路感模拟执行机构，并通过磁流变液阻尼器控制回正速度，保证方向盘的平稳；中国专利申请号为CN201420522322.8，专利名称为“一种复合式转向横拉杆”公开了一种复合式转向横拉杆，利用磁流变液的物理特性，在汽车爆胎时控制磁流变液黏度从而锁死横拉杆，减小了爆胎带来的危害。
根据磁流变液一系列优秀的特性，在汽车转向系统中其还具有较大的应用空间和价值。电液转向助力系统是一种较新颖的转向助力系统，其结合了电动助力转向系统和电控液压转向助力系统的优点，具有低能耗、经济性好、响应快、助力力矩较大、高速路感较好等优点。但是现有的电液转向系统仍采用传统的液压助力机构，整个系统能耗较高，且结构较为复杂、不便于安装与维护、制造和维修成本也相应的增加、路感与灵敏度之间不够协调。
发明内容
针对于上述现有技术的不足，本发明的目的在于提供一种基于磁流变液的循环球式电液转向系统及其优化方法，解决了传统转向系统中存在的能量浪费较大的问题，本发明利用磁流变液的物理性能实现助力作用，大大简化了系统的结构，同时提高了高速时转向路感的可控性。
为达到上述目的，本发明采用的技术方案如下：
本发明的一种基于磁流变液的循环球式电液转向系统，包括：机械传动模块、电动助力模块、磁流变液助力模块和助力控制模块；
所述的机械传动模块包括方向盘、转向轴、循环球转向器、转向摇臂、转向直拉杆、转向横拉杆、左转向节臂、左梯形臂、左转向节及左侧车轮、右转向节臂、右梯形臂、右转向节、右侧车轮；
所述转向轴的上端与方向盘相连，下端与循环球转向器输入端连接；所述循环球转向器包括转向螺杆、转向螺母齿条、循环球转向器壳体、齿扇以及循环钢球，其中循环钢球放置于转向螺母齿条与转向螺杆之间的密闭管路内；循环球转向器的输出端通过齿扇与转向摇臂的一端连接，转向摇臂的另一端通过转向直拉杆和左转向节臂相连，带动左转向节和左侧车轮偏转；左转向节臂经左梯形臂与转向横拉杆的一端相连；转向横拉杆的另一端与右梯形臂相连，右梯形臂经右转向节臂与右转向节相连，右转向节带动右侧车轮转向；
所述的电动助力模块包括助力电机和助力电机减速机构，所述的助力电机减速机构的输入端与助力电机相连，所述助力电机减速机构的输出端与转向轴相连；
所述的磁流变液助力模块包括磁流变液空腔、磁流变液材料、励磁线圈、电极板；
所述的磁流变液材料置于循环球转向器内的磁流变液空腔；所述的励磁线圈置于循环球转向器壳体的外部，励磁线圈通电产生的磁场方向与电极板通电形成的电场方向相互垂直；
所述的助力控制模块的输入端与转矩传感器、车速传感器、方向盘角位移传感器、位移传感器相连，输出端分别与助力电机、励磁线圈和电极板相连。
进一步地，所述的转矩传感器安装在转向轴上，通过转向轴获取驾驶员输入的转矩并将转矩信号传递给所述助力控制模块；所述的车速传感器安装在车辆上，用于获取车速信号；所述的方向盘角位移传感器安装在方向盘上，用于获得汽车转向时驾驶员输入的方向盘转角信号；所述的位移传感器安装在转向横拉杆上，用于获得转向横拉杆输出的位移信号。
进一步地，所述的循环球转向器为长方体；其中，转向螺母齿条的两端分别设置一个密封绝缘的磁流变液空腔，两个磁流变液空腔内充满磁流变液材料，并通过导液管相互连通。
进一步地，所述电极板的数量为两个，分别沿径向置于所述循环球转向器壳体内的前后两端，电极板的外部设有绝缘层，通电时两个电极板之间产生电场。
进一步地，所述励磁线圈截面为矩形且为完全一致的两对，两对励磁线圈沿轴向对称安装于循环球转向器壳体外部的两侧，每对励磁线圈沿径向置于所述循环球转向器壳体外部的上下两端，励磁线圈中电流方向保持一致且励磁线圈安装平面垂直于电极板安装平面，同一侧上下两个励磁线圈中间使用绝缘材料隔开。
