Modal Analysis of Automotive seating System Uday M. Jamdade 1, Sandip H. Deshmukh 2, Sanjay S. Deshpande 3 1 Sinhgad college of engineering, pune. 2 Sinhgad college of engineering, Pune 3 Asian academy of professional training, Pune. ABSTRACT The purpose of this study is to do the modal analysis of automotive seating system. A simple novel procedure has been used to solve the vibration problem of seat and determine its effect on human comfort through magnification factor or dynamic amplification factor. The aim of this present work is to find out the natural frequencies and magnification factor of seat component. The magnification factor shows the amplification of static amplitude in dynamic condition. This has been calculated at different excitation frequencies for fundamental frequency of the component. It has been observe that some of the components are critical from resonance point of view and shows higher dynamic amplification factor at the lower excitation frequency range. The lesser the magnification factor the better is the seat from dynamic point of view. We aim here to keep the magnification factor as low as possible. The natural frequencies of seat components have been found out by using Hypermesh and Nastran and dynamic amplification factor has been calculated with the help of analytical method. It is concluded that higher the natural frequency lower is the resonance between human body and seat components. This leads to increase the comfort of the occupant while riding. Keywords: - Natural frequency, Magnification factor, Amplification factor, Excitation frequency 1. INTRODUCTION The main aim of this project is to analyse an automotive seating system for vibration concern and to check whether it meets the final original equipment manufacturers requirements of modal frequency management concern. The seating system is made up of several component like head rest, arm rest, back rest, tracks etc. these component have their own natural frequency and in practice seat gets excited due to vehicle vibration i.e. engine vibration and external road condition. The road condition excites the automotive components from very low frequency to high frequency. These excitations are responsible for whole body vibrations and it is considered as source of discomfort while riding. It has been observed that the natural frequencies of the human body are of the order of 2 to 10 Hz. The mechanical model of the human body with resonance frequency range of various body section have been published by C.Druga in the article of vibration and human body [1]. This presented model has been used to study the resonance frequency range of human body. If the excitations coming from the seat matches with human body natural frequency then there will be resonance effect between body parts and seat component and it will reduce the comfort level of the occupant. Figure 1 Simple theoretical model of the resonance frequencies of human body[1] Volume 2, Issue 9, September 2014 Page 41
Vibrations influence the human body in many different ways. From an exposure point of view, the low frequency range of vibration is the most interesting. B.S. Shivakumara [2] has presented the work on study of vibration and its effect on the health of motorcycle rider. In this article the symptoms due to whole body vibrations and the frequency range at which they usually occur has presented. The principal interface between occupant and vehicle is the automobile seat and the effect of seat vibration on the human body has shown in Table1. Symptoms Natural frequency General feeling of discomfort 4-9 Head symptoms 13-20 Lower Jaw symptoms 6-8 Influence on speech 13-20 Lump in throat 12-16 Chest Pains 5-7 Abdominal pains 4-10 Urge to urinate 10-18 Increased muscle tone 13-20 Influence on breathing movements 4-8 Muscle contractions 4-9 Table 1: Symptoms due to whole-body vibration and the frequency range at which they usually occur [2] 2. FINITE ELEMENT MODEL OF CAR SEAT A finite element model of car seat has been constructed within this work. First, the vendor has supplied the solid geometrical model of car seat in IGES format. This model has developed in CATIA V5 software. Then, the CAD model has been pre-processed using Hypermesh 11 in which the geometry clean-up and model editing has been done. The finite element meshing done on seat component is followed by standard quality criteria. The seat is consists of 22 components amongst them 21 are shell component and only one is solid component i.e. Arm Rest. The shell component is meshed using first order quad and tria element and solid component is meshed using hex element. The seat component are made up of low carbon steel of modulas of elasticity is 2.1 10 5 N/mm 2, poisons ratio is 0.3 and density of material 7.8 10-9 tonne/mm 3. The Fig.2 shows the assembled finite element model of car seat. For the analysis purpose the individual seat component have been considered and results of natural frequency and magnification factor have been found out for individual component. Seat assembly frequency is not considered here; as such, consideration is important in full vehicle analysis. The aim here is limited to only characterizing the seat with respect to natural frequency requirements [3]. Figure 2 Finite element mesh model of car seat Volume 2, Issue 9, September 2014 Page 42
