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Dynamic analysis of steering system of the articulated vehicle in the heeled status
Available online at www.sciencedirect.com
Procedia Engineering 16 (2011) 540 – 545
International Workshop on Automobile, Power and Energy Engineering
Dynamic analysis of steering system of the articulated vehicle in the heeled status Zhiguo Zhaoa*, Chuansheng Sib, a b
Huaiyin Institute of Technology,Huai’an,Jiangsu,223001,china Huaiyin Institute of Technology,Huai’an,Jiangsu,223001,china
Abstract In order to research the dynamic characteristic when the articulated vehicle accelerates, brakes and steers, it is necessary to analyze the force of the front and the rear car body and establish the steering dynamic mathematical model and simulation model when the articulated vehicle is in the heeled status. Taking the FW - 6 underground service car as an example, the results of the numerical simulation when the initial velocity of the vehicles is 12m/s, the heeled angle of rear car body is 0° and the heeled angle of front car body is 8° show that the dynamic responses of the steering acceleration, steering angle and steering speed are strong, at the same time, the vehicle steering stability is seriously impacted.
© 2010 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Society for Automobile, Power and Energy Engineering Keywords: Articulated vehicle, heeling, steering system, dynamic characteristics
1. Introduction Articulated vehicle refers to the engineering vehicles that the front frame and the rear frame are connected by hinge joint and swinging rings. Articulated vehicle becomes the indispensable equipments of mining machinery and agricultural engineering [1], because it has maneuverable, flexible, multifunctional and economic superiority. The dynamic characteristic is very important for the articulated Vehicle when the vehicle accelerates, brakes and steers. In literature [2-5], there was only the dynamic characteristic study when vehicle moved smoothly, and the articulated vehicle was divided into two parts that is the front body and rear body then did the research by establishing the linear mathematical model,
* Corresponding author. Tel.:+86+517-83559166; fax: +86+517-83559166. E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.1122
541
Zhiguo Zhao and Chuansheng Si / Procedia Engineering 16 (2011) 540 – 545
ignoring the very dangerous rollover swing. Articulated vehicles have lateral dynamic characteristic. The rollover is very dangerous and even can threaten the operator. The rolling instability is caused by many factors, such as hang, tires, human factors, weight and size, but the most important factor is the rollover due to the uneven road. Therefore, to describe the vehicle roll behavior more comprehensively and more accurately, it is necessary to rely on more perfect car model to simulate the roll response. 2. Establishing the dynamic model When analyze the articulated vehicle steering dynamics, there are some assumptions: (1) ignoring the air resistance; (2) ignoring the friction that has little influences on the movement. With car forward initial direction as the X axis and anti-clockwise steering direction that is perpendicular to the X axis as Y axis, establish the level steering simplified diagram of the hinged steering vehicle (shown in chart 1).Among them: Or is hinge center, O1O2 are the centroids of the front and the rear bodywork respectively; a and b are the distances between the front and rear bodywork centroids to the hinge point respectively, mm; c, d are the distances between the front and rear shaft axes to the hinge point respectively, mm; 2e is distance between wheels, mm; w1 w2 are the angular velocities of the front and rear bodywork centroids respectively, rad/s; vx1 vy1 are the lateral and longitudinal velocities of front bodywork centroid respectively, m/s; vxvy are the lateral and longitudinal velocities of rear bodywork centroid respectively, m/s; is vehicle steering Angle °.
