Process Parameter, Geometric & Vibro-acoustic Variability: The Study of Causation in the Deep Drawing Process

Single-stage forming is widely used in the automobile industry due to shorter cycle times, cost-effectiveness and ease of implementation. However, achieving the desired dimensional accuracy of a designed part still remains a challenge as complex phenomena, including springback, are associated with the manufacturing process. For this reason, the process parameters such as the blank holder force are nowadays continuously adapted within the acceptable range during the deep drawing in order to produce defect-free parts. It is often seen that this results in both geometric profile and thickness variations as compared to the nominal part design. Although these variations are small and acceptable from a dimensional accuracy perspective, they can have a significant effect on the vibro-acoustic behaviour. A thorough understanding of the impact of deep drawing process parameters on geometrical variations of the manufactured part
and its resulting vibro-acoustic properties is therefore needed to improve the noise, vibration and harshness (NVH) behaviour of mass-produced components. However, such detailed knowledge covering the complete manufacturing process of deep-drawn parts is currently lacking. 

This research aims at providing insights into the complex relation between process parameters and the vibro-acoustic properties of deep-drawn components. To this purpose, two reference geometries are analysed numerically and experimentally: an oil pan look-alike component with a high draw ratio and a set of cylindrical cups. The geometry of the actual components is analysed using a white-light scanning process. It is observed that a geometry profile deviation up to 5 mm and a thickness variation of 40% occurred in the actual oil pan as compared to the nominal design. The importance of these geometrical variations for the vibro-acoustic behaviour is demonstrated by comparing the results of an experimental modal analysis and vibro-acoustic simulation models of the nominal design and of the geometries obtained from the scan of the physical part and from forming simulations. It is observed that the eigenfrequencies
of the actual part have deviations up to 14% as compared to those predicted for the nominal design. Besides, the vibration response of the actual part differs significantly from the one predicted by the numerical model obtained using the nominal CAD model. Similar differences are observed between the different numerical models for the radiated structure-borne and airborne noise.
These results illustrate the necessity to include geometry profile and thickness variations to improve the accuracy of vibro-acoustic simulation models.

 One of the methods to build high-fidelity finite element (FE) models, which accurately represent the behaviour of the actual system under study, is through a model updating procedure. A conventional model updating, tuning Young’s
modulus, density and damping ratios, does not lead to a good match between simulated and experimental results for deep-drawn components, where the mismatch between model and reality is predominantly caused by geometry variations. Hence, a new model updating process is proposed, where geometry shape variables are incorporated by carrying out morphing of the FE model. An optimisation procedure that uses the Global Response Surface Method (GRSM) algorithm to maximise diagonal terms of the Modal Assurance Criterion (MAC) matrix is presented, which is shown to result in a more accurate FE model. An additional advantage of the proposed methodology is that the CAD surface of the updated finite element model can be readily obtained after optimisation. 

Continuously adaptable blank holder force (BHF) systems not only cause deviations from the nominal part geometry but also induce a significant amount of variability in both the geometry and the functional performance of the component. The influence of BHF and friction coefficient on vibro-acoustic properties is investigated through forming simulations. The forming analysis
results—geometry profile and thinning—are used as an input to predict the vibroacoustic behaviour of the formed component. It is shown that the geometric profile and thickness variations are small but nevertheless significantly affect the vibration response and radiated noise. A similar analysis is carried out experimentally by comparing two nominally identical oil pan components. The
natural frequencies obtained in free-free boundary conditions vary up to 20% for the first six flexible modes, and significant differences in the mode shapes are observed. The resulting sound power levels between the two parts varied by 2 dB(A).

Finally, a set of cylindrical cups manufactured with different BHF is analysed to quantify vibro-acoustic variability within and between batches of deep-drawn components. It is observed that increasing the BHF reduces the mean vibration values, but increases the variance within the batch. A Design of Experiments (DOE) study, based on Taguchi orthogonal arrays and numerical simulations, is carried out to characterise the individual effects of process parameters on the response levels. The resulting correlation confirms the experimental observations
and simulation model can be used to select appropriate process parameters, in order to achieve the vibro-acoustic variability targets.