Sensitivity of ride comfort to Suspension characteristics of an off-road vehicle under road excitation

Transcription

1 Sensitivity of ride comfort to Suspension characteristics of an off-road vehicle under road excitation M. Zehsaz 1, F. Vakili-Tahami 2,. Fasihi 3,.. Majidi jirandi 4 1, 2, 3 epartment of Mechanical ngineering, University of Tabriz, Tabriz 51666, Iran 4 epartment of Mechanical ngineering, University of Payam Nour(PNU), Kerman, Iran 1 zehsaz@tabrizu.ac.ir 2 f_vakili@tabrizu.ac.ir 3 ali_fasihi 4 bstract This paper describes the influence of the suspension system parameters of an off-road vehicle on its ride comfort and dynamic control, as it moves along the road during the and braking. Ride comfort of the vehicle can be improved by controlling the vertical, as well as the pitch vibration. In this research the road roughness has modeled in nonstationary situation. The dynamic behaviour of the Off-road vehicle has been modeled using a system with 7 egrees of Freedom (OF) to indicate the effect of different parameters in rear and front of the vehicle. For this purpose, a computer code in Matlab has been developed to model the road profile and the dynamic behaviour of the vehicle. The results obtained using numerical methods show that the frequency of the resonance of the sprung mass decreases significantly by decreasing the stiffness. The numerical and analytical results also show that with decreasing the suspension system index, the ride comfort increases and handling becomes worse. lso the results show that the ride comfort is more sensitive to the rear of the suspension system and by increasing the mass on the rear suspension system, ride comfort can be improved. Keywords Road Roughness, Power Spectral ensity, Ride omfort, Suspension I. INTROUTION Nowadays, the increasing progresses of the technology and the need to more use of transporting devices have made the design of vehicles an important task. For today's vehicles, ride comfort and dynamic control, are crucial criteria for customers and also for the selection of an appropriate vehicle. For this reason, optimum design of a suspension system and studying the effect of its parameters on the ride comfort and dynamic control of a vehicle has a key role. Studying the effect of different parameters on the ride comfort and dynamic control of a vehicle provides an understanding of their sensitivity which in turn leads to an optimum design of the suspension system. In this way, any possible weaknesses and drawbacks of the vehicle can be solved before manufacturing the prototype. In the past years, many efforts have been made by different organizations to identify or classify the level or type of the road surfaces based on their unevenness profile. Motor Industry Research ssociation (MIR) using experimental work in measuring the roughness of roads and spectral analysis of different levels of roads has proposed an approximate relationship to determine spectral form of the road profiles [1]. International Organization for Standardization (ISO) has also proposed road roughness classification using the Power Spectral ensity (PS) values, as shown in Fig.1 [2]. The corresponding values are illustrated in Table 1 [3]. To study the dynamic behaviour of the vehicles, computer aided simulations using numerical models in time and frequency domains can be used which provide the accelerations to assess the ride comfort. In this respect, there should be also a criterion for evaluating human response to the vibrations at various frequencies. The international standard ISO2631 has recommended the boundary values for the vertical accelerations at sensivitive frequencies [4]. 422

2 Figure 1: lassification of surface roughness by ISO [2] Table1: lassification of the road roughness types according to ISO and the associated parameters [3] lassification and road roughness S K 0 / 10 6 Very good 2-4 Good 8-32 verage Poor Very poor m cycle Vibration detection of a vehicle is a subject which has been discussed in details by Motor Industry Research ssociation (MIR). In this frame, considering the findings of the Industrial Research ssociation regarding the human tolerances for the vibration can be useful. rief review of the vibration restrictions for human comfort goes back to the 1920 and was published in motor association calendar in Great works by the International Organization for Standardization (ISO) and other researchers has been made which are major contributions to the database in the information of vibration tolerances. These studies are focused on individual tolerate level [5]. For this purpose, the correlation between objective methods for determining ride comfort and subjective comments from crew who drive the vehicles were investigated. For objective measurements, the ISO 2631, S6841, verage bsorbed Power and VI2057 methods were used. The correlation between the different methods, measuring positions, measurement directions and calculation methods was determined. 423 It is concluded that all these methods can be used to specify and evaluate ride comfort, but that acceptable ride comfort limits vary according to the different conditions and also the type of the vehicle [6]. esigning the vehicle suspension systems is a complex process due to the necessity to meet several conflicting demands. The passenger comfort should be satisfactory, while the relative motion between the body of the vehicle (sprung mass) and two axels with wheels (the unsprung mass) must be limited to a reasonable value [7]. When designing vehicle suspension systems, it is wellknown that and characteristics required for good handling of a vehicle are not the same as those required for good ride comfort. ny choice of and characteristic is therefore necessarily a compromise between ride comfort and handling [8] Gobbi is used standard deviation of vertical accelerations and relative motion between wheel and vehicle body as a criterion for evaluating comfort and range of working space. His results indicate that optimization of suspension settings using one road and at a certain speed will improve ride comfort on the same road at other speeds. These settings will also improve ride comfort for other roads at the optimum speed as well as other speeds, although not as much as when optimization has been done for the particular road [9]. For experimental comparison of passive, semi-active on/off and semi-active continuous suspensions, Ivers and Miller have used RMS tire contact force as an indication of wheel hop and road holding capability [10]. ong Soo Kim and et al. [11] to identify and reduce a knocking noise from a rear suspension, the characteristics of a knocking noise have analyzed experimentally in the frequency domain. In this paper, to determine the excitation of irregular surface profiles, numerical methods are used to provide relationships which define the road roughness. These relationships have been used as input data to study the dynamic behaviour of an off-road vehicle. numerical model has been used to calculate the acceleration of masses in the model with 7 OF. lso, the acceleration curve of the sprung mass and the tire force curve have been used as criteria to assess the ride comfort and dynamics control of the vehicle respectively. II. RO ROUGHNSS In the early attempts to investigate the characteristics of the vehicle ride, excitation due to the road roughness in the form of sine waves, step functions, or triangular waves are used.

