Energy prediction models of belt conveyor systems towards speed control - Modellen om energie besparing te voorspellen van bandtransporteurs door snelheidsvariatie

(1)

Delft University of Technology

FACULTY MECHANICAL, MARITIME AND MATERIALS ENGINEERING

Department Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

This report consists of 63 pages and 2 appendices. It may only be reproduced literally and as a whole. For commercial purposes only with written authorization of Delft University of Technology. Requests for consult are only taken into consideration under the condition that the applicant denies all legal rights on liabilities concerning the contents of the advice.

Specialization: Transport Engineering and Logistics Report number: 2015.TL.7972

Title: Energy prediction models of belt conveyor systems towards speed control Author: T.H.A. Visser

Title (in Dutch) Modellen om energie besparing te voorspellen van bandtransporteurs door snelheidsvariatie

Assignment: Literature Confidential: no

Supervisor: D. He, Y. Pang

(2)

T

U

Delft

FACULTY OF MECHANICAL, MARITIME i MATERIALS ENGINEERING

Delft University of Teclinology Department of Marine and Transport Technology

Mekelweg 2 2528 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl Student: T. H. A. Visser

Supervisor: D. He, Y. Pang Specialization: TEL Creditpoints (EC): 10

Assignment type: Literature Report number: 2015.TEL.7972 Confidential: No

Subiect: Energy prediction models of belt conveyor systems towards speed control

In large scale bulk material handling applications, considerable power is consumed by belt conveyor systems. Taking the design and operation of belt conveyor systems into account, industry standards and norms provide the fundamentals of calculating the energy consumption. Meanwhile, diverse models have been developed to predict the energy utilized by conveyor systems and the potential energy savings. Recent researches have proven that belt conveyor speed control can be considered to be a feasible approach to realize energy savings in belt conveyor operations.

This assignment is to provide a survey of the standards/norms and models to calculate and predict energy consumption of belt conveyor systems. The models and theories of estimating the energy savings by means of belt conveyor speed control will be investigated. This literature survey should cover following:

- To summarize the design and operation aspects regarding the energy consumption and energy savings of belt conveyor systems

- To review the industry standards/norms and models with respect to the calculation and estimation of belt conveyor power consumption

- To describe the principle of belt conveyor energy savings by means of speed control )

- To survey the state of the art models and energy saving applications of belt conveyor speed control

This report should be arranged in such a way that all data is structurally presented In graphs, tables, and lists with belonging descriptions and explanations in text.

The report should comply with the guidelines of the section. Details can be found on the website.

(3)

2

Summary

In the recent years there have been a new focus on energy reduction using speed control as an answer to rising costs, pollution and global warming in the belt conveyor industry. Speed control can be used to lower the belt speed in to reduce energy consumption of the belt conveyor system.

Belt conveyors are designed around peak material flows. The peaks do not occur often. In case of lower material flow the belt is only partially loaded. In these cases the belt speed could be lowered to match this non-nominal material flow rate.

However, the energy estimations used during the engineering phase, which are based on standards, do not transfer well to calculate the energy use for speed control. The energy models in use during the engineering phase are generally based on a little overdesigned system, which means that the energy consumption seem higher than they would be in reality. Furthermore these standards are based on nominal values for the belt speed and the belt load, which vary during speed control. So the estimations of energy use are not accurate if these standards are used for speed control.

Many of the standards describe the energy use of a belt conveyor in great detail for a belt conveyor in steady state operation which operates at nominal values of its parameters. This is however not the case for speed control based situations. Research indicates that the resistance forces are dependent on the belt speed and belt load. It is shown that the coefficient of friction, which is used in two heavily used engineering standards, is dependent on both the belt load and the belt speed. Furthermore another method of calculation called single resistance method shows that the resistances of belt conveyor are dependent on the belt load and the belt speed. Researchers have taken upon themselves to build new energy estimation models which can be used in both engineering and operation phases. The first step is to determine whether the parameters used in standards are actually the right values for a project in use. If or when these values have been confirmed or updated they can be used in the right model to simulate the energy use in either passive or active speed control methods. Further research is needed to also implement these model in actual speed control method for operation.

