Chapter33 Detection of Stress-Stiffening Effect on Automotive Components Elvio Bonisoli, Gabriele Marcuccio, and Stefano Tornincasa Abstract In this paper experimental investigations of interference fit effects on the dynamic behaviour of assembled wheels are provided. The performed analyses on the automotive components take into account manufacturing pre-stresses and dimensional tolerances of mating parts. Experimental modal analysis is made on a set of components with identical nominal values to prove either the component or the assembly variability. For each mode a PCE-based meta model is developed upon a small sample of experimental observations and the interference fit level is estimated by means of the stress stiffening effect. The presented technique is aimed at improving the design and development of industrial components through the combination of established methodologies. The effectiveness of modal analysis, when combined with numerical/statistical approaches is pointed out. Keywords Stress stiffening effect • PCE meta-models • Experimental modal analysis • Design for modal assembly • Dimensional tolerances 33.1 Introduction The stress-stiffening effect is a well-known phenomenon which can be observed in many types of real structures such as columns, tendons, cable-roof structures, membranes and plates. Weinstein and Chien [1] obtained the fundamental frequency for a clamped square plate for increasing values of tension. In [2, 3] the authors demonstrated the possibility of estimating the axial loads of beams in a truss by using experimental dynamic responses. Computing the fundamental frequency of a vibrating plate under uniform tension received extensive attention in the literature. Timoshenko [4] solved the case of a circular plate taking into account the effect of tension in its middle plane. Weinstein and Chien [1] extended the approach presented by Bickley [5] and valid only for a small range of the tension, reducing the problem for a plate of any shape to the membrane one for the corresponding domain. In [6] theoretically exact solutions are given for the case of a circular plate, either clamped at the circumference or simply supported, with a large initial tension or compression of varying magnitude. The geometric stiffening normally needs to be considered for thin structures with bending stiffness very small compared to axial stiffness, such as shells, cables, and thin beams. Numerical formulations for beam elements are available [7, 8], whereas for 2D or 3D elements the stiffness matrix can be computed by the use of numerical integration. Generally speaking, the computational approach splits the global stiffness matrix Ktot in terms of two components, namely Kgeom and Kstress. The former is a conventional stiffness matrix of the structure, and the latter is a supplementary term that is generated by prestresses. The effect of stress stiffening is accounted for by generating an additional stiffness matrix. This approach predicts that for one-dimensional and two-dimensional models, the stress effects play an important role in bending dynamics while axial and torsional effects are negligible. If the stress state becomes compressive, then terms in the stiffness matrix might yield to a non-positive-definite total stiffness matrix which represents the buckling condition. Interference fit fastening is one of the most used type of connection for joining parts together in many branches of mechanical industry. The slightly different sizes of the two components being connected create semi-permanent and stiff E. Bonisoli • G. Marcuccio ( ) • S. Tornincasa Politecnico di Torino, Corso Duca degli Abruzzi, 24, Torino 10129, Italy e-mail: elvio.bonisoli@polito.it; gabriele.marcuccio@polito.it; stefano.tornincasa@polito.it H.S. Atamturktur et al. (eds.), Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04552-8__33, © The Society for Experimental Mechanics, Inc. 2014 335
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