Abstract
Accurate finite element models of mechanical systems are fundamental resources to perform structural analyses at the design stage. However, uncertainties in material properties, boundary conditions, or connections give rise to discrepancies between the real and predicted dynamic characteristics. Therefore, it is necessary to improve these models in order to achieve a better fit. This paper presents a systematic three-step procedure to update the finite element (FE) models of machine tools with numerous uncertainties in connections, which integrates statistical, numerical, and experimental techniques. The first step is the gradual application of fractional factorial designs, followed by an analysis of the variance to determine the significant variables that affect each dynamic response. Then, quadratic response surface meta-models, including only significant terms, which relate the design parameters to the modal responses are obtained. Finally, the values of the updated design variables are identified using the previous regression equations and experimental modal data. This work demonstrates that the integrated procedure gives rise to FE models whose dynamic responses closely agree with the experimental measurements, despite the large number of uncertainties, and at an acceptable computational cost.
Highlights
Machine tools are stationary, power-driven industrial devices used to manufacture workpieces under user and technological requirements
Three design variables are only significant for one natural frequency (f FEA5 ), namely the transverse stiffness kZ63 between the bed frame and foundations, and two stiffnesses between the modules of the machine tool, kZ13 and kY9
MAC5 and MAC6 are affected by the largest number of interactions
Summary
Power-driven industrial devices used to manufacture workpieces under user and technological requirements. The most demanded requirements are accuracy and precision, which mainly depend on the static deformation and dynamic behavior of the machine tool under variable cutting forces. Machine tool manufacturers devote strong efforts to perform the appropriate static, modal, and dynamic analyses of the machines, in order to determine the stresses and displacements, natural frequencies, and mode shapes. The final aim is to identify and analyze the vibration sources under different operating conditions, in order to minimize their effects on the surface finishing of the workpieces, stop the appearance of regenerative vibrations or chatter, and slow down the swift wear of the tools [2,3]. The FEM provides a discretized model of the machine tool, whose purpose is to reproduce the real behavior of the structure
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