Characteristics investigation and verification of permanent magnet slip coupling for hydraulic power steering application

Abstract

Permanent magnet slip coupling (PMSC) is a kind of contactless transmission device with the advantages of clutch function, continuous speed regulation and no mechanical wear. The PMSC was introduced into the hydraulic power steering system (HPS) to regulate the steering pump speed so as to improve the steering stability and reduce the energy consumption. To evaluate the designed PMSC electromagnetic characteristics and dynamic characteristics of the PMSC were investigated and verified. Two-dimensional finite element model of the PMSC was built to investigate the electromagnetic characteristics. The simulation results of induced electromotive force, induced current and electromagnetic torque demonstrated that the PMSC had excellent electromagnetic characteristics. The speed regulation circuit of the PMSC was developed to investigate the dynamic characteristics. The results indicated that the PMSC had excellent dynamic characteristics under the condition of high load, inferior dynamic characteristics under the condition of low load. The bench tests were carried out to verify electromagnetic characteristics and dynamic characteristics of the PMSC. It can be seen that the test results of the induced electromotive force and output speed of the PMSC were in consistent with the simulation results. The real vehicle tests were conducted and the results demonstrated that the permanent magnet coupling based electronically controlled hydraulic power steering system (P-ECHPS) greatly improved low-speed steering maneuverability and high-speed steering stability of heavy-duty vehicles.

Keywords

Permanent magnet slip coupling electromagnetic characteristics dynamic characteristics hydraulic power steering speed regulation circuit

1. Introduction

Although the electric power steering system (EPS) has been widely used in lightweight vehicles for its advantages of safety, energy saving and environment protection, there are some limitations for the application of EPS in heavy-duty vehicles, among which the existing vehicle power supply system in unable to provide enough steering assist power especially under the condition of pivot steering or low-speed steering because of high load on the front axis [1,2]. Recently, the heavy-duty vehicle is equipped with the hydraulic power steering system (HPS) due to the high level of assist steering torque and low cost [3]. However, HPS obviously has two disadvantages. One is the invariable assist characteristic independent of vehicle speed so that it cannot ensure low-speed steering portability and high-speed steering road feel [4]. The other is the considerable energy loss of overall hydraulic power steering system. Therein, the overflow loss of the steering pump is responsible for most of the loss [5]. For the above problems, one solution is that the variable displacement pump is employed instead of constant displacement pump to decrease the overflow loss [6], but it cannot realize variable assist characteristics. The traditional way to realize variable assist characteristics is by reducing the flow to the rotary valve at high speed, which could be regulated by means of electronically variable orifice in steering pump instead of the fixed flow orifice [7], and electronically controlled bypass valve in parallel with the rotary valve [8]. Based on the above analysis, the feasible approach to completely resolve the problems of HPS is making the steering pump run at appropriate rotation speed independent of the engine to output on-demand flow of hydraulic oil according to different driving conditions. Generally, the steering pump is fix-mounted on the engine to directly obtain steering power from the engine. It is reported that the mechanical coupling [9,10], the hydraulic coupling [11] and the magnetic coupling [12] integrated between the engine and the steering pump are used to regulate rotation speed of the steering pump according to vehicle speed and steering velocity. The magnetic coupling is more reliable and feasible than the mechanical coupling and the hydraulic coupling because of no mechanical wear and oil pollution [13–15].

Magnetic couplings are classified as the electromagnetic coupling [16–18] and the permanent magnetic coupling [19–21] according to different ways of excitation. The electromagnetic coupling regulates rotation speed of mechanical load by excitation current so that it consumes considerable electric energy [22], while the permanent magnetic coupling adjusts rotation speed of mechanical load by varying length or area of the air gap between the permanent magnet disc and the conductor plate via a mechanism [23,24] which is more complicated. Compared with the electromagnetic coupling, the permanent magnet coupling has higher power density and better dynamic performance [25]. Either electromagnetic coupling or permanent magnetic coupling transmits torque through the interaction between excitation magnetic field and induction magnetic field generated by induced current in the conductor plate [26,27]. Due to the induced current, the slip energy, that is energy difference between the input and output terminals, dissipates as heat, which results in low efficiency especially under large-slip conditions [28].

