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0Процессы и машины агроинженерных систем
УДК 631.3-51
Код ВАК 05.20.01 (новый код - 4.3.1)
EXPERIMENTAL RESEARCH ON THE LINEAR SYNCHRONIZATION CHARACTERISTICS OF
SELF-PROPELLED BOOM SPRAYERS
Wen Haojun*1'2, Liu Xinyue1, Wang Guoliang1 College of Mechanical and Electrical Engineering, Shihezi University, Shihezi Xinjiang China 832000; 2Key Laboratory of Northwest Agricultural Equipment of Ministry of Agriculture and Rural Affairs, Shihezi University, Shihezi Xinjiang China 832000.
*Email: 547273950@qq.com
Abstract. In this paper, a hydraulic drive system that utilizes a RTM valve is proposed to address the problem that self-propelled sprayers with a high ground clearance are prone to drift when driving in a straight line due in part to its large weight, high ground clearance and complex working conditions. Through a theoretical analysis of the impact of the RTM valve in the hydraulic system on the linear synchronization of the sprayer, a mathematical model of the hydraulic system is established, and the hydraulic system is simulated using the simulation software AMESim. According to the experimental results, under different load conditions, the speed errors are 2r/min and 105r/min respectively when the RTM valve is open and when it is closed, suggesting that the hydraulic drive system that has a RTM valve has clearly better synchronization than the one not having a RTM valve. To verify the reliability of the simulation results, a real vehicle test platform for the hydraulic drive system is built to conduct four-wheel speed tests. In the random test of driving sprayers in a straight line in the field, it is found that the maximum synchronous speed error is 5r/min, which meets the hydraulic drive requirements and verifies the responsiveness, accuracy and stability of the hydraulic drive system designed.
Keywords: self-propelled boom sprayer; hydraulic drive system; synchronization; AMEsim simulation; experiment.
Introduction
Modern agricultural and forestry plant protection machinery is developing towards safety, precision, high
efficiency and low energy consumption. The chassis of large-scale plant protection machinery widely adopts
hydraulic drive systems[1]. Foreign research on self-propelled sprayers with a high ground clearance started early,
and hydraulic power transmission systems are widely used. Most models are equipped with hydraulic four-wheel
drive systems and related research is quite mature. In recent years, domestic research has been gradually
conducted regarding self-propelled sprayers with a high ground clearance, but few studies have paid attention to
the drive systems of high clearance sprayers, most of which stay at the stage of two-wheel drives[2]. Based on
the characteristics of open and closed hydraulic drive systems, Ding Li et al. designed a closed hydraulic system
that comprises a variable displacement pump driving two quantitative hydraulic motors, but did not conduct 4
experimental research[3]. Tong Qin et al. analyzed the driving modes of vehicle chassis, used a single-pump four-motor natural shunt parallel system to drive, and examined the mathematical model and control method of the sprayer when driving in a straight line and turning[4]. Li Ze et al. designed a hydraulic drive system with a two-function diverter valve to study synchronization^]. Zhang Hua et al. built a hydraulic test bench to study synchronous control of a chassis hydraulic motor and made comparisons[6]. The synchronous control components involved in the above research, such as common synchronizing valves, are characterized by low accuracy of synchronization and high loss, and most of them are in the stage of experimental research and have not yet been put into practice, as the accuracy of synchronous control needs to be improved.
Therefore, a hydraulic drive system suitable for large-scale self-propelled boom sprayers with a high ground clearance is designed to improve the accuracy of synchronization in four-wheel straight-line driving mode, and an experimental platform is built to verify the stability and accuracy of the system designed.
Hydraulic drive system design
The unstable application rate of a sprayer is common, due in part to the complex and changeable environmental factors in field operations and the highly fluctuating loads, which will affect the quality of field operations. Hence, in order to ensure quality of work, the four-wheel speed of the sprayer should be adjusted in real time to adapt to the changing terrain, and the hydraulic system should be able to adjust the flow rate of each motor at the same time[7]. In order to make the system have better speed and load characteristics, and realize such functions as flow distribution, a hydraulic drive system that employs a RTM valve is designed. Its principles are illustrated in Fig. 1.
