Title page Investigation on the Influence of a Novel Redirector with By-pass Damping on the Performance of Load Sensing Steering System

The load sensing steering system of articulated loaders is prone to large pressure shock and oscillation during steering operations, affecting the stability of the steering system. To improve this phenomenon, an optimized structure of the redirector with by-pass damping is proposed, which adding orifices and throttle grooves to the original redirector. In the study, to control the steering load and working conditions, the steering load of the loader is replaced by using a pressure regulating valve. The simulation and experimental results shows that, compared with the traditional redirector, using the novel structure redirector with by-pass damping ensures good load sensing characteristics, the peak output pressure shock caused by the load unit step signal decreases from 65.04bar to 56.35bar, with a decrease rate of 13.4%, reducing the pressure oscillation of the hydraulic system. The pressure fluctuation time can be reduced from 2.09s to 1.6s, with a decrease rate of 23.4%, the output pressure oscillation decays faster, the smoothness of the steering operation is significantly improved.


Introduction
The loader is mainly used for loading and unloading materials and shoveling work within a certain range [1][2]. During the operation, frequent steering operations are required. The articulated loader is widely used due to its compact structure and easy operation. Scholars have conducted a comprehensive study on the steering system of  Jin-Shi Chen spreading@jlu.edu.cn 1 School of Mechanical and Aerospace Engineering, Jilin University, 130022, Jilin, China articulated vehicles using numerical analysis and simulation methods [3][4][5]. More accurate steering performance and the main parameters affecting the performance were obtained. During steering operation of the existing articulated loader, when the driver turns the steering wheel, there are some unstable situations such as shocks and oscillations in the hydraulic system, resulting in poor stability of the machine when starting and stopping the steering. The higher the steering wheel speed, the more obvious the shaking or shimmy of the fuselage [6][7]. The optimization of steering system performance has also become a focus of scholars' research. Reference [8] introduced the steering method into the study of the steering system, combined the dynamic model with the physical model, and used the NSGA-II algorithm to optimize the steering system for further improve the performance of the system. A novel steering system has been developed to improve the driving performance during steering [9]. References [10][11] optimized the articulated frame to obtain a more compact articulated frame steering system, improving steering flexibility.
For the unstable situation of the hydraulic system, the introduction of a steering system with independent control of the inlet and outlet ports has improved the steering stability and steering sensitivity under high torque [12]. The load sensing pump [13], the proportional variable pump [14]- [17] and other variable displacement pump were used to replace the fixed displacement hydraulic pump for the single-rod hydraulic cylinder steering system [18] - [21] and the double-rod hydraulic cylinder steering system [22] to build a closed-loop steering system. The displacement of the pump was controlled by the rotation speed of the steering wheel, which can supply oil on demand, reduce the loss of the steering system and improve the stability of the steering system. Caterpillar studied working and steering flow sharing hydraulic systems with the flow sharing valve [23]. The steering scheme of installing a by-pass proportional throttle valve at the outlet of a fixed displacement hydraulic pump was proposed in reference [24]. By-pass throttling reduces the outlet pressure of the hydraulic pump and the pressure shock of steering operating. Sany, Liugong and other companies mainly studied the improvement of the full-hydraulic steering system and load sensing hydraulic steering system with flow amplification valve [25][26][27]. EATON has done a lot of research on the structure optimization of the full hydraulic redirector, developed a full hydraulic redirector that can eliminate oil trapping [28]. Lanzhou University of Technology has done a lot of work on the development of the steering priority flow amplification valve and the structure optimization of the load sensing priority valve [29].
Based on the above research, scholars have researched and optimized hydraulic systems and components. Appropriately adjusted the oil supply pressure of the system, eliminated the oil trapped, which to some extent alleviated the pressure shock, oscillation and other instability of articulated vehicles during steering. However, under high speed condition, it is still difficult to control the pressure shock caused by the sudden flow changes, and the steering system will still have a large oscillation. For this reason, a redirector structure with by-pass damping is proposed.
The structure of this paper is as follows: Section 2 introduces the working principle of the redirector with by-pass damping. Section 3 deduces the relationship between the valve port area of the redirector and establishes a mathematical model. To research the relationship between the flow rate, the pressure and rotation speed of the redirector. In Section 4, the simulation model of the redirector with by-pass damping is established and verified the performance, the simulation results are obtained. Section 5 builds a simulation experimental platform and obtains experimental results of the by-pass damping redirector. Section 6 analyzes the dynamic characteristics and oscillation analysis of the novel redirector and the original redirector. Section 7 is the conclusion.