3 While these inputs could provide a basis for comparative evaluation of various designs, they could not serve as a valid basis for studying the actual ride behavior of the vehicle since surface profiles are rarely of simple forms. Later, it is found that ground profiles should be more realistically described as a random function. When the surface profile is regarded as a random function, it can be characterized by a power spectral density function [5]. There are two types of road profiles: stationary and ergodic [12]. In general, the real road profiles have a completely random nature, such as potholes or bumps, and therefore their shape does not follow a defined pattern. However, in this study, only the latter type of road is considered. The random fields are real-valued, zero mean, stationary, and Gaussian. Therefore, for their complete statistical description it is sufficient to specify their second-order moment. Here, this requirement is fulfilled by assuming that the road irregularities posses a known single-sided power spectral density (PS), say S u (k), where k = 2 / is a spatial frequency, corresponding to a harmonic irregularity with wavelength. ccording to many previous investigations on the subject [1], the geometrical profile of typical roads fits sufficiently accurately the following simple analytical form [13]: S u (K)= u K -n (1) Where n =3 for even roads and is 2 for uneven roads, K is wave number in cycle/m and u which is related roughness parameters based on ISO standards. The spectral density corresponding to the geometrical profile of typical roads the following relationships have been proposed [3]: K S (K ) ( ),K K K S (K ) ( ),K K n1 u 0 0 K0 n2 u 0 0 K0 In these equations, K is wave number in cycle/m, K o is the base wave number, S u (K) is the PS of the vertical displacement in m 3 /cycle, S u (K o ) is the PS in K o. The ISO recommendation for n 1 =3, n 2 =2.25 and K o = 1/2π are listed in Table 1. For different categories of road profiles, S o or Su(k) which are rated roughness parameters based on ISO standards and are given in Table 1 and 2, have been used. Table2: lassification of the road roughness by Robson and the proposed parameters [5] )2( In general case, the function of road roughness is regarded as a stationary random process in space domain, while a car is moving with the constant velocity. It is also a stationary random process in time domain. However, road roughness is a non-stationary random process in time domain while a vehicle is traveling at variable speeds. Therefore, the vibration caused by rough road surface should be considered as a non-stationary random process. quations (1) can be described in temporal frequency domain. For applying the road roughness conditions on dynamic model, two methods can be used [14]. First, generating a 3 road surface profile and moving the vehicle on it. In this case the roughness applied to the front and rear wheels or right and left ones would be the same only with a time delay. nother method is using the vibrating table (Shaking table) in which the road roughness can be applied to each one of the wheels through four plates of the tables. In shaking table, there is the possibility of defining independent roughness profiles for each one of the wheels. The latter method is more realistic in terms of the random nature of the road profile. Fig. 2 represent typical the simulation of road roughness in time domain while a car is running with the acceleration. Since a multi purposes vehicle (MPV) will pass over different road types based on ISO standards (from good urban paths up to very rough off-roads), PS values and ISO s for average type road have been selected and are used in this research with 120 mm maximum amplitude (Fig. 4). These results or road profiles have been used as input data to study the dynamic behavior or response of the vehicle. S0 0.5 lassification and road 10 8 m cycle roughness High way 3-50 Main road Rural Fig. 2: Time course of the road roughness in (a=3 m s2) 424