The hydraulic drive system is mainly composed of a variable displacement pump, a safety valve, a relief valve, a servo valve, a variable displacement piston, a shuttle valve, a proportional relief valve, a RTM valve and a hydraulic motor. The displacement of the variable pump is adjusted through the servo mechanism. When the hydraulic drive system is started, the oil is pumped out from the pump's outlet port, shunted by the RTM valve, and distributed to the four motors as per changes in external load. Then the oil of the four motors is collected and delivered to the pump's return port. Because of the bi-directional closed loop circuit and the bi-directional variable displacement pump, when the sprayer starts to drive backwards, the functions of the pump's inlet and outlet ports are interchanged, suggesting that the above-mentioned oil circuit is opposite to the forward direction of oil flow.
The RTM is the synchronous control component of the system. It consists of a metering orifice and a pressure compensator. The metering orifice is placed in the spool. It is used to divide the output flows that enter the RTM valve into different channels. To compensate for differences in load pressure, the pressure compensator is incorporated in the oil port of each actuator to eliminate the impact of load deviations on shunting errors, so that the actuators can execute at the same or proportional running speed to achieve a synchronization effect.
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1. Engine 2. Variable displacement pump 3.4. Fuel charge relief valve 5. Relief valve 6. Fuel tank 7. Filter 8. Charge pump 9. Two-position and three-way solenoid valve 10. RTM valve 11.12.13.14. Left front, right front, left rear, right rear hydraulic motors 19.20.21.22. Left front wheel, right front wheel, right rear wheel, left rear wheel101. Servo valve 102. Variable piston 103. Shuttle valve 104. Proportional relief valve
Fig.1 Schematic diagram of hydraulic system
Establishment of mathematical model of hydraulic system
In the variable displacement pump of the previously mentioned hydraulic system, the amount of flow of the pump can be controlled by using the servo valve to control the variable piston, thereby varying the displacement of the swash plate of the pump. Its structure is explained in Fig. 2.
X
1. Valve outflow 2. Valve inflow 3. Skid shoe 4. Cylinder block 5. Valve plate6. Spindle 7. Plunger 8. Valve
plate
Fig. 2 Variable pump control diagram
To clarify the relationships among main hydraulic component parameters, a linear mathematical model of the system was established and the following assumptions were made:
(1) The hydraulic oil pressure remains constant, regardless of pump flow pulsation;
0
9
A
P
8
7
(2) Each cavity of the hydraulic cylinder receives the same pressure, and the oil temperature and the bulk modulus of elasticity are constant;
(3) Regardless of pipeline pressure loss and pipeline dynamic effects
(4) Each oil passage window on the valve sleeve is rectangular, and the amount of openings on each valve port produced by the movement of the valve core is the same.
2.1 Spool valve flow equation
According to the assumptions, the four-way valve near the zero position can be linearized. The model is illustrated in Fig. 3. The flow equation of the four-way valve is:
Rl = kqxv kcPL
(1)
where qL —load flow, m3/s ; pL—load pressure, MPa; xv—spool displacement, mm; kq—flow gain; kq—flow-pressure coefficient.
Fig. 3 Linearized model of hydraulic control valve The force balance equation of the valve is:
Fo Ps^v = '
dt2 +f dt +Ksxv
(2)
where Av —the end area of the valve, m2; F0—regulator pressure spring preload; ps—output port pressure, MPa
mv —the sum of the mass of the moving parts of the valve and one third of the spring mass; xv—spool displacement, mm; f—viscous damping coefficient; Ks —the sum of regulator pressure spring stiffness and hydrodynamic stiffness.
2.2. Flow continuity equation of hydraulic cylinder
When considering the compressibility of the fluid, the closed cavity has flow in and out, volume change and
pressure effects. The flow balance equation of the compressible fluid is: 7
Zv-1 dV V dp
Qin-LQout = ~dt+~pJt
where V—the volume of the control cavity taken, m3 £ Qin—total flow into the control cavity, m3/s E Qout—total flow out of the control cavity, m3/s P—bulk modulus of elasticity of the fluid The flow from the valve port into the hydraulic cylinder:
Qi = Cic(Pi - Pi) +
V1 dp1 pe dt
+ CeciPi+Ai
dt
(4)
The flow from the hydraulic cylinder back to the valve port:
Qi = cic{pi - Pi) - ceciPi -
V2 dp2 pe dt
+ A7
dt
(5)
where Q1—flow from the valve port into the hydraulic cylinder, m3/s; Q2—flow from the hydraulic cylinder to the valve port, m3/s; A1, A2—the effective area of hydraulic cylinder, m2; xc—displacement of the piston in the hydraulic cylinder, m; Cic—internal leakage coefficient; Cec1—external leakage coefficient; V1—total volume from the valve to the oil inlet cavity of the hydraulic cylinder, m3; V2—total volume from the oil return cavity of the hydraulic cylinder to the valve, m3; —bulk modulus of the fluid, set as 7.0 x 108Pa
The volume of the two cavities of the hydraulic cylinder is:
Vi = VQi + AV(Xp) = VQi + Apx,
01 ~ np^C
V7 = V02 - AV(Xp) = V02 - Apxc
(6) (7)
where V01—the initial volume of the oil inlet cavity of the hydraulic cylinder, m3
V02—the initial volume of the oil return cavity of the hydraulic cylinder, m3
AV(xp)—the volume change when the piston moves, which is the function of piston displacement xp. That is, AV(Xp) = Apxc,Ap is the effective area of the piston.