This report also introduces its own theoretical energy model to hopefully accurately predict the energy savings of either passive or active speed control methods. This serves as a stepping stone towards a simulation model.

(4)

3

1 Introduction

1.1 Background of study

There has been a worldwide focus on energy reduction as the awareness of the impact of global warming grows. The transport sector has not been an exception to this. Improving energy efficiency and decreasing ambient pollution is a sector wide focus. There has been a focus on energy reductions of transport technology as a result. The belt conveyor sector has seen a surge in research into energy reductions of belt conveyors. A wide range of methods and technologies have begun to surface in the last decade or so. These developments focus on all the stages of the belt life cycle from new projects to sustainability of existing belt conveyor systems. This survey will focus on energy saving by concept of speed control, which will be introduced shortly.

1.1.1 Speed control

One of the main approaches to energy savings in belt conveyors in operation is speed control. The belt speed and belt load are specified for specific peak material flows. When the material flow is lower than this peak material flow the belt is not maximally filled. Normally a belt conveyor runs at the same speed (Lodewijks, Schott, & Pang, Energy Savings At Belt Conveyors By Speed Control). If the technology supports it, the conveying capacity of the belt conveyor can be adapted to the actual material flow by lowering the belt speed, effectively optimizing the belt fill by reducing the belt speed (Hilterman, 2008). So speed control is maximizing the belt fill by controlling the belt speed. This in turn reduces the energy consumption of the belt conveyor.

1.1.2 Reason for study

The methods to calculate the energy use for engineering design do not transfer perfectly to the operations side, especially not in an environment where the speed and the load of the belt conveyor are different from the nominal values determined in the engineering phase. This industry has become aware that the analytical tools available to reliably calculate the energy output are not sufficient. Thus the strategic approaches to energy savings could not be backed up by clear reasoning and metrics. Different organisations and individuals have taken upon themselves to develop new energy models to predict the energy use under different operational conditions more accurately. In doing so a clearer vision can emerge to which strategic approaches of energy savings are the most sound.

This study hopes to provide a coherent structure of energy consumption of belt conveyors. In doing so it also hopes to provide an insight to the path forward towards reliable energy models.

1.1.3 Scientific environment of study

As previously mentioned the energy calculations used for engineering do not transfer well to the operations side. There a multiple related factors for that.

The engineering process standards are used to determine the belt conveyor specifications. Among these specifications are the configurations of the belt and the drive motor. The speed is determined as a result of the specific cargo that needs to be transported. Energy use follows from that process. Most determined values of the belt conveyor belt are nominal values. This has problems for the energy calculation for the operations side.

(6)

5 Overestimation in the engineering process

It is common to somewhat overdesign the belt conveyor. This is done to make sure the belt conveyor holds up to extreme cases that do not occur frequently. One might even speculate that this favours the producers of belt conveyor parts. The result is that the energy calculations are also a little off.

Speed variation

During the engineering process the variables used are nominal values, so speed is considered constant or at least used as an average value. Furthermore the system is design for peak material flows.

During operations the speed may differ from the nominal values. As we will see later on the standards used in the engineering are not sufficient to calculate the energy accurately where different belt loads and speeds are employed.

Scientific response

As a result of these problems and the focus on energy reductions in the belt conveyor industry, people and organisations as a whole have started to expand on the standards used in the engineering process. Energy calculations needs to be more accurate in order to fully optimize operations.

1.2 Objective of work

This paper hopes to provide an overview of the different energy models. This overview will cover the basis of energy calculation, provided by different standards as well as an expansion these standards. Secondly it will cover the energy models in use to calculate energy use for speed control. And at last it will also provide a theoretical estimation of the energy savings of speed control.