4 Z 5 vertical displacement of vehicle body at center of gravity Z 6 - pitch angular displacement of vehicle body, Z 7 - roll angular displacement of vehicle body, q 1, q 2, q 3, q 4 - displacement inputs due to the road roughness at front and rear tires, respectively q 5 input due to the effect of or braking in the center of gravity Fig. 4: Road roughness profile for an average road type III- MTHMTI VHIL MOL To develop a dynamic model and to find the reaction forces, different methods can be used such as quarter vehicle model, half vehicle model and the full model of vehicle which is the most sophisticated one and takes into account the effect of pitch, roll and bounce caused by passing the vehicle over a road with random roughness profile. onsidering the goal of this research, a vehicle model M z z K z= F Q Z= z z z z z z z Q= q q q q q T with 7 degrees of freedom has been established and is shown in Fig. 5. In this model, each tire is modeled by a linear with stiffness k t and the damping effect of the tires is neglected since it is negligible. Other parameters in this model are defined as: M f, M r - unsprung masses and rear suspensions, respectively, K f, K r - stiffness s and rear suspensions, respectively, f, r - damping s and rear suspensions, respectively, M - mass of vehicle body, K t - stiffness s of tires, W a, W b - distances from the center of gravity to front and rear tires, respectively, Z 1, Z 2, Z 3, Z 4 - bouncing displacement of unsprung masses and rear suspension, T )3( Fig. 5: Vehicle model with 7 degrees of freedom The excitations that act on the back wheels are the same as the front wheels, but they have been delayed with the time period corresponding to the distance between the axis and vehicle speed [4]. ssuming that the pitch and roll motions are small so that: Sin( ) and the movements of the linear s and shock absorbers in the lateral and longitudinal directions are negligible compared to their movements in the vertical direction. The equations of motion for the vehicle model can be described as follows: In these equations the parameters are: Z- Output vector, [M]- Mass matrix, []- amping matrix, [K]- Stiffness matrix, [F]- xcitation force matrix and [Q]- xcitation vector, This can be defined as: z x, z x, z x z x, z x, z x, z x z x,z x,z x z x, z x, z x, z x t the same time the state- space equations are: X o = X + Q U Where X is the state variables and U is the input vector. )17( 425

5 IV. RI OMFORT N YNMIS ONTROL In fact, while a car is traveling at variable speeds such as starting, and braking and so on, the vibration excited due to the rough road should be simulated using non-stationary random vibration in time domain. Since this problem is very close to the real or actual situation, random vibration of a vehicle is a very important topic, and it is also significant in engineering [15]. Passengers of various vehicles are mainly exposed to whole-body vibrations due to the random road irregularities, which cause ride discomfort and fatigue. Since ride comfort is directly related to the vertical accelerations sensed by the passengers, decreasing these accelerations is the main aim of the research groups and automotive industries [4]. ue to the characteristics and requirements of the offroad vehicles, the worst classification "average type" has been selected and used to induce the excitations caused by road roughness. Fig. 6and 7 show the numerical results obtained based on 10 percent decreasing of the suspension system parameters for each solution. ifferent case studies have been given the following code names: : parameters : the : the : the : the Fig. 6 and 7 show the displacement of the mass during the and braking respectively. s it is shown, body displacements due to the variation of the suspension system parameters in two cases are insignificant. Fig. 7: omparison of the mass displacement during braking Table 3 and 4 represent the numerical results with decreasing 10 percent of the suspension parameters system. With reducing the of the and of the front and rear suspension system, the sprung acceleration curve has been reduced, meaning that the ride comfort has increased. In comparison between the stiffness of the and, the results show that the ride comfort relative to the is more sensitive to these changes and the the acceleration curve is reduced further. Knowing that decrease of the the acceleration curves will provide ride comfort and also decreasing the the curves showing exerted by the road will increase the dynamic control of the vehicle. The following results can be obtained from Table 3 and 4. The overall result of reducing the suspension parameters is decrease of the acceleration curves which in turn will increase the ride comfort. It can also be seen that reducing the rear stiffness or damping reduces the area under the front tire force and therefore it will increase the dynamic control of the vehicle. In general, the results of the two Tables show that reducing the stiffness of the rear suspension system is the best solution and can be regarded as optimum design. Fig. 6: omparison of the mass displacement during the acceleration 426