Working Principle
The research object of this paper is the coaxial flow rate amplification redirector, whose structure is shown in Figure 1 (a). It is mainly composed of three parts: housing, metering motor and rotary valve (including control spool and control sleeve). The control spool of the redirector is connected to the steering wheel, and the control spool rotates synchronously when the steering wheel is turned. There is a relative angular displacement between the control spool and the control sleeve. The input P opens after the control spool rotates a certain angle. The fluid enters through the input and pushes the metering motor to rotate. The metering motor is mainly used to ensure that the flow rate of oil delivered by the redirector is proportional to the steering wheel angle when the steering pump is working. If the steering pump is not working, the motor directly sucks oil from the oil tank and supplies it to the steering cylinder when rotating the steering wheel. The metering motor is mainly used to ensure that the flow rate of oil delivered by the redirector is proportional to the steering wheel angle when the steering pump is working; when the steering pump is not working, manually turn the steering wheel, the motor directly sucks oil from the oil tank and supplies it to the steering cylinder. The faster the rotation speed of the steering wheel, the greater the relative angular displacement of the control spool and control sleeve, the flow rate is greater, and the steering speed is faster. The rotary valve is mainly composed of a control spool with four groups of grooves and a control sleeve with ten groups of through holes. When the control spool rotates, the direction and flow rate of the oil are changed by the on-off and opening area of different grooves and through holes, as shown in Figure 1 (b). Figure 1 (c) is the principle diagram of the redirector. When the steering wheel is not rotated, the redirector is in the medium position, and the port P is disconnected to ports R and L. The oil enters the channel C through ports P and LS and returns to the tank through the port T. The steering rod drives the control spool to rotate when the steering wheel rotates to the left. The oil enters the even-column H of the C channel through the P port and reaches the metering motor, then output from the odd-column H through the B channel and the L port to the steering cylinder. The port T is closed, the channel A connects the port LS, port R and the fuel tank, and the left steering is completed. When the steering wheel rotates at high speed, the steering rod drives the control spool to rotate a large angle, the oil enters the channel B through flow rate amplification holes and is directly output from parts L and R of the redirector to the steering cylinder to complete the steering. When the redirector is in the medium position, the by-pass damping hole is not connected to the port R or L. When the steering wheel rotates, the port R or L is connected to the port T through the by-pass throttle hole K. At this time, the pressure shock and oscillation caused by the displacement of the cylinder can be reduced by by-pass damping to achieve smooth steering.

Calculation of the Opening Area
It is necessary to calculate the opening area of each port and channel when researching the performance of the redirector. For the convenience of calculation, the   The oil flow path of the redirector is divided into 7 modules. The opening area of the inlet module P-C is r is diameter of the hole， is the angle corresponding to the opening area.
The opening area of the flow rate amplification module 1.02 6 sin 2 18 1.5 sin 3( ) where 1 x , 2 x are displacements of two limit positions. The opening area of the metering motor module when the oil goes through the inlet and outlet H of the metering motor is where l is the side length of motor hole. The opening area of the working module H-R\L is The opening area of the return module R\L-T is where 1 The opening area of the load sensor module when oil through LS is where a is the transverse distance of opening area. The opening area of the by-pass module R\L-D is The opening area of the by-pass module D-K is where 2 2 arccos The opening area of the by-pass module K-T is  33  02  sin  sin  22  3  2  3  sin  2  3  3 sin 3 3 2arccos x l r r where 1 l , 2 l are distances between two limit positions and two holes, 3 l is the distance between the two holes. The relationship curve between the opening area of each module and the control spool displacement is shown in Figure 3.