1.3 Structure of work

This document will be grouped in three sections. Firstly the energy models, secondly speed control and third an estimation of the energy savings of the two different versions of speed control.

1. The first section will lay the groundwork for the energy calculations used in the two sections that follow it. Here the two different methods of energy calculations will be introduced. Followed by that the standards are further explored. From there the expansions upon the standards will be explored.

2. The second section will cover the theory of the two different methods of speed control. It will also cover some research that has covered this topic.

3. The third section will give a theoretical estimation of the energy savings of the two different methods of speed control.

1.4 Scope

This is a literature review research, as such it will mostly cover the established insights of the industry and the research that followed up on it. Nevertheless not all industry wide used standards will be spoken of in an in depth matter, only the ones most accepted or in use. The

(7)

6 research that is mentioned must provide a large merit to the development of energy models for speed control, not energy use models in general. The last section covering an estimation of the energy use. This estimation will be purely theoretical and will use the analytical building blocks covered before that. It will not use any experimental work or any new analytical insights.

(8)

7

2 Conveyor systems

In this section a short introduction will be given to belt conveyors in general. Different methods for energy savings will also be given. Among these possibilities there will be a further

exploration into speed control as a first step for the rest of this paper.

2.1 Basis of conveyor systems

In the figure below [Figure 1] a general graphic description of a belt conveyor is given.

Figure 1: Schematic graphic of a belt conveyor, (Drenkelford, 2013)

In a belt conveyor system energy is used to transport material from one place to another. The main components that make up a belt conveyor are the idlers, the head and tail pulleys, the take-up system and the belt. Other components are the frame and the loading chute

(Drenkelford, 2013). Energy must be spent to overcome friction forces where moving parts make contact with stationary parts. Friction also occurs within the belt and the belt load itself, due to elasticity (Drenkelford, 2013).

2.2 Energy savings methods

As this paper will later show in analytic form is that a large part of the energy consumption of belt conveyor stems from these parts (Alspaugh, 2004):

- Idlers resistance - Belt flexure - Load flexure

Also rubber indentation due to idler support and alignment. The energy consumption due to resistance for a non-incline belt is divided as follows (Alspaugh, 2004):

- Rubber indent (48%) - Idlers (26%)

- Alignment (17%) - Material flexure (4%)

(9)

8 Energy consumption will go up rapidly for belt with a certain lift. For example a belt conveyor with a length of 413𝑚 and a lift of 12𝑚 the energy consumption for lift will be 43% (Alspaugh, 2004).

For non-inclined and very long belt conveyors where the running of an empty system already takes a large part of the energy consumption (Alspaugh, 2004) a focus will need to be on the idler, belt and load.

In general energy savings can be the most favourable if one invest into the right components before the installation of a belt conveyor system. This is however not always quite possible for systems that are in operation. Retrofitting is a possibility, but that will take the belt out of operation for some time. This is might not be possible for some systems. For systems that are in operation speed control.

2.2.1 Energy savings methods

It is important to note that these development do not operate in a vacuum. Along with speed control other development also tackle issues of energy savings and efficiency. The following initiatives focus more on new engineering project, rather than improving existing ones. The main directions of can be summed up as the following (Poluektov, 2014), (Alspaugh, 2004):

- Routing optimization - Power distribution - Analysis and optimization - Efficient equipment

So far this chapter focussed on the engineering part and the general components involved. For the operations side it most of the time not possible to change components. Therefore different strategies for energy savings are needed. One of those is speed control.

(10)

9

2.3 Speed control

In the last decade or so the technology required for speed control has gone down considerably. The price of electricity has risen it the same period as well. That has made speed control more attractive over the years.

