[Abstract] By analyzing the relationship between the functional requirements of automotive steering systems and the operating principles of their corresponding mechanisms, and based on the characteristics that the tie rods of the steering knuckle arm ultimately drive the steering mechanism in a linear motion, this paper proposes using linear stepper motors to directly drive the left and right tie rods. This results in more direct control, faster dynamic response, and eliminates most mechanical or hydraulic components, making the structure simpler. By utilizing the control characteristics of linear stepper motors, the various control requirements of steering force changing with vehicle speed can be conveniently and fully met, while also improving steering accuracy. Its implementation also helps to improve the cost-effectiveness of high-performance automotive four-wheel steering systems.
I. Analysis of the Functional Requirements of Automobile Steering System and its Corresponding Mechanisms
The performance of a car's steering system largely determines the ease and comfort of vehicle handling, as well as the stability and smoothness of safe driving. It is also a crucial factor in reducing traffic accidents and improving road capacity. With the development of modern automobiles and related technologies, increasingly higher demands are being placed on the functionality of car steering systems. The following analysis, based on the operating principles of its corresponding mechanisms, addresses this issue:
1. The steering wheel operation requires both light and flexible handling, as well as a stable feel.
Because the frictional damping between the tires and the ground increases as vehicle speed decreases during steering, steering with a traditional mechanical steering system without power steering is quite difficult at low speeds. Therefore, power steering systems are now almost universally adopted. The required steering assist decreases as vehicle speed increases. However, at high speeds, the steering wheel requires very little force. To prevent minor disturbances to the steering wheel from causing the car to deviate from its course, to reduce the impact of uneven road surfaces hitting the steering wheels and causing "kickback," and to ensure the steering wheel automatically returns to center at the end of a turn to maintain stable straight-line driving, allowing the driver to maintain appropriate "road feel" during steering, a "counter-assist" effect is desired at high speeds, i.e., appropriately increasing the damping of the steering system.
2. It has high sensitivity to steering and can simplify its structure to reduce energy consumption.
When operating the steering system, the wheels are required to respond quickly so that the vehicle body can turn in time. In addition to minimizing the free travel clearance of each transmission mechanism of the steering system, the power control device used for steering assistance is also required to respond quickly. Currently, the power steering systems used are mainly hydraulic, pneumatic and electric. The first two have disadvantages such as high energy consumption and slow response. Although hydraulic power steering system is currently the most commonly used device in traditional automobiles, with the development of electric vehicles and according to the characteristics of various related controls [1] , it is more appropriate to use electronic control electric power steering system (EPS). Since the hydraulic power steering system eliminates the need for a constantly running oil pump, oil tank, pipeline, etc., the motor is only connected to the power supply to rotate when steering is required, which reduces energy consumption and makes the structure compact and reduces the vehicle weight. There is no need to replenish oil or worry about oil leakage, making the work more reliable. This is especially suitable for pure electric vehicles with limited onboard energy. The existing electric power steering system EPS uses a rotary motor, which requires electromagnetic clutch, gear reduction transmission and other mechanical mechanisms. It also has disadvantages such as complex mechanism, large space occupation and slow response speed. Given that the steering mechanism ultimately drives the tie rods of the steering knuckle arm in linear motion, this paper proposes to use linear stepper motors to directly drive the left and right tie rods, making the control more direct and the dynamic response faster.
3. The motion pattern of the steering wheels must be correct and stable.
That is, the deflection angles of the inner and outer steering wheels and the differential ratio of the driving wheels are required to be correct and stable. The ratio of the two should always maintain a certain relationship with the steering wheel angle to ensure that each wheel only rolls and does not slip when turning. By analyzing the motion process of the inner and outer steering wheels and driving wheels when the car turns, in order to ensure that each wheel only rolls and does not slip, all four wheels should rotate around the same center. Let L be the car wheelbase, B be the car track, and α and β be the deflection angles of the outer and inner steering wheels, respectively. Then the condition for the wheels to roll purely is: . This shows that the deflection angle α of the outer steering wheel must be less than the deflection angle β of the inner steering wheel, and at the same time, the inner and outer driving wheels must also meet the corresponding differential conditions [2] . In order to meet the deflection angle requirements of the inner and outer steering wheels, the left and right tie rods of the steering mechanism and the steering knuckle arm should form a trapezoidal relationship with the corresponding angle, i.e., a non-parallelogram relationship. This is also the basic method commonly used in various steering systems. In order to meet the differential requirements of the driving wheels, there are two types: mechanical differential and electronic differential. Mechanical differentials are a common method used in traditional automobiles, and their mechanisms are large and complex. Electronic differential systems (EDS), on the other hand, are implemented using electronic control and have many advantages. With the development of electric vehicles, especially the application of in-wheel motors, it will be the future direction for differential control of automotive drive wheels.
