Control method for composite transmission type dual-mode electric power steering gear of heavy duty vehicle

Abstract

The invention discloses a heavy duty vehicle composite transmission type dual-mode electric power steering gear control method which comprises the following steps: obtaining a motor target power torque relational expression according to the structure principle of an electric power steering gear; according to an actual measurement test condition, obtaining a characteristic function of a motor target power-assisted torque and hand power of a driver, a vehicle speed and a wheel steering angle; defining piecewise functions of the hand power of the driver under different working conditions of pivot steering, low speed, medium speed and high speed; substituting the hand power piecewise function of the driver into the target power-assisted torque characteristic function of the motor to obtain a key characteristic function calculation basic method of the target power-assisted torque of the motor, the vehicle speed and the wheel steering angle; and obtaining a function relational expression of the target current of the power-assisted motor along with the vehicle speed and the steering wheel torque. According to the scheme, the intelligent power-assisted characteristic function is improved, the power-assisted motor target current formula based on the vehicle speed change is deduced and used for steering gear motor current tracking control, the low-speed controllability and the high-speed stability of the vehicle are optimized, and a driver obtains good road feeling.

Description

Technical Field

[0001] The invention relates to the fields of electromechanical systems and motor vehicle applications, and in particular to a control method for a composite transmission dual-mode electric power steering device for a heavy vehicle. Background Art

[0002] In the automotive industry, with the continuous growth of the number of fuel vehicles, vehicle emissions are increasingly polluting the environment. At the same time, oil, as a non-renewable energy source, is also facing the crisis of depletion. Therefore, low-emission or zero-emission electric large-tonnage commercial vehicles have become the core development direction of today's wheeled vehicle technology due to their advantages of energy saving and environmental protection. Electric power steering technology (EPS) has been widely used in the field of domestic vehicles at home and abroad due to its significant advantages such as high integration, energy saving and high efficiency, but it is mostly used for family cars or passenger cars with steering loads ≤2t, while large-tonnage electric power steering technology suitable for electric buses, heavy trucks, special vehicles, etc. is still in a blank state, with urgent market demand and broad prospects.

[0003] In response to military needs, military wheeled vehicles have heavy single-axle loads, complex road conditions (such as trenches, off-road mountain roads, icy and snowy roads, and muddy roads), and harsh operating conditions. The chassis must not only meet the requirements of high mobility during road marches and operations, but also have good driving stability and off-road safety under extremely harsh road conditions. Among them, the steering system of wheeled vehicles is an important subsystem of the automobile chassis system, and its performance directly affects the vehicle's handling stability, driving comfort and driving safety. At present, the steering system of my country's military wheeled vehicles basically adopts a hydraulic power steering system, and the actuator is a recirculating ball hydraulic power steering gear. Therefore, the vehicle's steering return mainly depends on the steering positioning parameters, such as the kingpin castor angle and the kingpin inclination angle. When the positioning parameter error is large, the vehicle's return ability will become poor and unstable, thereby affecting the vehicle's maneuverability; for example, when the vehicle is driving at high speed, there will be a feeling of "floating" in the steering, that is, the steering assist is too large, which is determined by the principle of the recirculating ball hydraulic power steering gear. The steering pump in the hydraulic power steering system is powered by the engine. At high speed, the engine speed increases, the pressure of the hydraulic power steering system increases, and the steering assist naturally increases. Although the current new steering oil pump can achieve a decrease in oil pump flow pressure relief during high-speed steering, it cannot fundamentally solve the problem of "floating".

[0004] In order to improve the performance of the steering system and meet the driver's requirements for low-speed steering lightness, high-speed steering road feel and fuel economy, the automobile steering system has gone through four development stages: mechanical steering system (MS), hydraulic power steering system (HPS), electronically controlled hydraulic power steering system (EHPS) and electric power steering system (EPS).

[0005] The HPS system uses an engine-driven steering oil pump to provide hydraulic power, and achieves power steering through a steering control valve, solving the problem of excessive driver burden when the mechanical steering system is turning in situ and at low speeds. However, because its power assist effect is only related to the driver's operating force, the power assist characteristics are the same at different vehicle speeds, which can easily lead to "floating" steering when driving at high speeds. It is difficult for the driver to grasp the road feedback information and the steering road feel is poor.

