Does your lagging optimise your convey’s performance?
Flexco chief engineering Brett DeVries explains:
Conveyor lagging has long been used to both protect conveyor pulleys and to increase the available friction for driving the conveyor belt. A primary consideration in the choice of lagging is the coefficient of friction. Designers use the friction coefficient in the pulley wrap factor equation to calculate the drive capacity of the conveyor, so the behavior of lagging friction under real world conditions is of extreme interest.
Through advancements in research and testing, lagging is available in various designs with differing stated capabilities and strengths. As belt technology innovates with increasing tensions and more power delivered through the drive pulleys, a correct understanding of the source of friction – a primary consideration in the choice of lagging – is necessary.
Pulley lagging is available in a myriad of styles and materials. The most common types are autoclave rubber, sheet rubber, strip rubber, and ceramic imbedded in rubber (CIR). All exhibit different coefficients of friction by nature of their design, creating a confusing choice for the conveyor designer. Some established design charts for friction exist like those contained in CEMA’s Belt Conveyors for Bulk Materials 7th Ed., and the DIN 22101 standard, but they are generalised, come from best practices, and assume a constant coefficient of friction.
In contrast, values published by lagging manufacturers may vary significantly from the charts. Additionally, there is no standardised test for determining the lagging friction coefficient or an industry standard for applying a safety factor against slippage. So how does one decide which is the best choice of lagging for their conveyors?
Testing, testing, testing
The engineering team at Flexco, as part of their continuous efforts to improve not only their lagging solutions, but the lagging’s performance with other belt conveyor components, developed a test apparatus for measuring lagging friction in which friction coefficients are measured under uniform pressurised loading using a tensile test machine. Applied pressures range from 5 to 100 psi, including some measurements to 120 psi for various lagging types.
Five different types of cold bond strip lagging were measured to find the coefficient of friction versus increasing pressure. Test conditions were also varied. Each lagging type was measured under conditions termed “Clean & Dry”, “Wet”, or “Muddy”.
Determine a way to measure the friction
The test fixture was designed to be used with a standard 50kN tensile test apparatus. The test fixture used floating pressure plates that are guided by track rails along the bottom edge. Belt samples are secured to the pressure plates such that the bottom covers of the belts face inwardly towards each other. Between the pressure plates is the steel shear plate with lagging samples bonded to it.
The design of the fixture uses Newton’s principle of equal and opposite force reactions to assure the load is equivalent on each side. The pressure plates are substantially thick to prevent flexure. There is a load cell located between the large airbag and the first pressure plate to measure the applied load.
The tensile tester has a load cell attached to the shear plate via pin connection on the protruding tab. The effective area of the steel shear plate is 64 square inches. The airbag is capable of applying loads in excess of 6400 pounds, allowing for measurements to 100 psi if the entire area is used.
The test procedure consisted of placing the shear plate between the pressure plates. Air pressure was then applied and allowed to stabilise to the proper reading. Next, the crosshead translated vertically upward at 50.8 millimetres per minute for a distance of 6.35 millimetres, while data was recorded regarding the position of the crosshead and the vertical load measured. While the data from the pressure load cell was not dynamically recorded, it was observed from the digital display that it did not vary during the test. Each test set was a unique combination of conditions (clean & dry, wet, or muddy), lagging type, and pressure and was repeated five times. Compressed air was used to blow off debris or dust generated during testing.
Analyse Stage 1 results
The classical representation of the friction force between two solid objects is that there exists a static coefficient until the start of motion, which then quickly drops to a lesser value know as kinematic friction.
The lagging in these tests behaved differently. The measured extraction force vs. displacement curves do not contain a local maximum force with a rapid decay to a lower value as would occur in classical friction. Upon visual inspection, it was clear that there had been movement between the lagging and the belt samples, so the absence of a transition was not due to insufficient applied force or displacement. This indicated non-classical friction behavior.
This led to the question of how to measure a friction coefficient at all, since the pull force had not yet stabilised even though slip had clearly been observed. <Insert Figure 3: Pull force vs. Displacement, 60 psi, plain rubber lagging, clean & dry conditions.>
Another aspect observed was that a doubling in the pressure was not resulting in a doubling of the extraction force. See Figures 2 & 3. This violated classical friction theory which states there is a constant coefficient of friction, which is independent of pressure.
After additional research was done regarding the dynamics of a belt traversing a pulley with a 180° wrap, 6.35 millimetres of crosshead movement was selected as the measurement point for the lagging friction coefficient.
