Understanding Spring Failures: Curvature Correction Factors
For the past three years, SMI has been examining spring failures and making recommendations for preventing recurrence. One issue that comes up repeatedly is the location of the fracture origin on compression springs. I hear comments like, “They are all breaking at the same spot, right at the inner diameter,” and “There must be something wrong with the wire, or the tooling marks are abnormal at the ID.” Sometimes there is something “wrong” with the wire, and occasionally tooling marks that tear the wire surface can be the culprit. However, in reality, it is perfectly normal for a compression spring to initiate fracture at the ID.
The mechanics behind the stress distribution in compression springs show that there are two causes for the inner-diameter stress concentration: direct shear stress and wire curvature.
The principle stress on a compression spring results from the torsional shear stresses that act on the spring. This rotational stress is shown in Figure 1, below.
The maximum stress in straight wire due to torsion is:
The distribution of this stress across the wire is at a maximum at the surface. The torsional stress is in the direction of the applied force at the inner diameter and opposite to the applied force at the outer diameter, as seen in Figure 2, right.
Accompanying the torsional stress is a less significant operational stress, which is the result of direct shear and can be assumed uniform across the wire, as seen in Figure 3, right. This transverse shear stress does not account for the curvature of the wire.
The direct-shear component can be approximated by dividing the applied force by the wire cross-sectional area:
When this stress is added to the torsional shear stress, the total stress at the inner diameter becomes:
Where C is the spring index and C = D/d.
The (1 + 0.5/C ) correction constant is sometimes referred to as the “Kw 2 correction factor,” which can be used on springs that have had the set removed. The magnitude of this correction factor can be seen graphically in Figure 6, page 40. It should be noted that there are many correction factors available and that A.M. Wahl equates the direct shear component to 4.92P/d2.
When the two stress components are added, the stresses at the spring inner diameter are greater due to the direction of the applied stresses, as seen in Figure 4, above.
Because the effects of curvature in springs are of far greater importance than direct shear, A.M. Wahl created a curvature correction factor, Kw1, that is based on the fact that a spring behaves like a curved bar under torsion. In Figure 5, bottom left, it can be seen that as AA' and BB' are rotated relative to each other, the resulting shear stresses at A'B' will be greater than at AB. This effect increases with increasing curvature or decreasing spring index, as shown in Figure 6, below.
Therefore, the maximum stress at the spring inner diameter accounting for curvature is expressed as follows:
where
The Wahl correction factor, Kw1, not only takes into account the spring curvature, but also includes the direct-shear component of the applied stress. This factor is commonly used for springs in fatigue applications.
As would be expected, the stresses at the outer diameter of the spring are in the opposite direction and less than nominal. The total stress at the outer diameter can be calculated by multiplying the torsional stress by the following term:
Understanding the stress distribution in a compression or extension spring can help explain the orientation of the point of fracture initiation. Overstressed compression springs normally initiate fracture near the inner diameter because of the direct shear stresses and spring curvature. Of much greater concern is the spring fracture that does not originate at the inner diameter. More often, this type of fracture is the result of operational abuse or material deficiencies.