dV1 dt
dV7
dt Ap dt
(8)
Based on pL = p1- p2 and the simultaneous equation (8), the load flow continuity equation can be obtained:
dxc Vr dpL
where QL—load flow, and QL = Ql+Q2,m3/s
Q
Ctp —total leakage coefficient of the hydraulic cylinder, Ctp = Cic
Vr—total volume of the two oil cavities, m3
Regardless of nonlinear loads such as Coulomb friction and the mass of oil, according to Newton's second law, the force balance equation between the hydraulic cylinder and the load is established:
p1A1-p2A2 =rnt-^ + Bc-^ + Kxc + Fh (10)
where mt —total inertial load, kg Bc —total viscous load factor K—elasticity load, kg
Fl —the force of the swash plate on the variable cylinder, N
2.3 Flow continuity equation of axial piston pump
In accordance with the working principle of the plunger pump, its mathematical model is established. The rotational speed of its single plunger pump is:
ds (11)
v = — = RMsin(Mt)tan a ( )
where,«—the swing angle of the swash plate, °
m—the pump rotational angular velocity, rad/s R—the radius of the distribution circle of the plunger hole, m s—the stroke of the plunger in the cylinder, m
During the working process of the variable pump, with the rotation of the pump cylinder, the flow continuity equation in the plunger cavity is:
dpz P dV
-W-v^-^-^ (12)
where pz—pressure in the plunger cavity, MPa
P—the bulk modulus of elasticity of oil, set as 7.0 x 108Pa V—the volume of the plunger cavity, m3 Qo—single plunger output flow, m3/s
The flow change in the i-th plunger cavity is:
\2\Pz-Pyl P
Qi = sign(pz - pp)CdA(y)
where Cd —flow coefficient
p—fluid density, kg/m3 A(cp') —flow distribution area, m2
pp—the pressure of the pump port connected to the plunger cavity, MPa
2.4 Flow continuity equation of RTM valve
The structure diagram of the RTM valve is shown in Fig. 4. Regardless of the leakage flow of the orifice, the flow continuity equation at the oil inlet of the RTM valve is:
qp = qL + qR + qz + qM (14)
where qp, qL, qR, qz and qM are flows passing through the oil inlet P, oil outlet A, oil outlet B, oil outlet C and oil outlet D in the RTM valve, m3/s.