Mathematical Model of the Redirector
For the purpose of further analyzing the dynamic characteristics of the redirector with by-pass damping structure, the mathematical model of the redirector is established. The following assumptions are accepted, ignore the pipeline loss, internal leakage, friction and hydraulic force of the redirector which have little effect on steering performance. According to the structure and working principle of the redirector, the schematic diagram of the equivalent damping is shown in Figure 4.
The combination of the metering motor seal oil cavity and the hole and channel structure of the rotary valve realizes the oil distribution relationship of the redirector. The flow rate continuity equation of the metering motor without considering leakage is where m  is the angular velocity of motor, m D is the displacement of motor.
During the working process of the redirector, it is mainly subjected to pressure uniformly distributed in the radial direction [30]. Since the control sleeve of the redirector is rigidly connected to the rotor of the motor, the force condition of the redirector is the same as that of the metering motor. According to the working principle of the redirector, the viscous friction and drag torque between the control sleeve and control spool of the rotary valve are main loads of the motor. The viscous friction can be ignored because it is much smaller than the drag torque. The force balance equation of the motor is where i P is the pressure between each orifice in rotary valve.
The control spool and control sleeve of the redirector are expanded into a planar structure according to their axial direction. The displacement of the control spool is where f  is the angular velocity of the rotary valve.
The differential pressure and flow rate of the redirector inlet are where d C is the flow coefficient,  is density of oil. According to the previous research and analysis of priority valves and redirectors [31][32], the differential pressure of the redirector orifice is basically a constant value. The flow rate through the inlet is only related to the opening area of the rotary valve, that is, it is related to the rotation speed of the control spool of the steering gear, and has nothing to do with the electromotor speed and steering load.
The flow rate of the redirector through each damping hole can be expressed where i A is the area of orifice, i P  is the pressure drop through each orifice.
When the redirector is in the medium position, medium damping holes 2 R , 3 R are working, other damping holes are in a negative opening state, and LS P is low pressure.
When the redirector rotates, 2 R , 3 R are closed. The flow rate of each damping hole is 7 1 As can be seen from Figure 4, the differential pressure of oil through each damping hole is:

Simulation Method
As shown in Figure 2, all the circumferential movements of the redirector are converted into translational movements. To simplify model structure, the metering motor is replaced by a meter cylinder with an inlet and an outlet replacing seven closed chambers and only six inlet holes are considered for translation in the same direction.
In addition, the seven holes of the valve body corresponding to port H and the metering motor are equivalent to an inlet and a return port. The magnitude of the input force signal in the model represents the rotation speed of the steering wheel. The pressure regulating valve as equivalent load instead of the steering load. The model is established in accordance with the 7 oil circuit modules in Section 3. Figure 5 shows the simulation model of the redirector.   The main parameters of the simulation model are given in Table 1. The hydraulic pressure acting on the control spool can be offset, so the acting area of the two relative valve blocks should be kept equal, and all parameters of the valve port area must be consistent. According to Equations (1)~(9), the opening area formed by the relative movement of the control spool and control sleeve is set. When the metering cylinder is used to replace the metering motor, the measuring area of the cylinder is calculated by the displacement of the motor.

Simulation General Setting
The speed signal of the steering wheel is converted to the speed of translation

Validation of the Model
To verify whether the simulation model can well reflect the working principle and dynamic performance of the actual structure, the performance of the redirector with by-pass   damping under different working conditions is simulated and analyzed. Figure6 is the displacement curve of the control spool and control sleeve under the certain rotating speed signal. It can be seen from the curve that the control spool begins to move immediately when the force signal is applied. The control sleeve does not move at the beginning due to the dead zone between the control spool and control sleeve. When the rotation speed increases and the port P is opened, the opening area and the displacement difference between the control spool and control sleeve increase. When the rotation speed is 0, the opening area is reduced to close and the control sleeve has a slight lag in stop movement relative to the control spool. The simulation results show that the control spool and control sleeve of the redirector ensure good follow-up performance when the steering wheel speed increases. Figure 7 shows the differential pressure P  and the pressure loss / R L P P   of the redirector under the constant increase speed signal. It can be seen from curves that / R L P P   gradually increases with the increase of the redirector opening area , while P  remains at a constant value. The overflow area and flow rate of the redirector with the increase of the steering wheel rotating speed. However, / R L P P   increases with the overflow area increasing, because the overflow area gradient of each orifice is smaller than that of the flow rate.  represents to the actual structure of the redirector, which can reflect the working principle and have good follow characteristics.

