Friction_Models_for_Conveyor_Design_2009_JBSPT_WebVer

Bulk Solids and Powder – Science and Technology, Vol 4, (2009), No. 1, pp1 – 11.

A. Harrison

A Comparison of Friction Models for Conveyor Design Alex Harrison. PhD, FIE(Aust). Conveyor Technologies Ltd., a Member Company of Scientific Solutions Inc., Colorado, USA Summary Power consumption of long overland conveyors with a low slope component is examined in the paper. Rolling and position-dependent losses along a conveyor profile can significantly influence design of belting, take-up and drive requirements. Whilst the slope or gravitational component of belt tensions is definable, frictional components largely depend on an an understanding of mechanical loss factors involved with the motion. Existing methods for quantifying belt tension of long low-lift conveyors conveyors are reviewed in the paper. Belt tension prediction methods such as DIN 22101 and CEMA are compared to alternative understandings of the rolling problem at the idler interface. Alternative predictive methods have been formulated to accommodate accommodate the effects of belt speed, sag, rubber properties and vertical loading at the idler contact zone. Application of the various predictive methods has been compared to results of selected site measurements to examine the loss factors and to fine tune models. Running losses affect the transient behaviour of conveyors during starting and stopping, particularly the selection of take-up position for practical dynamic control of belt tension.

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INTRODUCTION

Conveyor design requires the determination of belt rating and system loads. Long overland and underground conveyors, conveyors with horizontal and vertical curves, and conveyors with regenerative characteristics are most critically influenced by rolling losses losses when the lift component is small by comparison to other losses. The problem of defining the losses along a given conveyor profile change over time. time. A valid calculation at one point in time can be invalidated at some later time by changes to conveyor component design and material properties. In a general sense, predicting conveyor belt tension cannot be considered a known science until methods exist to accommodate continually changing component characteristics. Since idler rolling losses and belting rubber properties change from supplier to supplier and from year to year, most available predictive design methods inadequately treat or even accommodate inputs for such variations. Added to the abovementioned evolution of conveyor component characteristics, design methodologies for long distance conveyors used used in non-conventional applications generally require new analytical analytical approaches. For example, 20 years ago a troughed conveyor for BHP’s HBI project at Port Hedland in Western Australia required a straight overland belt with incoming incoming iron ore and outgoing briquettes. Analysis of the tensions for this application required a new approach to predict belt tension and power. In 2006, prediction of the power and belt tension distribution was required for a long, downhill horizontallycurved pipe conveyor to be installed in Peru [1]. The pipe conveyor conveys different bulk materials in the upper and lower runs of the pipe belt, requiring analysis of the more complex resistances. These examples demonstrate that the bulk handling industry often requires solutions that are more advanced than the available design methods. For some of the above reasons, a conveyor’s power consumption is often different from the predicted design values. During the proving stage of any conveyor conveyor design proposal, it is important important to consider the impact of component variations on the prediction of effective tension at the drive. Even more important is the accommodation of variations in component losses as discussed above. An examination of the basis behind the commonly used design methods is instructive since it can show why the design calculations for conveyors can vary so widely. The topic of model methodologies and accuracy is as important to project engineering as is project costing; both intimately affect each other in sometimes competing ways that could result in an uneconomical project or one that fails to meet design goals.

