Lumped Parameter Model for Structural Analysis of Over-Constrained Multi-Legged Parallel Mechanism Supporting System Applied to Cryogenic Devices - Luca Piacentini; Luca Dassa; Diego Perini; Andris Ratkus; Toms Torims; Stefano Uberti (Machines)
While the design of a cryostat is being developed, one of the most relevant sub-systems is the internal supporting system that sustains the cooled component. According to the literature, the arrangement and number of supports chosen often result in a multi-leg over-constrained architecture. These are usually studied by means of finite element analysis tools alone, which makes studies like the optimization of supporting systems computationally expensive. This paper proposes a more structured and general analytical model compared to the existing models for this application. The proposed lumped parameter model allows designers to study the influence of external loads, pre-load, and cool-down on stress levels and deformation status of the supports of the cryogenic device as well as the consequent misalignment of the cooled component. The general lumped parameter model for n tie-rods of different shapes, dimensions, and materials is proposed. Two particularized models of eight and eleven supports are validated by comparing the results with those from standard finite element analysis software. Results show that the proposed model has a strong agreement with finite element simulations, and the median of relative errors is about 1.4%. This accuracy is obtained for models of randomly arranged supports, which proves the effectiveness of the model in predicting results even for non-symmetrical support configurations. Comparable and accurate results are obtained, which are about 130 times faster than in finite element analysis, thus proving the effective reduction in computational cost. Additionally, the proposed code lets designers change input parameters in a quicker and reliable way.