A new type of permanent magnet coupling called permanent magnet slip coupling (PMSC) is developed in this paper. To improve transmission efficiency of PMSC, the induced current is conducted out of the armature by three-phase windings. During the slip energy recycle, the induced current is adjusted to realize rotation speed regulation of mechanical load. This work is concerned with characteristics investigation and verification of PMSC. In this paper, the configuration and working principle of PMSC and permanent magnet coupling based electronically controlled hydraulic power steering (P-ECHPS) system was presented firstly. Then the analysis of electromagnetic characteristics was carried out based on finite element model of PMSC to evaluate the design of PMSC. The speed regulation control circuit of PMSC was designed and the dynamic characteristics were analyzed. The bench tests of PMSC were carried out to verify the rationality of the finite element model and the speed regulation circuit. Finally, the real vehicle tests were carried out to evaluate handing stability of the coach which is equipped with P-ECHPS system.

2. Mechanical structure and working principle

2.1. Mechanical structure

It can be found in Fig. 1 that the PMSC is consisted of the outer rotor, the inner rotor and the speed regulation circuit. The outer rotor is embedded with three-phase windings which are connected to the speed regulation circuit via slip rings and brushes. Several pairs of permanent magnets are pasted on the surface of the inner rotor to excite magnetic field. The outer rotor as the input terminal is connected to the engine by the driving shaft, and the inner rotor as the output terminal is connected to the steering pump by the driven shaft. The speed regulation circuit is used to control rotation speed of the inner rotor and recycle the slip energy.

Fig. 1.

Schematic diagram of PMSC.

2.2. Working principle

A constant air gap magnetic field is established by the permanent magnets in the inner rotor of PMSC. When the outer rotor is driven by the engine, the three-phase windings will cut the air gap magnetic field and induce three-phase alternating current which excites the induction magnetic field. Due to the interaction between the induction magnetic field and the air gap magnetic field, electromagnetic torque is generated and the inner rotor rotates along with outer rotor in asynchronous speed. Electromagnetic torque is determined by the strength of the air gap magnetic field and rotation speed difference between the inner rotor and the outer rotor. The speed regulation circuit converts induced alternating current into direct current to charge the super capacitor for slip energy recovery.

3. Finite element model and electromagnetic characteristics

3.1. Finite element model

For hydraulic power steering application, the PMSC was designed according to the requirements of speed regulation and torque transmission. Fractional-slot structure with 16 poles and 18 slots was adopted in the PMSC, which can effectively reduce the cogging torque and torque ripple [29]. The double short pitch concentrated windings were also chosen to improve waveform of the electromotive force and magnetomotive force [30]. Permanent magnets were mounted on the surface of the inner rotor to effectively reduce the leakage coefficient and obtain higher sinusoidal waveform of flux density [31]. The basic parameters of the PMSC are shown in Table 1.

Two-dimensional finite element model of PMSC was built in Ansoft as shown in Fig. 2 ignoring demagnetization effect of permanent magnet, the magnetic flux leakage, iron core hysteresis and eddy current loss.

Table 1
Parameters of PMSC

Parameter Value Parameter Value

Outside diameter of outer rotor D1/mm 180 Permanent magnet thickness h/mm 3.6

Inside diameter of outer rotor D2/mm 100 Pole-arc coefficient 0.8

Inside diameter of inner rotor D3/mm 40 Ferrite magnetic materials N35-UH

Axial length l/mm 100 Material of iron core DW465-50

Minimum air gap/mm 0.6 Conductor number per slot 60

Parameter	Value	Parameter	Value
Outside diameter of outer rotor D1/mm	180	Permanent magnet thickness h/mm	3.6
Inside diameter of outer rotor D2/mm	100	Pole-arc coefficient	0.8
Inside diameter of inner rotor D3/mm	40	Ferrite magnetic materials	N35-UH
Axial length l/mm	100	Material of iron core	DW465-50
Minimum air gap/mm	0.6	Conductor number per slot	60

Fig. 2.

Finite element model of PMSC.