[0006] The EHPS system adds an electronic control system to the HPS system. The electronic control unit adjusts the power assist of the hydraulic power assist system through the added solenoid valve according to the vehicle speed signal, thereby achieving a power assist effect in which the power assist torque changes with the vehicle speed. The EHPS also meets the driver's requirements for the lightness of the car's steering at low speeds and a good road feel at high speeds. However, due to the addition of electronic control units, vehicle speed sensors, solenoid valves, fluid distribution valves and other devices, the structure is more complex and the cost is higher. It is also unable to overcome the inherent defects of the traditional HPS, such as complex process, power assist characteristics affected by engine speed, energy consumption when not steering, easy leakage of hydraulic oil, high requirements for sealing, and frequent maintenance.

[0007] In view of the above problems, the present invention provides a new electric power steering control method, thereby solving various problems faced by the steering of heavy vehicles. Summary of the invention

[0008] The present invention aims at the deficiencies in the prior art and improves the intelligent power-assistance characteristic function, thereby obtaining a control method for a heavy-duty vehicle composite transmission dual-mode electric power steering device to provide a good road feel.

[0009] In order to achieve the above object, the present invention provides a control method for a heavy-duty vehicle compound transmission dual-mode electric power steering device, comprising the following steps: Step 1: According to the structural principle of the electric steering gear, obtain the motor target assist torque relationship; Step 2: According to the actual test results, the characteristic function of the motor target assist torque and the driver's hand force, vehicle speed, and wheel steering angle is obtained; Step 3: Define the piecewise function of the driver's hand force under different working conditions such as in-situ steering, low speed, medium speed and high speed; Step 4: Substitute the driver's hand force piecewise function into the motor target assist torque characteristic function to obtain the basic method for calculating the key characteristic functions of the motor target assist torque, vehicle speed, and wheel steering angle; Step 5: Obtain the functional relationship between the target current of the power-assisting motor and the vehicle speed and steering wheel torque.

[0010] Furthermore, step 1 specifically includes the following steps: Step 1.1: According to the structural principle of the electric steering gear, the transient output torque of the electric steering gear and the motor target assist torque There are the following relationships: ; Step 1.2: Ignore the steering guide mechanism, that is, the energy loss of the steering linkage: ; Step 1.3: From the above two equations, we get ; Where: Motor target assist torque The system calculation output value within the set unit time, the unit is N·m; To assist the primary transmission ratio, it is the system setting value; To assist the secondary transmission ratio, it is the system setting value; To assist the three-stage transmission ratio, it is the system setting value; is the steering gear positive efficiency, which is the system setting value and is between 0 and 1; is the driver's hand force, in N·m; is the steering wheel radius, which is the system setting value and the unit is m; is the transient steering resistance torque, in N·m.

[0011] Furthermore, step 2 specifically includes the following steps: Step 2.1: Decompose the steering resistance torque into the maximum steering resistance torque with speed and the transient steering resistance torque, and collect data from the steering system on the actual vehicle, take the steering angle data, where the steering gear torque is indirectly collected data, that is, collect the steering gear hydraulic power assist pressure value, and calculate it according to the calibrated maximum power assist pressure and maximum output torque; According to the actual vehicle data, the transient maximum steering resistance torque is obtained With speed There are the following relationships: ; According to actual test results, the dynamic load of a vehicle when it maintains straight-line driving on a complex road surface is significantly smaller than the stationary steering resistance torque, which is only about 30% of the stationary steering resistance torque. The value is 0.3; Step 2.2: Due to the transient maximum steering resistance torque Transient steering resistance torque It is approximately a linear relationship, and the relationship is as follows: ; Step 2.3, obtain the relationship: ; Step 2.4: The characteristic function of the motor target assist torque and the driver's hand force, vehicle speed, and wheel steering angle is obtained as follows: ; in: is the in-situ steering resistance torque, which is the system setting value and the unit is N·m; is the coefficient, the value is 0.3; is the outer wheel turning angle of the front axle, in radians; is the maximum steering angle of the wheel, which is the system setting value in radians.

