The tool MC-05 computes maximum operating torque and maximum angular deflection of a torsion spring. It also gives the angular spring rate and inside diameter of torsion springs after loading.

In addition, a tutorial on how to use the tool in computation is provided and a subject review on fundamental theories and useful formulas is presented.

**Example: A Helical Torsion Spring**

The input in the tool is

After clicking "Run", the results will be shown as follows in another page.

Maximum Operating Torque (T) = 2.84331333 N*m

Maximum Angular Deflection in Radians (θ_{rad}) = 1.72470407 rad

Maximum Angular Deflection in Revolution (θ_{rev}) = 0.29104381 rev

Angular Spring Rate in Radians (k_{θ,rad}) = 1.6485804 N*m/rad

Angular Spring Rate in Revolution (k_{θ,rev}) = 9.76936534 N*m/rev

Inside Diameter of Spring After Loading = 0.42020881 m

**Fig. 1** A helical torsion spring

Fig. 1 shows a typical helical torsion spring. The bending stress is in the form of

where

T: Torque

K: Stress-correction factor

I/c(=d^{3}/32): Section modulus (Circular cross-section)

Maximum bending stress occurs at the inner fiber and the stress-correction factor is

where C represents the spring index, which is

with d being the wire diameter and D being the spring mean diameter.

Maximum operating torque is determined by equating the bending stress to the yield strength (σ_{yield}). Properties of some torsion springs
wires are listed in Table 1.

**Table 1** Properties of some spring wires

The angular deflection in radians is

where

E: Young's modulus of the spring material

N_{a}: Number of active coils at no load, which is

Including the effect of friction, the angular deflection in revolution is

The angular spring rate is in the form of

After loading, the inside diameter of a torsion spring is

where

D_{i}=D-d: Inside diameter of a torsion spring at no load

1. R.G. Budynas and J.K. Nisbett, Mechanical Engineering Design, 2011, McGraw-Hill.

2. S.R. Schmid, B.J. Hamrock and B.O. Jacobson, Fundamentals of Machine Elements, 2014, CRC Press Taylor & Francis Group.

3. A.C. Ugural, Mechanical Design: An Integrated Approach, 2004, McGraw-Hill.