3.2. Electromagnetic characteristics

3.2.1. No-load condition

The simulation under the no-load condition was carried out to check the sinusoidal degree of back EMF waveform in outer rotor winding of the PMSC. In general, higher sinusoidal degree of back EMF waveform indicates smaller torque ripple.

The simulation results of back EMF and its Fourier decomposition are presented in Fig. 3 and Fig. 4 when the slip rotation speed is 200 rpm. It can be seen from Fig. 3 that the waveform of back EMF is near-sinusoidal. It shows that amplitude of the fundamental component is about 29 V and amplitudes of the harmonic components are so small, among which the amplitude of the third order harmonic component is the biggest and the amplitude is only about 4 V. The total harmonic distortion is low, which is conducive to the torque transmission. Due to the fractional-slot concentrated windings, fractional harmonic appears and the denominator of fractional harmonic is 4, the same as the number of pole-pairs.

Fig. 3.

Waveform of back EMF.

Fig. 4.

Fourier decomposition of back EMF.

3.2.2. Full load condition

With the requirement of the maximum power of the P-ECHPS system being considered, the rotation speed of the outer rotor was set as 700 rpm, the initial rotation speed of the inner rotor was 300 rpm and the mechanical load was 40.39 N ⋅ m.

The simulation result of three-phase induced current in Fig. 5(a) shows that the waveform of the three-phase induced current in outer rotor windings is near-sinusoidal and the effective values of the induced current of the A-phase, B-phase and C-phase windings are 11.7599 A, 11.7658 A and 11.7608 A respectively. The simulation result of electromagnetic torque in Fig. 5(b) shows that the absolute values of electromagnetic torque on the inner rotor and outer rotor are almost equal, the electromagnetic torque reaches the steady-state value of 40.39 N ⋅ m in the time of 50 ms, and the torque fluctuation is less than 2 N ⋅ m, which verifies the rationality of the PMSC in structural design. The simulation result of the inner rotor speed in Fig. 5(c) shows that rotation speed of the inner rotor reaches steady-state value of 646 rpm at a very fast rate and the speed fluctuation is less than 10 rpm which demonstrates good steady and transient performance of the PMSC.

Fig. 5.

Simulation results under full load condition.

4. Speed regulation circuit and dynamic characteristics

4.1. Speed regulation circuit

The air gap magnetic field of the PMSC is unable to be varied by altering the excitation current just like electromagnetic slip coupling. Therefore, the speed regulation circuit is used to regulate rotation speed of PMSC. The DC chopper speed regulation system based on fully-controlled power switch devices by PWM modulation technique has the advantages of fast response, strong anti-interference ability and wide range of speed regulation [32]. Therefore, the speed regulation circuit with DC chopper was adopted to control rotation speed of the PMSC in this paper. The schematic of speed regulation circuit is shown in Fig. 6. The PWM control was conducted by PID algorithm as shown in Fig. 7.

Fig. 6.

Schematic of speed regulation circuit.

The speed regulation circuit includes the three-phase bridge rectifier, the DC-DC booster. The three-phase bridge rectifier is linked with the three-phase windings of the PMSC to convert alternating current to direct current. The DC-DC booster is consisted of the inductance L, the switching device, the diode D and the filter capacitor C. IGBT is chosen as the switching device due to its high input impedance and low conduction resistance. The direct current Id after rectification can be adjusted by the duty cycle of IGBT by PWM modulation and the current in three-phase windings varies synchronously. Thus the output torque of the PMSC and the rotation speed of the inner rotor can be regulated. When the duty cycle turns large the output torque and output speed increases. On the contrary, when the duty cycle turns small the output torque and output speed decreases. The direct current after the boost is used to charge the battery or supply power for other vehicle electric appliances.

Fig. 7.

Control strategy of the PMSC.

4.2. Dynamic characteristics

Dynamic characteristics of the PMSC were investigated under the condition of high load and small slip and the condition of low load and large slip respectively, which are corresponding to the condition of pivot steering and the condition of straight driving respectively. Under the condition of high load and small slip, the input speed of the PMSC was set as 700 rpm corresponding to the idle speed of the engine, and the high-load torque was set as 40.39 N ⋅ m. Under the condition of low load and large slip, the input speed of the PMSC was set as 1800 rpm corresponding to the high speed of the engine, and the low-load torque was set as 3.75 N ⋅ m.