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RESEARCH ON CONVEYOR FRICTION COMPONENTS

A significant amount of research is published on the forces and resistances that contribute to running belt tension. References to researchers or organizations specifically investigating rolling resistance are reviewed. Two of the most commonly used design methods for first order calculation of a conveyor’s effective tension are the Conveyor Equipment Manufacture’s Association (CEMA) method [2] and the Deutsches Instit. Normung (DIN) Standard DIN 22101 [3]. Numerous variations of these design methods exist[4]. Some belt manufacturers use in-house conveyor design manuals for sizing a belt for a specific application. European belt suppliers model in-house design manuals after the DIN Standard [5]. CEMA, DIN and other design methods use approximations and conservative factors in the design calculations. The CEMA Handbook design method was developed in the 1960’s as an attempt to standardise on conveyor hardware and component supply. At that time, the belt manufacturer would usually carry out belt rating calculations. CEMA recognised that idler losses depend on bearings, seal type, diameter and temperature. Based on field tests, CEMA presents tables for determining the flexural behaviour of belting and the bulk materials, and provides formulas to separate the components of the motional resistance. For conveyors longer than 1000 m and for regenerative conveyors, the CEMA method needs to be used with caution. Downhill conveyor calculations are conservative. In 1980, Jonkers [6] presented a general paper on the theory of rolling resistance. Actual measurements of the components of rolling resistance and flexural losses of various bulk materials were published in 1987 by Harrison et. al [7] . Later it was recognized that the belt sag component of flexure is non-linear along a loaded belt and that sag plays an important role in the calculation of effective tension Te [8]. By the early 1990’s, research was focusing on power loss reduction and on increasing the efficiency of the belt conveyor through rubber property control. A paper from 1991 by Spaans [9] shows that the flexural losses due to the bulk material can be more than previously considered by designers, particularly in wide belts. Hager et. al (1993) published a paper on the percentage of each resistance component of a 1 km belt [10]. A paper on the effect of length, temperature and friction on overland conveyor tensions was published by Harrison in 1998 [11], which showed the application of the research referenced above. Specifically, the influence of rubber indentation and hardness on the rolling losses of conveyors as a function of temperature was examined and compared to CEMA and DIN calculations. Application of the methods was used on the analysis of a dual carry conveyor for Namakwa Sands project in South Africa [12]. Research over many years has shown that different rubber materials behave differently when placed in service on a conveyor. Many researchers not referenced in this paper have examined viscoelasticity. The nature of the rubber compound in relation to rolling and indentation losses is not trivial. A paper by Lodewijks [12] in 2003 shows that rubber loss factors can be measured after the rubber is made. From the research, CEMA’s KtTemperature curve shows similarity to the viscoelastic storage modulus E for frequencies between 0 – 10 Hz. Lodewijks provides a correction factor for the DIN 22101 rolling resistance factor. ’

Test rigs have always provided a way of validating theoretical models of rolling resistance. In 2003, Wheeler presented research on the main resistances of belt conveyors [14]. A test rig at The University of Newcastle, Australia, was developed to allow a separation of the components of rolling resistance, and particularly the bulk solid flexure resistance [15]. A new theoretical investigation of rolling contact with viscoelastic materials relevant to conveyor design was published in late 2006 by Qui [16]. This research indicates that for a load of 3 kN/m, with 100 mm idlers and a span in excess of 3 m the indentation rolling resistance is predicted to be 22 N/m. Belt sag is not included in the model solution of Qui. This result will be revisited later in the paper. Indentation and rolling resistance of belt conveyors is a field of considerable interest and economic importance. Many belt manufacturers realise the importance of rolling losses if a design cost can be reduced from the use of lower loss rubber belting. Lower rolling losses reduce conveyor friction and power. This fact is noted in the new DIN 22101 Standard of 2002. For example, a low loss rubber was compounded by the belt supplier for the Henderson Mine belts in Colorado. Following installation in 2000, the DIN friction factor was 0.0075 [17]. As stated in the reference, retro-fitting low resistance belts to existing long conveyors allows a flow-rate increase.