[0012] Furthermore, step 3 defines the driver's hand force Under different working conditions such as in-situ turning, low speed, medium speed and high speed, the piecewise function is as follows: ; in: The minimum force required by the driver to turn the steering wheel, in N·m; The maximum force that the driver will not exceed when turning the steering wheel, in N·m; is the vehicle speed, which is the value collected by the sensor in km / h.

[0013] Furthermore, step 4 is specifically to substitute the driver's hand force piecewise function into the motor target assist torque characteristic function to obtain the basic method for calculating the key characteristic function of the motor target assist torque, vehicle speed, and wheel steering angle: .

[0014] Furthermore, Motor target assist torque , further preferably, the output value within 50ms, in N·m; Power-assisted primary gear ratio , i.e. the transmission ratio of the planetary reducer assembly, preferably 7; Power-assisted secondary transmission ratio , i.e. the transmission ratio of the belt drive assembly, preferably 2.5; Power-assisted three-stage transmission ratio , i.e. the transmission ratio of the steering gear recirculating ball, preferably 24; Steering gear positive efficiency , preferably 0.81; Steering resistance torque , preferably in the range of 1800 to 4000, more preferably 1833, unit N·m; Speed , the preferred range is 0 to 120, unit is km / h; Front axle outer wheel turning angle , the preferred range is -0.54 to 0.54, in radians; Maximum steering angle of wheels , the preferred absolute value is 0.61, in radians; Steering wheel radius , preferably 0.21, unit is m.

[0015] Furthermore, step 5 is specifically as follows: taking into account the accuracy of the motor target current and the computing power of the single-chip computer, mainly considering the influence of the vehicle speed and steering wheel torque on the target current, ignoring the influence of the steering axle load, tire pressure and road adhesion coefficient, and obtaining: ; ; in: is the motor current target value, which is the motor target current calculated by the system, in A; It is the power assist curve function corresponding to different speeds; is the steering wheel torque function; is the steering wheel torque, which is the system design input value, and is further preferably 0 to 12, in N·m; , , , , , is the power assist curve coefficient, further preferably 0.014, 0.00005, -0.01213, 1, -0.00462, 0.6996; , , is the steering wheel torque function coefficient, further preferably 5.2, -72.8, 254.8; When the steering wheel torque is between 0 and 12 N·m, the power assist torque is determined according to the torque value. The moment of inertia, viscous damping coefficient and friction compensation of the steering system and the power assist motor are ignored. Considering the road feel simulation and the continuity of the motor current change, the functional relationship between the power assist motor target current and the vehicle speed and steering wheel torque is obtained as follows: .

[0016] The beneficial effects of this scheme can be known from the description of the above scheme:

[0017] (1) The intelligent power-assist characteristic function is improved. Based on the continuous power-assist curve of road feel and the driver's hand force at low, medium, medium-high and high speeds, the power-assist motor target current formula based on vehicle speed change is derived and used for steering motor current tracking control, which optimizes the vehicle's low-speed maneuverability and high-speed stability, allowing the driver to obtain a good road feel.

[0018] (2) The introduced road feel continuous power assist curve is conducive to reasonably adjusting the size of the steering assist according to the driver's operating habits and the vehicle's driving status. When driving at low speeds, such as moving the car in a parking lot, a large steering assist is provided to enable the driver to easily turn the steering wheel; when driving at high speeds, the assist is reduced to ensure steering stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is the power assist characteristic curve of the motor of the present invention. DETAILED DESCRIPTION

[0020] In order to clearly illustrate the technical features of this solution, this solution is described below through a specific implementation method.

[0021] A control method for a composite transmission dual-mode electric power steering device for a heavy-duty vehicle is provided. An intelligent power-assistance characteristic function is improved in the control system. The EPS power-assistance characteristic refers to the law that the power-assistance torque provided by the motor changes with the vehicle steering driving condition and system parameters, which directly affects the performance of the steering system. The intelligent power-assistance function is a transient target torque value of the steering resistance motor calculated according to the vehicle speed and the steering wheel angle in the transient time domain. According to the driver's hand conditions under different vehicle speeds and different steering angles, the power-assistance motor torque target values ​​under different vehicle speeds and different steering angles are obtained. The method includes the following steps: Step 1: According to the structural principle of the electric steering gear, the transient output torque of the electric steering gear and the motor target assist torque There are the following relationships: ; in: The system calculates the output value, which is the output value per unit time, in N·m; To assist the primary transmission ratio, it is the system setting value; To assist the secondary transmission ratio, it is the system setting value; To assist the three-stage transmission ratio, it is the system setting value; is the steering gear positive efficiency, which is the system setting value and is between 0 and 1; is the driver's hand force, in N·m; is the steering wheel radius, which is the system setting value and the unit is m; Ignoring the steering guide mechanism, that is, the energy loss of the steering linkage, the energy loss is: ; in: is the transient steering resistance torque, in N·m; From the above two formulas, we can get .

