Available online at www.sciencedirect.com
Physics Procedia 33 (2012) 1663 – 1669
2012 International Conference on Medical Physics and Biomedical Engineering
Study on Dynamical Simulation of Railway Vehicle Bogie Parameters Test-bench Electro-hydraulic Servo System Zhikun Lan1,2, Jian Su1, Guan Xu1, Xiaoning Cao1 1
College of Traffic, Jilin University, Changchun , China e-mail:
[email protected] 2 School of Vehicle Engineering, Changchun University, Changchun, China
Abstract Dynamical mathematical model was established for accurately positioning, fast response and real-time tracing of electro-hydraulic servo control system in railway vehicle bogie parameters test system with elastic load. The model could precisely control the output of position and force of the hydraulic cylinders. Induction method was proposed in the paper. Dynamical simulation verified the mathematical model by SIMULINK software. Meanwhile the key factors affecting the dynamical characteristics of the system were discussed in detail. Through the simulation results, high precision is obtained in application and the need of real-time control on the railway vehicle bogie parameters test-bench is realized .
2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [nameCommittee. organizer] ©©2012 Published by Elsevier B.V. Selection and/or peer review under responsibility of ICMPBE International Open access under CC BY-NC-ND license. Keywords: bogie; dynamical simulation; real time control; electro-hydraulic servo system.
1. Introduction As the walking mechanism of railway vehicle, the bogie was important to ensure the railway vehicle safety [1]. The anti-shearing stiffness, anti-bending stiffness and tensile stiffness of bogie were key factors of affecting the security, smoothness and stability of railway vehicle[2]. For testing these parameters of bogie, a new railway vehicle bogie test-bench was developed. The electro-hydraulic servo system (EHSs) is the only power output agency of the test-bench, whose stability, accuracy and efficiency is essential to the whole performance of the test-bench. So, dynamical mathematical model of EHSs was established to meet the need of test accuracy.
1875-3892 © 2012 Published by Elsevier B.V. Selection and/or peer review under responsibility of ICMPBE International Committee. Open access under CC BY-NC-ND license. doi:10.1016/j.phpro.2012.05.268
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2. Structure of bogie test-bench The parameters test-bench of railway vehicle bogie was consisted of mechanical system, EHSs and comprehensive test-control system. Fig.1 is the prototype of the new bogie test-bench. Mechanical system was the frame of the bogie test-bench, which was consisted of gantry, cross slidebed, the agency of fixing wheel and guiding rail. It mainly fixed the bogie and actuators of EHSs. EHSs was composed of 21 actuators and the connecting parts, which controlled the output of displacement and force of each actuator. Comprehensive test-control system was consisted of control-bed and computer, which controlled the moving of all actuators in EHSs. Dynamical model was mainly studied in this paper. Under the fixed frequency vibration, the parameters of bogie was tested. Fig.2 was the control system principle diagram of EHSs.
Fig.1 New bogie parameters test-bench 1-gantry;2-loading set;3-hydraulic system; 4-clamping set to wheel
Fig.2
ontrol diagram of electro-hydraulic servo system
1-force sensor;2-displacement sensor;3-power amplifier; 4-control unit;5-comparator;
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3. The mathematical model establishment of the EHSs in bogie test-bench EHSs imposed the electrical signal on the driving system of experimental subject. The servo hydraulic cylinder with the characteristics of high strength, high frequency response and low friction. For obtaining high stability, symmetrical hydraulic cylinder was adopted in the system. Fig.3 was the diagram of EHSs.
Fig.3 Diagram of valve-controlled cylinder system 1-force sensor;2-electromagnet;3- displacement sensor;4-amplifier;5-control unit
The dynamic characteristic of the valve-controlled hydraulic cylinder was up to the valve, the hydraulic cylinder and the load. Through analysis, for the sake of compact description and convenient application, a linear analysis method was applied, the characteristics of the minim movement at a certain steady-state were investigated carefully. Practices have proved powerfully that this linear analysis configuration was effective in wide work domains. 3.1 Flow and Pressure Equation of Servo Valve-Controlled Symmetric Hydraulic Cylinder In the EHSs of railway vehicle bogie parameters test-bench, four-way slide valve was adopted, so the flow of two oil chamber was given by the following formula[3]: Q1
Q2
A
dy dt
A
dy dt
V0 dp1 dt
V0 dp2 dt
Lm pL
Lm pL
L0 p1
L0 p2
(1)
(2)
Where Q1 was the input flow, m3/s, Q2 was the output flow, m3/s, A was the effective area of piston, m , V0 was the event volume of two chambers, V0 =2 V1 V2/( V1+ V2), m3, Lm was the internal leakage coefficient of the actuators, m3/(s·Pa),L0 was outer leakage coefficient of the system, m3/(s·Pa), PL was the difference between p1 and p2, Pa. According to the flow characteristic of four-way slide valve, the flow equations were following: 2
Q1 Q2
K q x K L p1 ( K q x K L p2 )
(3) (4)
Where Kq was the gain of slide valve in the stable operation-point, m3/(s·m), x was the displacement of valve core, m, KL was the coefficient of flow-pressure in the slide valve in stable operation-point, m3/(s·Pa). And then integrated the formula (1), (2), (3),(4), we can obtain:
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K q x K L p1
A
dy V0 dp1 dt dt
Lm pL
L0 p1
(5)
K q x K L p2
A
dy V0 dp2 dt dt
Lm pL
L0 p2
(6)
p2 )
(7)
Integrated (5) and (6), getting the formula as the following: dy V0 d 2 K q x K L ( p1 p2 ) 2 A ( p1 dt dt
p2 )
2 Lm pL
L0 ( p1
Simplify the formula(7) and getting the formula(8):
Kq x Where Km was the leakage coefficient of system, K m
A
dy V0 dpL dt dt L0
( Lm
2
(8)
K m pL
KL . )
3.2 Force Balance equation of Symmetric Hydraulic Cylinder Taking account of the nonlinear load such as spiral spring and air spring of railway vehicle bogie and ignoring coulomb friction and oil mass, according to Newton’s law of force and acceleration, the force balance equation of vertical hydraulic cylinders was given as the following: ApL
m
d2y dt 2
B
dy dt
K s y FP
Ff
mg
(9)
Where m was the mass of piston and load, kg, B was the viscous coefficient of cylinder and load,
N s / m , Ks was elastic coefficient, N/m, Fp was the air spring resistance, N, Ff was the load force, N. Air spring resistance Fp was nonlinear at certain extent. The gravity of piston and load was constant, the load force was nonlinear, adopting induction method dealt with Fp , Ff and mg. So mathematical model was simplified. Formula (9) transformed into formula (10).