本发明的系统，转向时，驾驶员输入的转矩依次带动方向盘、转向轴转动；助力控制模块(ECU)根据各传感器采集到的信号，输出助力电机控制信号控制助力电机进行助力，助力电机输出的电磁转矩经助力电机减速机构作用在转向轴上，实现第一级转向助力；转向轴带动循环球转向器的转向螺杆运动，转向螺杆推动转向螺母齿条沿轴向运动，转向螺母齿条通过齿扇驱动转向摇臂往复摇动；助力控制模块通过输出励磁线圈控制信号改变励磁线圈中电流大小，调整产生的磁场大小，进而控制磁流变液材料的特性，改变其在励磁线圈和电极板形成的相互垂直的电场中受到的洛伦兹力的大小，洛伦兹力施加在转向螺母齿条上，实现第二级助力效果。
本发明还提出了一种基于磁流变液的循环球式电液转向系统的优化方法，基于上述系统，包含以下步骤：
(1)建立电液转向系统模型、整车动力学模型和轮胎模型；
(2)选取车辆电液转向系统的转向路感、转向灵敏度和转向系统能耗作为性能评价指标；
(3)选取转向螺杆中心距r a、齿扇节圆半径r p、转向柱刚度K、电机转动惯量J m、励磁线圈匝数N、转向螺母有效面积A、齿扇转动惯量J c作为优化变量，以转向路感及转向系统能耗为优化目标，在转向灵敏度和转向助力范围的约束条件下，建立电液转向系统多目标优化模型；
(4)采用小生境多目标粒子群优化算法对电液转向系统的优化变量进行优化，根据优化算法得出最优解。
进一步地，所述的电液转向系统模型包括转向盘模型、循环球转向器模型、电动助力模块模型、磁流变液助力模块模型。
进一步地，所述的步骤(4)中的小生境多目标粒子群优化算法具体步骤如下：
4.1 初始化粒子种群m，随机生成初始位置X 0和初始速度V 0，粒子的初始个体最优位置P best＝X 0，外部集合N s为空，迭代次数t＝0；
4.2 计算每个粒子的目标函数，将非支配解存入外部集合中；
4.3 计算外部集合中每个粒子的适应度，按照联赛选择方法随机选择外部集合中的粒子作为历史全局最优位置G best；
4.4 根据公式(1)和公式(2)更新粒子的位置和速度，并用当前粒子群中的非支配解更新外部集合N s；
V i(t+1)＝V i(t)+c 1*r 1*(P best(t)-X i(t))+c 2*r 2*(G best(t)-X i(t))      (1)
X i(t+1)＝X i(t)+V i(t+1)                 (2)
式中，V i(t)、V i(t+1)分别为t时刻和t+1时刻粒子的速度，X i(t)、X i(t+1)分别为分别为t时刻和t+1时刻粒子的位置，c 1和c 2为学习因子，r 1和r 2为取值在0到1之间的随机数；
4.5 判断外部集合中的粒子数是否超过给定的最大容量，若超过则删除适应度值最小的粒子，否则进行下一步4.6；
4.6 在外部集合中根据变异概率，执行变异操作，搜索新产生的非支配解；
4.7 若满足终止条件，则停止搜索，从外部集合中输出Pareto最优解集，否则转步骤4.3再循环直至结束输出Pareto最优解集。
进一步地，所述步骤4.3中的计算采用如下公式：
Figure PCTCN2019116096-appb-000001
式中：F i为外部集合中个体X i的适应度；N s为小生境内的个体数量；S i为个体X i的共享度；f sh(d ij)为个体X i和个体X j之间的共享函数；α为控制共享函数形状的参数；σ share为初始指定的共享距离；d ij表示个体X i和个体X j之间的欧氏距离。
进一步地，所述步骤(3)具体包括：选取转向螺杆中心距r a、齿扇节圆半径r p、转向柱刚度K、电机转动惯量J m、励磁线圈匝数N、转向螺母有效面积A、齿扇转动惯量J c作为优化变量，则所述的小生境多目标粒子群优化算法中的向量空间为七维向量空间，且在初始的m个粒子的位置向量和速度向量组中，第i个粒子的位置X' i和速度向量V' i表示如下：