The result of the PMSC output speed under the high-load condition is shown in Fig. 8(a). Within the time of 0–150 ms, the PMSC output speed is about 635 rpm, and the speed fluctuation is less than 10 rpm when the duty cycle is set as 1. Within the time of 150–300 ms, the PMSC output speed is about 452 rpm, and the speed fluctuation is less than 2 rpm when the duty cycle is 0.94. Within 300–450 ms, the PMSC output speed is about 307 rpm, and the speed fluctuation is less than 8 rpm when the duty cycle is 0.89. When the duty cycle decreased to about 0.79, the PMSC is unable to drive the load, and the inner rotor stops running. In terms of dynamic response, the output speed of the PMSC increases from the initial speed of 300 rpm up to 635 rpm only in the time of 0.05 s, the output speed of the PMSC decreases from 635 rpm down to 452 rpm in the time of 0.04 s, then the output speed of the PMSC decreases from 452 rpm down to 307 rpm in the time of 0.07 s. The result indicates that the PMSC has excellent dynamic performance under the condition of high load.

The result of the PMSC output speed under the low-load condition is shown in Fig. 8(b). Within the time of 0–1.6 s, the steady output speed of the PMSC is about 300 rpm, and the speed fluctuation is less than 5 rpm when the duty cycle is set as 0.05. Within the time of 1.6–3.2 s, the steady output speed of the PMSC is about 400 rpm, and the speed fluctuation is less than 3 rpm when the duty cycle is set as 0.06. In terms of dynamic response, the output speed of the PMSC decreases from the initial speed of 600 rpm down to 300 rpm in the time of 0.5 s, then the output speed of the PMSC increases from 300 rpm up to 400 rpm in the time of 0.4 s, which indicates that the PMSC has poor dynamic performance under the condition of low load. Even though it takes 0.5 s that the output speed of the PMSC decreases from 600 rpm down to 300 rpm, it also meets the response requirement of the P-ECHPS.

Fig. 8.

The simulation result of the PMSC output speed.

5. Bench tests of PMSC characteristics

The PMSC prototype with speed regulation circuit and the test bench were developed to verify electromagnetic and dynamic characteristics of the PMSC as shown in Fig. 9. The test bench is consisted of variable-frequency motor, torque-speed transducer, PMSC prototype, magnetic powder dynamometer and control cabinet as shown in Fig. 9(a).

The speed regulation circuit is consisted of current transducer, three-phase bridge rectifier, IGBT, capacitor, controller, resistor, switching power supply in Fig. 9(b). The current transducer is used to detect current in the three-phase windings before the rectification. Due to the inductance of the three-phase windings the additional inductance is not needed in the DC-DC booster. The diode of the DC-DC booster is integrated inside the IGBT. Capacitance of the capacitor is 8 μF. The resistor in parallel with the capacitor is simulated as the vehicle electric appliance to recycle slip energy of the PMSC. The controller is used to realize closed-loop control of the PMSC output speed. The switching power supply is used to supply electric power for the current transducer and the controller.

Fig. 9.

Test system of the PMSC.

5.1. No-load test

No-load test was implemented under the condition of no electrical load and no mechanical load. No electrical load means that three-phase windings in the outer rotor of the PMSC are open. No mechanical load means that the dynamometer doesn’t applies load torque on the inner rotor of the PMSC.

Rotation speed of the variable-frequency motor was set as 200 rpm by the control cabinet. The induced electromotive force in the three-phase windings was generated. Due to open circuit of the three-phase windings in the outer rotor there was no induced current in the three-phase winding, so that the inner rotor was unable to be driven and the slip speed was 200 rpm.

The induced electromotive force in one of three-phase windings was measured by oscilloscope as shown in Fig. 10. From the figure, it can be seen that the waveform of induced electromotive force is near-sinusoidal which indicates that the developed PMSC prototype meets the design requirements. The amplitude of induced electromotive force is about 24 V which is basically consistent with the simulation result.

Fig. 10.

Induced electromotive force in one of three-phase windings.