C
t qL. qz
Fig. 4 RTM valve structure model The flow-pressure equations for the oil outlets A, B, C, D in the RTM valve are respectively:
qL = CaAixD I-{p-pA)
qR = CdA(X2) ¡2(p-pB)
--(15)
qz = CdA(x3) I-{p-pc)
qM = CdA(x4) I-(p-pD)
where Cd —flow coefficient of variable orifices
Pa, Pb, Pc> Pd —the oil pressure of the A, B, C, D outlets of the RTM valve, Pa
A(x1),A(x2) ,A(x3),A(x4)—the flow cross-sectional area of the A, B, C, D outlets of the valve, m2
x1, x2, x3, x4—the spool displacement of the proportional directional valve on the A, B, C, D outlets of the RTM valve, m
2.5 Flow continuity equation of hydraulic motor
Suppose that the internal and external leakage coefficients of the four-wheel motors are the same respectively. Then the continuity equation for RTM valve-hydraulic motor inlet flow is:
Rij - Cm(Pij - Pb) - CemPij-^Pij = ^m^m (16)
He
where qtj —the inlet flow rate of the wheel motor (equivalent to qL, qR, qz, qMin the RTM valve modeling formula), m3/s
Vm—wheel motor displacement, m3/rad
Mm—wheel motor shaft speed, rad/s
Pij—wheel motor oil inlet pressure (equivalent to pA, pB, pc, pD in the RTM valve modeling formula), MPa
V-i—total volume of the oil inlet cavity of the RTM valve-oil tube-the motor (suppose that the total volume of the oil inlet cavity from the RTM valve to the four motors is the same), m3
Cim, Cem—the internal and external leakage coefficients of the motor, respectively, (m3/s)/Pa
The motor-load torque balance equation is:
Vm(Pi - Pb) = Jm^m + ^m^m + Sign(Mm)Tf + TL (17)
where Jm—the moment of inertia of the motor shaft, kg • m3
Bm—viscous damping coefficient on the motor shaft, N-m/(rad/s)
Tf—equivalent to the frictional resistance torque on the motor shaft, N-m
TL—External load torque on the motor shaft, N-m
When driving in a straight line, the speed of the four wheels must be the same. In reality, however, the external torque and slip rate of each wheel are not the same. In order to study the linear synchronization characteristics, it is necessary to adjust the motor flow rate while meeting the linear slip rate, and the external load torque applied to the motor that affects the flow into the motor is different. Through the establishment of the above flow continuity equation and motor-load torque balance equation, further research is carried out in simulation and experiments.
Simulation verification and analysis
Since the load on each drive motor will be different with the reduction of liquid medicines during the working process of the sprayer, combined with the performance research of the hydraulic chassis in construction machinery, when carrying out simulation research, the driving system is subjected to different torques for simulation. In order to obtain reasonable simulation data, the motor is loaded with different torques to simulate the effect on different road surfaces. It can be seen from the literature that the friction coefficients of asphalt roads and cultivated fields are 0.02 and 0.12, respectively, the full load of the sprayer is 8500kg, the tire radius is 0.625m, and the total transmission ratio is 1. Substitute the above data in the following equation:
Fn = G sina + G cos a fz (18)
Tm=— (19)
m vn— v '
where G—the total gravity of the sprayer, N fz —the coefficient of rolling friction a—ramp angle (°) Tm—motor loading torque, N-m rw—rolling radius of a tire, m i—total gear ratio n—number of motors ^—drive system efficiency
Fig. 5 Simulation model of hydraulic drive system According to the above calculation, the corresponding loading torques are 26.56N-m and 159.38N-m on asphalt roads and cultivated fields, respectively. The sprayer needs to ensure the stability of straight-line driving during operation, so as to analyze the synchronicity of the sprayer when driving on both sides. As shown in Fig. 5, a simulation model of the hydraulic drive system is established, and different loads are applied on one side of the sprayer for simulation analysis. The simulation
parameters are displayed in Table 1.
Table 1 System simulation parameters
Parameter Value
RTM spool diameter/mm 10
RTM spool mass/kg 0.06
Spring pre-compression/mm 5.326
Fixed orifice aperture /mm 3.2
Variable orifice aperture/mm 7
Centering spring stiffness/(N • mm-1) 0.8
Variable orifice initial opening/mm 3
Flush valve set pressure/Mpa 3
Flush valve maximum opening area/mm2 30
Oil viscosity/cp 50
Oil density/( kg • m-3) 855
Oil modulus of elasticity/bar 17000
Engine speed/(r • min-1) 2800
Variable pump displacement^ mL • r-1) 300
Maximum working pressure/Mpa 40
Mechanical efficiency/% 85
Volumetric efficiency/% 95
Motor displacement^ cc • rev-1) 100
Moment of inertia/(fc^ • m2) 0.036
A sinusoidal load of 26.56N-m is applied to the left front and left rear wheels of the sprayer, and a load of 159.38N-m is applied to the right front and right rear wheels of the sprayer. The effect of unilateral torque change 13
on the synchronicity of sprayer drive with or without the RTM valve is analyzed. Under different loads, the motor speed of the driving system changes in the absence of the RTM valve. In the initial stage of motor startup, the speeds of the left front motor, left rear motor, and right front motor tend to stabilize after reaching the peak value within 0-0.5s. The speed is between 0 and 1 r/min, and the speed of the right rear motor is the highest. That is because the right rear motor has the lowest load, and the flow entering the motor is the largest, resulting in the most significant change in its speed with the flow rate. The fluctuation of the motor speed within 0-2s is relatively high. After 2s, the fluctuation tends to be stable at 205r/min.