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CONVEYOR DESIGN MODELS

Effective tension Te is defined as the sum of all resistances to motion referred to the drive. A drive can consist of one or more driving pulleys, and when two or more drive drums occur, the load sharing between drives needs to be considered. Irrespective of the load sharing, Te = (T1 – T2) where T1 represents the belt tension entering the drive and T2 is the belt tension exiting the drive. In general, all tension calculation methods deriving Te have a form : (1) Te = L g [R + B + V] + Q v’ + P + O where L = Length of conveyor (m). R = Rotating resistance of all idlers (kg/m), g = gravitational acceleration = 9.81 m/s^2. B = Belting and material flexure resistance (kg/m), carry and return runs lumped together, V = Material mass (kg/m) to be lifted a height H ; (H can be negative), Q v’ = Force to accelerate material (N), Q(kg/s), v’ = (belt speed - loading speed) (m/s). P = Force to rotate all Pulleys (N), O = Forces for all Other accessories, scrapers and special losses (eg. turnovers) (N). Although Equ.(1) seems simple and linear, all components except “H” have a variability related to either temperature, rubber properties or definitions regarding the various flexural resistances. From an engineering perspective, defining the various factors of the Te equation is not straightforward. This problem has existed for over 50 years and still research is being conducted to elucidate the various components of the force equation.

3.1

CEMA and DIN Method Comparison

Table 3.1 lists and compares the various rolling resistance factors, not including the total pulley rotating force or accessory forces such as cleaners. Where possible, equivalent terms are used to compare CEMA and DIN methods. For The CEMA method, Kt = CEMA factor for Temperature T, where Kt =1 (0 < T < 40 ºC), Kt = 3 (T = – 40 ºC). Kx = (Ks + Ki) = (belt sliding + idler drag) = 0.00068 (Mb + Mm) + Ai/Sc (kg/m) . Mb, Mm = mass of belt and material, respectively (kg/m). Ai = idler rotational drag, carry and return, including seals and bearings (kg). Sc = carry-side idler spacing (m). L, H = conveyor length and material elevation respectively (m). Ky = belt flexure + material flexure factor (0.016 to 0.035), from a CEMA table.

For the DIN method, the additional variables are required :

f = DIN friction factor, typically 0.01 < f < 0.04 (can be ~ 0.045 for pipe conveyors). C = Length factor (C = 1.9 at 80 m, C = 1.03 at 5 km). ct = DIN temperature factor ( ct = 1 at T = 20ºC, ct = 1.7 at T = - 40 ºC). Mc, Mr = mass of carry and return idlers, respectively (kg). Sr = spacing of return idlers (m). Ai* = [Mc/Sc + Mr/Sr] (kg/m).

Variable R B

CEMA

DIN 22101 (or ISO 5048)

Kt Kx Kt Ky Mb + 0.015 Mb Kt + Mm Ky

f ct C Ai* f ct C (2 Mb + Mm) cos δ (cos

V

Mm H/L

Table 3.1

δ

~1 if slope δ<18 º)

Mm H/L

Comparison of coefficients for CEMA and DIN methods.

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Some basic differences between the CEMA and DIN methods are indicated in Table 3.2. CEMA • Idler rotational resistance Ai is used for Kx • Idler mass (carry + return) lumped into Ai • Flexural factor Ky is tension dependent • Return belt flexure component is fixed at 0.015 • Kt is 3 at -40 ºC irrespective of length (<1 km) • Kt is 1 for 0ºC and higher • No global friction is required • For regenerative conveyors (H < 0), Ai = 0 • Sag running is 1.5% – 3%, by setting take-up Table 3.2

DIN • Idler mass correctly apportioned in Ai* • Idler mass (kg/m) for carry + return run • No separate flexural factor available • if cos δ =1, Te will be increased 5% • (ct.C) is 3.23 at – 40 ºC, for 80m belt • (ct.C) is 1.03 at + 40 ºC, > 5km belt • Global friction factor f (0.01 to 0.04) • Idler friction is not removed if H < 0 • Sag is assumed to be 1%

List of differences in the basics functions of the models.

The differences between the global calculation of Te for the basic CEMA and DIN methods is not subtle, and these differences can be examined more thoroughly when actual conveyors are modeled. Without separating the carry and return belt losses, the tension distribution around the belt will be in error. Nevertheless, Te will be suitable for determining a conveyor’s belt-line power using Pe = v Te (v is the belt speed ). In general, simple global methods for determining Te can be improved by independent calculation of carry and return run tensions, as well as by providing methods to accommodate use of new variables such component changes.

