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Garter Spring

garter spring
Tribology Wikipedia > Garter Spring

A Garter spring is a coiled steel spring that is connected at each end to create a circular shape, and is used in oil seals, shaft seals, belt-driven motors, and electrical connectors. There are several ways to connect the ends depending on the application: connector ends, loop connection and tapered end connection. Garter springs are generally divided in compression and extensions springs according to the direction of the radial load exerted, i.e., inwards, or outwards.

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Figure 1. Garter spring sketch.

Many lip seals count with a Garter spring for loading the seal tip against the shaft. The extra load provided by the Garter spring ensures that the stress relaxation of the seal material does not decay beyond the percolation limit of the contact. Because the load exerted by Garter spring is generally constant, i.e., the spring does not generally change its elongation while operating, Garter springs for shaft seals are often referred to as “constant load springs”.

Theoretical background

There is little written on garter springs. The following procedure estimates the radial load exerted by an extension garter spring when working under linear deflection:

1

Wire diameter d

2

Mean diameter of the helix D

3

Shaft diameter

D_s
4

Initial tension

P_I
5

Spring Working Length

L_0
6

Young’s modulus

E
7

Rigidity modulus

G

The following parameters can be deduced from the ones above:

8 Number of working coils n
9 Inside diameter of the Garter spring D_r_i
10 Increase in diameter when fitted  \Delta D = D_s - D_r_i \Delta D
11 Spring rate S
12 Spring Index c = D/d c
13 Correction Factor  k =(c + 0.2)/(c-1) k
14 Combined stress due to bending and torsion q
15 Additional stress due to initial tension q_I
16 Total stress   q_t = q_I + q q_t
17 Circumferential force P_c
18 Radial force unit per length P_r

The number of working coils can be deduced from the working spring length L:

n = \frac{L_0}{d}

Therefore, the inside diameter of the garter spring D_r_i (when both edges are attached together):

D_r_i =\frac{L_0}{\pi } = \frac{nd}{\pi } - d^*

(*sometimes d/2 is used instead. The difference between both option is usually not significant.)

The spring rate S is obtained from the following formula:

 S =\frac{d^4G}{8nD^3} = \frac{dG}{8nc^3}

The circumferential and radial loads are related by the following expression (see section below):

 P_r =\frac{2P_c}{D_s}

The force exerted radially by the garter spring when mounted is defined as follows:

 P{_c__{extension}} = P_I + S(\pi D_s-\pi D_r_i)

 P{_r__{extension}} = 2(\frac{P_I}{D_s}+\pi S(1-\frac{D_r_i}{D_s}))

 P{_c__{compression}} = S(\pi D_s-\pi D_r_i)

 P{_r__{compression}} = 2(\pi S(\frac{D_r_i}{D_s}-1))

Most extension springs are wound with initial tension  P_I .  This is an internal force that holds the coils tightly together.  Unlike a compression springs, which has zero load at zero deflection, an extension spring have an initial tension  P_I .

Figure 2. Load-deflection curve for helical spring with initial tension P_I.

It is important to estimate the total stress imposed on the spring due to torsion and bending  q_t . By comparing it with the yield strength of the spring material  \sigma_y it is possible to check if the spring works in the elastic deformation range.

The stress resultant from the spring elongation  q is estimated as follows:

q=(\frac{D_s-D_r_i}{D}+\frac{2}{1+\frac{2G}{E}}) \frac{Gk}{nc}

It is necessary to include the stress induced by the initial tension  q_I :

 q_I = \frac{8cP_Ik}{\pi d^2}:

The relaxation of the spring material is usually neglected but it sould be considered when operating at elevated temperatures.

Relationship between the circumferential and radial loads

Figure 3. Radial and circumferential load decomposition.

To calculate the radial load exerted by a Garter spring, the Hooke’s law is applied in the circumferential direction and the radial load is obtained from forces decomposition:

 P_r [\frac{N}{m}] = \frac{2P_c}{D_2} = \frac{2}{D_2}(P_I+k\pi (D_2-D_1))

Realtionship between radial  P_r [\frac{N}{m}] and circumferential  P_c [N] forces

 P_c [N] = \(\int_{s_1}^{s_2} P_r sin(\theta) \, ds\)

 P_c [N] = \(\int_{0}^{\pi/2} P_r sin(\theta)  \frac{D}{2}\, d\theta\)

 P_c [N] = P_r \frac{D}{2} [-cos (\theta)]_0^{\pi/2} = P_r \frac{D}{2}

 P{_{r__{tot}}} [N]= P_r [\frac{N}{m}] \pi D [m]

References

  1. “Chapter 8: Garter Springs,” in Design handbook: engineering
    guide to spring design, Barnes Group Inc, 1981, pp. 56–59.

Industrial Engineer with focus on Tribology and Sealing Technology. Team player with an open-minded mentality author of several scientific publications and an industrial patent. Interested in Lean Management, Innovation, Circular Economy, Additive Manufacturing and Connected Objects Technology.