During the test, as the slip speed gradually raised from 0 up to 1500 rpm, the induced electromotive force also increased. The relationship of RMS of induced electromotive force and slip speed is shown as Fig. 11 which means back EMF coefficient. It can be seen in the figure that the RMS of induced electromotive force is linear with slip speed, which is conducive to close-loop control of output speed of the PMSC.

Fig. 11.

Relation curve of induced electromotive force and slip speed.

5.2. Speed regulation test

Under the high-load condition, the variable-frequency motor speed was set as 700 rpm, and the load torque was set as 40.39 N ⋅ m. When the duty cycle varied from 0 to 1, output speed of the PMSC was recorded simultaneously. The relationship between the duty cycle and output speed of PMSC was presented under this condition, as shown in Fig. 12. From the figure, it can be seen that when the duty cycle reaches 0.8 the inner rotor starts to rotate, and the output speed increases linearly with the duty cycle. Compared with the simulation result, output speed of the PMSC prototype is a little less than output speed in the simulation when the duty cycle is 1, 0.94 and 0.89 respectively, which results from mechanical friction loss of the prototype and the test bench.

Fig. 12.

Relationship between output speed and duty cycle under the high-load condition.

Under the low-load condition, the variable-frequency motor speed was set as 1500 rpm, and the load torque was set as 3.75 N ⋅ m. The relationship between the duty cycle and the output speed of PMSC was presented under this condition, as shown in Fig. 13. From the figure, one can see that when the duty cycle is very little, the inner rotor begins to rotate, and the output speed increases linearly with the duty cycle.

Fig. 13.

Relationship between output speed and duty cycle under the condition of low load.

5.3. Dynamic response test

The PMSC is applied to regulate the rotation speed of the steering pump in the P-ECHPS system to realize low-speed steering portability and high-speed handling stability. Based on the variable assist characteristics, the rotation speed of the steering pump varies between 300 rpm and 600 rpm. When the vehicle is under the condition of low-speed steering, the rotation speed of the steering pump is 600 rpm and the driven torque of the steering pump is 40.39 N ⋅ m which corresponds to high load of the PMSC. Under the condition of none steering, the rotation speed of the steering pump is 300 rpm and the driven torque of the steering pump is 3.75 N ⋅ m corresponding to low load of the PMSC. To ensure steering agility, the response time must be less than 0.5 s when the rotation speed of the steering pump rises from 300 rpm to 600 rpm. To improve energy efficiency, the response time should be less than 1 s when the rotation speed of the steering pump drops from 600 rpm to 300 rpm.

Under the high-load condition, the initial speed of the PMSC was set as 300 rpm, and the target speed was set as 600 rpm. The actual speed of the PMSC was controlled to track the target value by the speed regulation circuit. The test result of the PMSC output speed is presented in Fig. 14. From the figure, it can be seen that output speed of the PMSC reaches to the steady value of 600 rpm within 0.25 s which is much less than the required time of 0.5 s. Compared with the simulation results, the growth trend of the output speed is consistent. It’s worth mentioning that the rise time is more than that in the simulation, which is due to mechanical friction loss of the prototype and the test bench.

Under the low-load condition, the initial speed of the PMSC was set as 600 rpm, and the target speed was set as 300 rpm. The actual speed of the PMSC was controlled to track the target value by the speed regulation circuit. The test result of the PMSC output speed is presented in Fig. 15. From the figure, it can be seen that output speed of the PMSC reaches to the steady value of 300 rpm within 0.8 s which is less than the required time of 1 s. By comparison, the downward trend is in accordance with the simulation and the fall time is equal to that in the simulation which indicates that the model of the designed PMSC has high accuracy.

From above test results, it can be drawn the conclusion that the PMSC has excellent dynamic performance under the condition of either high load or low load, which is conducive to steering agility.

Fig. 14.

Test result of the PMSC output speed when speed rises from 300 rpm to 600 rpm.

Fig. 15.

Test result of the PMSC output speed when speed drops from 600 rpm to 300 rpm.