Simulation Results
The dynamic characteristics of the redirector with by-pass damping are analyzed from three aspects: different steering wheel speed, different electromotor speed and different steering load. Figure 8 shows the simulation results of the redirector under different steering wheel speeds with no-load condition of electromotor speed is 708 r/min. It can be seen from the simulation curves that that the flow rate into the redirector increases with the increase of the steering wheel speed. The flow rate has a linear relationship with the opening area 1 A when P  remains stable, the redirector has good operating performance. The flow amplification holes are opened wen the rotation speed is 20r/min and 30r/min, and the flow rate increases rapidly. Besides, this part of the flow rate directly reaches outlet of the redirector without passing through the metering motor. Figure 9 shows the simulation results of the redirector under different electromotor speeds with no-load condition of steering wheel speed is 20 r/min. Change the electromotor speed, the flow rate into the redirector and the pressure of ports P, LS, L/R remain constant. This shows that the flow rate required by the steering system is constant and not affected by the electromotor speed when the steering wheel speed is fixed. Figure 10 shows the simulation results under no-load and heavy-load conditions with the steering wheel speed and electromotor speed are fixed. The output pressure and pressure shock of the redirector under heavy-load condition are higher than that of no-load, and the oil return pressure in both cases is the same. The output pressure and pressure fluctuation of the steering gear under heavy load are higher than that of no load, and the oil return pressure is the same in both cases. According to the analysis of simulation results, the change of load has no effect on the flow rate and differential pressure of the redirector with the same steering speed.
It can be seen from Figure10 that input the step signal, the rise time under no-load condition is 0.23s, which is shorter than 0.49s under heavy-load condition. The steering system response becomes slower when the load gets heavy.

Simulation Experiment Platform
Although the simulation model has been set according to the actual structural parameters, the influence of pipeline has been ignored. Therefore, it is necessary to verify the correctness of the equivalent load and the model by experiments. According to the simulation system model in Figure 5, the simulation experiment platform of by-pass damping redirector is established, as shown in Figure 11. When assembling the platform, the bending degree of pipelines should be reduced as much as possible to reduce the influence of pressure loss on the measured data. Sensors should be installed as close to the pressure point as possible. In the experiment, the angular velocity of the steering wheel is collected by a speed measuring instrument. Pressure sensors are used to collect pressure of the hydraulic pump, the inlet and outlet of the redirector and the port LS. Flow meters are used to collect the flow rate of the redirector inlet and outlet. The experimental instruments required are given in Table 2.

Experimental Results
Three steering conditions with different steering wheel speed, different electromotor speed and different steering load were used to test and analyze the performance of the redirector with by-pass damping. The steering condition in the experiment is consistent with the simulation steering condition to ensure the accuracy of the experiment result. Figure 12 shows the experimental results of redirector with by-pass damping under the no-load condition with the electromotor speed is 708r/min when the steering wheel speed is 8r/min, 20r/min, and 30r/min, respectively. It can be seen that when the steering wheel speed increases, the flow rate through the redirector increases, resulting in the increase of pressure at port LS and port L/R. The steering wheel speed is the main factor that affects the flow rate of the steering system. When the speed is higher, the inlet flow rate of the redirector changes more obviously with the increase of steering wheel speed. Figure 13 shows the experimental results under the no-load condition with the steering wheel speed is 20r/min when the electromotor speed is 708r/min,1200r/min, and 1870r/min, respectively. It can be seen from curves that when the electromotor speed increases, the flow rate through the redirector and the pressure at port P, port LS, port R/L are basically constant. It can be concluded that the required flow rate of the steering system is determined by the steering wheel speed rather than the electromotor speed. Figure 14 shows the experimental results under no-load and heavy-load conditions with the steering speed is 8r/min, and the electromotor speed is 708r/min, 1200r/min, respectively. The pressure at port P, port LS and port R/L increases significantly with the increase of steering load, while the pressure variation of port R is not obvious. Combined with the previous simulation analysis, the pressure of steering system increases, and the response slows down when the steering load increases.
Part of the simulation and experiment results are shown in Table 3, the maximum error is 11.1%, which proves that the simulation model has good accuracy. The model can be used to further analyze the steering performance.