Figure PCTCN2019116096-appb-000002
Figure PCTCN2019116096-appb-000003
进一步地，所述4.1和4.4步骤中P best表示的个体最优位置对应优化变量的向量空间为为：
Figure PCTCN2019116096-appb-000004
进一步地，所述4.3和4.4步骤中G best表示的粒子的历史全局最优位置对应优化变量的向量空间为：
Figure PCTCN2019116096-appb-000005
本发明的有益效果：
本发明与现有的电液复合转向系统相比，采用了磁流变液助力模块，大大简化了系统结构，解决了传统液压助力模块中的路感与灵敏度问题，同时利用磁流变液的物理特性有效提高了路感的可控性能。
本发明利用磁流变液与励磁线圈和电极板的结合代替了复杂的液压机构，产生相似助力效果的同时提高了系统的可靠性和可控性。
本发明的优化方法考虑了电液转向系统的多目标耦合，采用小生境多目标粒子群算法，同时对电液转向系统的转向路感、转向灵敏度和能耗进行优化，能够得到综合性能较好的优 化结果。
附图说明
图1为本发明系统的原理结构框图；
图2为本发明循环球转向器的A-A剖面图；
图3为本发明优化方法流程图；
图4为本发明所用算法流程图；
图中：1-方向盘，2-转角传感器，3-转向轴，4-转矩传感器，5-助力电机减速机构，6-助力电机，7-循环球转向器，8-励磁线圈，9-导液管，10-转向螺杆，11-转向螺母齿条，12-电极板，13-左侧车轮，14-左转向节，15-左转向节臂，16-左梯形臂，17-转向横拉杆，18-循环球转向器壳体，19-转向直拉杆，20-转向摇臂，21-齿扇，22-位移传感器，23-循环钢球，24-磁流变液空腔，25-磁流变液材料，26-位移信号，27-励磁线圈控制信号，28-助力电机控制信号，29-转矩信号，30-方向盘转角信号，31-车速信号，32-右侧车轮，33-右转向节，34-右梯形臂，35右转向节臂。
具体实施方式
为了便于本领域技术人员的理解，下面结合实施例与附图对本发明作进一步的说明，实施方式提及的内容并非对本发明的限定。
参照图1、图2所示，本发明的一种基于磁流变液的循环球式电液转向系统，包括：机械传动模块、电动助力模块、磁流变液助力模块和助力控制模块(ECU)。
所述的机械传动模块包括方向盘1、转向轴3、循环球转向器7、转向摇臂20、转向直拉杆19、转向横拉杆17、左转向节臂15、左梯形臂16、左转向节14及左侧车轮13、右转向节臂35、右梯形臂34、右转向节33、右侧车轮32；
所述转向轴3的上端与方向盘1相连，下端与循环球转向器7输入端连接；所述循环球转向器7包括转向螺杆10、转向螺母齿条11、循环球转向器壳体18、齿扇21以及循环钢球23，其中循环钢球23放置于转向螺母齿条11与转向螺杆10之间的密闭管路内；循环球转向器7的输出端通过齿扇21与转向摇臂20的一端连接，转向摇臂20的另一端通过转向直拉杆19和左转向节臂15相连，带动左转向节14和左侧车轮13偏转；左转向节臂15经左梯形臂16与转向横拉杆17的一端相连；转向横拉杆17的另一端与右梯形臂34相连，右梯形臂34经右转向节臂35与右转向节33相连，右转向节33带动右侧车轮32转向；
其中，所述的循环球转向器为长方体；其中，转向螺母齿条11的两端分别设置一个密封绝缘的磁流变液空腔，两个磁流变液空腔内充满磁流变液材料，并通过导液管9相互连通。
此外，所述的循环球转向器壳体18包围转向螺杆10、转向螺母齿条11、循环钢球23和齿扇21。
所述的电动助力模块包括助力电机6和助力电机减速机构5，所述的助力电机减速机构5 的输入端与助力电机6相连，所述助力电机减速机构5的输出端与转向轴3相连；