2.3.1 Dynamics of capacity, speed and belt load

Before the discussion of the different speed control types of speed control it is a good idea to understand the dynamics of belt load and speed control. The belt load is denoted as 𝑚𝐿′ in kg/m,

the capacity 𝑄 in MTPH and the speed 𝑣 in m/s. The relationship between these three variables is given as:

𝑚_𝐿′ ₌ 𝑄

3.6 ∙ 𝑣 (2.1)

For engineering purposes these values are all nominal values. But for operation the inflow of material (𝑄) might vary of time. The power consumption of the system has a 1:1 relation to the speed. So to optimize for energy efficiency it is advised to set speed as low as possible (even if friction will increase). Every belt has a maximum belt load. So if the capacity is at a maximum value the speed cannot be lowered without going over the maximum belt load. For lower values of the capacity (𝑄) speed can be set to such a value that maximum belt load is achieved.

Note however that there is no general agreement within the scientific community that setting the speed such that a maximum value of the belt load is achieved, will lead to a more energy efficient system in all instances (Lauhoff, 2005). Although the described method of maximum belt load via speed control is however the most general accepted strategy.

2.3.2 Passive and active speed control

For belt conveyors without the possibility of changing the speed of the belt the belt runs at a predetermined nominal value. This means that the belt has a filling degree lower than 100% in cases where the inflow of material is lower than the nominal value.

Passive speed control

With passive speed control the belt speed is constant for a certain amount of time where the maximum value of the inflow of material is known (Zhang & Xiaohua, Modeling and energy efficiency optimization of belt conveyors, 2011). The set speed is not (necessarily) at the nominal value though. This speed is decided upon before the belt conveying system is running. The speed is matched to the maximum expected value of inflow of material (Q). So the inflow of material could be lower than this maximum value.

Active speed control

The belt fill level and/or belt load is monitored continuously and the belt speed is also adjusted continuously with a closed loop control system to maximize the belt load to a predefined level. So active speed control continuously adjusts the belt speed to match the belt conveying capacity to the actual material flow by means of a control system (Hilterman, 2008).

(11)

10

2.3.3 Technological requirements

Conveyor belts without speed control use AC induction motors with a fixed running speed. Speed control systems need frequency converters. In the last ∓15 years the availability of high power frequency converters for AC motors has grown. Variable geometry chutes are needed (Hilterman, 2008) and need to be controlled actively in the case of active speed control. An active speed control needs an active control system as well, something the passive speed control does not need.

Later on this paper will take a look on the energy efficiency of AC motors in relation to speed control.

The active speed control has the most potential for energy savings on first look. But this type of speed control needs more technological investment. Also note that the maximum belt

acceleration is limited in cases of long belt conveyors (Alles, Conveyor Belt System Design, 1994). So this type of speed control is not the most suitable to rapid changes of inflow of material. Passive speed control can handle a faster change in material flow, given that it does not pass the maximum value it has set on. But passive speed control cannot gain any efficiency of the change of inflow of material.

To summarize:

- Active speed control is generally preferred if the change of flow in material is larger but more gradual.

- Passive speed control is generally preferred if the peak of material is pre-known and the change of flow in material is smaller. A change in flow in material influx is allowed to be faster.

(12)

11

3 Models for calculating motional resistance

3.1 Introduction and overview of energy models

In this section energy calculation models will be discussed. These models will form the basis for the sections that will follow it. This section will discuss various models where each of them can be categorised. This section will discuss the following topics:

1. Energy conversion models 2. Resistance based models 3. Standards

4. Coefficient of friction

5. Single resistance for friction based models

The various energy models can be categorized into two categories. These two are: - Energy conversion model

- Resistance based model

The latter is more in use in this industry. Nonetheless this section will give a short description of this type of model. Next up is the description of the resistance based model.

The standards that will be described in this section are all resistance based models. Three different standards will be discussed: ISO/DIN and CEMA.

After this part a coefficient of friction will be discussed. This coefficient of friction is based on two of the standards previously discussed. This is important in order to lay the groundwork or the speed control section. Lastly ‘single resistance for friction’ will be discussed which uses a different approach to friction than the earlier discussed standards.