Fig. 1. the level steering simplified diagram of the hinged steering vehicle
1) The longitudinal and lateral accelerations of the front bodywork:
ax1 = vx1 − v y11
(1)
a y1 = v y1 − vx11
(2)
2) The longitudinal and lateral accelerations of the rear bodywork:
a x = v x − v y 2
(3)
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Zhiguo Zhao and Chuansheng Si / Procedia Engineering 16 (2011) 540 – 545
a y = v y − v x 2
(4)
3) According to Newton's second law and fixed axis rotation laws of rigid body, for the front bodywork, here:
I xs1
d 2 a1 da − I xs11 + ms1h1 (v y1 + vx11 ) = (ms1 gh1 − K s1 )a1 − Cs1 1 dt 2 dt
I s11 − I xs1
d 2 a1 = ( Fy cos − Fx sin )a + ( Fs1 − FS 2 )(c − a ) + ( Fx1 − Fx 2 )e dt 2
(5)
(6)
4) According to Newton's second law, for the rear bodywork, here:
I xs 2
d 2 a2 da − I xs 22 + ms 2 h2 (v y + vx2 ) = (ms 2 gh2 − K s 2 )a2 − Cs 2 2 2 dt dt
I s 22 − I xs 2
d 2 a2 = Fy b + ( Fs 4 − Fs 3 )(d − b) + ( Fx 3 − Fx 4 )e dt 2
(7)
(8)
5) The lateral and longitudinal velocities of the front bodywork:
vx1 =
v y1 =
3vx − v y − 1a(3sin + cos ) − b2 2cos
(9)
2b + 1a(sin + cos ) − vx + v y 2sin
(10)
3. The numerical simulation and analysis 3.1. Research object Taking FW-6 underground service car as the research object. Concrete parameters: M=7850kg; ms1=2850kg; ms2=2000kg; m1=4350kg; m2=3500kg; e=0.75m; h1=0.55m; h2=0.35m; a=0.140m; b=0.30m; c=1.660m; d=1.74m; Ks1=Ks2=820N . m )-1; Cs1=Cs2=280 N . m . )-1; Ixs1=2053.015k . m2; Is1=3596.582k . m2; Ixs2=1962.632k ⋅ m2; Is2=4607.961k ⋅ m2 . It is possible to get the corresponding equations by substitution these parameters into the formulas from (1) to (10). In the new equations, variables are vx1 vy1 vx vy a1 a2 Fx Fy and all equations are about time variable t. Through getting different values of vx1, it is too easy to find that the remaining variables are the real-time dynamic characteristics about time variable. 3.2. Simulation model Here assume vx1= 12m/s. Using simulink [6] tool of matlab, create a simulation model shown in figure 2 of equation (1). Through this method, the simulation models of equations (2) to (10) can be listed in sequence, then according to the relationship of variable between equations, integrate them all together, and finally build the whole vehicle mathematical model that contains 10 equations.
Zhiguo Zhao and Chuansheng Si / Procedia Engineering 16 (2011) 540 – 545
Fig.2. simulation model
3.3. Solving analysis Setting the simulation time: from 0 to 14s. With sine steering that the amplitude is 0.01 (rad) and the cycle is 2(s) as the inputs, describe steering response when the vehicle’s speed is constant 12m/s. Run the Simulink program, and get the dynamic response of the front body lateral acceleration, shown in figure 3. In the figure, the dotted line represents dynamic response curve of the front bodywork lateral acceleration when the lateral angle of the front frame is 8° and the lateral angle of the rear frame is 0°. Solid line represents dynamic response curve of the front frame lateral acceleration when the lateral angle of the front frame and the rear frame are both 0°.
Fig.3. the dynamic response curve of the front frame lateral acceleration ay1
Fig.4 is dynamic response curve of the steering angle . The dotted line represents dynamic response curve of the steering angle when the lateral angle of the rear frame is 0° and the lateral angle of the front frame is 8°. Solid line represents dynamic response curve of the steering angle when the lateral angles of the front frame and the rear frame are both 0°.
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Zhiguo Zhao and Chuansheng Si / Procedia Engineering 16 (2011) 540 – 545
Fig.4. the dynamic response curve of the steering angle
Fig.5 is the dynamic response curve of steering speed vy1. In the figure, the dotted line represents dynamic response curve of the steering speed vy1 when the lateral angle of the rear frame is 0° and the lateral angle of the front frame is 8°. Solid line represents dynamic response curve of the steering speed vy1 when the lateral angle of the front frame and the rear frame are both 0°.