所述的磁流变液助力模块包括磁流变液空腔24、磁流变液材料25、励磁线圈8、电极板12；
所述的磁流变液材料25置于循环球转向器7内的磁流变液空腔24；所述的励磁线圈8置于循环球转向器壳体18的外部，励磁线圈8通电产生的磁场方向与电极板12通电形成的电场方向相互垂直；
所述的助力控制模块(ECU)的输入端与转矩传感器4、车速传感器、方向盘角位移传感器2、位移传感器22相连，输出端分别与助力电机6、励磁线圈8和电极板12相连。
其中，所述的转矩传感器4安装在转向轴3上，通过转向轴3获取驾驶员输入的转矩并将转矩信号29传递给所述助力控制模块；所述的车速传感器安装在车辆上，用于获取车速信号31；所述的方向盘角位移传感器2安装在方向盘1上，用于获得汽车转向时驾驶员输入的方向盘转角信号30；所述的位移传感器22安装在转向横拉杆17上，用于获得转向横拉杆输出的位移信号26。
其中，所述电极板的数量为两个，分别沿径向置于所述循环球转向器壳体内的前后两端，电极板的外部设有绝缘层，通电时两个电极板之间产生电场。
其中，所述励磁线圈截面为矩形且为完全一致的两对，两对励磁线圈沿轴向对称安装于循环球转向器壳体外部的两侧，每对励磁线圈沿径向置于所述循环球转向器壳体外部的上下两端，励磁线圈中电流方向保持一致且励磁线圈安装平面垂直于电极板安装平面，同一侧上下两个励磁线圈中间使用绝缘材料隔开。
本发明的系统，转向时，驾驶员输入的转矩依次带动方向盘、转向轴转动；助力控制模块根据各传感器采集到的信号，输出助力电机控制信号28控制助力电机进行助力，助力电机输出的电磁转矩经助力电机减速机构作用在转向轴上，实现第一级转向助力；转向轴带动循环球转向器的转向螺杆运动，转向螺杆推动转向螺母齿条沿轴向运动，转向螺母齿条通过齿扇驱动转向摇臂往复摇动；助力控制模块通过输出励磁线圈控制信号27改变励磁线圈中电流大小，调整产生的磁场大小，进而控制磁流变液材料的特性，改变其在励磁线圈和电极板形成的相互垂直的电场中受到的洛伦兹力的大小，洛伦兹力施加在转向螺母齿条上，实现第二级助力效果。
参照图3所示，本发明还提出了一种基于磁流变液的循环球式电液转向系统的优化方法，基于上述系统，包含以下步骤：
(1)建立电液转向系统模型、整车动力学模型和轮胎模型；
所述的电液转向系统模型包括转向盘模型、循环球转向器模型、电动助力模块模型、磁 流变液助力模块模型；
其中，电液转向系统模型为：
Figure PCTCN2019116096-appb-000006
式中，θ m、J m、B m、T m分别为助力电机的转角、转动惯量、阻尼系数、输出助力转矩，L A1 U A1、I A1、R A1分别为助力电机电枢的电感系数、电压、电流、电阻，K T1、K a、ω 1分别为助力电机的电压感应系数、比例系数、角速度，J lg为转向螺杆的转动惯量，θ lg为转向螺杆转角,B lg为转向螺杆的粘性阻尼系数，T S为转矩传感器测得的转矩值,F b为转向螺杆的轴向工作载荷，r a为螺杆力的中心距，m lm为转向螺母的质量，x m为转向螺母齿条的位移，B lm为转向螺母齿条的粘性阻系数，F lm为螺母齿条轴向力，T cs为齿扇转矩，r w为齿扇节圆半径，B cs为齿扇的粘性阻尼系数，θ cs为齿扇转角，T p为等效转向阻力矩，J c为齿扇的转动惯量，F MRF为磁流变液模块所提供的助力；
整车动力学模型为：
Figure PCTCN2019116096-appb-000007
轮胎模型为：
Figure PCTCN2019116096-appb-000008