[0022] Step 2: Define the driver's hand force by referring to industry standards and empirical data Under different working conditions such as in-situ turning, low speed, medium speed and high speed, the piecewise function is as follows: ; in: The minimum force required by the driver to turn the steering wheel, in N·m; The maximum force that the driver will not exceed when turning the steering wheel, in N·m; is the vehicle speed, which is the value collected by the sensor in km / h.

[0023] Step 3: Decompose the steering resistance torque into the maximum steering resistance torque with speed (i.e., the steering resistance torque at the maximum steering angle at different vehicle speeds) and the transient steering resistance torque (i.e., the steering resistance torque at different vehicle speeds and different steering angles), and collect data from the actual vehicle of the steering system, take the value of 0 steering angle data, as shown in Table 1, where the steering gear torque is indirectly collected data, that is, collect the steering gear hydraulic power assist pressure value, and calculate it according to the calibrated maximum power assist pressure and maximum output torque; Table 1 Dynamic load of a wheeled vehicle traveling in a straight line on a gravel road

[0024] The design value of the stationary resistance torque of this wheeled vehicle is 1833N·m. According to the actual test results, the dynamic load of the vehicle when maintaining straight driving on complex roads is significantly smaller than the stationary steering resistance torque, which is only about 30% of the stationary steering resistance torque. Based on the above-mentioned actual vehicle data, the transient maximum steering resistance torque is obtained. With speed There are the following relationships: ; in: is the in-situ steering resistance torque, which is the system setting value and the unit is N·M; The value is 0.3; The transient steering resistance torque is the steering torque of the vehicle at different speeds and steering angles. Transient steering resistance torque It is approximately a linear relationship, and the relationship is as follows: ; in: is the outer wheel turning angle of the front axle, in radians; is the maximum steering angle of the wheel, which is the system setting value and the unit is radian; So we have: ; The characteristic function of the motor target assist torque and the driver's hand force, vehicle speed, and wheel steering angle is as follows: .

[0025] Step 4: Substitute the characteristic function of step 3 into the piecewise function of step 2 to obtain the basic method for calculating the key characteristic functions of the motor target assist torque, vehicle speed, and wheel steering angle, as shown below: .

[0026] Where: Motor target assist torque The system calculates the output value in N·m, which is the output value per unit time, preferably within 50ms; Electric steering gear primary transmission ratio is the system design value, i.e. the transmission ratio of the planetary reducer assembly, preferably 7; Electric steering gear secondary transmission ratio is the system setting value, i.e. the transmission ratio of the belt assembly, preferably 2.5; Electric steering gear three-stage transmission ratio is the system setting value, i.e. the transmission ratio of the steering gear circulating ball, preferably 24; Steering gear positive efficiency (0-1) is the system setting value, preferably 0.81; Steering resistance torque is the system setting value, in N·m, preferably in the range of 1800 to 4000, more preferably 1833; Speed is the sensor collection value, the unit is km / h, the preferred range is 0 to 120; Front axle outer wheel turning angle , the unit is rad, the preferred range is -0.54 to 0.54; Maximum steering angle of wheels is the design input value, in rad, and the preferred absolute value is 0.61; Steering wheel radius It is the system setting value, in m, and preferably 0.21.

[0027] Step 5: The controller obtains the target current of the motor according to the vehicle speed, steering resistance torque and steering wheel torque, so that the motor assist torque changes with the vehicle speed and steering wheel torque. Therefore, it is very important to obtain the functional relationship between the target current of the assist motor and the vehicle speed and steering wheel torque.