3.2 Energy conversion based methods

The models split the energy use up into three parts (Zhang & Xiaohua, Modeling and energy efficiency optimization of belt conveyors, 2011):

1. The power to run an empty conveyor belt (𝑃𝑒𝑐)

2. The power to run a belt which is loaded on the horizontal parts (𝑃ℎ)

3. The power to run load which either declines or amends (𝑃𝑙)

4. Power to run the accessories (𝑃𝐴𝐶𝑆)

The total power to run a belt conveyor can be stated as:

𝑃𝑇= 𝑃𝑒𝑐+ 𝑃ℎ + 𝑃𝑙+ 𝑃𝐴𝐶𝑆 (3.1)

The Japanese standard (JIS B 8805 - Japanese Standard - Rubber belt conveyors with carrying idlers - Calculation of operating power and tensile forces, 1992) can be categorized as an energy conversion method.

Later on it can be noted that the ISO/DIN methods of resistance based methods can easily be split up and be transformed into energy conversion methods.

(13)

12

3.3 Resistance based models

For these models the overall resistances to motion of a belt conveyor comprises are grouped. It is assumed that the belt runs in steady state and no acceleration of the material takes place, thus all forces come from overcoming friction. The mentioned groups are as follows (Zhang & Xiaohua, Modeling and energy efficiency optimization of belt conveyors, 2011):

1. Main resistances 2. Secondary resistances 3. Gradient resistances 4. Special resistances

The main resistances are the resistances that occur along the whole belt and make up the largest part of the resistances given a flat belt. For a belt with a big height difference gradient resistances can be higher. Secondary resistances only occur at specific places. For long conveyor belts secondary resistances do not contribute much to the overall belt friction, and as such both ISO and DIN calculate the secondary resistances as a fraction of the primary resistances. The special resistances are belt specific and do not occur at every belt conveyor.

The standards DIN 22101 (DIN 22101: Gurtförderer für Schüttgut – Grundlagen für die Berechnung und Auslegung (Belt conveyors for bulkmaterials – Fundamentals for calculation and design), 1982), ISO 5048 (ISO 5048: Continuous mechanical handling equipment -- Belt conveyors with carrying idlers -- Calculation of operating power and tensile forces, 1989) and CEMA (CEMA: Belt Conveyors for Bulk Materials, 2002) all us this split.

In the next part all three of these standards will be discussed. There will be clear similarities between the DIN and the ISO standard. As such a comparison between the two models will be made.

From friction to power

The difference between the two models is that one describes the total power and the other the friction. To overcome this difference the total resistance of the resist based method can be multiplied with the belt speed to calculate the required power.

3.4 ISO 5048

The next section will cover the content of ISO 5048, second edition (ISO 5048: Continuous mechanical handling equipment -- Belt conveyors with carrying idlers -- Calculation of operating power and tensile forces, 1989) and all the mentioned formulas originate from this document. The overall resistances to motion of a belt conveyor comprises various resistances, these will be classified into the following five groups:

5. Primary resistances (𝐹𝐻)

6. Secondary resistances (𝐹𝑁)

7. Special main resistances (𝐹𝑠1)

8. Special secondary resistances (𝐹𝑠2)

(14)

13 The total resistance is the sum of those four resistance forces:

𝐹 = 𝐹_ℎ+ 𝐹_𝑛+ 𝐹_𝑠𝑡+ 𝐹_𝑠 (3.2)

Note that this standard splits up special resistance into main and secondary. Special main resistances occur along the whole belt, while special secondary resistances occur only at a specific place.

Whereby the special resistance forces are grouped together as 𝐹𝑠 = 𝐹𝑠1+ 𝐹𝑠2.

The main resistances 𝐹ℎ and 𝐹𝑠1 occur continuously along the length of the belt conveyor.

The secondary resistances 𝐹𝑛 and 𝐹𝑠2 are only present locally.

Slope resistance can both occur locally or continuously along the length of the belt conveyor depending on where the belt runs on a slope.