6. Real vehicle tests of steering maneuverability and stability

Real vehicle tests were carried out to evaluate steering maneuverability and stability of the vehicle equipped with P-ECHPS system in comparison with HPS system. In the real vehicle tests, steering maneuverability was evaluated by the pivot steering test, and steering stability was evaluated by the high-speed sinusoidal steering test. A coach was chosen as the test vehicle with the maximum front axis load of six thousand kilograms. The PMSC was mounted in the engine compartment instead of the air condition compressor as shown in Fig. 16.

Fig. 16.

The test vehicle.

The test system was constructed including the steering dynamometer, the gyroscope, the acquisition instrument, the controller of P-ECHPS system and power supply system as shown in Fig. 17. The steering dynamometer was used to acquire the signal of steering angle and steering torque. The gyroscope was used to acquire the signal of lateral acceleration and yaw velocity. The controller was used to control the output speed of the PMSC to adjust the output flow of the steering pump according to the signal of vehicle speed, steering angle velocity and steering torque, so as to realize variable assistance and avoid overflow loss of the steering pump.

Fig. 17.

Experimental apparatus.

6.1. Pivot steering test

The pivot steering tests were implemented in the case of the HPS system and the P-ECHPS system respectively. In the pivot steering test, the test vehicle parked on the flat road, and the driver turned the steering wheel in the whole loop. During the test, the steering torque and steering angle was acquired. The relationship between the steering angle and steering torque is presented in Fig. 18. The results shows that average steering torque of the vehicle equipped with the P-ECHPS system is about 9 N ⋅ m, the same as the vehicle equipped with the HPS system, which indicates that the vehicle equipped with P-ECHPS system has good steering maneuverability.

Fig. 18.

Relationship between steering angle and steering torque.

6.2. High-speed sinusoidal steering test

The high-speed sinusoidal steering tests were respectively implemented under the condition of the HPS system and the P-ECHPS system. In the high-speed sinusoidal steering test, the vehicle traveled straightly at the speed of 80 km/h, the driver turned the steering wheel with the period of 5 seconds at a certain steering angle under which the maximum lateral acceleration was less than 0.2 g. During the test, the steering torque and lateral acceleration was acquired. In the relationship between lateral acceleration and steering torque, the torque gradient with respect to lateral acceleration indicates the central steering feeling when lateral acceleration is 0 g, the torque gradient with respect to lateral acceleration indicates the natural steering feeling when lateral acceleration is 0.1 g. Generally, the bigger the torque gradient is, the better the steering stability is. The relationship between lateral acceleration and steering torque is presented in Fig. 19. Based on the data of the steering torque and lateral acceleration, the torque gradient under the P-ECHPS system and the HPS system was respectively calculated when lateral acceleration was 0 g and 0.1 g as shown in Table 2. From the figure and the table, it can be seen that the torque gradient under the P-ECHPS system increases by 32.4% compared with the HPS system when lateral acceleration is 0 g, and the torque gradient under the P-ECHPS system increases by 39.9% when lateral acceleration is 0.1 g. The test results indicate that the high-speed steering stability of the vehicle is greatly improved by introducing the PMSC to regulate the speed of the steering pump.

Fig. 19.

Relationship between lateral acceleration and steering torque.

Table 2

Comparison of torque gradient between P-ECHPS and HPS

Condition	Type
	HPS	P-ECHPS	Growth rate
0 g	9.38 N ⋅ m/g	12.42 N ⋅ m/g	32.4%
0.1 g	3.03 N ⋅ m/g	4.24 N ⋅ m/g	39.9%

7. Conclusions

To improve the high-speed steering stability and reduce the energy consumption of heavy-duty vehicles the permanent magnet coupling based electronically controlled hydraulic power steering (P-ECHPS) system was built and the permanent magnet coupling (PMSC) was designed. Electromagnetic characteristics and dynamic characteristics of the PMSC were investigated and verified by bench test. Real vehicle tests were carried out to evaluate the PMSC on the improvement of steering maneuverability and stability of the vehicle. Based on the research results, the following conclusions can be drawn.

The fractional-slot structure, double short pitch concentrated windings, surface mounted permanent magnets were adopted in the design of the PMSC. Two-dimensional finite element model of the PMSC was built. The simulations of electromagnetic characteristics were respectively implemented under the no-load condition and full-load condition. The results of induced electromotive force, induced current and electromagnetic torque demonstrated that the PMSC had excellent electromagnetic characteristics.