[0028] Taking into account the accuracy of the motor target current and the computing power of the single-chip computer, the influence of vehicle speed and steering wheel torque on the target current is mainly considered, while the influence of steering axle load, tire pressure and road adhesion coefficient is ignored, and the following is obtained: ; ; According to the industry standards and experience of heavy-duty vehicle steering system design, the maximum steering wheel torque is 12N·m. When the steering wheel torque is greater than 12N·m, the motor assists with the maximum torque. When the steering wheel torque is between 0 N·m and 12N·m, the assist torque is determined according to the torque value. The maximum current of the assist motor is 130A. Ignoring the moment of inertia, viscous damping coefficient and friction compensation of the steering system and the assist motor, considering the road feel simulation and the continuity of the motor current change, the three-dimensional characteristic curve of the assist motor target current is obtained as follows: ; in: is the motor current target value, in A, which is the motor target current calculated by the system; It is the power assist curve function corresponding to different speeds; is the steering wheel torque function; is the steering wheel torque, in N·m, which is the system design input value, and is further preferably 0 to 12; , , , , , is the power assist curve coefficient, further preferably 0.014, 0.00005, -0.01213, 1, -0.00462, 0.6996; , , is the steering wheel torque function coefficient, further preferably 5.2, -72.8, 254.8; The motor assist characteristic curve is as follows: Figure 1 As shown, the horizontal axis is the steering wheel torque, and the vertical axis is the motor assist current. There are multiple curves in the figure, corresponding to different vehicle speeds.

[0029] The steering gear device is powered by 24±4VDC, with an overall rated power of 2500W, a maximum output torque of 9000N•m, a maximum input shaft stroke of -720°~720°, dual CAN communication interfaces, and dual working modes of position and power assistance and active return function.

[0030] The communication protocol of the steering device is: using the CAN 2.0B communication protocol. Among the 8 data bytes of the sending frame and the returning frame, 1 byte is used to clearly indicate the working mode of the device, and 2 bytes are used to indicate the angle data. The specific explanation of the communication protocol data bits is shown in Table 2, Table 3 and Table 4:

[0031] Table 2 Transmit frame data bit explanation

[0032] Table 3 Return frame data bit explanation

[0033] Table 4 Explanation of working mode (1 means valid, 0 means invalid)

[0034] It should be noted that those skilled in the art can easily understand that the heavy-duty compound transmission dual-mode electric steering gear involved in the present invention can be applied in the above-mentioned manner in steering systems of different types of wheeled vehicles, whether manned or unmanned.

[0035] Technical features not described in the present invention can be achieved through or by adopting existing technologies and will not be described in detail herein. Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by ordinary technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A control method for a heavy-duty vehicle compound transmission dual-mode electric power steering device, characterized in that: The following steps are involved: Step 1: According to the structural principle of the electric steering gear, obtain the motor target assist torque relationship; Step 2: According to the actual test results, the characteristic function of the motor target assist torque and the driver's hand force, vehicle speed, and wheel steering angle is obtained; Step 3: Define the piecewise function of the driver's hand force under different working conditions such as in-situ steering, low speed, medium speed and high speed; Step 4: Substitute the driver's hand force piecewise function into the motor target assist torque characteristic function to obtain the basic method for calculating the key characteristic functions of the motor target assist torque, vehicle speed, and wheel steering angle; Step 5: Obtain the functional relationship between the target current of the power-assisting motor and the vehicle speed and steering wheel torque.

2. The control method of the heavy-duty vehicle compound transmission dual-mode electric power steering device according to claim 1 is characterized in that: Step 1 specifically includes the following steps: Step 1.1: According to the structural principle of the electric steering gear, the transient output torque of the electric steering gear and the motor target assist torque There are the following relationships: ； Step 1.2: Ignore the steering guide mechanism, that is, the energy loss of the steering linkage: ； Step 1.3: From the above two equations, we get ； Where: Motor target assist torque The system calculation output value within the set unit time, the unit is N·m; To assist the primary transmission ratio, it is the system setting value; To assist the secondary transmission ratio, it is the system setting value; To assist the three-stage transmission ratio, it is the system setting value; is the steering gear positive efficiency, which is the system setting value and is between 0 and 1; is the driver's hand force, in N·m; is the steering wheel radius, which is the system setting value and the unit is m; is the transient steering resistance torque, in N·m.