3.2

Modified CEMA and DIN Methods

Both CEMA and DIN calculation methods describe ways to separate loss calculations in any element along the conveyor. Separate calculations of the carry and return belt tension will produce a more reliable tension distribution, particularly in long conveyors. In order to produce separate calculations for the carry and return sides of a belt using the CEMA method, separate Kx and Ky values need to be determined. A modified CEMA method, referred to as CMOD, contains these changes. With respect to the DIN Standard, the idler mass Ai* already contains the separate lengthnormalised carry and return idler losses. Keller [17] describes the separation of the carry and return run losses from the main resistance of the DIN Standard [ 3, 5]. In general, separate calculations for the carry and return runs of either CMOD or DIN can be cast in the form : 2 L

L

T1 =

∑ j=0

Tx(j) +

∑ Tx(j) + T

o

(2)

j= L

where Tx(j) is the tension exiting every element of length “j” along the profile. Within each summation, a variable z = r (or c) can be used to set different return or carry run component values, respectively. Pretension To is usually added by a take-up force, which is often placed behind the drive at j = 0 or L, depending on the profile. Normally, T2 = To for a positive slope conveyor. The take-up force needs to be adjusted to ensure that drive slip is prevented, or alternatively to ensure that running belt sag at the lowest tension point is ideally between 1% and 3%. In all cases, long conveyors require a take-up to remove belt stretch which results from distributed motional resistance. Furthermore, independent computation of carry and return motional resistance is essential if both runs of the conveyor carry a bulk material, as was noted earlier [1]. To demonstrate the differences in tension distribution between CMOD and DIN methods, an example conveyor is examined using computer graphics to show differences in the models. The example conveyor is 8.184 km long, has an overall fall of -158 m, conveys Q = 1000 T/h of coal at a speed of 4 m/s. For CMOD calculations, Ai = 170 gm/roll. Note that these modified models do not contain an input for belt rubber properties. Figure 3.1 shows the example conveyor 1 profile. Values of CEMA Kx and Ky are shown on the figure. Figures 3.2 and 3.3 show a comparison between CMOD and DIN tension distributions, respectively. DIN friction has been set so that the power for both conveyors is equal, allowing distribution differences to be observed.

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Figure 3.1

Figure 3.2

Profile of example conveyor 1.

CMOD tension distributions for example conveyor 1.

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Figure 3.3

A. Harrison

DIN tension distributions for example conveyor 1.

In discussing Figures 3.1 to 3.3, it should be noted that downhill components of force in this conveyor profile reduce the overall power since Te is reduced by gravity effects. However the power is not negative and the conveyor is not regenerative. The fall slope of bulk material is only 1.93%. Setting Ai = 0 as CEMA recommends for regenerative conveyors is not allowed with the CMOD method. In order to establish an equivalence between a CMOD and DIN methods, the DIN factors are manually set at f carry = 0.0098 and f return = 0.0093. These factors depart from traditional DIN values of 0.016 for such a conveyor. Regular DIN values of 0.016 would result in a power consumption of 884 kW, compared to the CMOD power of 538 kW at the belt line. All power calculations above do not include mechanical drive losses. With respect to the graphs showing the distribution of tension along the belt profile, quite a difference is observed between the two methods, even though the power and terminal point tensions are made equal through the use of adjustable DIN factors for carry and return runs. The origin of the difference is related to elemental length adjustments of Kx and Ky values derived from CEMA tables [2], and separated to model a 35 degree trough and a 15 degree vee-return belt. No such equivalent input occurs in the basic DIN Standard formulation. This example shows that the belt forces around the conveyor will have differing influences on structural elements such as vertical and horizontal curves, depending on the model being used. In addition, the differences in belt tension between the models will change dynamic accelerations during starting and stopping, depending on profile. The CEMA and DIN methods do not allow indentation losses to be separately predicted. Both DIN and CMOD do not allow inputs for the viscoelastic effects of belt rubber indentation losses.