The speed regulation circuit of the PMSC was developed and the PWM control was implemented by PID algorithm. Dynamic characteristics of the PMSC were investigated. In the aspect of speed regulation response, the PMSC had excellent dynamic performance under high load condition. When PWSC was under low load condition, speed regulation response was inferior by comparison, for which the deceleration of PMSC mainly depended on load braking. However, the response time from maximum speed to minimum speed ramained less than 0.5 s. In general, the PMSC had the ideal dynamic performance with the speed regulation circuit and met the response requirement of P-ECHPS system.

The bench tests were carried out to verify electromagnetic and dynamic characteristics of the PMSC. The test result indicated that the induced electromotive force was sinusoidal which is in consistent with the simulation result. Under the high load and low load condition, the relationship between duty cycle and output speed of the PMSC was basically in accordance with the simulation result. Although the speed response in the bench test was slightly lower than that in the simulation, the dynamic characteristic met the requirements of steering agility of the P-ECHPS system.

From the results of the real vehicle tests, it can be seen that the vehicle equipped with P-ECHPS system had good steering maneuverability. In the high-speed sinusoidal steering test, the torque gradient under the P-ECHPS system increased by 32.4% and 39.9% respectively when lateral acceleration is 0 g and 0.1 g, which demonstrated that the P-ECHPS system was inductive to greatly improve high-speed steering stability of heavy-duty vehicles.

Footnotes

Acknowledgements

This research was supported by National Natural Science Foundation of China (Grant No. 51605199, No. 51275211), Natural Science Foundation of Jiangsu Province (Grant No. BK20160527) and Six Talent Peak Funding Projects in Jiangsu Province (Grant No. 2019-GDZB-084), Special fund for the transformation of scientific and technological achievements in Taizhou (Grant No. SCG201904).

References

Zhao

Luan

and Wang

, Parameter optimization design of vehicle E-HHPS system based on an improved MOPSO algorithm, Advances in Engineering Software 123 (2018), 51–61.

Zhao

Luan

and Wang

, Parametric optimization of novel electric-hydraulic hybrid steering system based on a shuffled particle swarm optimization algorithm, Journal of Cleaner Production 186 (2018), 865–876.

Nishimura

and Matsunaga

, Analysis of response lag in hydraulic power steering system, JSAE Review 21(1) (2000), 41–46.

Tang

Jiang

and Gong

, Optimal design of variable assist characteristics of electronically controlled hydraulic power steering system based on simulated annealing particle swarm optimisation algorithm, International Journal of Vehicle Design 73(1) (2017), 189–207.

Lee

Park

Lee

and Park

, Effects of FTP-75 mode vehicle fuel economy improvement due to types of power steering system, International Journal of Automotive Technology 10(6) (2009), 771–776.

Chen

and Zhang

, Simulation and experimental research for the energy saving steering pump based on the special speed offsetting, International Journal of Vehicle Design 72(2) (2016), 175–192.

Kozuma

Arita

and Tsuda

, Development of energy saving power steering, in: Proceedings of the 6th JFPS International Symposium on Fluid Power, JFPS, Tsukuba, 2005, pp. 297–300.

Xia

and Jiang

, An electronically controlled hydraulic power steering system for heavy vehicles, Advances in Mechanical Engineering 8(11) (2016), 1–11.

Tokumoto

, Development of energy-saving pump for hydraulic power steering, JSAE Review 18(3) (1997), 310–313, doi:10.1016/S0389-4304(96)00011-2.

10.

Chirag

Jaypal

and Anand

, Energy efficient hydraulic power assisted steering system (E2HPAS), SAE Paper, 2012-01-0976.

11.

Murty

Gopalakrishnan

and Namuduri

, Magnetorheological coupling based hydraulic power steering: Low-cost solution for fuel economy improvement, SAE International Journal of Passenger Cars-Mechanical Systems 2(1) (2009), 219–228.

12.