Fig.5. dynamic response curve of steering speed vy1
From Fig.3 to Fig.5, it is obvious that, dynamic responses of steering acceleration, steering Angle and steering speed are rather strong because of lateral phenomenon. That is the lateral phenomenon seriously affects the vehicle steering stability. 4. Conclusion 1) We established the mathematics model and simulation model of the steering system when the hinged car is in the lateral status. 2) Taking the FW-6 underground service car as an example, conduct the numerical simulation under the conditions that the vehicle initial velocity is 12m/s, the lateral angle of the rear frame is 0° and the
Zhiguo Zhao and Chuansheng Si / Procedia Engineering 16 (2011) 540 – 545
lateral angle of the front frame is 8° and obtained the dynamic response curves of steering acceleration, steering angle and steering speed when hinged vehicle is steering and in a certain lateral status. 3) The simulation results show that in the front frame heeled circumstance, dynamic response of the whole car with lateral phenomenon is rather strong and the steering stability is seriously influenced.
References [1] Jianjun Dong, Wenming Zhang, Boqiang Shi. General of Underground Mining Articulated Dump Truck and Market in China. Coal Mine Machinery, vol.28, no.12, pp.1-3, 2007. [2] Jinyue Tian, Huixing Jia. Dynamic Simulation of the Overturning of Articulated Vehicles. Transactions of the Chinese Society for Agricultural Machinery, vol.37, no.7, pp.26-29, 2006. [3] Meirong Zhao, Kai Chang, Xi Yang. Analysis of the Steering Feature for Mine Articulated Vehicles. Mechanical Engineering & Automation, no.4, pp.100-104, 2009. [4] Jianchun Wang. Dynamical mathematical model of in situ steering of articulated vehicles. Construction Machinery, no.6, pp.86-90, 2008. [5] Minzhen Ye. Study of steering Procedure of Articulated Frame and Design of Steering System. Construction Machinery, no.11, pp.9-11, 1997. [6] Hongli zhang. Building of Complicated Non-linear Module in MATLAB. Journal of Xinjiang University (Natural Science Edition), no.1, pp.419-222, 2004.
545
Procedia Engineering 16 (2011) 540 – 545
International Workshop on Automobile, Power and Energy Engineering
Dynamic analysis of steering system of the articulated vehicle in the heeled status Zhiguo Zhaoa*, Chuansheng Sib, a b
Huaiyin Institute of Technology,Huai’an,Jiangsu,223001,china Huaiyin Institute of Technology,Huai’an,Jiangsu,223001,china
Abstract In order to research the dynamic characteristic when the articulated vehicle accelerates, brakes and steers, it is necessary to analyze the force of the front and the rear car body and establish the steering dynamic mathematical model and simulation model when the articulated vehicle is in the heeled status. Taking the FW - 6 underground service car as an example, the results of the numerical simulation when the initial velocity of the vehicles is 12m/s, the heeled angle of rear car body is 0° and the heeled angle of front car body is 8° show that the dynamic responses of the steering acceleration, steering angle and steering speed are strong, at the same time, the vehicle steering stability is seriously impacted.
