Reducing pitch angle and suspension jounces of a truck when braking on railway crossing by control of semi-active suspension

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This paper presents pith plane dynamic model of a cargo truck. Numerical simulations for determination of a pitch angle and deflection in front and rear suspension under braking on railway crossing are conducted.

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Nội dung Text: Reducing pitch angle and suspension jounces of a truck when braking on railway crossing by control of semi-active suspension

International Journal of Mechanical Engineering and Technology (IJMET) Volume 10, Issue 03, March 2019, pp. 1584–1592, Article ID: IJMET_10_03_159 Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=3 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed REDUCING PITCH ANGLE AND SUSPENSION JOUNCES OF A TRUCK WHEN BRAKING ON RAILWAY CROSSING BY CONTROL OF SEMI- ACTIVE SUSPENSION N. L. Pavlov Department of Combustion Engines, Automobile Engineering and Transport, Faculty of Transport, Technical University of Sofia, 8 Kliment Ohridski Blvd., 1000 Sofia, Bulgaria ABSTRACT This paper presents pith plane dynamic model of a cargo truck. Numerical simulations for determination of a pitch angle and deflection in front and rear suspension under braking on railway crossing are conducted. The change of the braking force is presented by trapezoidal form, similar to the theoretical law of variation of braking deceleration in the braking diagram of road vehicles. For the railway crossing profile trapezoidal function is used too. The numerical simulations are carried out in program field of MATLAB. After conducting tests for determination of a braking dynamics and braking properties of a truck in road conditions, the pith plane model is validated. Possibilities for pitch angle and suspension jounces reduction are given. A fifth wheel assembly, displacement sensors and data acquisition system are used in the road tests. Key words: Dynamic model, truck, simulation and road test Cite this Article: N. L. Pavlov, Reducing Pitch Angle and Suspension Jounces of a Truck When Braking on Railway Crossing by Control of Semi-Active Suspension, International Journal of Mechanical Engineering and Technology 10(3), 2019, pp. 1584–1592. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=3 1. INTRODUCTION Road transport and commercial vehicles are constantly being studied and improved, and proof of this is the availability of various publications on the topic. Along with the fuel economy and the exploitation efficiency of the road freight transport [1, 2 and 3], the problems of the dynamics of commercial vehicles are a question of present interest [4, 5]. When the road vehicles are under braking on the vehicle body acts a powerful disturbance as a torque. Its magnitude is proportional to the inertia force and, on the other hand to the mass centre height of the vehicle [6, 7 and 8]. The action of the torque is accompanied by longitudinal tilting of the vehicle body (pitch angle) due to the presence of elastic suspension. This results in http://www.iaeme.com/IJMET/index.asp 1584 editor@iaeme.com
N. L. Pavlov redistribution the normal reactions of the front and rear wheels. The phenomenon is most pronounced in vehicles with a short base and a high mass centre, for unladed trucks or tractors with a detached semitrailer. When the ground vehicles brakes, the wheel suspension travel may be spend and shocks may occur as a result of the inclusion of the jounce stops at maximum suspension deflection [9]. The phenomenon is known as a suspension "slam" or "jounce", which is an amalgamation of the words jump and bounce. In suspension terminology, it means the most compressed condition of a spring. These phenomena are even more pronounced when vehicle passing through convex irregularities such as some railway crossings (Fig. 1). This type of crossings has a profile corresponding to a single bump of triangle or trapezoidal irregularity. Figure 1 A primer of a railway crossing like single road irregularity 2. DYNAMIC MODEL In order to find the pitch angle and the suspension deflection values when the truck simultaneously braking and crossing over the railway, the dynamic model based on the authors’ model presented in [9] used to study the braking only, without any road irregularities. The present model is shown in Fig. 2. It takes into account the mass of the vehicle, its moment of inertia around the transverse axis, the elasticity of the front and rear suspension and the damping of the shock absorbers. The railway crossing is presented as irregularity with trapezoidal form. Figure 2 Dynamic model of a truck when braking on railway crossing Braking is a process of creating and control the artificial resistance of the vehicle motion. The braking of the vehicle is mainly accomplished by creating braking moments from the brake http://www.iaeme.com/IJMET/index.asp 1585 editor@iaeme.com