4. Possesses corresponding safety and reliability.
When a car is involved in a collision, the steering wheel and other related devices should be able to mitigate or prevent injury to the driver. Furthermore, if the power steering system fails or malfunctions, it should still allow for manual steering.
5. Minimize the turning radius and improve stability during high-speed cornering.
To reduce the turning radius at low speeds, facilitate parking at low speeds or driving through narrow passages, and improve driving stability at high speeds or under crosswinds, high-performance four-wheel steering [2] is required.
Based on the above analysis, and considering that the tie rods of the steering knuckle arm ultimately drive the steering mechanism in linear motion, two automotive steering system control mechanisms are proposed here, using linear stepper motors to directly drive the left and right tie rods, in order to improve the rapid response of the steering system and meet the functional requirements of providing corresponding power assistance at different vehicle speeds. To explain the structural principle of this steering system, a necessary explanation of the linear control motor is required first.
II. Introduction to Linear Control Motors
The so-called linear motor is actually a rotary motor that is split and straightened along the radial direction. It is a thrust device that directly converts electrical energy into linear mechanical motion. In terms of control theory, the use of linear motors in linear displacement mechanisms will make control more direct and dynamic response faster. Furthermore, by eliminating many mechanical transmission parts, the mechanical structure is simpler, eliminating mechanical backlash, which is beneficial to improving accuracy, transmission stiffness, energy conversion efficiency, and reducing noise. In order to improve the control accuracy and fast response of CNC servo systems, the author proposed an invention patent for a CNC servo device driven by a constant temperature linear motor as early as 1986 [3] . More than ten years later, various ultra-high speed precision CNC machine tools driven by linear motors [4] began to emerge one after another. For example, they were exhibited at the 1996 Chicago International Manufacturing Technology Exhibition (IMTS-96'). Experts in the industry around the world called this type of machine tool "the next generation of new machine tools".
In terms of working principle, linear motors are similar to rotary motors, also including DC, AC, stepper, and permanent magnet types. Structurally, they come in various forms such as moving-coil, moving-iron, flat-plate, and cylindrical, meaning linear motors can evolve into more types than rotary motors. Applications range from large-scale projects like maglev trains and linear pile drivers to smaller applications like remote-controlled electric curtains and plotter displacement mechanisms, spanning a wide range of technological fields. Furthermore, the motor's structural form can be selected to best suit the needs of the application. With the continuous development and improvement of modern direct torque control technology, mechatronics, and related technologies, the application fields of linear motors will become increasingly widespread. The cross-fertilization, integration, and fusion of multiple technologies in a specific field is one of the important trends in contemporary technological development.
Figure 1 shows a schematic diagram of a three-phase linear stepper motor. The moving and stationary components of the linear motor are equivalent to the rotor and stator of a rotary motor. Both the moving and stationary components have toothed slots as shown in the figure, and are formed by stamping and stacking silicon steel sheets. The tooth pitch of the moving and stationary components must satisfy a certain relationship. Let the number of phases of the motor be m, and the tooth pitch of the moving component be b, then the tooth pitch of the stationary component p = (k + 1/m)b, where k is any positive integer. For the convenience of the motor winding leads, it is usually made as a moving iron type, that is, the component with the winding coil is the stationary component, which is fixed to the motor housing, while the moving component can be fixed vertically by a linear rolling guide, allowing it to move horizontally, or it can be directly connected to the mechanical component being driven for linear displacement. The motor's shape can be made into various forms such as a rectangle or cylinder, depending on the needs. The stepper motor operates according to the principle of variable reluctance, that is, it follows the "principle of minimum reluctance"—magnetic flux always closes along the path of least reluctance. When the moving component is positioned relative to the stationary component as shown in the diagram, energizing phase A winding will cause the magnetic field force generated by the phase A poles to reduce the magnetic circuit resistance, thus exerting a magnetic pull force to the right on the moving component. This forces the salient pole teeth of the moving component to align with the salient pole teeth of phase A as much as possible. Consequently, the moving component moves to the right by 1/3 of the moving component tooth pitch b (i.e., the position where phase C aligns with the moving component teeth in the diagram). If the three-phase windings A→B→C are energized sequentially, the moving component will shift to the right; while if the energizing sequence is B→A→C, the moving component will shift to the left. The smaller the tooth pitch of the moving component is made according to the manufacturing process and precision, the smaller the displacement (pulse equivalent) per pulse will be. The above describes the three-phase single three-step energizing method. In actual use, a three-phase six-step or three-phase double three-step energizing method is generally used. The energizing sequence of the three-phase six-step method is: A→AB→B→BC→C→CA→A; the energizing sequence of the three-phase double three-step method is: AB→BC→CA→AB. The pulse equivalent of the three-phase six-step method is half that of the three-phase three-step method.
