Modal Continuity Optimization Techniques

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1 Modal Continuity Development Process with the Help of Optimization Techniques Hemendra Singh Engineer Venkatesh Selvam Manager Mohamed Sithik Senior Manager Abbreviations: BIW: Body in white, TBIW: Trim Body in white, FRF: Frequency response function, Keywords:Modal Continuity, Modal Discontinuity, OptiStruct, FRF, Torsion, Bending, Mode shape, Shape Optimization, gauge optimization Abstract Compared to Physical tests, Virtual validation methodologies arevery economical in developing a vehicle in today s competitive automotive world. To support the vehicle architecture development, automotive industries are trying to develop new methods and processes to refine their vehicle to its excellence. A refined vehicle is the result of a refined structure. To facilitate the structural performances, vibration characteristics remain an important parameter to evaluate the behavior of the structure at its natural frequencies. Modal continuity which defineses refinedness of a mode is one such important characteristic to be justified in the vehicle structure it also affects the vehicle NVH and durability performance. Hence, modal continuity is one of the performance factors which are being tracked in the concept stage of vehicle structure development. The study conducted establishes a generalized methodology to control the modal discontinuity in a vehicle structure by optimizing the gauges (thickness) of panels and shape of panels using OptiStruct solver and RADIOSS for verification. The FREQ4 card has been used in the optimization and imaginary component of acceleration is being controlled to approach continuity in the structure. Since the study conducted aims to develop a methodology for performance improvement by modal continuity optimization, it does not emphasize on weight reduction. The performance characteristics can be attained with significant reduction in weight, by using Topology and shape optimization techniques available in OptiStruct& by reinforcing the structure locally wherever required with reinforcements. Introduction Vibration is a general phenomenon in mechanical systems. All mass elastic systems have natural frequencies. A few of the lower order frequencies are of interest because the higher ones are more highly damped. For one frequency, a system vibrates in a particular way, depicted by the relative amplitude and phase at various locations mode of vibration. Different systems exhibits different mode shapes according to their mass and stiffness distribution. Among all the mode shapes bending and torsion remain the fundamental shapes (or common shapes) of systems with unconstrained boundary conditions. A vehicle follows the same too, but sometimes the non-uniformity in the shapes of these modes resulting from asymmetry or non-uniformity in structure s stiffness and mass distribution poses a challenge to the vehicle architects. In order to avoid these problems, at the design stage it is necessary to buildthe structure accurately and analyze its response to anticipated disturbances and to endow symmetry and uniformity to the structure to make it behave as per expectation. This paper explainsa process to control the non-uniformity in the mode shapes of a vehicle. The mode shape of the vehicle can be controlled by keeping in check the imaginary component of the responses in frequency response analysis, as presented in the studies in this paper.first study is about torsion discontinuity elimination from the body in white structure using the optimization process and second study shows the way weight optimization is done while keeping the amplitu desin check during bending mode. 1

2 Procedure Torsion Discontinuity Definition: Torsion discontinuity is referred as the movement of C-ring (in case of hatchbacks) or D-ring (in case of minivans)during torsion mode in Y-direction coupled with Z-direction, wherethe movement in Y- direction becomes undesirable as it causes the durability issues. The torsion discontinuity in the structure is determined by frequency response e analysis, where the 4 points at four corners of the C-ring/D-ring are excited in Z-direction and imaginary component of acceleration at the excitation locationsare plotted for Y- direction. If the acceleration at top and bottom locations on either side of the C-ring/D-ring are in-phase i.e. bothare positive or both negative then the structure is said to be continuous, otherwise discontinuous. In this study, four points on the C-ring/D-ring as shown in Fig:1 are taken and frequency response analysis deck in OptiStruct is created for point mobility where the body in white (BIW) is excited at these four points and responses are taken at the excitation points respectively. For the sake of simplicity two points either only on left hand side or on right hand side can be considered if the design variables are symmetric about XZ-plane. FREQ4 card, is a dynamic excitation card available for Frequency response analysis, which excites the point at the natural frequencies of the system. This card plays a major role in this methodology because of its capability to excite the system only at the natural frequencies. From the past studies, an approximate range of frequency for first torsion mode is determined and FREQ4 card is defined appropriatelykeeping in mind that the adjacent modesdo not interfere with the frequency range defined in the FREQ4 card. Also, the torsion mode frequency and the adjacent mode frequencies were constraineddiligently to avoid interference of torsion mode with the adjacent mode. Lateral acceleration at the top and bottom points is controlled to bring the amplitudes in phase to control the discontinuity in the structure. Discontinuity is eliminated by bringing top and bottom lateral accelerations in phase. In this particular study the panels in the vicinity of C-ring and D-ring of the BIW were considered to get the desired nature of the torsion mode. Controlling the Bending frequency response In another similar study where the objective is weight reduction while keeping the accelerations within the target level, the acceleration in the frequency response analysisat bending frequency is controlled using the same methodology and significant mass reduction was achieved. This particular frequency response optimization was based on cross mobility analysis where the system is excited at one location and the response is taken at any other location/ locations. In this study, the excitation point is at front rail and the response points are at front rail&pillars as shown in Fig: 2. Again the accelerations were controlled by using the same optimization setup as explained in the previous study. The design variables are defined as per the manufacturing constraints, the allowable for panels thicknesses and the packaging space available for shape optimization.majorlyunderbody panels were considered for optimization and all the frequency targets as well as amplitude targets were achieved with significant mass reduction. Fig:1 2