3. MODAL ANALYSIS OF SEAT COMPONENTS The goal of modal analysis in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during free vibration. The natural frequency is nothing but the frequency with which the any object will vibrate if disturbed and allowed to vibrate on its own without any external force. In this work, we are dealing with the free-free analysis i.e. no external force is applied on the component at the time of analysis. All the real life objects have infinite natural frequencies but finite element analysis can compute natural frequencies equal to degrees of freedom of the FE model only and the lowest natural frequency is known as fundamental frequency. The damping is usually neglected for free vibration analysis because most mechanical structures are under damped and usually damping ratio is below 10% which indicates the difference in results of ω d and ω n of about 0.5%. Damping makes calculations difficult and hence for usual applications damping neglected. In this work, Hypermesh 11 and MSC Nastran Version 2010 is used to calculate the natural frequencies of the components. The below Fig.3 shows the upper cross member of a seat has first fundamental frequency is 148.6396 Hz and it is vibrating along the Y direction and the mode shape of cross member at respective frequency. Figure 3 Modal analysis of upper cross member The armrest of a seat has first fundamental frequency is 1089.34 Hz and vibrating mode is a rotation along the z direction. The Fig 4 shows the mode shape of armrest at respective frequency. Like this, all seat component modal analysis has been performed by using Hypermesh and Nastran results of their first natural frequencies are shown in table 1. The inputs to the simulation software were material properties like modulas of elasticity, poisons ratio, material density. The thickness of all components is uniform and it is set as 1.5 mm. Like this we have calculated natural frequencies for thickness 1also and 2mm also. Figure 4 Mode shape of armrest Volume 2, Issue 9, September 2014 Page 43
Table 2: Nastran results of natural frequencies of components at thickness 1.5mm PART NAME NATURAL FREQUENCY fn Arm rest 1089.3431 Arm rest supporter 561.8069 Back rest tube 76.23876 Bracket 320.3762 Bolt cover 1111.900 Cushion tube 933.9595 Front cross member 121.6736 Front hook 715.8678 Head rest 330.6113 Lower riser 127.2086 Lower track 340.575 Lower tube 674.9133 Rear hook 493.3223 Reinf bracket 412.0648 Release tube 69.9563 Riser 104.6722 Riser tube support 12003.837 Support bracket 2150.489 Upper cross member 148.6396 Upper recliner bracket 288.9352 Upper track 218.6329 The natural frequencies of seating components have been kept much higher than human body frequencies, so that at assembly level the possibility of resonance between components and body parts are minimised and that will lead to increase the comfort level of occupants. However, some components are in critical zone for example riser and backrest tube, their natural frequency is near to human sensitivity range i.e. 1 to 80Hz. Sufficient isolation of vibration has achieved and components are showing the wide range of natural frequencies. By just looking at the results table we will not understand the impact of these natural frequencies, for this we need to calculate the dynamic amplification factor For each component for design consideration point of view this will help us to decide the frequencies of seat components. 4. ANALYTICAL RESULTS OF MAGNIFICATION FACTOR Dynamic magnification factor is defined as the ratio of the dynamic deflection at any time to the static deflection, which would have resulted from the static application of the external load. For all practical systems subject to harmonic excitation, the transient vibrations die out within the matter of short time, leaving only the steady state vibrations. Thus, it is important to know the steady state behaviour of the system when subjected to different excitation frequencies. The magnification factor is denoted by MF. It is a factor by which the zero frequency deflection is to be multiplied to get the amplitude [4], [5]. ω Excitation Frequency in rad/sec ω n Component Natural Frequency in rad/sec ξ= 0.2 (Damping ratio) The amplitude of vibration is mainly depending upon the excitation frequencies; it varies with the change in excitation