式中，I z为汽车质量对z轴的转动惯量，ω r为横摆角速度，φ为车身侧倾角，N r、N β、N φ、N δ分别为单位横摆角速度、单位质心侧偏角、单位侧倾角速度、单位前轮转角对z轴的力矩，u为纵向速度，m为整车质量，I x为悬挂质量对x轴的转动惯量，β为质心侧偏角，α为前轮侧偏角，δ为前轮转向角，I xz为悬挂质量对x、z轴的惯性积，d为轮距，G P为螺杆到前轮传动比，h为悬挂质心至侧倾轴线的距离，L p、L φ分别为单位侧倾角速度、单位侧倾角对x轴的外力矩，Y r、Y β、Y φ、Y δ分别为单位横摆角速度、单位整车侧偏角、单位侧倾角、单位前轮转角引起的地面侧向反作用力，k 1为前轮侧偏刚度，E 1为弧度因子。
(2)选取车辆电液转向系统的转向路感、转向灵敏度和转向系统能耗作为性能评价指标；
(3)选取转向螺杆中心距r a、齿扇节圆半径r p、转向柱刚度K、电机转动惯量J m、励磁线圈匝数N、转向螺母有效面积A、齿扇转动惯量J c作为优化变量，以转向路感及转向系统能耗为优化目标，在转向灵敏度和转向助力范围的约束条件下，建立电液转向系统多目标优化模型；
所述的电液转向系统多目标优化模型为：
Figure PCTCN2019116096-appb-000009
式中，f 1(X)为转向系统能耗，f 2(X)为转向路感，g 1(X)为转向助力范围，g 2(X)为转向灵敏度。
(4)采用小生境多目标粒子群优化算法对电液转向系统的优化变量进行优化，根据优化算法得出最优解；
参照图4所示，所述的小生境多目标粒子群优化算法具体步骤如下：
4.1 初始化粒子种群m，随机生成初始位置X 0和初始速度V 0，粒子的初始个体最优位置P best＝X 0，外部集合N s为空，迭代次数t＝0；
4.2 计算每个粒子的目标函数，将非支配解存入外部集合中；
4.3 计算外部集合中每个粒子的适应度，按照联赛选择方法随机选择外部集合中的粒子作为历史全局最优位置G best；
4.4 根据公式(1)和公式(2)更新粒子的位置和速度，并用当前粒子群中的非支配解更新外部集合N s；
V i(t+1)＝V i(t)+c 1*r 1*(P best(t)-X i(t))+c 2*r 2*(G best(t)-X i(t))       (1)
X i(t+1)＝X i(t)+V i(t+1)                   (2)
式中，V i(t)、V i(t+1)分别为t时刻和t+1时刻粒子的速度，X i(t)、X i(t+1)分别为分别为t时刻和t+1时刻粒子的位置，c 1和c 2为学习因子，r 1和r 2为取值在0到1之间的随机数；
4.5 判断外部集合中的粒子数是否超过给定的最大容量，若超过则删除适应度值最小的粒子，否则进行下一步4.6；
4.6 在外部集合中根据变异概率，执行变异操作，搜索新产生的非支配解；
4.7 若满足终止条件，则停止搜索，从外部集合中输出Pareto最优解集，否则转步骤4.3再循环直至结束输出Pareto最优解集。
其中，所述步骤4.3中的计算采用如下公式：
Figure PCTCN2019116096-appb-000010
式中：F i为外部集合中个体X i的适应度；N s为小生境内的个体数量；S i为个体X i的共享度；f sh(d ij)为个体X i和个体X j之间的共享函数；α为控制共享函数形状的参数；σ share为初始指定的共享距离；d ij表示个体X i和个体X j之间的欧氏距离。
其中，所述步骤(3)具体包括：选取转向螺杆中心距r a、齿扇节圆半径r p、转向柱刚度K、电机转动惯量J m、励磁线圈匝数N、转向螺母有效面积A、齿扇转动惯量J c作为优化变量，则所述的小生境多目标粒子群优化算法中的向量空间为七维向量空间，且在初始的m个粒子的位置向量和速度向量组中，第i个粒子的位置X' i和速度向量V' i表示如下：
Figure PCTCN2019116096-appb-000011
