Company : CEMA & Elastotec
Conveyor drives and drive pulleys are a key part of the conveyor system, providing the power transmission required to move material. Engineers rely on guidelines from the Conveyor Equipment Manufacturers Association (CEMA) to design these drive systems effectively, employing mathematical techniques like Euler’s equation. However, while this approach focuses on preventing loss of traction, it overlooks potential wear and tear on critical components like the belt and pulley lagging. This paper aims to describe this issue, highlighting the need for a balanced approach that considers both loss of traction and localized slip which can result in wear and damage.
The relatively simple Euler Capstan Equation helps engineers define how much traction the drive pulley can transfer without fully slipping. The Euler Eequation looks at the wrap angle and contact friction on a drive pulley to define the torque transfer limit based upon the entry and exit belt tension ratio.
Euler Capstan Equation:
CEMA uses the Euler Capstan Equation in a different form to define the allowable tension change for active pulleys and provides coefficients of friction between pulley surface or lagging and belt surface.
CEMA does not specify where these coefficients of friction come from, but these friction values have historically been known to be conservative to cater for all potential design conditions. Due to these conservative friction limit values, conveyor designers suspect the allowable tension change is underestimated and therefore conveyor design could be more efficient.
There’s some hesitancy from pulley lagging manufacturers to provide more accurate coefficients of friction values to be used with this method. The Euler method described by CEMA only looks at the capability of lagging and belt to transfer torque without loss of traction but does not define the shear stress, normal pressure and potential localized slip that occurs at the belt to pulley interface.
Before moving onto defining more accurate lagging coefficients of friction, it is important to address the limitation of the simple Euler method adopted by CEMA regarding considering potential damage of lagging and belt.
Designers, lagging specialists and belt specialists are not only interested in power transmission capacity, but also achieving maximum service life of the belt and the lagging.
There’s not a lot of knowledge in this area. To get a better understanding, it is necessary to:
Along the arc of contact between the belt and the drive pulley, the belt tension changes from T1 (entry) to T2 (exit). Considering a positive drive power transmission, the belt contracts as the tension decreases around the arc of contact towards the exit. The pulley lagging and belt cover’s flexibility and friction between them are responsible for keeping both surfaces interlocked during the simultaneous belt contraction and shear transfer.
Both lagging and belt are subject to stresses in both the normal and shear directions. The interaction between them results in a developed friction (normal stress/shear stress). The shear stress increases towards the T2 exit point but the normal pressure decreases as the belt tension also reduces towards the exit. Where the friction developed intersects with the friction limit then localized movement or slip occurs. This localized slip can lead to wear and damage of both the pulley lagging and belt cover.
At the same time, these cyclic normal and shear stresses can fatigue lagging and potentially belt splices causing premature failure of these components. When these stresses exceed the endurance limit of what the lagging and the splices can tolerate, there’s a risk of fatigue failure.
A conveyor designed using the traditional Euler\CEMA method can successfully transfer drive power but may still have localised slip or fatigue of pulley lagging and belt splices that negatively affect the life of the components.
The example below shows an analysis of the stresses at the pulley lagging to belt interface. This example shows a drive pulley design with a CEMA wrap factor of 0.38 (Euler utilization of 87%) which is satisfactory according to CEMA 7 Table 6.114 however:
Friction coefficients are used to ensure satisfactory traction but are also applicable to the localised slip assessment (dotted lines in first graph in example above).
It is noted that the friction coefficient is constant for a lagging type. Testing has identified that the friction varies depending upon normal pressure, slip speed and slip distance. This has been generally referred to as variant friction and through extensive testing, several variant friction models have been developed to replicate the complex behaviour.
There’s a need for more accurate friction coefficients but there’s no clear guide on:
CEMA provides a simple conservative guide on friction coefficients but does not specify the test method and the detailed definition of how they are derived.
Pulley lagging manufacturers are adopting testing methods that resemble what happens on a conveyor by applying a normal pressure between a lagging and belt samples and measuring the force to extract the belt under varying speed and distances.t. Comparing Normal force applied (N) to the behaviour of the Shear force required to overcome the friction (F) provides an insight on the variant friction coefficients. The shear force tends to reach a plateau after which further displacement does not result in a higher shear force required.
Friction coefficient is the max Shear stress that that can be obtained from the interaction of the lagging and the belt.
Pulley lagging and belt cover are both viscoelastic materials. When testing for max shear force, different stages of ‘slip’ can be defined. In the first zone, there is lagging and belt cover deformation with initial shear force applied, then zone 2 where surfaces have some localized areas where relative slip, and the final zone where the surfaces are fully mobilized and no further shear resistance can be attained.
This combined with the fact that the maximum shear resistance and friction attained is dependant upon the normal pressure applied. This is referred to as a variant friction model.
Going by the definition, the coefficient of friction reported should be where the max shear force is achieved. This means that some slip between lagging and belt would be allowed with the potential of lagging and belt damage. To reduce the risk of lagging and belt damage, the reported friction coefficient reported should be the beginning of section 2 value before any damaging slip occurs.
Zone 1 |
| Shear force increasing with displacement. Almost no risk of lagging belt damage. |
Zone 2 |
| Shear force still increasing. Some belt, lagging potential damage due to macros lip. |
Zone 3 |
| Shear force maximum achieved. High risk of belt, lagging damage due to macro slip. |
The test results of Shear force F vs Displacement are shown below.
There are two key aspects of selecting driven pulleys for conveyors, power transfer without slip and ensuring the service life of both the pulley lagging and belt. Different mathematical models are used for each of them. There is no mathematical model that can be used for both purposes simultaneously.
Using the Euler\CEMA method will ensure power transfer without slip, but may result in localized slip resulting in excessive wear and fatigue.
It is therefore recommended that driven pulleys are designed using Euler\CEMA method but in addition, potential wear and damage to the pulley lagging and belt should be checked through a more comprehensive analysis to determine if localized slip and potentially excessive fatigue stress within the pulley lagging is present. If there’s a risk of local slip or fatigue, a change in the conveyor design should be implemented to eliminate.
Conversely, it also recognized that under different circumstances, the Euler\CEMA method will be overly conservative and prevent the full potential power transfer potential from being achieved.
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