frequency. Vehicle while moving along the road experiences the wide range of excitation frequency of vibration due to some irregular road profiles. In this case, we have considered wide range excitation frequencies vary from 3Hz to 1000Hz. The MF has been calculated by using the formula 1 for different excitation frequencies ( ) like 3Hz, 32Hz, 100Hz, 500Hz and 1000Hz and ( n) has been given in the table as f n for respective components. The results has been observed for different excitation frequencies and given in below table 3. Like this we have calculated the magnification factor for thickness 1 and 2 mm of component but the calculations are not shown here. The effect of change in thickness has shown in the graph plotted below. Volume 2, Issue 9, September 2014 Page 44 (1)
PART NAME f n MF MF MF MF MF @3Hz @32Hz @100Hz @500Hz @1000Hz Arm rest 1089.343 1.000006 1.000690 1.00780 1.23396 2.5033 Arm rest supporter 561.8069 1.000026 1.00260 1.0299 2.42560 0.4381 Back rest tube 76.23876 1.0014 1.33483 1.1299 0.0237 0.00584 Bracket 320.3762 1.00008 1.01611 1.0974 0.6387 0.11323 Bolt cover 1111.900 1.000006 1.00132 1.0074 1.2227 2.45474 Cushion tube 933.9595 1.000009 1.00188 1.0106 1.34356 2.20935 Front cross member 121.6736 1.00055 1.118424 2.1467 0.0261 0.02550 Front hook 715.8678 1.00004 1.00320 1.0182 1.7140 0.97063 Head rest 330.6113 1.00007 1.01512 1.0910 1.70310 0.01328 Lower riser 127.2086 1.0005 1.10771 2.0210 1.0688 0.01642 Lower track 340.575 1.00007 1.0142 1.0854 0.7715 0.12967 Lower tube 674.9133 1.00001 1.0036 1.0205 1.8526 0.7495 Rear hook 493.3223 1.00003 1.00675 1.0391 2.4610 0.3112 Reinf bracket 412.0648 1.00004 1.00970 1.0569 1.4765 0.2006 Release tube 69.9563 1.0016 1.18762 0.08404 0.0199 0.004916 Riser 104.6722 1.00075 1.1638 2.5511 0.0456 0.01106 Riser tube support 1203.83 1.000005 1.0011 1.0063 1.14482 2.2006 Support bracket 2150.489 1.00007 1.0003 1.09160 0.69717 0.1206 Upper cross member Upper recliner bracket 148.6396 1.00037 1.0775 1.6394 0.09612 0.0225 288.9352 1.00009 1.0198 1.12228 0.4736 0.09030 Upper track 218.6329 1.00017 1.0350 1.2320 0.2310 0.0499 Some observations have been made from above table which are given as below. If the excitation frequency is much lower than component natural frequency, in this case the Magnification factor is much near to 1 and at such situation dynamic amplitude is same as the static amplitude. If the excitation frequency of vibration of the vehicle is much higher than the component natural frequency then the dynamic amplification factor is less than 1 and higher is the excitation frequency the dynamic amplification factor is close to zero i.e. the dynamic amplitude vibration is very much lower than the static amplitude vibration. Volume 2, Issue 9, September 2014 Page 45
In practice, the vehicle will experience the wide range of excitation frequency so at particular excitation frequency some of the components of seat show the resonance effect. It is observed that the lower range of excitation frequencies i.e. in between 1-80HZ will have a significant effect on human body, as human body is sensitive in the range 1-80Hz of vibration. We do not have any control on excitation frequency of vibration and if we keep the component natural frequency in the range of human sensitivity there will be a possibility of resonance between human body and seat components due to excitations frequency of vibration and it will lead to decrease the comfort of the passenger and driver. Thus, it is better to keep the component natural frequency much higher than lower range of excitation frequency and much away from the human range of sensitivity for better vibration isolation. From the above results table the components that are showing the Magnification factor in the range of 0-1 those are safe from dynamic point of view as in dynamic Magnification factor can be visualized as amplification of static results due to dynamic loads. Thus, lesser is the Magnification factor better safe is the design from dynamic point of view. 4.1 Frequency Response Curve The dimension less plot of magnification versus frequency ratio has been shown in below Fig. 5. These curve reveal a lot of interesting and useful information regarding the behaviour of the system to sinusoidal excitation. The frequency response curve gives the response of the system to various frequencies. In this work the frequency of seat component have been calculated at different thickness of the component like 1mm, 1.5mm and 2mm. Below curves shows the response of upper cross member. Here natural frequency of upper cross member ( n) is constant and only variable is excitation frequency i.e. ( ). We have considered as 3 Hz, 32Hz, 50Hz, 100Hz, 150Hz...600Hz, 700Hz, 800Hz, 1000Hz. The magnification factor is calculated for this excitation frequencies and effect of this have been shown in below