Reducing Pitch Angle and Suspension Jounces of a Truck When Braking on Railway Crossing by Control of Semi-Active Suspension mechanisms on the wheels [10]. Due to friction in the contact path, a tangential reaction Rx directed opposite of the direction of motion arises under the action of the braking moment. Then in braking mode for the differential equation of motion along x-axis is obtained: mx  Rx (1) Since the mass center of the vehicle lies above the center of elasticity of the suspension at any distance, the inertia force that is always directed against the acceleration, in the case of braking, creates torque. Because the trucks have elastic suspension of the body on the wheels, the resulting torque deflects the suspension elastic elements and tilts the vehicle forward at an angle θ around the center of elasticity – c. e. If the center of mass (m) is relocated to the point C placed in the horizontal plane of the center of elasticity (c. e.) it will not affect linear z-axis oscillations. To study the angular oscillations during braking, it is necessary to add the torque (moment) M = Fj.h (Fig. 3). After reducing the inertial force Fj and relocating the center of gravity to the plane of the center C, also is necessary to reduce the coordinate system in an appropriate manner. This is accomplished by relocating the start of the x-z coordinate system at a distance h, at point C, which is accepted as a new coordinate of the mass center. Figure 3 Dynamic model after reduction of inertia force and adding the torque M = Fj.h The torque M is added as a disturbance in the differential equation of the angular displacement around the y-axis. The change of the braking torque is presented by trapezoidal form, similar to the theoretical law of variation of braking deceleration in the braking diagram of road vehicles. The differential equations of motion of vertical and angular displacements are:     mz  1 z  a   2 z  b  c1 z  a   c 2 z  b   (2) c1 q1  c 2 q 2  1 q1   2 q 2     J  1 a z  a   2 b z  b  c1 az  a   c 2 bz  b   (3) c1 aq1  c 2 bq2  1 aq1   2 bq 2  M where q1 and q 2 are the coordinates of the road irregularities respectively under the front and rear axle of the truck, and also their derivatives q1 and q 2 , i.e. the velocities with which the wheels of the truck are moved along the vertical axis. For the inertia force can be writing: http://www.iaeme.com/IJMET/index.asp 1586 editor@iaeme.com
N. L. Pavlov F j  m. j  Rx  Rx1  Rx 2 (4) where j is braking deceleration; Rx1 and Rx2 are the longitudinal reactions in the contact between the wheels and the road under braking. In the used model the following assumptions have been accepted [9]: - the characteristics of the elastic and damping elements are linear; - the vehicle moves horizontally; - the aerodynamic drag is ignored; - the rolling resistance forces are ignored; - the influence of the inertia moments of the rotating parts is ignored; - the body angle is small (up to 15 °) and sin   , cos  1 . The dimensions of the railway crossing are given in Fig. 4 below: Figure 4 Dimensions of the railway crossing 3. NUMERICAL SIMULATIONS The simulations were performed using MATLAB with the given in Table 1 parameters: Table 1 Simulation parameters Parameter Symbol Value Unit Full mass of the truck m 7500 kg Moment of inertia J 33582 kg.m2 Front suspension stiffness c1 166600 N/m Rear suspension stiffness c2 230625 N/m Distance h 1,2 m Distance a 2,32 m Distance b 1,93 m Static load – front axle Gw1 33,355 kN Static load – rear axle Gw2 40,221 kN The minimal and maximal damping coefficients of suspension β1 and β2 are defined in the work [9]. The accepted values for the front suspension are: β1low=9520 N.s/m β1high=30000 N.s/m For the rear suspension: http://www.iaeme.com/IJMET/index.asp 1587 editor@iaeme.com
Reducing Pitch Angle and Suspension Jounces of a Truck When Braking on Railway Crossing by Control of Semi-Active Suspension β2low=12300 N.s/m β2high=35000 N.s/m The simulation results of a pith angle and suspension deflection with two different damping coefficients are shown in Fig. 5 and Fig 6. Figure 5 Effect of the shock absorber damping ratio (β) on the pitch angle θ when the truck brakes on the railway crossing with maximum acceleration j=8 m/s2. Subscribe l when βlow, h when βhigh In the figures 5 and 6 can be seen how increasing the damping reduce the truck pitch angle and eliminate the suspension jounce. Figure 6 Effect of the shock absorber damping ratio (β) on the front z1 and rear z2 suspension deflection when the truck brakes on the railway crossing with maximum acceleration j=8 m/s2. Subscribe l when βlow, h when βhigh. The black line shows the maximum of the dynamic suspension travel deflection The principal diagram of a possible control system for reducing the pitch angle and suspension jounce is shown in Fig. 7. The controller receives signals from the displacement sensors and generates control signals to the shock absorbers. http://www.iaeme.com/IJMET/index.asp 1588 editor@iaeme.com