Tang

Jiang

Geng

and Xu

, Dynamics of electromagnetic slip coupling for hydraulic power steering application and its energy-saving characteristics, Journal of Central South University 22(5) (2015), 1994–2000.

13.

Lubin

Mezani

and Rezzoug

, Simple analytical expressions for the force and torque of axial magnetic couplings, IEEE Transactions on Energy Conversion 27 (2012), 536–546.

14.

Lubin

Mezani

and Rezzoug

, Experimental and theoretical analyses of axial magnetic coupling under steady-state and transient operations, IEEE Transactions On Industrial Electronics 61 (2014), 4356–4365.

15.

Budhia

Boys

Covic

and Huang

, Development of a single-sided flux magnetic coupler for electric vehicle IPT charging systems, IEEE Transactions on Industrial Electronics 60(1) (2013), 318–328.

16.

You

Barahona

Chai

and Cutululis

, Frequency support capability of variable speed wind turbine based on electromagnetic coupler, Renewable Energy 74 (2015), 681–688.

17.

You

Barahona

Chai

Cutululis

and Wu

, Improvement of grid frequency dynamic characteristic with novel wind turbine based on electromagnetic coupler, Renewable Energy 113 (2017), 813–821.

18.

Jiang

Tang

and Geng

, Electromagnetic and torque characteristics of electromagnetic slip coupling applied to hydraulic power steering system for heavy-duty vehicles, Journal of Computational and Theoretical Nanoscience 12(6) (2015), 1069–1075.

19.

Dolisy

Mezani

Lubin

and Leveque

, A new analytical torque formula for axial field permanent magnets coupling, IEEE Transactions on Energy Conversion 30 (2015), 892–899.

20.

Kang

and Choi

, Parametric analysis and experimental testing of radial flux type synchronous permanent magnet coupling based on analytical torque calculations, Journal of Electrical Engineering and Technology 9 (2014), 926–931.

21.

Yang

and Ma

, Numerical calculation of the outer thickness of double-solid rotor asynchronous permanent magnetic coupling by finite element method, International Journal of Materials & Product Technology 39(3-4) (2010), 339–346.

22.

Tang

Huang

Zhang

Jiang

Cai

and Sun

, Field-oriented control of energy-regenerative electromagnetic slip coupling, IEEE Access 6 (2018), 52169–52178.

23.

Canova

and Vusini

, Design of axial eddy-current couplers, IEEE Transactions on Industry Applications 39 (2003), 725–733.

24.

Hogberg

Jensen

and Bendixen

, Design and demonstration of a test-rig for static performance-studies of permanent magnet couplings, IEEE Transactions on Magnetics 49(12) (2013), 5664–5670.

25.

Lubin

and Rezzoug

, Steady-state and transient performance of axial-field eddy-current coupling, IEEE Transactions on Industrial Electronics 62(4) (2015), 2287–2296.

26.

You

Barahona

Chai

and Cutululis

, A novel wind turbine concept based on an electromagnetic coupler and the study of its fault ride-through capability, Energies 6(11) (2013), 6120–6136.

27.

Razavi

and Lamperth

, Eddy-current coupling with slotted conductor disk, IEEE Transactions on Magnetics 42 (2006), 405–410.

28.

Mouton

and Kamper

, Modeling and optimal design of an eddy current coupling for slip-synchronous permanent magnet wind generators, IEEE Transactions on Industrial Electronics 61 (2014), 3367–3376.

29.

Fornasiero

Bianchi

and Bolognani

, Slot harmonic impact on rotor losses in fractional-slot permanent-magnet machines, IEEE Transactions on Industrial Electronics 59(6) (2012), 2557–2564.

30.

Zhu

Zhao

and Ling

, Comparative investigation of concentrated winding and vernier double-stator permanent-magnet motors, International Journal of Applied Electromagnetics and Mechanics 53(3) (2017), 387–395.

31.

El-Refaie

Zhu

Jahns

and Howe

, Winding inductances of fractional slot surface-mounted permanent magnet brushless machines, Compel-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 28(6) (2009), 1590–1606.

32.

Zhao

and Lee

, High-efficiency high step-up DC-DC converters, IEEE Transactions on Power Electronics 18(1) (2003), 65–73.