graph. The damping value is consider as a 0.2 and it is observe that for higher excitation frequency the magnification tend to zero or the amplitude of vibration become very small. If the natural frequency of the component is higher and the excitation frequency is lower then magnification factor is one or more close to one i.e. the dynamic amplitude of vibration is equal to static amplitude of vibration. Figure 5 : Frequency response curve of upper cross member 5. VALIDATION OF SIMULATION RESULT OF NATURAL FREQUENCIES BY ANALYTICAL METHOD The natural frequency of standard system like beam, plates can be found out by using mathematical approach. The fundamental frequency of typical beam configuration will be calculated by formula [4], which is given below. f n Frequency in Hz E Modulas of Elasticity in N/mm 2 I Area moment of Inertia in mm ρ Density of material in tonne/mm 3 A Cross sectional area in mm 2 Volume 2, Issue 9, September 2014 Page 46 (2)
L Length in mm n i - constant Constant n i is different for different modes of frequencies, this is obtained by solving the governing differential equation for number of iterations [5]. The obtained by analytical way is the exact. Constant n i is given below for common configurations in table Table 4: Constants for common configurations [4] Configuration Mode 1 Mode 2 Mode 3 Fixed-Free (Cantilever) 3.52 22.0 61.7 Fixed-Fixed 22.4 61.7 121 Free-Free 22.4 61.7 121 Cushion tube is integral part of seat assembly; in practice, it will give support to the cushion of seat pan. The geometry of cushion tube is like a beam of circular cross section fixed at the both end to the side cross member. Here we have considered free-free condition though it is fixed at both ends because for simulation we have considered a free-free analysis condition. The dimensions and properties of cushion tube are as follows, Length L = 485 mm Radius Thickness R = 18.1 mm t = 1 mm Modulas of elasticity E = 2.1 10 5 N/mm 2 Area moment of inertia I = π/64 (d o 4 - d i 4 ), I = 113.72 mm 4 Therefore, by using the equation (2) and constants mentioned in table (4), the results for first two modes are, f n for first mode = 1001 Hz f n for second mode = 2757 Hz Like this we have calculate the natural frequencies of cushion tube for thickness 1.5mm and 2mm. The simulation results and analytical results of cushion tube are given in below table 5. It is observed that the analytical results and FEA results of cushion tube are in a close agreement. The error between exact and FEA have been calculated by, Table 5: Cushion tube frequencies for different thicknesses Mode Thickness t = 1mm Thickness t = 1.5mm Thickness t = 2mm Exact FEA Exact FEA Exact FEA Mode 1 1001 933 1001.6 933.95 1002.24 934.21 Mode 2 2757 2421 2758 2421.74 2760.55 2422.59 It has been observed that the error for mode is 6.7% and it is same for each condition i.e. the variation in thickness does not change the error for first mode. For second mode, the error is 12.2 %. This is because FE models have low stiffness at higher frequencies, so in order to get correct natural frequencies in higher modes, the mesh should be very fine. It has been also observed that the analytical results and simulation results of cushion tube are in a close agreement. 6. CONCLUSION In this dissertation work, a methodology to analyse seating system using finite element method is presented. If the excitation frequencies are in the range of human sensitivity range i.e. 1-80Hz, then some of the components of seat have a higher value of magnification factor, it means it has high amplitude of vibration in dynamic condition. The seat components natural frequencies should be beyond the lower range of excitation frequencies and human frequency range of sensitivity as it will effect on human body comfort. It is also concluded that higher the natural frequency lower is the resonance between human body and seat components and the lesser the magnification factor better safe is the seat from dynamic point of view. This leads to increase the comfort of the occupant while riding. Volume 2, Issue 9, September 2014 Page 47
REFERENCES [1] C.Druga, D. Barbu. S. Lache, Vibration and the Human body, Fascicle of Management and Technological Engineering, VI (XVI), 2007. [2] S. Shivakumara, V. Shridhar, Study of Vibration and its Effect on Health of the Motorcycle Rider, Online Journal of Health and Allied Sciences, IX (II), 2010. [3] C. Mehta, V. Tewari, Seating Discomfort of Tractor Operators- A Critical Review, International Journal of Industrial Ergonomics, 25, pp. 661-674, 2000. [4] N. S. Gokhale, S. S. Deshpande, S. V. Bedekar, A. N. Thite, Practical Finite Element Analysis, First Edition, Finite to Infinite, Pune, 2008. [5] S. S. Rao, Mechanical Vibration, Addison and Wesley publishing, Second Edition, 2000. Volume 2, Issue 9, September 2014 Page 48