Active Suspension Analysis of Full Vehicle Model Traversing over Bounce Sine Sweep Road
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1 Journal of Advances in Vehicle Engineering 1(1 ( Active Suspension Analysis of Full Vehicle Model Traversing over Bounce Sine Sweep Road Parviz Tomaraee* Department of Agricultural Machinery, Faculty of Agriculture, Ankara University, Ankara, Turkey (Manuscript Received: 12 November 2015; Revised: 15 January 2016; Accepted: 20 January, 2016 Abstract Semi-active and active suspensions influencing the vertical dynamics of vehicles enable improvement of ride comfort and handling characteristics compared to vehicles with passive suspensions. 7 DOF full vehicle model considering roll and pitch is presented for the objective vehicle. Hybrid CarSim-Simulink was adopted to achieve the effect of active suspension for the condition of road profile with bounce sine sweep road. The results are presented in terms of ride and handling performance criteria such as tire deformation, damping factor, damping force, jounce, roll, and pitch. The results show that the performance criteria are function of road profile input and that the designed active suspension configuration drastically affects the vibration attenuation and decrement of induced oscillations. Keywords: Active suspension; CarSim; Full vehicle model; Ride comfort Introduction A continuous domain of vehicle engineering discipline is to achieve an optimal level of handling and ride that are two contradictory parameters to be achieved. A substantial characteristic for maximization of ride comfort is to minimize the vehicle body acceleration. Ride safety and improved handling characteristics can be achieved by reduced dynamic wheel load fluctuations. Vehicle suspension system performance is analyzed through the ability to provide improved road handling and improved passenger comfort given that the application of passive components can only offer a compromise between these two conflicting criteria by providing spring and damping coefficients with fixed rates [1]. A vehicle's suspension system typically consists of springs and shock absorbers that help to isolate the vehicle chassis and occupants from sudden vertical displacements of the wheel assemblies during driving. A well-tuned suspension system is important for the comfort and safety of the vehicle occupants as well as the long-term durability of the vehicle's electronic and mechanical components. The conventional vehicle suspension systems include of mechanical elements of spring and viscous dampers that are responsible of vehicle ride and handling functions wherein the coefficients of these elements should be determined and provided to operate within a broad spectrum of operational range. A satisfactory ride comfort requires soft spring while this may have the drawback of poor road holding. Furthermore, for the open-loop passive systems there is no * Corresponding author. P Tomaraee (* Department of Agricultural Machinery, Faculty of Agriculture, Ankara University, Ankara, Turkey p.tomaraee@gmail.com choice than to deal with the resonance frequency. With the introduction of sensors, actuators and microelectromechanical controlling devices, it has been possible to define active suspension systems with far efficient performance. The vibration performance of a vehicle, so-called ride comfort, is extremely reliant on the natural frequencies and mode shapes of the vehicle. The aim of the suspension system is to separate the vehicle body from the road inputs. Suspension systems serve a dual target one of which is t help to the vehicle stability/handling and braking for good active safety and driving comfort, and the second one is to keep vehicle passengers comfortable and reasonably well isolated from road noise, bumps, and vibrations. Active suspension systems adopt electronic monitoring of vehicle conditions added with some instruments to adjust and decide the motion and to directly control the motion of the car in on-the-go condition. Ride comfort in wheeled- vehicles usually rely on a configuration of vertical motion (heave and angular motion (pitch and roll. Suspension elements between the car body and wheels provide forces that excite heave, pitch and roll motions. While fully active suspension systems are power-demanding, passive suspension systems are incapable of providing reduced sprung mass motions at frequencies both above and below the wheel frequency modes and do not assist independent control of heave, pitch and roll motions. A precise vehicle dynamics model has to exemplify the actual vehicle characteristics and to be validated with vehicle dynamics simulation software and an instrumented real experimental car and in the case that the behavior of the vehicle is not predicted when designing a vehicle, it can result in inopportune handling behavior and dangerous maneuver such as 49