6 Table 3: The numerical results based on 10 percent decreasing of the suspension system parameters during the acceleration curve displacement curve of front tire displacement curve tire parameters Table 4: The numerical results based on the 10 percent decreasing of each suspension system parameters during braking parameters displacement curve tire displacement curve of front tire curve V. OMPRISON OF NUMRIL RSULTS WITH FRQUNY OMIN NLYSIS The dynamic behavior of the vehicle can be characterized by considering the input-output relationships. The input may be any of the excitations or combination thereof. The output most commonly of interest will be the vibrations on the body. The ratio of the output and input amplitudes represents a "gain" for the dynamic system. The term "Transmissibility" is often used to denote the gain. Transmissibility is the nondimentional ratio of the response amplitude to the excitation amplitude for a system in steady-state forced vibration. The magnitude ratio of the transfer function is used in a similar fashion to denote the gain, although this term is normally reserved for use with linear systems [5]. The most efficient method for solving stationary random response of a linear system is the transfer function. However, it is not suitable for solving nonstationary random response. Therefore, a new method in frequency domain needs to be proposed [15]. The input caused by and braking is independent from other inputs. Fig. 8, 9, 10 and 11 show the power spectral density of the sprung mass acceleration. The first peak of the acceleration curve shows the resonance frequency of the sprung mass and the second peak shows the resonance frequency of the unsprung mass, on the other hand unsprung mass frequency is more than sprung mass frequency. The domain of the mass displacement decreases when the ratio of the unsprung mass frequency to the mass frequency increases. This ratio has small variation in comparison with the results obtained using numerical method. Therefore, displacements show negligible variation in different conditions (Fig. 6 and 7). Fig. 8: omparison of the acceleration power spectral density of the vehicle body during (stationary) 427

7 The first and second maximum points at the deceleration curve during braking (Fig.10) are increased when compared with the acceleration curve (Fig.8). This means that during the acceleration, due to the shifting of the load from front to the rear of the vehicle, and also due to the increase of the equivalent load on the rear suspension, the ride comfort increases. The result given in Table 5 and 6 also approves this fact. Fig. 12, 13 and 14 show the acceleration power spectral density () of the sprung mass in the natural frequency domain of the sprung mass, between natural frequencies domain of sprung mass and unsprung mass and in the natural frequency of unsprung mass, respectively. The changes trend of curves is the same for both acceleration and braking states. Table 6: The analytical results based on 10 percent decreasing separately of each suspension system parameters during braking curve(nonstationary) curve(stationary) parameters Fig. 10: omparison of the acceleration power spectral density of the vehicle body during braking (stationary)) Table 5: The analytical results base 10 percent decreasing separately of each suspension system parameters during curve(nonstationary) curve(stationary) parameters Stimulations usually include a wide domain of frequencies. Regarding the sprung mass, frequency is low, so system isolates high frequency inputs. ut low frequency stimulations are applied on vehicle body, thus they cause resonance in the frequencies close to the natural frequency. In the frequencies lower than the sprung mass frequency, the variations are negligible (Fig. 8, 9, 10 and 11). ut the first peak of the acceleration curve decreases with decreasing the stiffness of the suspension system and increases with decreasing the damping (Fig.12). Fig. 12 shows that the resonance frequency of the sprung mass decreases more by decreasing the stiffness of the rear suspension. amping of the front suspension system is larger than the damping of the rear suspension system in the initial design of the vehicle which results in more increment of the curve peak which is shown in Fig. 12. However, the the and curves is increased near the mass frequency but this increment is due to the fact that and curves have lower amounts 428

8 in a wide domain between resonance frequencies of the sprung mass and unsprung mass (Fig.12 and 13). Fig. 14 shows that by reducing the parameters, natural frequency of the unsprung masses has been reduced and therefore the isolation occurs at a lower frequency and the ride comfort is improved. lso, Tables 5 and 6 show that the ride comfort has been increased by decreasing the suspension system parameters. Fig. 16: omparison of the acceleration power spectral density of the vehicle body in the natural frequency domain of the sprung mass Fig. 12: omparison of the acceleration power spectral density of the vehicle body during (stationary) Fig. 17: omparison of the acceleration power spectral density of the vehicle body in the natural frequencies domain between sprung mass and unsprung mass Fig. 14: omparison of the acceleration power spectral density of the vehicle body during braking (stationary) 429