III. Structural Principle of Automobile Steering System Controlled by Linear Stepper Motor
The steering system controlled by a linear stepper motor is a further improvement on the aforementioned electronic power steering system EPS [1]. That is, the linear stepper motor replaces the rotary motor used by the EPS to assist the rack in the steering gear, eliminating the electromagnetic clutch, reduction mechanism and its transmission components, making its structure more compact, control more direct and response faster. In order to facilitate the implementation of high-performance four-wheel steering (4WS) mechanism, two structures are proposed here: the system controlled by the linear stepper motor can be used in the front wheel steering mechanism of the traditional two-wheel steering (2WS) system or four-wheel steering (4WS); the system controlled by the linear stepper motor is mainly used in the rear wheel steering mechanism of four-wheel steering. The details are as follows:
1. Automotive steering system that uses a linear stepper motor to control power steering.
As shown in Figure 2, the moving part of its linear stepper motor is directly connected to the steering rack. The entire linear stepper motor is mounted on the steering rack mechanism, taking up almost no space. It is also a linear stepper motor added to the original simplest unassisted mechanical steering system. The linear thrust of the linear stepper motor directly assists the driver's steering torque. Since the assistance to the steering gear is not very large and the linear displacement of the rack is not long, a small linear stepper motor is sufficient to drive it. Its control principle is basically the same as that of EPS, except that the motor drive needs to be changed to the aforementioned stepper motor pulse distribution method. For specific implementation, refer to the electronic controller ECU and its control logic in the relevant EPS [1] , and use the relevant sensors in EPS. That is, control the displacement of the linear stepper motor according to the steering wheel angle signal, use the steering wheel angle signal to realize closed-loop control, accurately control its displacement, and provide corresponding assistance according to the vehicle speed. At low speeds, a large amount of steering assistance is provided, which decreases as the vehicle speed increases, and stops when the vehicle speed reaches a certain range. However, at high speeds, a "reverse" assistance to the steering system is desired, i.e., an appropriate increase in steering system damping. This is difficult to achieve with existing steering systems, but it is easily accomplished using a linear stepper motor. According to the working principle of a linear stepper motor, simply keeping the motor energized provides a certain self-locking force to the linear displacement device, and controlling the magnitude of the current changes the magnetic pull between the stationary and moving parts. Therefore, the amount of steering assistance can be controlled according to the vehicle speed signal. As the vehicle speed increases, the winding current decreases, and the steering assistance decreases accordingly. When the vehicle speed exceeds a certain threshold (generally 30 km/h), steering assistance is canceled, i.e., power to the linear stepper motor is stopped. When the vehicle speed reaches a certain level, it is desirable to gradually increase the damping of the steering system. This allows the linear stepper motor windings to remain energized, generating a self-locking force, and controlling the current changes the damping of the steering system. This achieves a steering wheel operation that is both light and responsive, as well as stable and reliable.
2. Automotive steering system that uses a linear stepper motor to control steering force.
As shown in Figure 3, this design further simplifies the steering system structure by eliminating all transmission chains between the steering wheel and the tie rods, including the gear input shaft torsion bar and rack and pinion. A steering wheel angle sensor is installed inside the steering wheel, with appropriately increased rotational damping, and is independently located in the driver's cab. The moving parts of the linear stepper motor are directly connected to the left and right tie rods. The electronic controller controls the left and right displacement of the linear stepper motor moving parts based on the steering angle signal and vehicle speed signal, transmitting the force through the tie rods and steering knuckle arms to control wheel steering. While ensuring system reliability, this design offers advantages such as simpler structure, smaller footprint, lower cost, more direct control, and faster response. However, if the system malfunctions, the car will be unable to steer. It is the preferred solution for the rear-wheel steering mechanism in a four-wheel steering (4WS) system. Its application is expected to further improve the cost-effectiveness of automotive four-wheel steering (4WS) systems.