© 2010 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Society for Automobile, Power and Energy Engineering Keywords: Articulated vehicle, heeling, steering system, dynamic characteristics
1. Introduction Articulated vehicle refers to the engineering vehicles that the front frame and the rear frame are connected by hinge joint and swinging rings. Articulated vehicle becomes the indispensable equipments of mining machinery and agricultural engineering [1], because it has maneuverable, flexible, multifunctional and economic superiority. The dynamic characteristic is very important for the articulated Vehicle when the vehicle accelerates, brakes and steers. In literature [2-5], there was only the dynamic characteristic study when vehicle moved smoothly, and the articulated vehicle was divided into two parts that is the front body and rear body then did the research by establishing the linear mathematical model,
* Corresponding author. Tel.:+86+517-83559166; fax: +86+517-83559166. E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.1122
541
Zhiguo Zhao and Chuansheng Si / Procedia Engineering 16 (2011) 540 – 545
ignoring the very dangerous rollover swing. Articulated vehicles have lateral dynamic characteristic. The rollover is very dangerous and even can threaten the operator. The rolling instability is caused by many factors, such as hang, tires, human factors, weight and size, but the most important factor is the rollover due to the uneven road. Therefore, to describe the vehicle roll behavior more comprehensively and more accurately, it is necessary to rely on more perfect car model to simulate the roll response. 2. Establishing the dynamic model When analyze the articulated vehicle steering dynamics, there are some assumptions: (1) ignoring the air resistance; (2) ignoring the friction that has little influences on the movement. With car forward initial direction as the X axis and anti-clockwise steering direction that is perpendicular to the X axis as Y axis, establish the level steering simplified diagram of the hinged steering vehicle (shown in chart 1).Among them: Or is hinge center, O1O2 are the centroids of the front and the rear bodywork respectively; a and b are the distances between the front and rear bodywork centroids to the hinge point respectively, mm; c, d are the distances between the front and rear shaft axes to the hinge point respectively, mm; 2e is distance between wheels, mm; w1 w2 are the angular velocities of the front and rear bodywork centroids respectively, rad/s; vx1 vy1 are the lateral and longitudinal velocities of front bodywork centroid respectively, m/s; vxvy are the lateral and longitudinal velocities of rear bodywork centroid respectively, m/s; is vehicle steering Angle °.
Fig. 1. the level steering simplified diagram of the hinged steering vehicle
1) The longitudinal and lateral accelerations of the front bodywork:
ax1 = vx1 − v y11
(1)
a y1 = v y1 − vx11
(2)
2) The longitudinal and lateral accelerations of the rear bodywork:
a x = v x − v y 2
(3)
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Zhiguo Zhao and Chuansheng Si / Procedia Engineering 16 (2011) 540 – 545
a y = v y − v x 2
(4)
3) According to Newton's second law and fixed axis rotation laws of rigid body, for the front bodywork, here:
I xs1
d 2 a1 da − I xs11 + ms1h1 (v y1 + vx11 ) = (ms1 gh1 − K s1 )a1 − Cs1 1 dt 2 dt
I s11 − I xs1
d 2 a1 = ( Fy cos − Fx sin )a + ( Fs1 − FS 2 )(c − a ) + ( Fx1 − Fx 2 )e dt 2
(5)
(6)
4) According to Newton's second law, for the rear bodywork, here:
I xs 2
d 2 a2 da − I xs 22 + ms 2 h2 (v y + vx2 ) = (ms 2 gh2 − K s 2 )a2 − Cs 2 2 2 dt dt
I s 22 − I xs 2
d 2 a2 = Fy b + ( Fs 4 − Fs 3 )(d − b) + ( Fx 3 − Fx 4 )e dt 2
(7)
(8)
5) The lateral and longitudinal velocities of the front bodywork:
vx1 =
v y1 =
3vx − v y − 1a(3sin + cos ) − b2 2cos
(9)
2b + 1a(sin + cos ) − vx + v y 2sin
(10)
3. The numerical simulation and analysis 3.1. Research object Taking FW-6 underground service car as the research object. Concrete parameters: M=7850kg; ms1=2850kg; ms2=2000kg; m1=4350kg; m2=3500kg; e=0.75m; h1=0.55m; h2=0.35m; a=0.140m; b=0.30m; c=1.660m; d=1.74m; Ks1=Ks2=820N . m )-1; Cs1=Cs2=280 N . m . )-1; Ixs1=2053.015k . m2; Is1=3596.582k . m2; Ixs2=1962.632k ⋅ m2; Is2=4607.961k ⋅ m2 . It is possible to get the corresponding equations by substitution these parameters into the formulas from (1) to (10). In the new equations, variables are vx1 vy1 vx vy a1 a2 Fx Fy and all equations are about time variable t. Through getting different values of vx1, it is too easy to find that the remaining variables are the real-time dynamic characteristics about time variable. 3.2. Simulation model Here assume vx1= 12m/s. Using simulink [6] tool of matlab, create a simulation model shown in figure 2 of equation (1). Through this method, the simulation models of equations (2) to (10) can be listed in sequence, then according to the relationship of variable between equations, integrate them all together, and finally build the whole vehicle mathematical model that contains 10 equations.