It can be seen from Fig. 6a that under the conditions of different loads with the RTM valve, the four motors tend to stabilize quickly after reaching the peak value in the starting acceleration phase. It can be seen from Fig. 6b that the maximum speed error of the four motors is 2.0r/min, and the minimum error is 0.3r/min after 5s.
Oi
PWMM*»
left front motor left rear motor right front motor right rear motor
6
time/s
2.0 1.5
1.0-)
0.5
in
left front motor left rear motor right front motor right rear motor
0.0 -0.5 -1.0 -1.5 -2.0
I
6
time/s
a. Has RTM valves for different loads b. Speed error curve
Fig. 6 has RTM valves for different loads
left front motor left rear motor right front motor right rear motor
6
time/s
left front motor left rear motor right front motor right rear motor
4 6
time/s
Fig.7 One-side step load RTM free valve
Fig.8 Single step load with RTM valve
120
100 -
80 -
60
40
20
0
2
8
10
0
2
4
8
10
300
120
100
e 200
80 -
150
60
40
50
20 -
0
0
2
8
10
0
2
8
Following the above simulation results, a step load of 718N-m is applied to one side of the sprayer at 5s. In the absence of the RTM valve, on the side loaded with 718N-m, the motor speed suddenly drops down to 0, while the motor speed increases linearly on the side without step load. At 6.5s, the motor speed stabilizes at 205r/min, and the speed error reaches 105r/min, so the sprayer may deviate during driving. In the presence of the RTM valve, the sudden increase of step load in 5 s makes the motor speed overshoot, but it quickly becomes stable, and the maximum speed error is 2r /min. To sum up, the hydraulic drive system that uses a RTM valve has clearly better synchronization than the one not having a RTM valve.
Real vehicle test results
The designed hydraulic drive system is mounted on the self-propelled sprayer. The test site is in the field road of Sanfenchang Erlian, Shihezi City in Xinjiang, with a driving speed of 4km/h. The parameters of the gasliquid mixed suspension is adjusted before the test. For the test instrument, SR-RPM6000 speed sensor is used to measure the speed signals of the four tires. The installation location of the sensor is shown in Fig. 9.
1. Speed sensor 2. Tester3. PC terminal (including test analysis system and processing system)
Fig. 9 Sensor installation location
A reflective strip is pasted on the circumference with a radius of 20cm from the axis of the four hubs, and the infrared signal of the rotational speed sensor is aligned with the reflective strip placed on the rotating shaft to be measured, and a safe non-contact RPM measurement is performed on the tire. The speed change curves of the four wheels after the RTM valve is opened are obtained, as shown in Fig. 10a.
1
3
left front wheel left rear wheel right front wheel right rear wheel
10
time/s
left front wheel left rear wheel right front wheel right rear wheel
a. Speed change curve
b. Test synchronization error curve
Fig. 10 Test curve
Compared with the simulation curve, due to the rolling resistance between the wheel and the ground, the external leakage of the hydraulic connector and the internal leakage of the hydraulic motor, the system pressure fluctuates to a certain extent, which results in a rise in the test curve fluctuation. It takes a long time to stabilize, about 3 s.
The experimental synchronization error curve is shown in Fig. 10b, which is expressed by the M1D curve here. It can be seen from the figure that the test synchronization error of the right rear wheel is the largest, about 5.0 r/min, which meets the straight-line driving requirements of the sprayer chassis, and further verifies the correctness of the theoretical analysis.
Conclusions
(1) A hydraulic drive system suitable for large-scale self-propelled boom sprayers is designed to tailor to the four-wheel straight-line driving requirements of the sprayer under different working conditions. Conforming to the working principle of its hydraulic pump, main hydraulic valve and hydraulic motor, a mathematical model is established, and a simulation model of the hydraulic drive system of the sprayer is built based on the AMEsim simulation software. The simulation results have verified the accuracy of the model.
(2) By analyzing the simulation results, when different loads are applied to the four motors and different step loads are applied to the one-side motor, the synchronization error of the four motors is 0-2r/min, which is superior to the hydraulic pressure without the RTM valve in terms of synchronicity and meets the requirements of straight-line driving.
(3) The actual vehicle test results of the hydraulic drive system show that the errors of the four motors are all less than 5r/min, which verifies the practicability, stability and reliability of the hydraulic system involved.
80 -
60
40
20
0
0
5
15
20
References
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