3 Results and Discussion Fig: 2 Torsion Discontinuity: The project aims to eliminate the torsion discontinuity in the first torsion mode with maximum mass reduction or minimum mass penalty as is the case in all optimization studies. The targets are achieved but with the mass penalty of 1.7%.The mass penalty are then recovered by trading-off the thickness with the shapes (section) of the panels and by placing the reinforcements. As shown in the Fig: 3 (b), the rear-most ring of the vehicle which possess some lateral movement (movement in Y-direction) when excited in Z-direction - in the initial or baseline model, was optimized to the structure which does not possess such lateral movement in torsion mode. This behavior was also confirmed graphically as shown in the Fig: 3 (a) where the peaks in the baseline structure at the top and bottom locations (as shown in fig 1) on either sides of the ring are out of phase i.e. one peak is in negative direction and the other is in positive direction. But in the optimized structure, the peaks on either side of the ring are in phase i.e. both are either positive or negative. Fig: 3 (a) Fig: 3 (b) 3

4 Controlling the Bending frequency response: This study aims for mass reduction while retaining the existing bending behavior (baseline bending behavior) by controlling the amplitudes at FEM & pillar locations, at bending frequency.with the relaxation of 10% in targets, significant mass reduction of 3.5% and 5% were achieved in two different studies with different sets of design variables.fig:4show the plots for benchmarked concept models and concept models with mass reduction. Fig: 4 Concept 1 is one of the benchmarked model having highest peak values but low mass and concept 2 is another benchmarked model having lowest peak values but with high mass.the objective in simple terms was to achieve the comparable performance as in concept 2 with mass comparable to the concept 1.Concept 3 and Concept 4 are the models with lower mass than Concept 1 model and comparable peak values with concept 2 model. Benefits Summary The frequency response optimization method presented here can be used extensively for vehicle architecture development as well as for weight optimization.this optimization process is efficient as it takes relatively less time for analysisbecause of the capability offreq4 card to excite the system at natural frequencies.also the use of FREQ4 card enables us to properly track the mode and optimize for only that particular mode. Challenges Setting up the deck for the process requires intensive care for isolating the modes so as to avoid interference with the adjacent modes, as the interference with other modes may cause the optimizer (OptiStruct) optimizing the mode which is out of the scope of the study. Future Plans We are aiming to refine the processs further and implement it in TBIW, at subsystem levels and in addressing the discontinuity in bending mode. Conclusions Using this methodology, with proper selection of design variables and optimization processes viz. gauge, shape, topology, topography, significant performance improvement or mass reduction or both performance improvement and mass reduction can be achieved. ACKNOWLEDGEMENTS The Authors would like to thank Partha Datta, Director, Chrysler India Automotive Pvt limited for encouraging the breakthrough technologies. Our GMs Subbi Pisupati& Rama Vallurupalli for supporting with technical guidance and last but not the least Mohamed Sithik for his support and guidance. 4

5 REFERENCES [1] Gradient-based Methods for Optimization, Prof. Nathan L. Gibson, Oregon state University [2] Gradient Based Optimization Methods, Antony Jameson, Department of Aeronautics and Astronautics, Stanford University [3] Frequency Response Analysis, Jungwon Yoon, School of Mechanical & Aerospace Engineering. [4] Analysis of Frequency Response and Fatigue of Car Body by Random Loading, Xiting Wang, School of Mechanical Engineering, Shenyang University of Technology, Shenyang, China [5] OptiStruct Help Manual 5

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