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| NB: This is a basic guide - actual performance will be affected by the components in the system | |
The 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):
Where: K is the Spring Constant (Nmm-1) and c is the Displacement (mm).
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 x E x w x t/p3
Where: E is the Elastic Modulus for the material (kNmm-2), w is the width, t is the thickness (mm) and p is the wave pitch (mm).
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 x 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 x c x K
Where: n is the Number of waves, c is the Compression of waves (mm) and K is the Spring Constant (Nmm-1).
The axial assembly force (N) is given by: A = FR x u
Where: m is the Coefficient of Friction
The Torque (Nm) is given by: T = FA x d/2
Where: d is the Diameter (mm).
It is important to note the wide range of spring constant and hence forces and torques that can be designed for a given ring size. Empirical research shows that the wave compression range for the elastic properties varies depending on the wave geometry. The typical range for elastic properties is from 3%-7% of wave height compression but for light duty rings, specifically designed for mounting bearings, the elastic limit can be as high as 50% with a usable range of 20% to 40%.
This will normally involve rings designed to achieve the minimum percentage
of spring compression at which bearing retention can be guaranteed when at maximum
clearance, leaving the remainder of the spring compression range available to handle any external radial loads, machining tolerances or dimensional changes caused by differential thermal expansion of the mating components. Most tolerance rings would be designed such that the elastic zone was maximised.This caters for maximum component tolerances and differential expansion
In a typical electric motor bearing mount: Alumina housing, 608 bearing, H9 tolerance on the bore and a temperature range of 20°C to 100°C an HVL22x7SS tolerance ring with a 0.33mm wave height would be used giving a radial clearance of 0.297mm to 0.320mm across the machining tolerance range.
‘Light duty’ variants of the standard ring design design are available which allow some axial movement of the bearing where, for example, pre-loading is used. The standard ‘heavy duty’ ring design provides axial retention and is used where higher eccentric radial loads are expected.
In some instances, e.g. when being used as a torque limiter it is useful to
deliberately design for the plastic zone so that large variations in component
size will have minimal effect on the torque at which slip occurs. The ring is designed such that the crests of the waves embed slightly into the mating component and the base of the waves acts as a bearing surface and slips against the mating surface. Rings can be designed to slip either on the shaft or the bore, depending on materials, surface finish and hardness issues etc.
Rings coated with a proprietary dry lubricant have been developed to provide further enhanced performance and to eliminate the need for a greasing station on assembly lines.
Similar in principle to torque slip design designs bur designed to ensure that minimum torque is maintained across component tolerances and operating temperature range. A safety factor of 3 is recommended for normal environments and X6 for shock loaded environments.
Normally Tolerance Rings and Strip are supplied in either Carbon Steel or Stainless Steel but can also be supplied in Inconel, Monel, Incalloy, Phynox, Copper-Beryllium and other suitable materials.
Hardness affects the point at which material will yield (elastic limit): For special OEM designs we can heat treat carbon steel to a variety of hardness levels to achieve the desired characteristics. Varying grades of other material hardness can be used to obtain the desired characteristics.
Many thousands of specifications for different Rencol tolerance rings exist. The table indicates typical combinations only. We often create specific designs for high volume applications. Rings of 300mm+ diameter are routinely produced. Beyond this tolerance strips can be supplied (10 or 50m coils) for cutting and fitting as required.
For a typical bearing fit (OD to housing) the chart shows the relaxation of machining tolerances and reduction of press fit forces when using tolerance rings compared to conventional interference fit into steel housing with various tolerances on the bore.
For a ball bearing in an aluminum housing the differential thermal expansion will quickly reduce the force needed to disassemble and at fairly moderate temperatures for many applications, the bearing will be loose. A correctly designed tolerance ring in a simple fixing application or bearing assembly utilises the elastic range of wave compression to compensate and maintain a positive retention force to much higher temperatures.
The tolerance ring tends to center a bearing or other parts with each wave pushing towards the centre. With a free mounting arrangement eccentricity will usually be in the region of 2-3% of radial clearance.
In applications with cyclical loading, e.g. mounting a belt pulley to a shaft, safety factors must be considered. For normal applications we recommend a safety factor of 3 be introduced to calculations, or in extreme cases, e.g. rapid reversal of direction or frequent stop-start, a factor of 6.
The HV style ring is “open” in the free state so that when installed inside a bore the ring will conform to that bore and be self retaining. The ring sits in the housing with waves on the inside to be compressed by the outer diameter of the mating part.
SV style rings have a free-state diameter smaller than the shaft diameter over which they
are to be installed, so that when mounted to the shaft, the rings conform to and become
self-retaining on the shaft. The ring sits on the shaft with waves on the outside to be compressed by the bore of the housing.
Tab rings help to prevent the tolerance ring “walking out” in high vibration environments.
Single piece ring but with multiple band of waves giving increased performance. This simplifies the machining requirements on mating components.
The HVL style may be described as a very light duty HV style ring. It is often characteristic of this ring to not have a circular shape in free state.
HV ring with flanged end used for axial load control or limiter, e.g. in steering column collapse mechanisms.
Modified wave form to give greater contact area and improved slipping surface. Designed to eliminate the need for pre-torque cycle. Improved slip torque control over increased number of slip cycles.
Free Arrangement
This arrangement will not provide axial support to the ring in either direction, so the assembly machine must be fixtured to “back up” or axially locate the ring temporarily while the mating components are assembled. The Tolerance Ring will be subjected to all radial loading and should be selected with appropriate capacity.
Centered Arrangement
This arrangement provides a groove in the housing for HV rings or a groove in the shaft for SV rings. These grooves capture the ring axially on both sides and simplify assembly. When the shoulder (stepped) diameter is held close to the nominal diameter, the following advantages occur:
- Improved alignment of parts during installation
- Improved concentricity due to low radial clearance at the shoulder
- Excessive radial loads and shock loads can be accommodated since the Tolerance Ring is protected in its own cavity. The corrugations will deflect until the shoulder or stepped diameter contacts the mating member. Additional loading will be transmitted through the step and will not act to further deflect or crush the corrugations.
Piloted Arrangement
This arrangement is similar to the centered arrangement at a lower cost. With the exception
of piloting for alignment, this method may provide the advantages of the centred arrangement when the stepped diameter is held close to the nominal diameter of the mating component.
Assembly Procedure Considerations
The “tops” of the corrugations (The I.D. on HV style rings or the O.D. on SV rings) are formed with a rounded contour , which assists as a lead-in edge during assembly. It is very important that the lead-in edge of the mating parts is contoured with a generous radius or a shallow (15°) chamfer. Sharp corners on the lead-in edge could dig in and mar the Tolerance Ring, sacrificing performance.
Best results of assembling mating parts are achieved by using an arbor press and fixturing the parts to hold them squarely in place during assembly. The fixture also needs to ensure that eccentricity during assembly is less than 10% of the nominal radial clearance. Except for very light duty rings, aligning the parts by hand and/or hammering the assembly together jeopardises alignment and performance. If misalignment occurs during assembly, there is a tendency for the lead-in edge of the mating part to flatten corrugations in one area of the Tolerance Ring.
When using the centred arrangement, a small radius (re) and adequate groove width should be used to ensure that the Tolerance Ring may be properly seated on the cylindrical surface, the groove needs to be deep enough to ensure the ring is not dislodged during assembly.
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