9 Table 7: The analytical results based on 10 percent decrease of the suspension system parameters during the acceleration area tire force tire force parameters 30584* * * * * *102 Fig. 18: omparison of the acceleration power spectral density of the vehicle body in the natural frequency domain of the unsprung mass VI. ISUSION The results show that the the tire force curve increases more by decreasing the rear damping (see Table 7 and 8), and this represents the importance of the optimization of the suspension system. This means that the vibration domain of the forces has been increased and the dynamic control of the vehicle has been decreased * * * *10 2 Table 8: The analytical results based on 10 percent decreasing of the suspension system parameters during braking area tire force tire force If the criterion is based on the reduction amount of the area under the acceleration curve, with reducing the parameters of the front suspension system, ride comfort has been improved more, but if the criterion is based on the ratio of the amount of reduction in suspension parameters to the reduction of the the acceleration, the results show that ride comfort improves more by reducing the rear suspension parameters. This criterion is seemed to be more appropriate because with decreasing the rear, the dynamic control is more increased comparing with the other cases. In other words, dynamic control is more sensitive to the rear suspension system. parameters 22131* * * * * * * * * *

10 VII. ONLUSION The comparison between the results obtained using numerical methods and frequency domain analysis show that the ride comfort has increased with decreasing stiffness and damping s of the suspension system. espite the increase in the peak of the spectral density curve on the natural frequency of the sprung mass with decreasing the front and rear damping s, in a wide range of natural frequencies for sprung and unsprung masses, this increase is covered and curves show lower values comparing with values obtained for the first case. omparing the effects of the and damping s, ride comfort has more sensitivity to the value of the s. If the the acceleration curve with lower damping and s show negligible change, better results have been obtained using lower due to the lower peak in acceleration curve. omparing between acceleration and braking with equal and constant acceleration, both numerical analysis and frequency domain analysis show that due to the shifting of the equivalent mass, the acceleration exerted on the vehicle body in braking is considerable and therefore the rear suspension system is more sensitive to the variation of the mass and this reflects the sensitivity of the ride comfort to the rear suspension system. Knowing the sensitivity of the suspension system to the variation of the equivalent mass and considering the fact that by reducing one of the suspension parameters (rear or front), the effect of the equivalent mass on the suspension system of the other side of the vehicle reduces, the acceleration response of the vehicle body on this system increases and therefore the dynamic control increases. [7] Segla S. and Reich S Optimization and comparison of passive, active, and semi-active vehicle suspension systems. 12 th IFTOMM word congress, june, esancon(france). [8] ls P.S, Theron N.J, Uys P.. and Thoresson M.J The ride comfort vs. handling compromise for off-road vehicles. Journal of Terramechanics. Vol. 44. pp [9] Uys P., ls P.S, and Thoresson M.J Suspension setting for optimal ride comfort of off-road vehicles traveling on road with different roughness and speeds. Journal of Terramechanics, vol 44, pp [10] Uys P., ls P.S, and Thoresson M.J riteria for handling measurement. Journal of Terramechanics. Vol. 43. Issue 1. Pp [11] Kim,., ae, K., hang, S. and Ryu, J Optimal Rear Suspension esign for the Improvement of Ride omfort and Suspension Noise," S Technical Paper , doi: / [12] Sayers, M.W. and S.M. Karamihas, The Little ook of Profiling, asic Information about Measuring and Interpreting Road Profiles. University of Michigan Transportation Research Institute (UMTRI). 1st dn., National Highway Institute, Federal Highway, OS G. and P, US., ISN , pp: [13] Verros G., Natsiavas S. and Papadimitriou esign Optimization of Quarter-car Models with Passive and Semi-active Suspensions under Random Road xcitation. Journal of vibration and ontrol, No. 11, pp [14] enasciutti,. Tovo, R Spectral Methods for Lifetime Prediction under Wide and Stationary Random Processes. Int. J. Fatigue, Vol. 27, pp [15] Zhang L-J, L -M and Wang Y.S, Study on nonstationary randon vibration of a vehicle in time and frequency domains. International Journal of utomotive Technology, NO.3. pp RFRNS [1] odds,. J. and Robson, J The escription of Road Surface Roughness. Journal of Sound and Vibration, 31(2), [2] smailzadeh,. and Taghirad, H ctive vehicle suspensions with optimal state feedback control., International Journal of Mechanical Science, S Transactions. [3] Steinwolf, Random vibration testing eyond PS Limitations, Sound and Vibration, ynamic Testing Reference Issue, September 2006, pp [4] Mirzaei M. and Hassannjad R pplication of genetic algorithms to optimum design of elasto-damping elements of a halfcar model under random road excitation. J. Multi-body ynamics, Vol. 221, part k. [5] Gillespie T.., Fandamentals Of Vehicle yanamics. Society of utomotive ngneers, Inc,. [6] ls P.S The applicability of ride comfort standards to off-road vehicles. Jjournal of Terramechanics, Vol 42, pp