Answer :
Designing a helical torsion spring involves calculating the spring constant from the relationship between torque and deflection, selecting wire dimensions according to design constraints, and ensuring material stress limits are not exceeded. The rod diameter to mount the spring must provide clearance and support, typically being less than the inner diameter of the coil spring.
The question pertains to the design of a helical torsion spring using stainless steel wire for an application that requires a specific torque after a given deflection. To approach this problem, we must refer to the standard guidelines for spring design. These usually involve calculations related to the spring constant, material properties such as the shear modulus, and geometrical constraints such as wire diameter and coil radius. The question specifies the use of ASTM A313, type 302 stainless steel, a common spring material known for its strength and corrosion resistance.
First, we determine the required spring constant by analyzing the torque and deflection relationship. The spring constant k is given by the derivative of force with respect to length ($k = dF/dl$) for a coil spring, and for a torsion spring, it is the derivative of torque with respect to angular deflection $(k=dt/d heta)$. The spring constant helps to relate the torque exerted by the spring to the angle of twist.
A critical aspect of spring design is ensuring that the stresses within the spring do not exceed the material's yield strength, to avoid permanent deformation. The shear modulus of the material, alongside other factors like the wire and coil dimensions, will influence the torsion constant. This follows the method of dimensions which describes how the torsion constant depends on the shear modulus, radius, and length of the wire.
The diameter of the rod (mandrel) on which to mount the spring is typically less than the inner diameter of the coiled spring, providing sufficient clearance while maintaining support. The steps to design the torsion spring are as follows:
- Determine the required spring constant based on the torque and deflection data.
- Select an appropriate wire diameter using standard spring design equations and ensuring it fulfills the outside diameter constraint.
- Calculate the mean coil diameter, and using that, the diameter of a rod on which the spring can be mounted, considering manufacturing tolerances and proper fit.
Specific details about calculations and standard formulae are typically found in reference texts on mechanical design or spring design handbooks, which should be consulted for comprehensive guidance.