Research Article MODAL COUPLING EFFECT FROM MODAL ALIGNMENT PERSPECTIVE FOR LIGHT COMMERCIAL VEHICLE Chavan U. S.*, Sandanshiv S. R., Joshi S.V. Address for Correspondence Department of Mechanical Engineering, Vishwakarma Institute of Technology, Pune, Maharashtra, India E Mail umeshschavan@rediffmail.com ABSTRACT This paper presents the effect of each sub-system on overall vehicle from modal alignment perspective. In this work light commercial vehicle is considered for a case study. Modal analysis of all the aggregates like chassis frame, load body, cab, front and rear axle, propeller shaft and exhaust system are carried out on basis of rigid body and flexible body model. Finally, Modal alignment charts are prepared which shows the resonant points and coupling present in vehicle aggregates. These charts are very useful tool in dynamic analysis of whole vehicle. Results are validated in both rigid and flexible body models. KEYWORDS: Campbell chart, Light commercial vehicle, Modes, Modal alignment chart, Natural frequency, Resonance. I. INTRODUCTION Further, resonant points are found with Due to increase in competition, driver comfortness is taken as one of the main design consideration. Driver comfort has been affected due to increase in vibration, due to exciting forces which occurs mainly from subsystems and road disturbance [1]. One of the main vibration characteristic is natural frequency, when this match with exciting frequency resonance occurs. In vehicle if one of the subsystems s or aggregates natural frequency matches with other subsystems (cab, engine, exhaust, chassis frame, load box, propeller shaft, front axle and rear axle etc.) natural frequency resonance occurs. This phenomenon is called as modal coupling effect. Modal alignment chart is prepared for recognizing the resonant points in vehicle subsystems. First, rigid body method is used for modeling and analysis and then results are correlated with flexible body method for light commercial vehicle. For both methods modeling is done by using Hypermesh 8.0 and analysis is carried by Msc-Nastran software. rotating systems like propeller shaft and wheel rpm using its forced frequency by Campbell charting tool. These results are useful for guiding the vehicle designer and further modifying the design to avoid these critical points. II. MODELING Rigid body method (RBM) [2] for preparation of models boundary nodes are taken from the geometry of the subsystems. All the points are connected and giving the properties to the models and its cross section by using hyper beam tool (used for giving the properties to the beam element). The models of front suspension, rear suspension, chassis frame, load box, cab, engine and exhaust system are prepared. Finally all the models are assembled for making the full vehicle model as shown in Fig.1. Flexible body method (FBM) has been used for preparing the model of complete system level. Finite element technique is used which contains the meshing of components as shown in Fig.2.
Fig. 1 Complete systems Fig. 2 Complete systems flexible body model Front suspension [4] contains the number of mount bracket on front and rear side, and its components involving inner rim, outer rim, connections. Rims-inner and outer also anti hub, brake drum, caliper mounting bracket, roll bar are mesh with shell type of element stub axle, bearings, front axle beams, anti roll like quad type of element all remaining with bar, leaf springs, shock absorber, suspension solid tetra mesh. Front suspension has 105689
elements. Bearings are provided on two times, on one side for providing rotation to front wheels it is provided on front and rear side of the hub. Rbe2 element is provided on two rows of the nodes and at the centre node 1d rbe2 element is used and after connection zero element length is provided in hm software. Rotating motion along y axis is making free for the representation of the rotation. Rear suspension [5], [8] consist of inner rim, outer rim, axle tube, differential gear box, hub, bearing, leaf spring, suspension mount brackets, shock absorber mount bracket. Meshing elements are same as front suspension. Rear suspension has 115702 elements. Chassis frame [7] contains the long member, cross member, gusset, engine mount cross member, connections and total eight cross members are used. Long member is the main component of the chassis frame, which was used