Zhiguo Zhao and Chuansheng Si / Procedia Engineering 16 (2011) 540 – 545
Fig.2. simulation model
3.3. Solving analysis Setting the simulation time: from 0 to 14s. With sine steering that the amplitude is 0.01 (rad) and the cycle is 2(s) as the inputs, describe steering response when the vehicle’s speed is constant 12m/s. Run the Simulink program, and get the dynamic response of the front body lateral acceleration, shown in figure 3. In the figure, the dotted line represents dynamic response curve of the front bodywork lateral acceleration when the lateral angle of the front frame is 8° and the lateral angle of the rear frame is 0°. Solid line represents dynamic response curve of the front frame lateral acceleration when the lateral angle of the front frame and the rear frame are both 0°.
Fig.3. the dynamic response curve of the front frame lateral acceleration ay1
Fig.4 is dynamic response curve of the steering angle . The dotted line represents dynamic response curve of the steering angle when the lateral angle of the rear frame is 0° and the lateral angle of the front frame is 8°. Solid line represents dynamic response curve of the steering angle when the lateral angles of the front frame and the rear frame are both 0°.
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Zhiguo Zhao and Chuansheng Si / Procedia Engineering 16 (2011) 540 – 545
Fig.4. the dynamic response curve of the steering angle
Fig.5 is the dynamic response curve of steering speed vy1. In the figure, the dotted line represents dynamic response curve of the steering speed vy1 when the lateral angle of the rear frame is 0° and the lateral angle of the front frame is 8°. Solid line represents dynamic response curve of the steering speed vy1 when the lateral angle of the front frame and the rear frame are both 0°.
Fig.5. dynamic response curve of steering speed vy1
From Fig.3 to Fig.5, it is obvious that, dynamic responses of steering acceleration, steering Angle and steering speed are rather strong because of lateral phenomenon. That is the lateral phenomenon seriously affects the vehicle steering stability. 4. Conclusion 1) We established the mathematics model and simulation model of the steering system when the hinged car is in the lateral status. 2) Taking the FW-6 underground service car as an example, conduct the numerical simulation under the conditions that the vehicle initial velocity is 12m/s, the lateral angle of the rear frame is 0° and the
Zhiguo Zhao and Chuansheng Si / Procedia Engineering 16 (2011) 540 – 545
lateral angle of the front frame is 8° and obtained the dynamic response curves of steering acceleration, steering angle and steering speed when hinged vehicle is steering and in a certain lateral status. 3) The simulation results show that in the front frame heeled circumstance, dynamic response of the whole car with lateral phenomenon is rather strong and the steering stability is seriously influenced.
References [1] Jianjun Dong, Wenming Zhang, Boqiang Shi. General of Underground Mining Articulated Dump Truck and Market in China. Coal Mine Machinery, vol.28, no.12, pp.1-3, 2007. [2] Jinyue Tian, Huixing Jia. Dynamic Simulation of the Overturning of Articulated Vehicles. Transactions of the Chinese Society for Agricultural Machinery, vol.37, no.7, pp.26-29, 2006. [3] Meirong Zhao, Kai Chang, Xi Yang. Analysis of the Steering Feature for Mine Articulated Vehicles. Mechanical Engineering & Automation, no.4, pp.100-104, 2009. [4] Jianchun Wang. Dynamical mathematical model of in situ steering of articulated vehicles. Construction Machinery, no.6, pp.86-90, 2008. [5] Minzhen Ye. Study of steering Procedure of Articulated Frame and Design of Steering System. Construction Machinery, no.11, pp.9-11, 1997. [6] Hongli zhang. Building of Complicated Non-linear Module in MATLAB. Journal of Xinjiang University (Natural Science Edition), no.1, pp.419-222, 2004.
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