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HYBRID CONVEYOR DESIGN MODEL

Modern developments in low indentation loss rubber materials cannot be adequately accommodated into existing models as an input parameter. Even with the DIN method which allows a variable friction factor input, there is no easy way to convert rubber loss factors into a component of the friction factor. Hybrid models combine the basic mechanics of motion with established methodologies of Equ. (1) and Equ.(2) above. Using previous notations where possible, T is temperature, z = c or r representing carry and return indices, and Tx(j) is the tension exiting a length element L(j) comprising rolling and gravitational losses. Predictive loss equations for each length element “j” can be defined as follows :

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Element j :

Tx(j) = g L(j) [R(j) + {BI(j) + BF(j)} + MF(j) + V(j)] + Qv(j) + P(j) + O(j)

Idlers :

R(j) = Kt [Ks(j) + Az(j) (v/2) exp(- c T) / Sz(j) ] : a, b, c are fractions

Indentation :

BI(j) =(d tanδ v / g f (idz)) . (g (Mb + Mmz(j)) Sz(j))

a

b

e

1.33

: d, e are fractions

tanδ = Rubber Loss(T) = f (v, Sz(j), τ) + f (T) as functions

(3)

(4)

(5) (6)

τ = Viscoelastic time constant of rubber cover at a frequency = v/Sz (Hz). f (idz) = k1. idz + k2, is a function of idler diameter id, z = carry or return. a

n

Belt Flexure :

BF(j) = m’ Kt (Mb + Mmz) Sz(j) / L(j)

Material Flex:

MF(j) = (p + q v) (1.66 Sc(j)/Sr(j))

s

: m’, n are fractions

: for material on the carry side

(7) (8)

(0.003 < m < 0.008), n =3/2, (0.2 < p < 3) kg/m (0.02 < q < 0.6) kg-s/m^2, (1 < s < 3) is a real value

Variables R(j), BI(j), BF(j), MF(j) and V(j) have units of kg/m, and material flexure coefficients p, q and s are best obtained by measurement. [8, 16]. The same statement is true for the other factors. In the above set of equations, trivial variables such V, Qv, P and O has been omitted. Since 1986, field tests and laboratory measurements have been used to determine approximate functions for the way various loss factors behave. For example, we know that the idler rolling loss is a function of its temperature and grease type, seal friction, its diameter, speed and normal or vertical loading. Belt indentation factors are more elusive to obtain unless one works in a rubber compounding factory. From equation (3), the indentation factor is proportional to the normal load to a power of approximately 1.33, and it is also a function of belt speed to a power “e” and inversely proportional to idler diameter. Viscoelastic loss factor “tanδ” is a function of temperature and is similar to the Kt curve of CEMA, except that it is modified to account for belt cover flexing frequency. Many rubber manufacturers compound belt rubber covers using differing ratios of the various substances used in rubber calendaring. Mechanical tests indicate that the ratios and substances are variables, however the cured rubber exhibits a mechanical set of properties that can be tested to obtain necessary viscoelastic constants. Numerous references discuss rubber properties. To be sure of the constants of a particular elastomer, its mechanical properties should be measured. The method used in this paper is based on the indentation frequency variable in Equ. (6) coupled to a temperature dependence which can be measured for various rubber types. In summary, a conveyor design using the hybrid method discussed above will predict the general losses along a conveyor as a function of velocity, vertical or normal load on idlers, belt rubber type and material flexure. The hybrid method is used commercially in program BeltVS8 (2008) to compare the various available models. Hybrid models can be adjusted to accommodate new types of low-loss rubber and this model is seen as another tool when evaluating designs.

5.0

HYBRID MODEL APPLICATION AND EXAMPLE

The best way to demonstrate the application of the hybrid model is to display a computer-generated graph from software that contains the coding for CEMA, CMOD, DIN and the new hybrid algorithm “Non-Lin”. Rubber properties are used by the “Non-Lin” method to determine indentation losses. For example conveyor 1 shown in Figure 3.1, the Non-Lin hybrid model produces Pe(T) curves which are shown in the attached Appendix. Appendix Graphs1 and 2 show the differences in power as a function of temperature for belting rubber consisting of an SBR/Natural rubber blend and Natural rubber, respectively. The results of using Non-Lin modeling on example conveyor 1 can be viewed and will not be discussed further.

