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How to calculate tolerance stack-up
April 12th, 2022
What is tolerance stack-up, why does it matter, and what can be done about it?
Tolerance stack-up is something that needs to be addressed in every bearing assembly. Its calculation is the starting point for assessing what tolerance compensation measures may be used to make your assembly work as intended. The following advice includes a simple explanation of the issues, the calculation method and – most importantly – what we can do as a result to optimise your system.
Tolerance stack-up
When ordering components for an assembly, you will specify their required dimensions. In practice, most manufacturing processes are unable to guarantee that the components in a batch will each have precisely the same dimensions. The manufacturing tolerance is the amount by which a dimension is allowed to vary. If we take, for example, a shaft for a rotating bearing assembly, the manufacturing tolerance will set an upper and a lower limit for the shaft’s diameter.
Consider an assembly in which the shaft will be inserted into a bore within a housing structure. If the shaft diameter is too large, it will not fit into the bore. If it is too small, it will rattle due to existing clearance. Those extremes need to be avoided.
But the bore will also vary in diameter, as the housing has its own manufacturing tolerance. We need to make sure that the shaft and the bore are a good fit – not too tight and not too loose – even when maximum and minimum size variants are combined. In other words, when the widest shaft joins with the narrowest bore, or the narrowest shaft joins with the widest bore.
Next, we introduce a third component: a plain bearing (also known as a bushing) between the shaft and the bore. The thickness of the bearing material also has a manufacturing tolerance. The tightest fit comes from a combination of the maximum shaft diameter, maximum bearing material thickness and minimum bore diameter. The loosest fit comes from a combination of the minimum shaft diameter, minimum bearing material thickness and maximum bore diameter. These situations are summarised in Figure 1.
This combination of individual tolerances is what we call tolerance stack-up. It needs to be calculated and understood if we are to make the components fit together and interact in a way that works for the application.
Figure 1a. Tolerance stack-up tightest fit
Figure 1b. Tolerance stack-up loosest fit
What kind of fit do you need?
The aim is to achieve the right engineering fit between the assembly’s components. In bearing assemblies, the fit will largely determine the amount of torque needed to create movement.
At the tight end of the fit spectrum, we have interference fits (also known as press fits). In these, the shaft diameter will always be at least slightly larger than that of the bore. For some applications you will need such a high level of interference that the mating components are fixed firmly together and no relative movement between them is possible. In others, the interference will need to be lower so that movement is possible. The higher the interference, the more torque is needed for movement.
At the loose end of the fit spectrum, we have clearance fits. In these, there will always be at least a slight gap between the shaft and bore.
There are also intermediate cases, known as 0/0 fits. These permit a small amount of clearance, but not so much free play as to allow rattling. Further, they allow a small amount of interference, but not so much as to create excessive torque.
The three main types of fit are illustrated by the application examples in Figures 2, 3 and 4, in which the plain bearings are highlighted in red.
Figure 2. Side door hinge
A profiled side door hinge for a vehicle (Figure 2) needs an interference fit. The resulting compression between the hinge pin, housing and plain bearing determines the torque. The system needs to be engineered so that the torque is low enough to allow easy opening and closing of the door. At the same time, it must be high enough to prevent unwanted movements of an opened door.
The timing belt tensioner in an engine (Figure 3) needs a clearance fit with the right amount of free play to enable smooth running. An interference fit here would result in too much torque and rapid wear.
Figure 3. Belt tensioner
Figure 4. Seat height adjustment mechanism
In a seat height adjustment mechanism (Figure 4), there are several sets of bearings with much scope for bore size variation and for misalignments. During assembly, pre-tensioning is applied via multiple links to reduce the amount of clearance. The result is a 0/0 fit with enough free play to allow for misalignments. There should be enough torque to avoid rattling, but not so much as to require a large effort from the user when adjusting the seat.
Tolerance stack-up calculation
Calculating the tolerance stack-up in a bearing assembly (as shown in Figure 5) involves two very simple and straightforward equations.
Figure 5a. Tolerance stack-up, max interference
The first is to determine the maximum interference – which can also be described as the minimum clearance. This is calculated as:
Minimum bore diameter
Minus double the maximum plain bearing material thickness
Minus maximum shaft diameter
The second equation determines the minimum interference – which can also be described as the maximum clearance. This is calculated as:
Maximum bore diameter
Minus double the minimum plain bearing material thickness
Minus minimum shaft diameter
Figure 5b. Tolerance stack-up, min interference
Tolerance compensation
Once you have calculated the tolerance stack-up, what does it tell you? Using their specialised knowledge and experience, Saint-Gobain’s engineers can assess the data against the assembly’s construction and application. Their assessment will determine how much interference or clearance will be a problem. They will use calculation programmes to see which combination of bearing materials, structures and shapes will best meet the challenge.