ApL m
d2 y dy B Ks y F dt 2 dt
Where F was an equivalent substitution, F= Ff+ Fp+mg. Combining the formula (8) and (10) after Laplacian transform as the following:
Kq Y ( s)
A 2
(
the system output function was given
Km s (1 )F A2 1 s2 2 0 1)( 2 s 1)
X (s) s r
(10)
0
0
(11)
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Where
0
was oscillation frequency,
2 ( K m B A2 ) K sV0 , (1 ) V0 m 2 A2
0
0
was damping ratio,
2 Km , Ks Km , 1 2 . 2 Km B , r 1 2 2 V A K V 1 2 0 2 0 V (1 s 0 ) m 0 2 2 A In the EHSs, the formula of valve core displacement was given as the following: 1
0
X=(U i -K H Y)K a K sy K q
(12)
Where U i was input voltage, V, K H was feedback gain, V/m, K a was electric conversion gain, mA/V.
K sy was slide valve core displacement gain, K sy
s2 2 mf
coefficient,m3/ ·mA.
1 2 mf
, m/ mA, K q was slide valve flow
s 1
mf
3.3 Dynamical simulation of EHSs Combining formula (11) with formula(12), the control system principle diagram was given as Fig. 4. We established the mathematical model of EHSs based on Simulink software[4]. For conveniently simulating, these parameters in the model were initialized as the table I.
Fig.4 Control system principle diagram Table I simulation parameters KH
Kq
0.98
2.71
B
2.10e3
m
1100
Km
1.5e-11 A
Ka
1.26 Ks
2.26e-2 7.0e7
V0
6.8e-3
8.0e8
mf
mf
320
0.5
The dynamical simulation was carried out in Matlab7.0. As shown in Fig.5, a step signal was input into the system, which goes through about 0.15s vibrating and then gradually gets steady. When simulation carries out to 0.2s, the vibration disappears, so the simulation curve denotes that the system shortly gets steady state and the system performance is excellent.
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Zhikun Lan et al. / Physics Procedia 33 (2012) 1663 – 1669 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1
0
0.05
0.1
0.15
0.2
0.25
Fig.5 System dynamical simulation
When one of all parameters is changed, the system dynamical performance changes with it. So simulation testified the adaptability of system model. Fig.6, Fig.7 and Fig.8 show the dynamical is respectively changed. Each affects characteristic of the system when parameters KH Kq and differently the time from vibration to steadiness of the system. 4. CONCLUSION In the paper, in order to testify the property of EHSs and avoid labor intensity, the mathematical model of the railway vehicle bogie EHSs is established. Through objectively and comprehensively analyzing factors which affect the system stability and efficiency, We simulate the mathematical model in Matlab7.0. The simulation results distinctly demonstrate that the model can meet the need of fast, effective and real-time control on the railway vehicle bogie EHSs. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1
Fig.6 KH=0.62
0
0.05
0.1
0.15
0.2
0.25
Zhikun Lan et al. / Physics Procedia 33 (2012) 1663 – 1669 0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Fig.7 Kq=1.356 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1
Fig.8
0
0.05
0.1
0.15
0.2
0.25
=160
References [1]Li Fu-yi, “Hydraulic technology and hydraulic servo system,” Harbin Engineering University Press, Harbin, 1992. [2]B.M.Eikhoff, J.R.Evans. “A Review of Modeling Methods for Railway Vehicle Suspension Components”, Vehicle System Dynamist ,1995, Vol24 (3):pp.469-496. [3]Wang Xing-yu, Su Jian, “Modeling and Analysis of Hydraulic Pressure Servo for Railway Vehicles Bogie Test Bench”, Chinese Hydraulics and Pneumatics, 2009(6),pp.8-11. [4]Li Zi-guang, You Zhang-ping, “Study on dynamical simulation of hydraulic servo system based on Simulink”, Chinese Jounal of Construction Machinery, Vol.2, No.1, Jan.2004,pp.30-34
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