Analyse Stage 2 results
Using 6.35 millimetres of crosshead movement as the threshold for developing friction, the coefficient of friction vs. pressure test results of each combination of lagging type and conditions were graphed. Exponential curves were fit to the data to allow for automated calculation of the coefficient of friction.
The curves showed a general downward trend in coefficient of friction as the pressure increased, except for the medium and full ceramic lagging samples. For these, it was observed that the coefficient of friction peaked at 30 psi. It is inferred that this is the requisite pressure for the 1mm tall surface nubs to fully engage with the belt. After the peak, the ceramic plots all trended downward like the other samples.
Using the fitted exponential curves, it was possible to consolidate several of the lagging types onto one graph to illustrate the relative friction performance.
- Clean & Dry – conditions were as optimal as possible. The lagging and belt were in new condition.
- Wet – conditions are dew-like. Water was sprayed onto the lagging with a trigger sprayer until water dripped from the lagging. This data does not represent lagging that is hydroplaning or immersed in water.
- Muddy – samples were painted with an Illinois basin coal fines slurry. The slurry was a mixture of clay and coal particles of unknown distribution. Ratio by weight was 3:2 coal fines to water.
Discuss the results
These results showed a strong dependence of lagging friction on pressure. In practice, pressure arises from the belt tension wrapped around the pulley. Where p = 2 x T/(BW x D), we see that wrap pressure is a function of belt tension. Since drive pulleys remove tension and thereby, pressure, from the belt, the results show that the coefficient of friction is changing as the belt traverses.
Applying the results
So what should a conveyor designer do? The new data suggests the reason the pulley wrap factor equation has worked is because of generous safety factors in the assumed friction coefficient, especially at pressures below 70 psi. However, since available friction is pressure dependent, it is difficult to know the actual safety factor and correct results are not assured using this equation when pressures increase.
Ideally, the equation would be modified to include pressure-dependent friction. However, an analysis shows it cannot be solved by conventional means. An approximation method must be employed.
Utilise an approximation method
Friction force is usually expressed as coefficient of friction multiplied by a normal force. Normal force is distributed over the apparent area of contact and could be expressed as a pressure. So, pressure multiplied by the coefficient of friction is the friction force per unit area between the two apparent areas, otherwise known as shear stress. Conceptually, this could be considered the grip or traction that the lagging has on the belt.
Graphs (Figures 7-9) were made showing the theoretically available driving shear stress. Curves were created from multiplying pressure by the measured coefficient of friction equations.
As the pressure increases, the available shear stress increases, but at a diminishing rate. The graphs suggest maximum grip for each of the different lagging styles. This is predicted by the origin of the friction force. Friction force arises from adhesion in the areas of true contact between surfaces. True contact area is much less than the apparent contact area for most substances and can linearly increase with increasing pressure. But not rubber. Since it is homogenous and soft, true contact quickly approach apparent contact area. If the true contact area is approaching the apparent contact area, and friction is the result of adhesion forces between the surfaces, then there will be a limit at the maximum shear stress value those adhesion forces can sustain.
From a practical standpoint, the goal of the conveyor designer is to assure the belt will be driven under all foreseeable conditions. One method to achieve this is to use a safety factor. Once the effective shear stress required to drive the belt is known, it can be compared against a theoretical maximum available value and a design safety factor calculated.
It should be noted that there are three ways to increase the safety factor.
- Increase the T2 This can be an inefficient way to improve safety factor in some cases since the available shear stress increases slowly at higher tensions.
- Change the lagging type. Full ceramic lagging showed the best performance for pressures exceeding 50 psi.
- Increase the pulley diameter or wrap angle to increase the contact area. Pulley diameter plays a pivotal role in driving the belt as compared to the pulley wrap factor equation. With the new method, traction is being increased by placing more lagging area in shear due to the extra circumference generated by a larger diameter.
This improved method for calculating conveyor drive capacity is based on the induced shear stress at the interface of the belt and lagging. It originates from measured coefficient of friction data and a modern understanding concerning the origin of rubber friction. It provides the designer with improved accuracy and confidence. Gone are the assumed coefficients of friction that do not match measured data. The improved method also captures and quantifies two intuitive concepts: there is an upper bound for frictional adhesion and larger pulley diameters have more traction.
A consequence of this approach is the potential for the designer to avoid excessive T1 tension by increasing the pulley diameter or adjusting the lagging type. Since T1 tension commonly guides the selection of the belt minimum tension rating, reducing it may save on belting costs. Depending on the length of conveyor, large savings may be possible by selecting a lower tension rated (and less expensive) belt and choosing instead to invest in a larger diameter pulley and ceramic lagging.