See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/269342602 Modelling and Validation of Vehicle Ride Comfort Model Article in Applied Mechanics and Materials · June 2014 DOI: 10.4028/www.scientific.net/AMM.554.515 CITATIONS READS 7 963 3 authors, including: Saiful Anuar Abu Bakar Pakharuddin Mohd. Samin Universiti Teknologi Malaysia Universiti Teknologi Malaysia 31 PUBLICATIONS 129 CITATIONS 62 PUBLICATIONS 600 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: Novel Strategy to enhance the efficiency of electric vehicle powertrain using electro mechanical continuously variable transmission. View project AI CONTROL TECHNIQUES APPLIED TO AN ABS APPLICATIONS View project All content following this page was uploaded by Saiful Anuar Abu Bakar on 19 March 2019. The user has requested enhancement of the downloaded file. Applied Mechanics and Materials Vol. 554 (2014) pp 515-519 Online available since 2014/Jun/02 at www.scientific.net © (2014) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMM.554.515 Modelling and Validation of Vehicle Ride Comfort Model Saiful Anuar ABU BAKAR1, a, *, Pakharuddin MOHD. SAMIN2,b Azhar ABD. AZIZ1,c , 1 Automotive Development Centre (ADC), Universiti Teknologi Malaysia, 81310 Skudai Johor. 2 Department of Aeronautics, Automotive and Ocean Engineering, Universiti Teknologi Malaysia, 81310 Johor, Malaysia a saiful@fkm.utm.my, bpakhar@fkm.utm.my, cazhar@fkm.utm.my, Keywords: Ride model, full vehicle model, 7DOF vehicle ride model Abstract. This paper presents the development of a validated seven degrees of freedom (7DOF) of vehicle ride comfort model for a Malaysian made passenger vehicle. The mathematical equations of the ride model, which consists seven degrees of freedom, are represented. Ride test known as pitch mode test was conducted to validate the reliability of the developed simulation model. The test was conducted using a fully instrumented test vehicle where the sensors installed were used to gather information on vehicle’s vertical and pitch motions. The data collected are used to tune certain parameters value in the simulation model, to ensure the developed simulation model can be used to represent the ride dynamics behaviour of the test vehicle. The result shows that the developed simulation model is capable in representing the ride dynamics behaviour of the test vehicle. Introduction Vehicle dynamics models tend of fall into of two categories. The first uses a multi-body approach to generate the equations of motion, where the vehicle is described as a collection of rigid bodies connected by appropriate joints and internal forces and subject to external forces. The second equation of vehicle dynamics modelling is known as simplified model. They are three main types of simplified vehicle model often used in vehicle dynamics analysis namely quarter car, half car and full car models. In quarter car model, only up-down movements of the sprung and unsprung masses are assumed and the role of the control arm is completely ignored. While, half car model is a combination of two-quarter car models that included the rotational effects of pitch or roll as well as bounce is sprung mass motions. For the full vehicle model, it can be divided into a ride model to simulate road bump test and a handling model to simulate vehicle cornering or braking behaviour. Full vehicle modelling is more preferred in studying vehicle’s ride comfort performance (and also to test the developed control algorithm) rather than the quarter car model or the half car model. This can be looked by others researchers work. [1,2,3,4]. In this study, a ride model is derived based on Ikenaga (2000) and later being validated by the experimental data. The validation on the developed model is necessary in order to make sure that the developed model is valid to be used in order to further study vehicle’s ride dynamics or to study advance suspension system. Mathematical Modelling of Ride Comfort Model A vehicle’s ride model is derived based on the work done in [5]. The ride model consists of seven degrees of freedom namely roll, pitch, bounce and vertical motion of each four wheels. Figure 1 show the vehicle’ ride model. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 103.1.71.85-07/07/14,07:17:08) 516 Mechanical and Materials Engineering Fig. 1 Seven degree of freedom of vehicle ride model Based on the 7DOF of ride model in Figure 1, the displacements of the sprung masses are given by; a Z sij = Z b + car θ car − Li α car 2 (1) with Z sij is the total sprung mass displacement (i =f for front, r for rear and j=l for left, r for right), is the sprung mass vertical displacement at the center of gravity, θ car is the roll angle and α car is the pitch angle. The distance of centre of gravity to the front axle and rear axle are given by L f and Zb Lr respectively. The forces acting at each of the suspension ( Fij ) is the sum of the spring force ( Fsij ) and damper force ( Fdij ) . The suspension forces are given by (2) Fij = F sij + F dij The spring forces, Fsij in each of the suspension system are given by; (3) F sij = K sij ( Z uij − Z sij ) with K sij is the spring stiffness of the spring, Z uij and Z sij are the unsprung mass vertical displacement and the sprung mass vertical displacement respectively at each side of the vehicle. The damper forces, Fdij are given by; . . (4) F dij = C sij ( Z uij − Z sij ) . . with C sij are the damping coefficient of the dampers, Z uij and Z sij are the unsprung mass vertical velocity and the sprung mass vertical velocity respectively. For the vehicle tires, it is modelled as a spring and the force acting at tires is usually known as dynamic tire loads, Ftij . For each tires, their dynamic tire loads are given by; Applied Mechanics and Materials Vol. 554 Ftij = K tij ( Z rij − Z uij ) 517 (5) where K tij , Z rij , and Z uij , are the tire stiffness, road input displacement and unsprung mass displacement respectively. Using Newton’s Second Law at the vehicle’s sprung mass, the body vertical acceleration, Zb can be determined by F fl + F fr + Frl + Frr = M b Zb (6) where M b is the total mass of the vehicle. Angular acceleration during the roll effect, θcar is given by; a a ( F fl + Frl ) car − ( F fr + Frr ) car = I xxθcar 2 2 (7) where a is the vehicle’s track width and I xx is the moment of inertia about x-axis. The angular acceleration while the vehicle is in pitch effect, αcar it is given by; ( Frl + Frr ) Lr − ( F fl + F fr ) L f = I yyαcar (8) with I yy are the vehicle’s wheelbase and moment about y-axis respectively. Acceleration of each wheel can be calculated using Ftij − Fsij − Fdij = M uij Zuij (9) with M uij are the unsprung masses at each corner of the vehicle. The vehicle ride comfort model was developed using equations (1) to (9) using Matlab/Simulink. Validation of Vehicle Ride Model The developed vehicle ride model was validated with an experimental vehicle in order to determine the model’s reliability in representing an actual vehicle’s ride behaviours. A Malaysian made vehicle was used in validating the developed simulation model. In vehicle’s instrumentation preparations, several types of transducers were used and there are three-axis sensor that measure vertical, longitudinal and lateral acceleration as well as the rotational motions (roll, pitch and yaw). The three-axis sensor was located approximately at the centre of gravity of the vehicle. An amount of 8 units of single axis accelerometer were installed at each corner of the vehicle, at the sprung and unsprung masses. The accelerometers were used to measure vertical acceleration of vehicle’s sprung and unsprung masses when the vehicle hit the bump. A multi-channel Dewetron data acquisition system was used for the data collection. A pitch test was performed during the experiment. In pitch test, a bump with the dimensions of 2.4m in length, 0.4m in width and 0.075m in height, was used and arranged perpendicularly to the vehicle’s driving direction. A speed of 20km/h was used during this test. In this pitch test, the front wheels will hit the bump followed by the rear wheels. Table 1 shows the vehicle parameters used for the simulation model and Figures 2 to 5 shows the validation results between the experimental and simulation data. It can be seen that there is a good correlations between the simulation and experimental data; in terms of responses’ trends. 