2 P. Tomaraee / Journal of Advances in Vehicle Engineering 2(1 ( rollover [2]. There are studies documented in literature dealing with full vehicle models for suspension and handling control [3-6]. A study contributed in controller performance for Active Front Wheel steering System (AFWS for armoured vehicle with a 14 DOF model of armoured vehicle that was used to control the vehicle's dynamic responses particularly in yaw rate, yaw angle, lateral acceleration and lateral displacement by using a simple PID controller. The responses from the vehicle model was then compared with ones from CarSim software to ensure that the model is verified [7]. A three-dimensional dynamic model for simulating various motions of two-wheel-steering vehicles was constructed in an investigation wherein the model had 16 independent degrees of freedom (DOF that comprise of three modules: a vehicle body of six DOF, four independent suspensions mounted at every corner of the car body, and four tire models linked with each suspension. This full vehicle model was implemented in a MATLAB toolbox and then was validated using some experimental data. It is concluded that the full vehicle model could be easily adopted for the performance study of the guidance controller as well as the dynamic motion analysis of the vehicle [8]. In another investigation, a strategy was proposed containing genetic algorithm based optimization solution to improve the main design parameters of a semi active suspension for a two axle full off road vehicle while the aim is to reduce the maximum bouncing acceleration of the sprung mass. Due to the significance of ride comfort for off road vehicles, reducing the settling time and peak to peak of the vertical, pitch and roll acceleration would bring about a better ride comfort performance [9]. The aim of the present paper is to use 7 DOF full vehicle model to analyze the active suspension system for the objective vehicle traversing over bounce sine sweep road. The mathematical model of the full vehicle suspension system is presented. The coupled CarSim and Matlab Simulink approach is adopted to analyze the performance of active suspension system on the road profile introduced under ABS braking strategy. 2. Mathematical Modeling The road surface irregularities are the main source of vibrations to the vehicle system and a suitable representation of these irregularities is needed in order to investigate the vehicle dynamic behavior satisfactorily (Fig. 1. The ride performance parameters are the body acceleration and displacement, damper displacement and wheel acceleration. The full vehicle model includes the body bounce x, body roll ϕ, body pitch θ, hops at x 1, x 2, x 3, and x 4 and independent road excitations y 1, y 2, y 3, and y 4. The full vehicle suspension system is represented as a linearized seven degree-of-freedom (DOF system that consists of a single sprung mass (car body connected to four unsprung masses (front-left, front-right, rear-left and rear-right wheels at each corner. It should also be noticed that the suspensions between the sprung mass and unsprung masses are considered as linear viscous dampers and spring elements, while the tires are modeled as simple linear springs without damping (Fig. 1. A full car vibrating model has 7 DOF and a set of seven equations of motion can be presented as following: Figure 1. 7 DOF full vehicle model for the suspension system 50
3 P. Tomaraee / Journal of Advances in Vehicle Engineering 2(1 ( mx c ( x x b a c ( x x b a f f c ( x x b a c ( x x b a r r k ( x x b a k ( x x b a f f k ( x x b a k ( x x b a 0 r r (1 I b c ( x x b a b c ( x x b a x 1 f f b c ( x x b a b c ( x x b a 1 r r b k ( x x b a b k ( x x b a 1 f f x x b k x x b a b k x x b a k w 1 2 ( ( 0 1 r r R I a c ( x x b a a c ( x x b a y 1 f f a c ( x x b a a c ( x x b a 2 r r a k ( x x b a a k ( x x b a 1 f f a k ( x x b a a k ( x x b a 0 2 r r (2 (3 m x c ( x x b a k ( x x b a f 1 f f x x ( 1 2 R tf ( k k x y w w m x c ( x x b a k ( x x b a f 2 f f x x ( 1 2 R tf ( k k x y w w (4 (5 m x c ( x x b a k ( x x b a k ( x y 0 (6 r 3 r r t r 3 3 m x c ( x x b a k ( x x b a k ( x y 0 (7 r 4 r r t r 4 4 The equations of motion developed are valid for the passive system and it should be noted that when the active suspension is applied, there is another external actuator force that functions between the sprung and unsprung mass at each corners. Therefore in the above-developed equations, an extra term representing the active force should be inserted while the authors excluded them in order to avoid the over-extension of the paper. 3. Active Suspension System Active suspension system deals with the active vibration control principle that is the active application of force in an identical and contrasting manner to the forces imposed by external vibration. With this application, a precision industrial process can be preserved on a platform of vibration-free. 51 The active suspension is a common type of suspensions system that control the vertical motion of the wheels relative to the chassis or vehicle body when compared to passive suspensions where the motion is defined by the road profile input. Active suspension systems measure the forces exerted to the wheels and continuously modify the connections between the chassis and tire in order to maintain the chassis level and absorb the energy associated with the vertical motion of the wheels which is referred as energy harvesting/energy recapturing. Active suspensions can be categorized into two main groups: pure active suspensions and semi-active suspensions wherein semi-active suspensions differ shock absorber control to comply with road irregularities, active suspensions adopt some particular varieties of actuator to increase and decrease the chassis motion. The aforementioned developments in the industry of vehi-