3. The control method of the heavy-duty vehicle compound transmission dual-mode electric power steering device according to claim 2 is characterized in that: Step 2 specifically includes the following steps: Step 2.1: Decompose the steering resistance torque into the maximum steering resistance torque with speed and the transient steering resistance torque, and collect data from the actual vehicle of the steering system to obtain the zero steering angle data, where the steering gear torque is indirectly collected data, that is, collect the steering gear hydraulic power assist pressure value, and calculate it according to the calibrated maximum power assist pressure and maximum output torque; According to the actual vehicle data, the transient maximum steering resistance torque is obtained With speed There are the following relationships: ； According to actual test results, the dynamic load of a vehicle when it maintains straight-line driving on a complex road surface is significantly smaller than the stationary steering resistance torque, which is only about 30% of the stationary steering resistance torque. The value is 0.3; Step 2.2: Due to the transient maximum steering resistance torque Transient steering resistance torque It is approximately a linear relationship, and the relationship is as follows: ； Step 2.3, obtain the relationship: ； Step 2.4: The characteristic function of the motor target assist torque and the driver's hand force, vehicle speed, and wheel steering angle is obtained as follows: ； in: is the in-situ steering resistance torque, which is the system setting value and the unit is N·m; is the coefficient, the value is 0.3; is the outer wheel turning angle of the front axle, in radians; is the maximum steering angle of the wheel, which is the system setting value in radians.

4. The control method of the heavy-duty vehicle compound transmission dual-mode electric power steering device according to claim 3 is characterized in that: Step 3: Define the driver's hand force Under different working conditions such as in-situ turning, low speed, medium speed and high speed, the piecewise function is as follows: ； in: The minimum force required by the driver to turn the steering wheel, in N·m; The maximum force that the driver will not exceed when turning the steering wheel, in N·m; is the vehicle speed, which is the value collected by the sensor in km / h.

5. The control method of the heavy-duty vehicle compound transmission dual-mode electric power steering device according to claim 4 is characterized in that: Step 4 specifically involves substituting the driver's hand force piecewise function into the motor target assist torque characteristic function to obtain the basic method for calculating the key characteristic functions of the motor target assist torque, vehicle speed, and wheel steering angle: 。 6. The control method of the heavy-duty vehicle compound transmission dual-mode electric power steering device according to claim 5 is characterized in that: Motor target assist torque , further preferably, the output value within 50ms, in N·m; Power-assisted primary gear ratio , i.e. the transmission ratio of the planetary reducer assembly, preferably 7; Power-assisted secondary transmission ratio , i.e. the transmission ratio of the belt drive assembly, preferably 2.5; Power-assisted three-stage transmission ratio , i.e. the transmission ratio of the steering gear recirculating ball, preferably 24; Steering gear positive efficiency , preferably 0.81; Steering resistance torque , preferably in the range of 1800 to 4000, more preferably 1833, unit N·m; Speed , the preferred range is 0 to 120, unit is km / h; Front axle outer wheel turning angle , the preferred range is -0.54 to 0.54, in radians; Maximum steering angle of wheels , the preferred absolute value is 0.61, in radians; Steering wheel radius , preferably 0.21, unit is m.

7. The control method of the heavy-duty vehicle compound transmission dual-mode electric power steering device according to claim 3 is characterized in that: Step 5 is as follows: taking into account the accuracy of the motor target current and the computing power of the MCU, mainly considering the influence of vehicle speed and steering wheel torque on the target current, ignoring the influence of steering axle load, tire pressure and road adhesion coefficient, and obtaining: ； ； in: is the motor current target value, which is the motor target current calculated by the system, in A; It is the power assist curve function corresponding to different speeds; is the steering wheel torque function; is the steering wheel torque, which is the system design input value, and is further preferably 0 to 12, in N·m; , , , , , is the power assist curve coefficient, further preferably 0.014, 0.00005, -0.01213, 1, -0.00462, 0.6996; , , is the steering wheel torque function coefficient, further preferably 5.2, -72.8, 254.8; When the steering wheel torque is between 0 and 12 N·m, the power assist torque is determined according to the torque value. The moment of inertia, viscous damping coefficient and friction compensation of the steering system and the power assist motor are ignored. Considering the road feel simulation and the continuity of the motor current change, the functional relationship between the power assist motor target current and the vehicle speed and steering wheel torque is obtained as follows: 。

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