The RENCOL® Tolerance Ring is a precision spring steel device, comprising a thin strip into which corrugations, or waves, are formed, each of which will act as a spring. This strip is then rolled into a ring.
Within the elastic limit of the waves that make up a tolerance ring, simple spring theory applies i.e. Force (N) -- F = K · c
The factors influencing K include: Material specification represented by Young’s Modulus, Material thickness, Wave pitch, Wave width, Wave shoulder shape, Wave thinning, Plannish width, Plannish thickness, Wave root radii. Wave crest radii
Of these, for a given wave shape, the two major factors are thickness and wave pitch.
So the Spring Constant (kNmm-1) is given by: K = 4.8 · E · w · t/p3
The cubic power relationship allows for the possibility to engineer a very wide range of spring stiffness. The complex wave geometry with a formed wave and closed ends gives rise to a rigid structure, allowing very high spring stiffness to be achieved with corresponding high forces possible.
From FEA models it can be seen that the wave shoulders make the main contribution to the stiffness. This is one of the reasons why rings with multiple bands of waves around the circumference are often used in high torque applications.
In tests using rigid steel gauges, a duplex ring with 2 sets of waves gives 1.7 times the torque of a single banded ring of the same dimensions.
The rings are specifically designed for each application by varying the complex ring geometry, material thickness, hardness, etc. to create an appropriate spring constant and hence a pre-determined retention forces and/or slip torques. Radial Load (N) is given by: FR = n · c · K
The axial assembly force (N) is given by: A = FR · u
The Torque (Nm) is given by: T = FA · d/2