4 P. Tomaraee / Journal of Advances in Vehicle Engineering 2(1 ( cle system suspensions and particularly the actuators have enabled the automotive manufacturers to provide a better performance of ride comfort and vehicle stability/handling by maintaining the tires perpendicular to the road and following the road profile irregularities and generating effective net traction force due to the continuous tire-ground contact. The mounted devices on the vehicle can determine chassis motion from devices while the obtained data can be further analyzed online to adjust the vehicle kinetics that can affect both the vehicle ride and driving performance. The system is able to control roll and pitch changes in different driving operational modes such as cornering, accelerating, and braking. As aforesaid, active suspensions adopt isolated actuators that can apply pre-determined force on the suspension to recover the riding characteristics. The disadvantages of such strategy are being expensive, extra devices and the requirement for control and maintenance constantly. 4. CarSim-MATLAB Simulink CarSim simulates a complete 3D vehicle-suspension multibody model, concerning the car vertical dynamics, as well as the lateral and longitudinal motions. It delivers is of efficient approaches for simulating the performance of passenger vehicles and light-duty trucks. CarSim is a preferred tool for analyzing vehicle dynamics, developing active controllers, calculating a car s performance characteristics, and active safety systems. In addition to VS Commands (the built-in scripting language, it can run with custom programs (MATLAB, Visual Basic, C/C++ using VS API (application program interface. CarSim is a software tool for simulating and analyzing the dynamic behavior of two-axle vehicles. Integration of CarSim into a vehicle development program can help engineers at all levels make better decisions regarding potential vehicle changes ranging from the sprung mass CG location to a tire design change, to the effectiveness of a new electronic stability controller. Simulink is a block diagram environment for multidomain simulation and Model-Based Design. It supports simulation, automatic code generation, and continuous test and verification of embedded systems. Simulink provides a graphical editor, customizable block libraries, and solvers for modeling and simulating dynamic systems. It is integrated with MATLAB, enabling you to incorporate MATLAB algorithms into models and export simulation results to MATLAB for further analysis. It is also referred to a graphical programming environment for modeling, simulating and analyzing multidomain dynamic systems. Its main interface is a graphical block diagramming tool and a adjustable set of block libraries. It provides close-fitting integration with the rest of the MATLAB environment and can either create MATLAB or be scripted from it. Simulink is widely used in automatic control and digital signal processing for multidomain simulation and Model-Based Design. In Simulink, it is very straightforward to represent and then simulate a mathematical model representing a physical system. Models are represented graphically in Simulink as block diagrams. A wide array of blocks are available to the user in provided libraries for representing various phenomena and models in a range of formats. One of the primary advantages of employing Simulink (and simulation in general for the analysis of dynamic systems is that it allows us to quickly analyze the response of complicated systems that may be prohibitively difficult to analyze analytically. Simulink is able to numerically approximate the solutions to mathematical models that might considered complex to be solved. In general, the mathematical equations representing a given system that serve as the basis for a Simulink model can be derived from physical laws. In this page we will demonstrate how to derive a mathematical model and then implement that model in Simulink. Figure 2. CarSim-Simulink model considering damping factor, damping force, tire deformation and jounce 52
5 P. Tomaraee / Journal of Advances in Vehicle Engineering 2(1 ( Figure 3. Active car suspension outputs in Simulink Table 1. Model parameters Description Unit Sprung mass 1370 kg Unsprung mass (front 80 kg Unsprung mass (rear 80 kg Suspension damping coefficient 2045 N s/m Suspension stiffness coefficient N/m Tire stiffness coefficient N/m Roll Inertia (I xx kg-m 2 Pitch Inertia (I yy kg-m 2 Yaw Inertia (I zz kg-m 2 Table 2. Function block parameters: Semi-active suspension controller Description Value Optimal control gain K Optimal control gain K Optimal control gain K Optimal control gain K Spring Stiffness (front (N/m Spring Stiffness (front (N/m Gain 1 1 Gain Variable damper upper limit 40000(N-s/m Variable damper lower limit 10 (N-s/m 53
6 P. Tomaraee / Journal of Advances in Vehicle Engineering 2(1 ( The fusion of both approaches would enable to analyze different procedures of vehicle kinetics such as stability, ride, handling, braking/acceleration, etc. for variety of two axle vehicles. Figs. 2 and 3 represent the CarSim-Simulink developed model and active car suspension outputs in Simulink, respectively. 