Common Formulas

The distance from the groove to the end of the shaft or housing is known as edge margin.
Edge margin is a calculated distance based on the relationship between the edge margin (y) and the groove depth (d). When y/dbiggerequal.gif (145 bytes)3, the groove will withstand the maximum thrust load as indicated in the Rotor Clip catalog specification page for that particular size and type of retaining ring.

Example: SH-50 external retaining ring installed on a cold-rolled steel shaft. The catalog specifications for this ring call; for a minimum edge margin of 0.048" and a groove depth of 0.016." Our formula is as follows:

calculating edge margin

stress gradients for retaining rings

Finite Element Analysis shows stress gradients for a retaining rings in an application with insufficient edge margin. When loaded, the high stress region extends over the entire groove wall to the end of the shaft (or housing) and the groove wall actually distorts.Under these conditions, the ring would buckle, possibly leading to catastrophic failure.
There is sufficient edge margin for the groove to withstand the maximum thrust load of 550lbs. listed in the catalog specifications.
If an application requires an edge margin less than the recommended specifications, it is necessary to calculate the thrust load (Pg)-capacity of the groove, to determine if the reduced margin is capable of handling the anticipated thrust load. The following formula applies (Note: see Correction Factors table for Gf value; Yield Strength of Groove Material for sy value; Edge Margin Graph for K1 value; Nomenclature Table for remaining catalog specifications):

calculating thrust load

edge margin chart

For this example, assume that the edge margin will only be half the listed catalog value or, y/d=1.5. The above equation is as follows:

calculating thrust load

yield strength of groove material

 

 

correction factors for retaining rings




Beveled Retaining Rings



Beveled rings are designed to function in the groove when positioned within a range of seating depths from the bottom of the groove (maximum insertion) to a recommended position of half way up the groove depth (minimum insertion). The complementary groove and ring bevel allow the ring to function like a wedge when it makes contact with the retained part. The ring exerts an axial force against the retained part, taking up the play and, consequently, reducing the clearance between parts to zero. If the sum of the assembly tolerances consisting of the retained part width (B), the groove location (A) and the ring beveled edge (U) exceed the end play take-up capacity of the ring, two conditions may potentially occur:

1.) The ring will be seated less than half way down the groove depth, compromising the thrust load capacity of the assembly.

2.) The ring will be seated at the groove bottom and play will be present.

GROOVE LOCATION The outer groove wall with the beveled edge locates the groove. The distance from a fixed shoulder to the outer beveled groove wall is A. The machining tolerance associated with locating the groove is A. The width of the retained part/parts is B. U is the beveled thickness at the base of the bevel and is specified in our VHO and VSH specification tables.
max insertion min insertion

DETERMINING RING FEASIBILITY
The feasibility of a beveled ring should be evaluated first. The built-up tolerances of the system must be less than or equal to the take-up capacity of the ring. For Example: A bearing must be retained on a 3" shaft using a VSH-300 Rotor Clip retaining ring. The bearing width is 1.000/0.995. Before the location can be determined, we would need to know the acceptable machining tolerance (A), which we will designate as +.003/-.000 for the sake of this example. Compute the sum of the tolerances:

B (Bearing Width Tolerance Range) =  Bmax - Bmin .005
A (Acceptable Machining Tolerance Range) =  Amax - Amin.003
U (Beveled End Thickness Tolerance Range from catalog spec) =  Umax - Umin .004
=  .012


The sum of the tolerances is less than the take-up capacity of the ring (.0135), confirming the fact that the ring will in all assemblies seat within the acceptable limits of half way down to all of the way down the groove.

COMPUTING GROOVE LOCATION
The following equations determine the distance from the defined shoulder (plane of reference) to the top of the far groove wall (A):

Amin Bmax + Umax + d/2 tan 15 (Corresponding to minimum groove engagement)
Amax Bmin + Umin + d tan 15 (Corresponding to maximum groove engagement)

Using the values from the above example, we compute Amin and Amax as follows:

Amin .000+.073 + .102/2 tan 15

(Note: .073 U value and .102 d value, per catalog spec)

Amin 1.087

Amax .995 + .069 + .102 tan 15

Amax 1.091

Anom = (Amax + Amin )/2 (Amax - Amin )/2

A 1.089 .002

Reviewing our stack up of tolerances, we assumed .003" for machining. Our calculated groove location allows for more leniency (.004") in the tolerance. Checking the again, we find the assembly is still within the .0135 limit for end play take-up.

From known ring dimensions, retained part dimension(s), required groove depth and designated machining tolerance, the groove can be easily located for assemblies meeting the primary requirement d/2 tan 15.
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