Finite element model updating of a commercial vehicle seat by response surface method

Since the vibration on the seat has a high impact on human comfort and health, the comfort of the seat is very important in the vehicles manufactured. One of the important domains of seat comfort is the resonance frequency of the seat and it is demanded that the seat resonance frequency is above a certain value. This demanded value greatly affects the structure of the seat. The finite element analysis method is being used widespread by the demands that come from the OEM (original equipment manufacturers) and it is more effective method about detecting deficiencies by analyzing the seat. Because at the beginning phases of the seat design the prototyping method is a time taking, difficult and expensive process as the experimental process. When the vehicle is being manufactured, all designs are prepared in a predictive manner and then converted into physical parts. Here, the design of the seats made by using the finite elements method is very important without making the projected seat design into a physical part. It is very important that analyzes made are closer to the tests performed on the seats that are made into physical parts in order to make progress and reliable results. Because it is time consuming and costly to manufacture the prototype of the seat in the beginning stages of the projects and to determine the characteristics related to the experimental work. Despite the advantage of the finite element method has the disadvantage of matching the experimental results. Thus it is necessary to increase the accuracy of the finite element model, and to update the model. This is the model updating technique that goes for true matching of the experimental and theoretical results. For that the component material properties, dimensions, rigidity of the interconnection points are accepted as parameters and tried to harmonize with the experimental data by updating them. First, the seat frame will be modal analyzed. Later, each corresponding element will be added to the seat frame and will be analyzed how these elements affect properties. After that, the best parameter values determined and will be detected what value range they are. This seat is modeled first in CAD environment, and then meshed in Hypermesh finite element program and finite element model is created. Modal analysis is performed with the Optistruct program, which creates the seat model in Hypermesh program. In addition, a force is applied by a hammer to the manufactured physical seat and modal analysis measurement is made by accelerometer. These measurements made on the seat were also tested at a separate level of the layers on the seat in order to examine the effect of the seat's layers on the modal frequency. These layer levels are: 1. the structure of the frame alone, 2. the seat backboard is added to frame, 3. the foam added to the frame with the backboard, 4. the whole seat. The modal parameter of each layers here are experimentally measured separately. Since the measurement is made by accelerometer after applying the force, the results that obtains are accelerance frequency response function. So, the accelarance frequency response function is turned into reseptance frequency function with the required formulation. By curve fitting method, the obtained reseptance frequency function is turned to a data set which contains more data point. Subsequently, modal measurement of the complicated state of the seat is performed in the finite element model and the frequency response function is obtained. The seat on finite element model is adjusted through the seat used on the modal test. For finding the necessary parameters that will use in the updating method, couple seat changes made to see the effects on the modal frequency. First parameters set is defined. These parameters set is important for the model updating and if necessary later these parameters can be changed with new parameters sets. Once these parameters are set, a range is set for these parameters. An experiment set is obtained for the parameters in this range by the central composite design method. Central composite design is useful for calculating quadratic equations. For this obtained set of experiments, analysis was made by Optistruct program for each data with finite element analysis program and these results are examined in Hypergrapgh program. For the results that is obtained from the finite element model, the difference function is calculated which shows the difference of finite element model results and experimental measurements. For the data set obtained by central composite design, a response surface is formed with the results obtained in the analysis program. The method used to update the seat finite element model and the experimental results is the response surface method. Response surface method is used for optimization of problems which affected from many parameters by using statistical and mathematical models. For obtain a mathematical model on the surface response method, parameters were chosen and a range is determined with central composite design. For each data point, the results have been obtained for both fore-aft and lateral directions with the finite element analysis program. With the response surface method, analysis of variance, model summary and coefficients are obtained as statistical values, and mathematical model is obtained. On the mathematical model, the linear, quadratic and cross values and their coefficients are obtained. On the model summary, R2 values show how the mathematical model is accurate for the model datas. Also P values shows the parameters are negligible if it is high. So on the mathematical model, P values of the some of the cross and quadratic values is high, backward elimination method is applied and the mathematical model is made plainer. On the graphic the values obtained from mathematical and experimental results is compared and if the line that goes from the points is around 45o, it reflects the mathematical model is represent the system well. Also for the third degree polynomials cubic models has been applied. To apply the cubic model certain quantity of data point has to be used which has been obtained from central composite design. Also backward elimination will applied to the cubic models. On the surface response method the optimum points are found which makes the best value for the lowest difference on the finite element results and experimental result. For the optimum values the frequency response functions are obtained again and compared with experimental results to see the how the mathematical model represent the real system. More appropriate values are determined for the surface parameters that are fitted by the response surface method and these values are reflected in the finite element model. Best values are looked for which makes better both the fore-aft and lateral direction. For some data point, some values makes better result for the fore-aft direction but make worse for the lateral direction. So, the optimum values searched for the ones which makes better at the same time for both fore-aft and lateral directions. This model will help in the construction of the finite element model on the similar seats for detecting dynamic properties. So the parameters of the seats can be predicted in the next times, without the necessity of the manufacturing prototypes and testing them.