5. Results and Discussion The model parameters are used for every configuration and their numerical values which are typical for passenger vehicle are summarized in Table 1. Furthermore, function block parameters for semi-active suspension controller are tabulated in Table 1. Road centerline evaluation based on bounce sine sweep is presented in Fig. 4 as well as the schematic vehicle travelling over the objective road profile in CarSim software environment. Fig. 5 shows tire deformation, damping factor, damping force and jounce in time domain. Jounce is the fourth derivative of the position vector with respect to time, with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively; hence, the jounce is the rate of change of the jerk with respect to time. In vehicle dynamics terminology, jounce is the motion caused by a wheel going over a bump and compressing the spring. During the jounce, the wheel moves up toward the chassis. Jounce can be simulated by sitting on the bumper and pushing down on the vehicle. The vehicle should jounce equally on both sides. By comparing Figs. 4 and 5, it can be seen that based on the road profile, where the bump height is great, there is a great portion of tire deformation and by decrease of road profile height, there is a decrease in tire deformation magnitude. However, due to the increased frequency of road profile, the tire deformation cyclic frequency increases. By further increase of the bump frequency, the resonance frequency occurs and the tire deformation magnitude increases again. Based on the definition given for the jounce and the road profile given in Fig. 4, the trend seen in jounce variations with respect to time is also justifiable. Fig. 5 also presents the damping force variations that are used in the closed-loop active suspension system and where the damping force is used to attenuate the oscillations created. The damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance. This variations of this factor can also be seen in Fig. 5 where the effect of road profile input is included. The vertical force variation in time domain is presented in Fig. 6 for front and rear tires. There is a complete harmony between the left and right side of tires in front and rear components. Similar to the tire deformation trend presented in Fig. 5, tire vertical force increases in the beginning of motion where the bump height is great, but then it decreases owing to the reduction in irregularity height. The vertical forces increase again where the frequency in bumps increase that the trend is in compliance with that of tire deformations. (a (b (c (d Figure 5. a Tire deformation, b Jounce, c Damping force and d Damping factor variations in time domain 54
7 P. Tomaraee / Journal of Advances in Vehicle Engineering 2(1 ( Figure 6. Vertical force variation in time domain Figure 7. Vehicle vertical acceleration for center of gravity (a (b Figure 8. Pitch and roll outputs of the vehicle in time domain Vehicle vertical acceleration for center of gravity has also been presented (Fig. 7 that is significant from the ride comfort perspective. The chassis acceleration gives an understanding of how the chassis would provide the ride comfort given that the force that passengers might feel is closely correlated with the vertical acceleration multiplied by the sprung mass. Pitch and roll variations are demonstrated in Fig. 8. Pitch has increased at first significantly but then decreased that is due to the vehicle road profile. Roll has also increased in time domain in contradictory to pitch variation trend. 6. Conclusion Semi-active and active suspensions influencing the vertical dynamics of vehicles enable improvement of ride comfort and handling characteristics compared to vehicles with passive suspensions. 7 DOF full vehicle model considering roll and 55
8 P. Tomaraee / Journal of Advances in Vehicle Engineering 2(1 ( pitch is presented for the objective vehicle. Hybrid CarSim- Simulink was adopted to achieve the effect of active suspension for the condition of road profile with bounce sine sweep road. The results are presented in terms of ride and handling performance criteria such as tire deformation, damping factor, damping force, jounce, roll, and pitch. The results show that the performance criteria are function of road profile input and that the designed active suspension configuration drastically affects the vibration attenuation and decrement of induced oscillations. References [1] Ikenaga S., Lewis F.L., Campos J., Davis L. Active suspension control of ground vehicle based on a full-vehicle model. In American Control Conference. Proc. of the IEEE, 2000; 6: [2] Setiawan J.D., Safarudin M., Singh A. Modeling, simulation and validation of 14 DOF full vehicle model. In Instrumentation, Communications, Information Technology, and Biomedical Engineering (ICICI-BME, 2009 International Conference on.ieee, 2009: 1-6. [3] Min D.J., Jung M.R., Kim M.Y., Kwark J.W. Dynamic Interaction Analysis of Maglev-Guideway System Based on a 3D Full Vehicle Model. International Journal of Structural Stability and Dynamics, 2006; [4] Sun W., Gao H., Yao B. Adaptive robust vibration control of full-car active suspensions with electrohydraulic actuators. Control Systems Technology, IEEE Transactions on 2013; 21(6: [5] Tchamna R., Lee M., Youn I. Attitude control of full vehicle using variable stiffness suspension control. Optimal Control Applications and Methods 2015; 36(6: [6] Soudbakhsh, D., Eskandarian, A., & Chichka, D. (2013. Vehicle collision avoidance maneuvers with limited lateral acceleration using optimal trajectory control. Journal of Dynamic Systems, Measurement, and Control, 135(4, [7] Bin Mansor M., Hudha K., Kadir Z., Amer N.H. Active front wheel steering system for 14 DOF armoured vehicle model due to firing force disturbance. In Control Conference (ASCC, th Asian. IEEE, 2015:1-6. [8] Min K., Byun Y.S., Kim, Y.C. Modelling and validation of 16 DOF full vehicle model for guidance control. International Journal of Vehicle Systems Modelling and Testing 2015; 10(4: [9] Ben Lahcene Z., Faris W.F., Ihsan S.I., Darsivan F.J. Optimisation and control of semi active suspension using genetic algorithm for off road full vehicle. International Journal of Vehicle Systems Modelling and Testing 2014; 9(3-4,
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