Figure PCTCN2019116096-appb-000012
其中，所述4.1和4.4步骤中P best表示的个体最优位置对应优化变量的向量空间为为：
Figure PCTCN2019116096-appb-000013
其中，所述4.3和4.4步骤中G best表示的粒子的历史全局最优位置对应优化变量的向量空间为：
Figure PCTCN2019116096-appb-000014
本发明具体应用途径很多，以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以作出若干改进，这些改进也应视为本发明的保护范围。

Claims (10)

  1. 一种基于磁流变液的循环球式电液转向系统，其特征在于，包括：机械传动模块、电动助力模块、磁流变液助力模块和助力控制模块；
    所述的机械传动模块包括方向盘、转向轴、循环球转向器、转向摇臂、转向直拉杆、转向横拉杆、左转向节臂、左梯形臂、左转向节、左侧车轮、右转向节臂、右梯形臂、右转向节、右侧车轮；
    所述转向轴的上端与方向盘相连，下端与循环球转向器输入端连接；所述循环球转向器包括转向螺杆、转向螺母齿条、循环球转向器壳体、齿扇以及循环钢球，其中循环钢球放置于转向螺母齿条与转向螺杆之间的密闭管路内；循环球转向器的输出端通过齿扇与转向摇臂的一端连接，转向摇臂的另一端通过转向直拉杆和左转向节臂相连，带动左转向节和左侧车轮偏转；左转向节臂经左梯形臂与转向横拉杆的一端相连；转向横拉杆的另一端与右梯形臂相连，右梯形臂经右转向节臂与右转向节相连，右转向节带动右侧车轮转向；
    所述的电动助力模块包括助力电机和助力电机减速机构，所述的助力电机减速机构的输入端与助力电机相连，所述助力电机减速机构的输出端与转向轴相连；
    所述的磁流变液助力模块包括磁流变液空腔、磁流变液材料、励磁线圈、电极板；
    所述的磁流变液材料置于循环球转向器内的磁流变液空腔；所述的励磁线圈置于循环球转向器壳体的外部，励磁线圈通电产生的磁场方向与电极板通电形成的电场方向相互垂直；
    所述的助力控制模块的输入端与转矩传感器、车速传感器、方向盘角位移传感器、位移传感器相连，输出端分别与助力电机、励磁线圈和电极板相连。
  2. 根据权利要求1所述的基于磁流变液的循环球式电液转向系统，其特征在于，所述的转矩传感器安装在转向轴上，通过转向轴获取驾驶员输入的转矩并将转矩信号传递给所述助力控制模块；所述的车速传感器安装在车辆上；所述的方向盘角位移传感器安装在方向盘上；所述的位移传感器安装在转向横拉杆上。
  3. 根据权利要求1所述的基于磁流变液的循环球式电液转向系统，其特征在于，所述的循环球转向器为长方体；其中，转向螺母齿条的两端分别设置一个密封绝缘的磁流变液空腔，两个磁流变液空腔内充满磁流变液材料，并通过导液管相互连通。
  4. 根据权利要求1所述的基于磁流变液的循环球式电液转向系统，其特征在于，所述电极板的数量为两个，分别沿径向置于所述循环球转向器壳体内的前后两端，电极板的外部设有绝缘层，通电时两个电极板之间产生电场。
  5. 根据权利要求1所述的基于磁流变液的循环球式电液转向系统，其特征在于，所述励磁线圈截面为矩形且为完全一致的两对，两对励磁线圈沿轴向对称安装于循环球转向器壳体外部的两侧，每对励磁线圈沿径向置于所述循环球转向器壳体外部的上下两端，励磁线圈中电流方向保持一致且励磁线圈安装平面垂直于电极板安装平面，同一侧上下两个励磁线圈中间使用绝缘材料隔开。
  6. 一种基于磁流变液的循环球式电液转向系统的优化方法，基于上述权利要求1至5中任意一项所述的系统，其特征在于，包含以下步骤：
    (1)建立电液转向系统模型、整车动力学模型和轮胎模型；
