The CEMA Horsepower Equation

Belt Conveyor Design

The CEMA Horsepower Equation

Development of a new Conveyor Power Prediction Methodology
The 7th edition of Belt Conveyors for Bulk Materials (known as “The Belt Book”) includes a new con­veyor power prediction methodology using “Large Sample Indentation Test” (LSIT) data. This article provides background and insight into how LSIT data is used to design conveyors, and describes the relation between this and the older conveyor power prediction methods. It also illustrates the use of LSIT data by using it to predict indentation losses in a recently commissioned conveyor system.
(ed. WoMaMarcel - 07/10/2015)
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The “CEMA Universal” or “Small Sample” Method

Empirical methods like the classic CEMA formulation give good results when the design parameters are close to the experimental data from which the empirical formulations were derived. The classic CEMA method works fairly well even outside the experimental parameter range as long as the temperature is above zero and the belt rubber compounds are similar to the compound tested by Penn State in 1954. Because of the inherent limitations of empirical methods, a number of researchers have proposed semi-analytical and theoretical methods of predicting conveyor power consumption [7 - 10].

In 1989 Conveyor Dynamics, Inc (CDI) commissioned two overland conveyors at the Channar Mine in Western Australia. Before commissioning this system, a number of major firms predicted that CDI had undersized the motors. After commissioning, CDI showed that the friction factor on the straight overland was on­ly 0.0098 and the friction factor on the horizontally curved belt was 0.011 [11]. Later, the friction even fell to 0.0085. This marvelous result (less than half of the recommend DIN standard base friction) surprised everyone. The conveyor had exceeded even CDI’s expectations, and convinced CDI to invest in developing a new method of predicting conveyor power.

In 1990 Syncrude Canada realized that they had a number of issues with their conveyors stemming from the fact that their power consumption was vastly different from the CEMA predictions. To solve this problem, Syncrude awarded CDI a contract to invent a new theoretical model of conveyor power consumption capable of explaining the strange behavior they observed in their conveyors [12]. Our earlier model is described by Nordell in [13].

The model we use now is a two-di­mensional plane-strain semi-analytical model that allows us to engineer the most energy efficient conveyors operating in the world today including the worlds’ longest single flight conventional belt conveyor [14].

In 2006 Overland Conveyor Co (OCC) proposed a simpler idler-belt interaction model but instead of a 2D plain stress model, they chose a 1D spring-dashpot model which, unlike the CDI formulation, neglects shear stress [15].

Both CDI and OCC’s indentation models are classified as “Small Sample Indentation Tests” (SSIT) because they require the engineer to measure the viscoelastic properties of a “small sample” of rubber used in the bottom cover of a conveyor belt. The rubber is characterized using master curves of G' (elastic stored energy) and G'' (energy lost to heat) as functions of time, temperature, and frequency. Both methods predict the indentation losses in a uniformly loaded slice of belt (shown in Fig. 1 with width ∂z). In this figure the belt is not rebounding as fast as it compresses. This causes the rubber entering the idler roll to push harder on the roll than the rubber leaving the idler which in turn, creates a force (indentation loss) that resists belt motion.

Fig. 1: Rotating cylinder on viscoelastic foundation.

The total resistance to motion is the sum total of the resistances contributed by all the ∂z thick slices in a belt cross section. The pressure on each slice depends on the load the slice is supporting, the stiffness of the belt, and the trough angle.

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