for the Load carrying member. Two C channels are used on left and right side of the frame. Long member is manufactured with the help of pressing operation. The thickness is same throughout. The shell element was used for the meshing of the long member. Cross members are also meshed with the help of 2d shell elements and are connected with the help of bolts which has been represented as beam 1d elements and Rbe2 elements. The main function of the gusset is to connect the long member to the cross member. Gusset is meshed with the help of 2d shell elements. Chassis frame has 130515 numbers of elements. Load box [3] which contains the long runner, cross members of the load box, tire guards, side members on both sides, for the mounting of the load box cleats are provided which was connected with chassis frame with the brackets and connected with nuts and bolts most of the components of the load box are mesh with 2d shell mesh. The main components of the cabs [3] are front and rear walls, left and right side doors, upper roof, mounting brackets. Walls, doors and roofs mesh with shell and brackets with 3d solid element and connecting with bolts by showing with 1d beam element. Cab and load box having 312754 and 143990 elements respectively. Components involve in the meshing of the exhaust system model was muffler, hanger, flexible bellow (its function is to isolate the vibration from engine to the exhaust and exhaust to Engine), mounting channel, chambers. Muffler, hanger, mounting channel, chambers are mesh with 2d element. For the damping of vibration flexible bellow is used. Here values of the stiffness s are given on six directions i.e. three on translational and three on rotational directions, for the representation of these stiffness s one spring element called as cbush is used. Propeller shaft [8] having the main function to transmit the power from engine to differential gear box in rear axle. The main components of the propeller shaft become flange yoke, tube 1 and tube 2, mid ship tube, tube yoke. Flange yoke, mid ship tube and tube yoke with solid and tubes with shell mesh. Exhaust and propeller shaft have 8356 and 16112 elements respectively. Engine, radiator, spare wheel, steering gear, driver, co-driver is made with point masses at the c.g. locations. III. MODAL ANALYSIS Modal Analysis was used for finding of the mode shapes and natural frequencies [9] which are essential for finding out the resonance points.
Table 1 Modal analysis results Type of mode Rigid (Hz) Flexible ( Hz) Type of mode Rigid (Hz) Flexible ( Hz) Full vehicle, 1 st 2.35 2.29 Rear axle, 1 st tramp 10.8 10.42 torsion Front axle, 1 st tramp 2.85 2.96 Exhaust 1 st longitudinal 12.55 12.01 Exhaust, 1 st lateral 3.98 3.93 Front axle, 1 st lateral 12.7 12.67 Exhaust, 2 nd lateral 4.01 3.96 Cab, 2 nd bounce 12.95 12.71 Engine, 1 st lateral 4.44 4.50 Exhaust, 1 st rolling 14.31 14.23 Engine, 1 st 4.98 4.76 Rear axle, 1 st hop 14.91 14.88 longitudinal Load body 1 st torsion 5.90 5.82 Propeller shaft, 2 nd vertical 15.01 14.95 bending Load body 1 st lateral 6.23 6.07 Exhaust, 1 st yaw 16.34 15.34 Front axle, 1 st hop 6.34 6.16 Exhaust, 2 nd yaw 16.54 15.66 Propeller shaft, 1 st 6.45 6.264 Exhaust, 1 st pitching 17.90 16.87 lateral Cab, 1 st bounce 6.58 6.55 Engine, 1 st yaw 21.56 19.41 Load body, 2 nd lateral 6.90 7.038 Engine, 1 st pitching 23.54 21.41 Engine, 1 st bounce 7.98 7.75 Load body, 1 st vertical 24.1 22.42 bending Exhaust, 1 st translation 8.01 7.77 Cab, 1 st vertical bending 25.01 24.3 about Z Propeller shaft, 1 st 8.13 7.78 Load box, 2 nd vertical 25.03 24.8 vertical bending bending Exhaust, 2 nd translation about Z 8.31 8.22 Modal alignment chart: Resonant points in vehicle are represented with modal alignment chart which indicates the information in X and Y direction. X direction contains the information of frequency in Hz. And Y direction i.e. on the left side column indicates the name of the sub system as shown in Fig.3. This chart represents the frequencies up to 25 Hz. This is lower natural frequency. Fig.3 and Fig.4 represents the symbols and its explanation which is used for the representation of mode shapes with respect to system and subsystem. If two or more related subsystems mode shapes matches then it creates the modal coupling, which is not desired. Modal alignment chart is the valuable tool for finding the modal coupling in automotive industry.
