Numerical and Experimental Modal Analysis Applied to an Optical Test System Designed for the Form Measurements of Metre‐Scale Optics

Abstract

The work focuses on the structural design and performances of a unique optical test system (OTS) used for measuring metre-scale optical surfaces. The investigation was carried out through a modal analysis. Two sets of results are presented. Both modal analysis of the entire OTS and transmissibility function related to its use as an optical system are carried out and analysed. The OTS is used for the measurements of the form accuracy at nanometre level of metre-scale concave surfaces. The OTS is a four and half-metre-tall mechanical structure made of bolted aluminium profiles, two structural platens, two dedicated precision positioning supports, a test piece, and a state-of-the-art laser interferometer. The OTS was numerically modelled and fully instrumented with triaxial accelerometers. The results of the modal analysis highlight the natural modes of the entire OTS. Both numerical and experimental methods are designed. The investigation methods are iterative. Indeed, a preliminary numerical model is created using finite element analysis (FEA). FEA results enable the determination of the dynamic range and suitable locations of accelerometers that are mounted onto the OTS for the experimental validation of the FEA model and further to carry out the transmissibility study. Natural frequencies, damping ratios, and mode shape values are obtained and scrutinized. These results are used for refining the FEA model. In fact, the lack of symmetry and the use of feet are identified as the key design feature that affects the OTS. The correlation between experimental and numerical results is within five percent for the first four modes. The results of the transmissibility study highlight the specific natural modes that influence the OTS measurement capability. Overall, the study enables to guide engineers and researchers towards a robust design using a validated and methodical approach.

A Comparative Analysis of Optimization Algorithms for Finite Element Model Updating on Numerical and Experimental Benchmarks

“…This case study originates from a unique OTS setup designed and assembled at the Precision Engineering Institute Laboratory of Cranfield University. This is discussed in detail in [36]; only the main aspects are recalled here for completeness.…”

“…In total, 24 locations (highlighted by the red dots The identified natural frequencies (up to the fourth mode, defined in the 0-50 Hz range) are reported in Table 2. The locations of the four sensors were changed between hammer hits as explained in [36], only maintaining one at a fixed location for reference and applying five hits per sensor layout. In total, 24 locations (highlighted by the red dots in Figure 2a) were used for the triaxial sensor, considering all the main frame joints and four points below the lower platen.…”

“…The FE Model utilized for this study is the same as that described in [36]. This was realized in ANSYS Mechanical APDL (Figure 5a).…”

Analysis of Vibration Characteristics of Electro-hydraulic 3-UPS/S Parallel Stabilized Platform

“…There are three methods to study the vibration characteristics: simulation analysis method [15][16][17], theoretical analysis method [18] and experimental analysis method [19]. The simulation analysis method is to analyze the vibration characteristics after solving the characteristic value of the finite element analysis of the structure [20][21][22]. Therefore, it is widely used in analyzing vibration characteristics of complex mechanical systems.…”