Stiffness estimation of planar spiral spring based on Gaussian process regression

Area of Science:

• Mechanical Engineering
• Materials Science
• Robotics

Background:

• Planar spiral springs are vital for miniaturizing motor-based elastic actuators.
• Traditional beam bending theory yields significant errors in calculating spring arm stiffness compared to finite-element analysis (FEA).
• Errors are attributed to the spiral length term in existing stiffness calculation formulas.

Purpose of the Study:

• To amend the spiral length term in stiffness calculations for planar spiral spring arms and complete springs.
• To improve the accuracy of stiffness prediction for miniaturized elastic actuators.
• To develop a more reliable method for designing planar spiral springs.

Main Methods:

• Training two Gaussian process regression models using FEA data for spring arms and double-arm springs.
• Utilizing datasets of 216 spring arms (varying radius, pitch, wrap angle) and 180 double-arm springs (varying width).
• Validating the models through simulations of various spring designs and experimental testing on a prosthetic ankle-foot spring.

Main Results:

• Reduced prediction errors to below 0.5% for spring arms and 2.8% for complete springs compared to FEA.
• Achieved a 3.25% error for a manufactured planar spiral spring in a powered ankle-foot prosthesis compared to measured stiffness.
• Demonstrated the effectiveness of Gaussian process regression in correcting stiffness calculation inaccuracies.

Conclusions:

• The proposed amendment, based on trained Gaussian process regression models, significantly enhances the accuracy of planar spiral spring stiffness calculations.
• This method provides a reliable approach for the dimensional miniaturisation of motor-based elastic actuators.
• The validated models offer a practical tool for the precise design of planar spiral springs in advanced applications.