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Conveyor example 2 will be discussed in this section. Example conveyor 2 has a 5% incline for its 16.8 km length. Figure 5.1 shows the profile of the conveyor example 2 with relevant parameters of the b elt.

Figure 5.1

5.1

Example conveyor 2, a 16.8 km long slope belt with a 5% slope.

Example Conveyor 2 with SBR Rubber Belt

Figure 5.2 shows the variation of Pe(T) for SBR rubber compound. Turnovers are not used on this belt and the pulley covers were compounded with a low resistance rubber. Example conveyor 2 is a well documented conveyor in North America. In fact, the calculations for this conveyor by a CEMA method would have prohibited its construction, however due to the development of a low loss rubber by the belt supplier [6], this conveyor is currently running with a DIN f actor of f = 0.0075. Using SBR rubber, the Non-Lin Hybrid model correctly predicts power for an empty belt when compared to measurements. The conveyor was measured and the equivalent DIN factor extracted by the belt supplier to compare the performance of the conveyor with traditional methods. For the loaded case of 2000 t/h, the Non-Lin model with SBR rubber as the pulley cover rubber predicts about 10% more power than the measured value. Measurements were taken at 20 C. Figure 5.2 shows the result. With respect to SBR rubber in this application, computed values of (g*BI) and (g*BF) in Eqs. (6) and (7) are reproduced on the figures. For rolling indentation, the loss is BI = 5.07 N/m and BI = 0.8819 N/m for carry and return runs respectively. For the 16.8 km belt, the total rolling resistance is 100 kN. Belt sag and flexure loss amounts to 248 kN, Bulk material (ore) flexure amounts to 42 kN, and total idler rotational drag is 86 kN. A summation of the above forces gives the motional resistance of 477 kN. From Figure 5.2, the force to elevate the bulk material is 543 kN. In other words, the conveyor power consumed by rolling losses alone is 47%.

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Figure 5.2

A. Harrison

Power vs. Temperature for various models, with SBR rubber belt compound.

Qui’s analysis [16] of rolling indentation loss has been examined in relation to the above findings. Applying the normal loads from example conveyor 2 to Qui’s paper (1800 N for carry side, 660 N for return side), one obtains rolling resistances of 7 N/m (carry) and 2.5 N/m (return), which translate to a total indentation rolling loss of 159 kN at 3 m/s. Qui used a viscoelastic material of unknown type however its tanδ = 0.2. Qui’s curves used 100 mm idlers, whereas the above conveyor uses 178 mm diameter idlers. Larger diameter idlers will reduce indentation according to Equ. (5) and so Qui’s solution may be plausible after normalisation.

5.2

Example Conveyor 2 with SBR-Natural Rubber Blend

Figure 5.3 shows the graph of Pe(T) for example conveyor 2 in which a blend of SBR/Natural rubber compound is used for the belt covers. Comparing Pe(T) results shows that the Non-Lin model closely follows the measured power for the loaded condition, and Pe(T) for the empty belt is slightly below measured values and the DIN curve. From the Non-Lin model, indentation resistance is BI = 76 kN which is 25 kN below the SBR value. Summing all the rolling losses together from Figure 5.3 gives 429 kN, which is 48 kN less than the SBR case and results in a power saving of 227 kW. For the above Non-Lin model, the frequency of rubber deformation was 1.36 Hz (see Equ. (6), and the temperature was 20 C. Comparing the Non-Lin model curve of Pe(T) to CEMA and CMOD solutions shows that the CEMA method predicts about 1500 kW more power at 20 ºC. CEMA cannot take into account rubber properties and so its predictions are overly conservative.

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Figure 5.3

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Power vs. temperature for a SBR/Natural rubber blend.

