The tool MC-03 computes maximum applied load, maximum deflection, and spring rate of a compression spring.
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 Compression Spring
The input in the tool is
After clicking "Run", the results will be shown as follows in another page.
Maximum applied load (F) = 22.00685412 newton(N)
Maximum deflection (δ) = 0.00362228 m
Spring rate (K) = 6075.41349199 N/m
Total number of active coils (Na) = 8
Solid length (Ls) = 0.495 m
Pitch at free length = 0.118125 m
Fig. 1 A helical compression spring
Fig. 1 shows a typical helical compression spring. A helical compression spring is subjected to both transverse and torsional shear. The total shear stress is in the form of
d: Wire diameter
D: Spring mean diameter
F: Applied axial load
Kd = (2C+1)/(2C) : Shear stress multiplication factor
with C = D/d being spring index
Due to the curvature effect, the stress at the inside surface is higher than that at the outside surface. If the curvature effect is included, the shear stress multiplication factor is replaced by the Bergstrasser factor
The spring deflection is
G: Elastic shear modulus
Na: Number of active coils (See Table 1)
Table 1 Formulas for compression springs with different end conditions
Then the spring rate is given by
For springs in parallel, the spring rate is
For springs in series, the spring rate is
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.