Front Axle 1 st Hop and Cab 1 st Bounce at 6.5 Hz. Engine 1 st Bounce and Exhaust 1 st Trans. @ Z at 8Hz Front Axle 1 st Lateral and Cab 2 nd Bounce at 13 Hz Engine 1 st Bounce and Propeller Shaft 1 st Vertical Bending at 8 Hz Rear Axle 1 st Hop and Propeller shaft 2 nd Vertical Bending at 15 Hz. Fig.3 Modal alignment chart-rigid body method Front Axle 1 st Hop and Cab 1 st Bounce at 6.5 Hz. Engine 1 st Bounce and Exhaust 1 st Trans. @ Z at 8Hz Front Axle 1 st Lateral and Cab 2 nd Bounce at 13 Hz Engine 1 st Bounce and Propeller Shaft 1 st Vertical Bending at 8 Hz. Rear Axle 1 st Hop and Propeller shaft 2 nd Vertical Bending at 15 Hz. Modal alignment chart-flexible body method Fig.4
Forced frequency: Forced frequency is finding by using following formulas. For Engine, ( Min. * 0.5 for1/ 2order * 2) Frequency for Minimum = (60) Frequency for Maximum = ( Max. * 0.5For1/ 2order * 2) (60) For Propeller shaft, Propeller Shaft (Minimum) = ( EngineMin. ) ( FirstGearRatio) For Wheel, Pr opellershaft ( Min.) Frequency for Propeller Shaft (Minimum) = 60 (PropellerShaft( Min.)) Wheel for Min. Engine Rpm = ( Cons tantgearratio) Frequency for Wheel (Min. Engine ) = ( WheelforMin. Engine ) (60) Table 2 Engine Frequency Results For Different Orders with Min. and Max. Order (min.) Freq, (Hz), (min) (max) Freq, (Hz), (max) Half 700 12 2800 47 1 st 700 23 2800 93 1.5 th 700 35 2800 140 Campbell chart: It was plotted for frequencies are plotted with respect to engine representing the resonance when natural frequency intersects with forced frequency. Campbell chart was plotted with X values as Engine. This starts from the minimum engine which is 700 rpm and ends at maximum engine rpm which was at 2800 rpm. Y direction represents the frequency (Hz) as shown in Fig 5. Horizontal lines represent the natural frequencies of subsystems. Exciting frequencies are found from engine rpm which maximum and minimum rpm as shown in Fig.6. Total six gear ratios are included in this chart; from this gear ratios propeller shaft operating frequencies are calculated. Wheel or tire operating frequencies are shown in Fig. 7and calculated by using engine rpm, gear ratios and constant gear ratio. It was between propeller shaft and differential gear of 4.857. If operating frequency lines are intersect with horizontal natural frequency line this point is was represented as engine orders. For called as resonant points. We also knew at propeller shaft or drive lines operating which rpm this resonance occurs
Engine Half Order Engine 1st Order Engine 1 st Pitching at 21.41 Hz at 1280 rpm Engine, 1 st Yaw at 19.41Hz at 1160 rpm Exhaust 1 st Pitching at 16.87 Hz at 1010 rpm. Exhaust 1 st Yaw at 15.34 Hz at 930 rpm. Exhaust, 2 nd Yaw at 15.66 Hz at 950 rpm. Propelle r Shaft 2 nd Vertical Bending at 14.95 Hz at 901 rpm Exhaust 1 st Rolling at 14.23 Hz with 900 rpm Exhaust 1 st Longitudinal at 12.01 Hz at 728 rpm Campbell Chart, Engine Vs Frequency, for Engine Order Fig. 5 Campbell Chart, Engine Vs Frequency, for Engine Order 6 th GEAR 5 th GEAR Engine 1 st Pitching at 21.41 Hz with 4 th, 5 th and 6 th Gear Engine 1st Yaw at 19.41 Hz at 3rd, 4th, 5th and 6th gear 4 th GEAR 3 rd GEAR Rear axle,1st Hop at 14.88 Hz at 3rd, 4th and 5th gear. Rear axle 1st Tramp, 10.42 Hz at 2nd, 3rd and 4th gear. 2 nd GEAR Propeller shaft 1st Vertical bending 7.78 Hz at 2nd and 3rd gear Engine 1 st Bounce at 7.75 Hz at 2 nd and 3 rd Gear Propeller shaft 1st Lateral 6.26 Hz at 1st, 2nd and 3rd gear Engine 1st Longitudinal, 4.76 Hz at 1st and 2nd gear Engine 1st Lateral, 4.5 Hz at 1st and 2nd gear 1 st GEAR Campbell Chart, Engine Vs Frequency, for Propeller Shaft Gears Fig. 6 Campbell Chart, Engine Vs Frequency, for Propeller Shaft Gears