518 Mechanical and Materials Engineering Table 1 Vehicle Parameters Mb 1250 kg Ksfr 17900 N/m Mufl 50 kg Ksrl 17900 N/m Mufr 50 kg Ksrr 17900 N/m Murl 50kg Csfl 3100 Ns/m Murr 50 kg Csfr 3100 Ns/m a 1.5 Csrl 3100 Ns/m L 2.6 Csrr 3100 Ns/m Ixx 289 kgm^2 Ktfl 23000 N/m Iyy 3300 kgm^2 Ktfr 23000 N/m Izz 13350 Ktrl 23000 N/m Ksfl 17900 N/m Ktrr 23000 N/m Jerk 1000 800 600 Jerk (m/s^3) 400 200 0 -200 0 0.5 1 1.5 2 2.5 3 3.5 -400 -600 -800 -1000 Time Simulation Experiment Fig. 2 Jerk response Vertical Acceleration 15 Acceleration (m/s^3) 10 5 0 0 0.5 1 1.5 2 2.5 3 3.5 3 3.5 -5 -10 -15 -20 Time Simulation Experiment Fig. 3 Vertical acceleration response Vertical Displacement 0.04 Acceleration (m/s^3) 0.03 0.02 0.01 0 0 -0.01 0.5 1 1.5 2 2.5 Time Simulation Experiment Fig. 4 Vertical displacement response Applied Mechanics and Materials Vol. 554 519 Pitch Rate 0.35 0.3 0.25 Pitch Rate (rad/s) 0.2 0.15 0.1 0.05 0 -0.05 0 0.5 1 1.5 2 2.5 3 3.5 -0.1 -0.15 -0.2 -0.25 Time Simulation Experiment Fig. 5 Pitch rate response Conclusions The validations of the simulation model of 7DOF of the ride model were done, by comparing the simulation’s results with the results gained from the experiments. Pitch test was done to measure the vehicle’s ride performance. The road inputs that were used in the built 7DOF model were able to create the required effect (vertical and pitch motions) and this can be seen clearly by looking at a good correlations between the simulation and experimental results. This shows that the derived equations and the built model can be used to represent 7DOF of a full car in order to study the vehicle’s ride performance. However, certain parameters such as the moment of inertia need to be fined tuned if the model wants to be used for further research works. This is in order to minimize the error between the simulation results and the experimental results, which will further create a reliable and more accurate model. Acknowledgements The authors wish to acknowledge the financial support of Ministry of Science Technology and Innovation, Malaysia, Automotive Development Center, UTM for the support, PROTON Malaysia for the donation of PROTON PERSONA being used as the experimental car and finally the staffs of Department of Aeronautic and Automotive, Faculty of Mechanical Engineering, University Technology Malaysia. References [1] Chike,C.,Shim,T. “ 14 Degree of Freedom Vehicle Model for Roll Dynamics Study “, SAE Paper No.2006-01-1277, 2006. [2] Hudha,K, “Non-parametric Modeling and Modified Hybrid Skyhook Groundhook Control of Magnetorheological Dampers for Automotive Suspension System”, Ph.D Thesis, Universiti Teknologi Malaysia (2005). [3] Jun Wang, David A. Wilson, Wenli Xu, David A. Crolla, “ Active Suspension Control to Improve Vehicle Ride and Steady-State Handling.” 44th IEEE Conference on Decision and Control, 2005. [4] Ossama Mokhiamar, Masato Abe.” Effects of model response on model following type of combined lateral force and yaw moment control performance for active handling safety”, JSAE Review 23(2002) 473-480. [5] Ikenaga.S., Lewis.F.L., Campos.J., Davis.L. “Active Suspension Control of Ground Vehicle based on Full-Vehicle Model ”, AACC Paper, 2000. Mechanical and Materials Engineering 10.4028/www.scientific.net/AMM.554 Modelling and Validation of Vehicle Ride Comfort Model 10.4028/www.scientific.net/AMM.554.515 View publication stats