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 (θrad) = 1.72470407 rad
Maximum Angular Deflection in Revolution (θrev) = 0.29104381 rev
Angular Spring Rate in Radians (kθ,rad) = 1.6485804 N*m/rad
Angular Spring Rate in Revolution (kθ,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
K: Stress-correction factor
I/c(=d3/32): 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 (σyield). Properties of some torsion springs wires are listed in Table 1.
Table 1 Properties of some spring wires
The angular deflection in radians is
E: Young's modulus of the spring material
Na: 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
Di=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.