    (2)选取车辆电液转向系统的转向路感、转向灵敏度和转向系统能耗作为性能评价指标；
    (3)选取转向螺杆中心距r a、齿扇节圆半径r p、转向柱刚度K、电机转动惯量J m、励磁线圈匝数N、转向螺母有效面积A、齿扇转动惯量J c作为优化变量，以转向路感及转向系统能耗为优化目标，在转向灵敏度和转向助力范围的约束条件下，建立电液转向系统多目标优化模型；
    (4)采用小生境多目标粒子群优化算法对电液转向系统的优化变量进行优化，根据优化算法得出最优解。
  7. 根据权利要求6所述的基于磁流变液的循环球式电液转向系统的优化方法，其特征在于，所述的电液转向系统模型包括转向盘模型、循环球转向器模型、电动助力模块模型、磁流变液助力模块模型。
  8. 根据权利要求6所述的基于磁流变液的循环球式电液转向系统的优化方法，其特征在于，所述的步骤(4)中的小生境多目标粒子群优化算法具体步骤如下：
    4.1初始化粒子种群m，随机生成初始位置X 0和初始速度V 0，粒子的初始个体最优位置P best＝X 0，外部集合N s为空，迭代次数t＝0；
    4.2计算每个粒子的目标函数，将非支配解存入外部集合中；
    4.3计算外部集合中每个粒子的适应度，按照联赛选择方法随机选择外部集合中的粒子作为历史全局最优位置G best；
    4.4根据公式(1)和公式(2)更新粒子的位置和速度，并用当前粒子群中的非支配解更新外部集合N s；
    V i(t+1)＝V i(t)+c 1*r 1*(P best(t)-X i(t))+c 2*r 2*(G best(t)-X i(t))  (1)
    X i(t+1)＝X i(t)+V i(t+1)  (2)
    式中，V i(t)、V i(t+1)分别为t时刻和t+1时刻粒子的速度，X i(t)、X i(t+1)分别为分别为t时刻和t+1时刻粒子的位置，c 1和c 2为学习因子，r 1和r 2为取值在0到1之间的随机数；
    4.5判断外部集合中的粒子数是否超过给定的最大容量，若超过则删除适应度值最小的粒子，否则进行下一步4.6；
    4.6在外部集合中根据变异概率，执行变异操作，搜索新产生的非支配解；
    4.7若满足终止条件，则停止搜索，从外部集合中输出Pareto最优解集，否则转步骤4.3再循环直至结束输出Pareto最优解集。
  9. 根据权利要求8所述的基于磁流变液的循环球式电液转向系统的优化方法，其特征在 于，所述步骤4.3中的计算采用如下公式：
    Figure PCTCN2019116096-appb-100001
    式中：F i为外部集合中个体X i的适应度；N s为小生境内的个体数量；S i为个体X i的共享度；f sh(d ij)为个体X i和个体X j之间的共享函数；α为控制共享函数形状的参数；σ share为初始指定的共享距离；d ij表示个体X i和个体X j之间的欧氏距离。
  10. 根据权利要求6所述的基于磁流变液的循环球式电液转向系统的优化方法，其特征在于，所述步骤(3)具体包括：选取转向螺杆中心距r a、齿扇节圆半径r p、转向柱刚度K、电机转动惯量J m、励磁线圈匝数N、转向螺母有效面积A、齿扇转动惯量J c作为优化变量，则所述的小生境多目标粒子群优化算法中的向量空间为七维向量空间，且在初始的m个粒子的位置向量和速度向量组中，第i个粒子的位置X' i和速度向量V' i表示如下：
    Figure PCTCN2019116096-appb-100002
    Figure PCTCN2019116096-appb-100003
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