N. L. Pavlov Figure 7 Principal diagram of a pitch angle control system Kpitch is a controller; Sp, Sz1 and Sz2 – sensor signals; 1 – brake pedal; 2 – pedal displacement sensor; 3, 4 – front shock absorbers; 5, 6 – rear shock absorbers; 7 – front axle displacement sensor; 8 – rear axle suspension sensor 4. MODEL VALIDATION For model validation was conducted road tests with real truck (Fig. 8). The distance, speed and acceleration of the truck when braking were measured by using “fifth wheel” measuring device (Fig. 9). Displacement sensors on front and rear axle, brake air pressure sensors and speed sensor for wheel slip determination were mounted on the truck (Fig. 10). The procedure of the road test is described in work [11]. Some numerical simulation results of braking on horizontal road are compared with the results obtained in the road tests (Fig. 11 and 12). Figure 8 The truck in road tests conditions http://www.iaeme.com/IJMET/index.asp 1589 editor@iaeme.com
Reducing Pitch Angle and Suspension Jounces of a Truck When Braking on Railway Crossing by Control of Semi-Active Suspension Figure 9 “Fifth wheel” measuring device assembly and data acquisition devices in the cabin a) b) Figure 10 Brake air pressure sensor 1a, truck speed sensor 1b, front axle displacement sensor 2a, rear axle displacement sensor 2b Figure 11 Measured and calculated - results for the pitch angle when braking http://www.iaeme.com/IJMET/index.asp 1590 editor@iaeme.com
N. L. Pavlov Figure 12 Measured and calculated - results for the front suspension deflection z1 and the rear suspension deflection z2 when braking Road tests have not been conducted on a railway crossing, but the author's opinion is that conducted test on horizontal road gives sufficient information for model validation. 5. CONCLUSIONS The paper presents a dynamic model allowing the study of the pitch angle and the suspension deflection when a truck braking on a railway crossing. The braking process was simulated using MATLAB program and validated with road brake tests. The principle of the pitch angle and suspension deflection reducing is outlined and a scheme of the control system is presented. ACKNOWLEDGMENTS This work was supported by Research and Scientific Centre of Technical University of Sofia, Bulgaria. REFERENCES [1] Kunchev, L. Methodology for selection the truck route. Engineering for Rural Development - Proceedings, Jelgava, Latvia, 2017, pp. 263-272. [2] Stoilova, S. and Kunchev, L. Application of the graph theory, AHP method and cost benefits analysis for route selection of a road train. Journal of the Balkan Tribological Association, 1, 2016, pp. 1041-1056. [3] Ivanov, R., Georgiev, K., Kadikyanov, G. and Staneva, G. An experimental research on the wear of truck tire. Transport Problems, 10(4), 2015, pp. 91-98. [4] Ivanov, R., Avramov, E. and Ivanova, D. Modeling of the reactions, acting on the tires and studying the stability of two axle’s lorry in case of unsteady motion. Proceedings BulTrans, Sofia, Bulgaria, 2013, pp. 58-63, In Bulgarian. [5] Kubo, P., Paiva, C., Larocca, A. and Dawson, J. Quantification of the vertical load applied to the pavement during braking maneuver of a commercial vehicle. Journal of Transportation Engineering, 142(4), 2016, pp. 1-4. [6] Karapetkov, St., Mihailova, M., Pehlivanov, S. and Moneva, I. Modeling the movement of a car when braking taking into account the oscillations around mass center. Announcements of Union of Scientists, Sliven, 11(2), 2006, pp. 70-71, In Bulgarian. http://www.iaeme.com/IJMET/index.asp 1591 editor@iaeme.com
Reducing Pitch Angle and Suspension Jounces of a Truck When Braking on Railway Crossing by Control of Semi-Active Suspension [7] Revin, A. The necessity of accounting for the dynamics of the vehicles pitch angle under braking with the assessment of the stability of motion. Izvestiya VolgGTU, 10(113), 2013, pp. 28-30, In Russian. [8] Revin, A. Body dynamics and stability of the vehicle during braking. Avtomobilnaya promyshlennost, 11, 2013, pp. 13-13, In Russian. [9] Pavlov, N. Possibilities for control of semi-active shock absorbers in order to reduce cases of suspension jounces when braking. Trans Motauto World, 3(1), 2018, pp. 19-20. [10] Dimitrov, S. and Kunchev, L. Motor vehicle theory. Sofia: TU – Sofia, 2016, pp. 180, In Bulgarian. [11] Pavlov, N., Sokolov, E. and Kochev, H. Braking performance of commercial vehicle with pneumatic actuated braking system – a method and equipment for road tests. Proceedings BulTrans, Sozopol, Bulgaria, 2015, pp. 130-134, In Bulgarian. http://www.iaeme.com/IJMET/index.asp 1592 editor@iaeme.com

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