CONCLUSIONS

A new non-linear hybrid model “Non-Lin” shows that power consumption of long conveyors can be predicted if the type of belt rubber is known or if the rubber’s tan δ is obtained. Results from the new model have been compared to traditional CEMA and DIN solutions. Whereas DIN allows input of a friction factor for a conveyor after the fact to show true friction factors, it is more difficult to predict the DIN friction factor in advance and impossible to input a rubber type to produce a DIN factor at the design stage. Development of the Non-Lin model solution has taken many years and is backed up by field measurements. Test work has provided general data for Nitrile, Chloroprene, Neoprene, SBR, Natural and special rubber blends as inputs to the model. Up to the present, the model contains material properties data for coal, lignite, ore, gravel, limestone, cement, iron pellets and sand. The model has been used on conveyor design with low loss rubber and conveyors carrying material both ways.

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References [1 Harrison, A, Cemento Peru Pipe Conveyor Audit, Scientific Solutions Inc. Report 1503, 7/7/2005. [2] Conveyor Equipment Manufacture’s Association, Belt conveyors for bulk materials, Ed. 6, 2005. [3] DIN 22101, Stetigfoerderer. Gurtfoerderer fur Schuttgutter, Deutsches Instit. Normung, August 2002. [4] International Standards Organisation, ISO 5048, [5] ContiTech, Conveyor belt system design, Ed 4, 1990, edited by Dr.Ing. R Alles. 6] Jonkers, CO, Indentation rolling resistance of belt conveyors, Fordern u Heben, April, Nr 4, 1980, pp 312-316. [7] Harrison, A, Teo, LH, Roberts, AW, Measurement of belt-idler interactions and material flexure coefficients for design of troughed conveyor systems, Bulk Solids Handling, Vol 7, No 3, 1987, pp 367-371. Also see Mechanical Engineering Transactions, Vol ME12, No 3, 1987, pp 196-202. [8] Harrison, A, Dynamic sag instabilities in long underground belt conveyors, International Mechanical Engineering Congress, Sydney, Australia, 8-12 July 1991, pp 24-30. [9] Spaans, C, The calculation of main resistances of belt conveyors, Bulk Solids Handling, Vol 11, No 4, 1991, pp 809-826. [10] Hager, M, Hintz, A, The energy saving-design of belts for long conveyor systems, Bulk Solids Handling, Vol 13, No 4, 1993, pp 749-758. [11] Harrison, A, Overland conveyors : effect of length, temperature and friction model on conveyor tensions, Bulk Solids Handling, Vol 18, No 1, 1998, pp 65-68. [12] Spriggs, GH, Short, GG, The design and implementation of the LSL/Tekpro dual carry overland conveyor, Bulk Solids Handling, Vol 23, No 6, 2003, pp 392-396. [13] Lodewijks, G, Determination of rolling resistance of belt conveyors using rubber data : fact of fiction? Bulk Solids Handling, Vol 23, No 6, 2003, pp 384- 391. [14] Wheeler, C, Analysis of the main resistances of belt conveyors, PhD thesis, The University of Newcastle, Australia, 2003. [15] Wheeler, C, Bulk solid flexure resistance, Bulk Solids Handling, Vol 25, No 4, 2005, pp 220-225. [16] Qui, X, Full two-dimensional model for rolling resistance : hard cylinder on viscoelastic foundation of finite thickness, J. Eng. Mech., Vol 132, No 11, 2006, pp 1241-1251. [17] Keller, M, The impact of the German Standard DIN 22101 on belt conveyor design, 2007, Private communication, pp 1-7,

This paper was published by Vogel/Germany in the Journal : Bulk Solids and Powder – Science and Technology, Vol 4, (2009), No. 1, pp1 – 11.

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APPENDIX – Power – Temperature Comparisons for Example Conveyor 1

Graph 1.

Graph 2.

Example conveyor 1 Power vs. T for Natural/SBR rubber covers.

Example conveyor 1 Power vs. T for Natural rubber covers.

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Friction_Models_for_Conveyor_Design_2009_JBSPT_WebVer

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