Analysis of Dynamic Characteristics and Oscillation
According to the force equation and flow continuity equation of the redirector and steering load during the steering process ·11· Figure 15 The schematic of redirector mathematical model where V is the chamber volume of the equivalent load, E is the effective bulk modulus of oil, F is the external load, () ut is the speed of the equivalent load response, B is the viscous damping, c  is the leakage coefficient of the equivalent load.
The redirector with by-pass damping has the pressure-flow rate linearization equation of steering load Gains of the two structure redirectors are Undamped natural frequencies are System damping ratios are The pressure overshoot is Figure 16 Flow rate through by-pass orifices.

Figure 17
Pressure of the equivalent load inlet.
According to the Routh-Hurwitz stability criterion, it is known that both systems formed by the two redirectors are stable.
Based on above equations, when the steering load F increases, L P increases, c K decreases, n  ,  will decrease and the pressure overshoot p M will increase. The number of system oscillations increases, the stability decreases, and the adjustment time increases. Therefore, the sudden increase of the steering load will lead to the system oscillation. If the opening area 8 A of the orifice 8 R increases, c K ,increases,  will increase and the pressure overshoot p M will decrease. the number of oscillations will decrease, and the corresponding stability of the system will increase. In this study, 12   , 12 PP MM  , and the overshoot of the redirector with by-pass damping is relatively small. The severity of system oscillation will be determined by the damping ratio  . The smaller  , the more severe the oscillation. The decay speed of the oscillation process is determined by n  . The larger n  , the faster the decay will be. According to the above analysis 12 nn Therefore, compared with the original redirector, the output pressure oscillation decays more quickly and the system is more stable when a step signal is input to the redirector with by-pass damping. Figure 16 shows the flow rate curve through the by-pass loop under different steering wheel speeds of no-load condition with electromotor speed is 708 r/min. The by-pass loop flow rate is 0.66L/min, 3.15L/min, 6.03L/min when the steering wheel speed is 8r/min, 20r/min, 30r/min, respectively. Accounting for 16.5%, 18.6% and 19.1% of the total flow rate into the redirector, respectively. The simulation results prove that the flow rate through by-pass loop increases with the increase of steering wheel speed, but the increase rate decreases. The proportion of flow rate through by-pass loop is relatively stable. Figure 17 shows the equivalent load inlet pressure simulation curves of the two redirectors under no-load and heavy-load conditions with electromotor speed is 708 r/min. Under no-load condition and the steering wheel speed is 20r/min, compared with the original redirector, the equivalent load inlet pressure overshoot of the redirector with by-pass damping reduces from 8.6bar to 7.9bar. Under heavy-load condition, the pressure overshoot reduces from 65.04bar to 56.35bar, with a decrease rate of 13.4%. The pressure oscillation duration is reduced from 2.09s to 1.6s, with a decrease rate of 23.4%. The research work in this paper can make a certain contribution to the stability optimization of articulated vehicle steering technology.

Conclusions
In this paper, to reduce the pressure oscillation and enhance the stability of the articulated vehicle steering system, a novel redirector with by-pass damping is proposed. The steering load is equivalent replaced to make the research conditions more convenient control. Through the simulation and experimental research and analysis of the novel redirector under different working conditions, the following conclusions can be concluded: (1) For the redirector with by-pass damping, the peak value of the equivalent load inlet pressure is reduced from 65.04bar to 56.35bar under heavy-load condition during steering. Compared with the original redirector, the overshoot is reduced by 13.4%, which reduces the number of system oscillations. system is more stable.
(3) For the redirector with by-pass damping, the flow rate through by-pass loop increases with the increase of steering wheel speed, but the increase rate decreases. The proportion of flow rate through by-pass loop is relatively stable. Therefore, the by-pass damping structure has little effect on the supply of flow rate during steering.

Availability of data and materials
The datasets supporting the conclusions of this article are included within the article.