Table 3 Results for propeller shaft and tire with frequency Gear Ratio Propeller (Min.) Propeller (Max.) Tire (Min.) Tire (Max.) Propeller (Min.) Frequency, Propeller (Max.) Frequency Tire (Min.) Frequenc Tire (Max.) Frequency, Hz Hz, Hz y Hz 6.9 101.44 405.79 20.887 83.54 2 7 0.34 1.39 4.02 174.12 696.51 35.851 143.40 3 12 0.59 2.39 2.39 292.88 1171.54 60.302 241.20 5 20 1.00 4.02 1.46 479.45 1917.80 98.713 394.85 8 32 1.64 6.58 1 700 2800 144.12 576.48 12 47 2.40 9.60 0.766 913.83 3655.35 188.14 752.59 15 61 3.13 12.54 Rear axle 1st Tramp of 10.42 Hz at 6th gear Front Axle 1st Hop of 6.16 Hz at 4th, 5th and 6th gear Front Axle 1 st Tramp at 2.96 Hz with 3 rd,4 th and 5 th Gear 3 rd GEAR 1 st GEAR 6 th GEAR 5 th GEAR 4 th GEAR 2nd GEAR Campbell Chart, Engine Vs Frequency for Wheel with Gear Ratios Fig. 7 Campbell Chart, Engine Vs Frequency for Wheel with Gear Ratios IV. RESULTS AND DISCUSSIONS found by using engine rpm per gear ratio and Natural frequencies by modal analysis are shown in Table1. Important mode shapes and natural frequency are given in appendix. Modal alignment and Campbell charts are prepared on the basis of rigid and flexible body model. In Engine frequency formula 0.5 includes for half order. Rpm of propeller was wheel rpm with propeller rpm per constant gear ratio. Results of engine and propeller and wheel frequencies are shown in Table 2 and Table 3 respectively. For explanation of Campbell chart for engine order refer Fig.5 which shows the intersecting points (resonant points). Also, Fig. 6 and Fig. 7 represent the
resonant points for propeller and wheel rpm at different gear ratios. Here the commercial vehicle and its subsystems, modes of vibrations were analyzed. Rigid body method and flexible body method used for modeling and modal analysis of subsystems and complete systems. Modal analysis was done for finding the mode shapes and natural frequencies. Results of rigid body methods are verified with flexible body methods. By both the methods results modal coupling shown in Table 4. Table 4 Modal coupling results from modal alignment chart Coupled subsystems and its modes Modal coupling frequency, Hz Front axle 1 st hop and cab 1 st bounce 6.5 Engine 1 st bounce and Exhaust 1 st translation about Z 8 Engine 1 st bounce and Propeller shaft 1 st vertical bending 8 Rear axle 1 st Hop and Propeller shaft 2 nd vertical bending 15 Front axle 1 st lateral and cab 2 nd bounce 13 Table 5 Resonant frequencies with engine rpm Type of mode Resonant frequency, Hz Engine, rpm Order type Exhaust 1 st longitudinal 12.01 728 1 st Exhaust 1 st rolling 14.23 900 1 st Propeller shaft 2 nd vertical bending 14.95 901 1 st Exhaust 1 st yaw 15.34 930 1 st Exhaust 2 nd yaw 15.66 950 1 st Exhaust 1 st pitching 16.87 1010 1 st Engine 1 st yaw 19.41 1160 1 st Table 7 Resonant frequencies with wheel rpm Type of mode Resonant frequency, Hz Gear number Front axle 1 st Tramp 2.96 3 rd, 4 th and 5 th Front Axle 1 st Hop 6.16 4 th, 5 th and 6 th Rear axle 1 st Tramp 10.42 