Research on Theoretical Basis of Design Optimization of Flexible Hinges and Flexible Body Mechanisms

Expanded

Flexible hinges have gained significant attention in precision devices due to their ability to transmit motion or energy through elastic deformation instead of rigid components. Compared to traditional motion hinges, flexible hinges offer advantages such as high motion resolution, no friction, no lubrication, and a simple manufacturing process. They have been widely used in various precision devices, including projection lithography objective lenses, silicon wafer workbenches, electronic scanning microscopes, space optical remote sensors, and precision and ultra-precision processing. The key parameters of compliant mechanisms, like flexible hinges, directly impact the dynamic characteristics and positioning accuracy of the end. Therefore, extensive research has been conducted to understand the flexibility of flexible hinges. This paper aims to study the flexibility matrix of straight beam rounded flexure hinges, analyze its parameters, and provide a theoretical basis for their design and optimization.

Flexibility Matrix of Straight Beam Rounded Flexure Hinges:

The straight beam rounded flexure hinge consists of a straight beam sheet structure with rounded corners at the hinge's ends to avoid stress concentration. The main geometric parameters include hinge height (h), hinge length (l), hinge thickness (t), and hinge fillet radius (r). To analyze the in-plane deformation of the hinge, an analytical calculation method based on the cantilever beam theory is derived. This method establishes a closed-loop analytical model for the in-plane flexibility matrix of the flexible hinge. Additionally, a simplified calculation formula for the flexibility matrix is provided when the ratio of hinge corner radius to thickness (r/t) is given.

Finite Element Verification:

To validate the derived analytical formula, a finite element model of the straight beam rounded flexure hinge is established using UGNX NASTRAN software. The simulation results of the finite element model are compared with the analytical values of the flexibility matrix parameters. The relative error between the two is analyzed for different variations in the hinge's structural parameters, such as the ratio of hinge length to thickness (l/t) and the ratio of hinge corner radius to thickness (r/t).

Results:

The analysis shows that for l/t ratios greater than or equal to 4, the relative error between the analytical and simulated values of the flexibility matrix is within 5.5%. However, for l/t ratios less than 4, the relative error is relatively large due to the inability to simplify the cantilever beam into a slender beam. This indicates that the closed-loop analytical model is more suitable for large l/t cases.

Regarding the ratio r/t, the analysis reveals that when 0.1 ≤ r/t ≤ 0.5, the relative error between the analytical and simulated values can be controlled within 9%. Additionally, when 0.2 ≤ r/t ≤ 0.3, the relative error can be controlled within 6.5%. These findings demonstrate the accuracy and applicability of the closed-loop analytical model for the flexibility matrix.

The closed-loop analytical model developed in this study provides a theoretical basis for the design and optimization of straight beam rounded flexure hinges. The analysis demonstrated that the model can accurately predict the flexibility matrix parameters when considering variations in hinge length, thickness, and corner radius. These findings will contribute to the advancement of compliant mechanisms and their applications in precision devices.