To achieve a certain level of performance from the bearing assembly, such as a very specific torque range, strict individual component tolerances and a strict tolerance stack-up may be needed. One way of achieving this is to specify more precise manufacture of the components, but this adds greatly to their expense. The other is to use the tolerance compensation capabilities of Saint-Gobain’s NORGLIDE® Bearings, RENCOL® Tolerance Rings and SPRINGLIDE™ Spring Energised Bearings.
These three Saint-Gobain product ranges have been developed to cover the many different application challenges. As well as compensating for tolerances, they also compensate for misalignments in assemblies – allowing systems to be produced more easily and cost-effectively.
NORGLIDE® Bearings
NORGLIDE® sliding bearings are designed with a layer of self-lubricating, low-friction PTFE which ensures smooth motion. This is combined with a choice of metals and filler compounds in various configurations to create a wide range of NORGLIDE® materials suited to different applications.
An important property of NORGLIDE® in relation to tolerance compensation is its sizeability. The radial thickness of the bearing can be altered by a sizing process in which an oversized pin is pushed through it. For each application, a specific NORGLIDE® material can be chosen with the right balance of sizeability, load capability and other factors.
The thickness and viscoelasticity of the PTFE, combined with appropriate sizing, compensates for manufacturing tolerances. Sizing can be precisely calculated to produce a particular amount of torque. The greater the interference fit, in terms of the shaft’s oversize compared to the inner diameter of the bearing, the higher the torque.
The many applications of NORGLIDE® Bearings include automotive side door hinges, timing belt tensioners and seat height adjustment mechanisms.
RENCOL® Tolerance Rings
A RENCOL® Tolerance Ring is essentially a device for joining cylindrical mating components, such as a shaft and its housing bore. Its shape features waves or other projections which act as springs. These are compressed during assembly to create a force that holds the components together.
The specific geometry of the tolerance ring can be chosen to create different amounts of force and hence different levels of torque. Applications range from static, high-torque structures, which are not normally expected to move, to relatively freely moving, lower-torque systems.
They are used, for example, in fastening of bearing and motor mounts, rotational adjustment of component positions, and hinges for armrests.
SPRINGLIDE™ Spring Energised Bearings
In some situations, the tolerance stack-up is too large for NORGLIDE® to compensate. A RENCOL® Tolerance Ring can compensate for greater tolerances. However, it cannot be used in applications requiring low friction. For this reason, Saint-Gobain has combined RENCOL® and NORGLIDE® into a single product offering both high compensation tolerance and low friction: SPRINGLIDE™ Spring Energised Bearings.
In SPRINGLIDE™ Spring Energised Bearings, a polymer layer containing a PTFE compound is bonded to spring steel. As in a RENCOL® Tolerance Ring, the bearing’s shape includes projections – such as waves, ribs or fingers – which act as springs. The force these apply, combined with the friction-reducing properties of the polymer layer, can be set to produce the level of torque you require.
Importantly, SPRINGLIDE™ Spring Energised Bearings keep the sliding force within your specified range, even in the face of unpredictable misalignments, varying loads and changing conditions.
An illustration of this solution’s application is shown in Figure 6 for a vehicle seat’s head restraint height adjustment mechanism. The bores of the plastic housing into which the two height-adjustable bars are inserted vary in diameter with temperature. In addition, the bars are never quite parallel. As a result of these factors, the bars’ sliding characteristics change through the seasons. In summer, as the plastic becomes softer and relaxes, they move easily and sometimes unintentionally. In winter, as the plastic becomes hard and contracts, they may require a large force for adjustment. With SPRINGLIDE™ Spring Energised Bearings, the sliding force is optimised and remains consistent.
Figure 6. Head restraint
SPRINGLIDE™ Spring Energised Bearings are a relatively new solution with huge potential for further applications.
Tailored to your needs
NORGLIDE®, RENCOL® and SPRINGLIDE™ are not single products. Each can be supplied in an enormous variety of geometries, materials and other configurations – custom-designed to meet the specific requirements of your application. Our engineers will work closely with you at all stages to understand and meet those needs precisely.
To discuss your challenges with us, engineer to engineer, use our contact form or email us at: makingabigdifference@saint-gobain.com.