6 th Table 6 Resonant frequencies with propeller shaft rpm Type of mode Resonant frequency, Hz Gear number Engine 1 st lateral 4.5 1 st and 2 nd Engine 1 st longitudinal 4.76 1 st and 2 nd Propeller shaft 1 st lateral 6.26 1 st, 2 nd and 3 rd Engine 1 st bounce 7.75 2 nd and 3 rd Propeller shaft 1 st vertical bending 7.78 2 nd and 3 rd Rear axle 1 st tramp 10.42 2 nd, 3 rd and 4 th Rear axle,1 st hop 14.88 3 rd, 4 th and 5 th Engine 1 st yaw 19.41 3 rd, 4 th, 5 th and 6 th Engine 1 st pitching 21.41 4 th, 5 th and 6 th
Rotating subsystems generate the operating frequency or exciting frequency when it matches with one of the related subsystems natural frequency it creates resonance. In this work Campbell chart for rotating systems like engine rpm, propeller shaft rpm and wheel rpm is plotted for resonant frequency. Table 5 shows the resonant frequency for engine rpm. If natural frequency of exhaust 1 st longitudinal matches with engine operating frequency at 12.01 Hz and at 728 rpm resonance occur. V. REFERENCES [1] Krystof P. Jankowski, Peter G. Dodd, David Periam, Darrell Hancock Jr."Analytical Investigation of Light Truck Low Frequency Vibration Issues", SAE International, SAE paper 981170, 1998 [2] I. M. Ibrahim, D.A. Crolla and D.C. Barton "Effect of Frame Flexibility on the Ride Vibration of Trucks, Department of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, U.K. 1995 [3] Subrato Dhar, William E. Hohnstadt and Jeffrey D. Green "Integrated Modular Methodology-Philosophy and Strategy to Build Full Vehicle Finite Element Model", SAE International, paper 2002-01-3072, General Motor Corporation. 2002 [4] Nitin Y. Wani and Vinod K. Singh "Design Evaluations on IRS Axle System NVH through Analytical Studies" SAE International, SAE Paper No. 2005-01- 2289, Visteon Corporation. 2004 [5] Hisanori Tachibana, Kazuhiko Goth, and Hitomi Sakai "Vibration Analysis of Drive Line and Suspension Using Finite Similarly, propeller shaft and wheel resonant frequency are getting from table 6 and 7 respectively. If engine 1 st lateral mode matches with propeller shaft operating frequency at 4.5 Hz and in 1 st and 2 nd gear which shows resonance. As axles are coupled with wheels, if any operating frequency matches with axles natural frequency it shows resonance. From the above table, front axle 1 st tramp matches with wheel operating frequency at 2.96 Hz in 3 rd, 4 th and 5 th gear. Elements Models", SAE International paper 931306, Toyota Motor Corp. 1993 [6] Ichiro Kido, Akeru Nakamura, Takeshi Hayashi and Makoto Asai "Suspension Vibration Analysis for Road Noise Using Finite Element Model", SAE International, paper 1999-01-1788, Toyota Motor Co., 1999 [7] Hiroshi Takata, Mitsuo Iwahara and Akio Nagamatsu "An Analysis of Idling Vibration for a Frame Structured Vehicle", SAE International, 2003-01- 1611, Isuzu Motors Japan, Vehicle Research and Experiment Dept., Test Planning Section and Hosei University, Faculty of Engineering, Department of Mechanical Engineering. 2003 [8] Zhaohui Sun, Glen Steyer and Mark Ranek FEA Studies on Axle System Dynamics", SAE International, paper 2002-01-1190, American Axle and Manufacturing, Inc. 2002 [9] Thomas D. Gillespie, Heavy Truck Ride, SAE International, paper 850001, The university of Michigan (Transportation Research Institute). 1985 VI. APPENDIX: Mode shapes and Natural frequency