In the next few sections takes a closer look to each of these resistance forces.

3.4.1 Main resistances (FH)

The different aspects of primary resistance are the following can be split up based on the resistance of the belt and the idler bearings. The resistance of the belt can be further split up in three subcategories. So to sum it up we have the following primary resistances:

a) Rotational resistances of the carrying and return strands of idlers due to friction in the idler bearings and seals

b) Belt advancement resistance due to pressing down of the idlers into the belt and the recurring flexing of the belt and the material.

3.4.2 Secondary resistances (FN)

The secondary resistances do not occur along the length of the conveyor belt but locally. For long centre-belt conveyors (for example over 80 meters) the secondary resistances are clearly less than the main installation resistances and can be calculated in a simplified manner without risk of too serious an error. For this purpose, a coefficient 𝐶 is introduced as main resistance factor dependent on the length of the belt conveyor. The coefficient 𝐶 is given by the following formula:

𝐶 =𝐹𝐻+ 𝐹𝑁

𝐹_𝐻 (3.3)

If the conveyor length, L, is over 80m this coefficient C can be calculated using the following equation:

𝐶 =𝐿 + 𝐿𝑜

𝐿 (3.4)

(15)

14 For conveyor belts shorter than 80m the secondary resistances need to be calculated rather than estimated. The secondary resistances comprise of the following:

a) Inertial and frictional resistances due to the acceleration of the material at the loading area;



0



bA VQ

F



I

 

v v

(3.5)

b) Resistance due to friction on the side walls of the chute at the loading area; The will be later noted as: Frictional resistance between handled material and the skirtplates in the acceleration area:

2 2 2 2 0 1 2 v b Schb I g l F v v b



            (3.6) 𝑊ℎ𝑒𝑟𝑒 𝜇₂= 0,5 to 0,7. And 𝑙_{𝑏,𝑚𝑖𝑛}=𝑣2−𝑣02 2∙𝑔∙𝜇1 Where 𝜇₁ = 0,5 to 0,7.

c) Resistance due to the wrapping of the belt on the pulleys

The will be later noted as: Wrap resistance between belt and pulleys - for fabric carcass belts:

9 140 0, 01F d F B B D    _  _   (3.7)

- for metal carcass belts:

F d F 12B 200 0, 01 B D    _  _   (3.8)

d) Pulley bearings resistance with the exception of the driving pulley bearings

The will be later noted as:: Pulley bearing resistance (not to be calculated for the driving pulleys: 0 0, 005 t T d F F D   (3.9)

3.4.3 Special main resistances (Fs1)

The special main resistances occur along the length of belt conveyor, which consists of the following:

a) Drag resistance due to forward tilt of the idler in the direction of belt movement; - For carrying idlers equipped with three equal length rollers: 𝐹𝑔𝐿

(16)

15 b) Resistance due to friction against chute flaps or skirtplates, if these are present over the

full length of the belt

2 2 2 2 1 v gL I g l F v b



   



  (3.10) Where 𝜇₂= 0,5 to 0,7.

3.4.4 Special secondary resistances (Fs2)

The special secondary consists of the following:

a) Resistance due to friction with belt and pulley cleaners;

3

t

F

  

A

 

(3.11)

Where 𝜌 is normally between 3 ∙ 104_{and 10 ∙ 10}4_𝑁/𝑚2

b) Resistance due to friction with chute flaps or skirt plates, if these are present on only a certain part of the belt.

c) Resistance due to inversion of the return strand of the belt; d) Resistances due to discharge ploughs:

a a

F

 

B k

(3.12)

𝑊ℎ𝑒𝑟𝑒 𝑘_𝑎 is normally 1500 𝑁/𝑚

e) Resistance due to trippers.

3.4.5 Slope resistances (FSt)

Slope resistance is Fst resistance due to lifting or lowering of the material on inclined conveyors. This resistance can be negative for declining conveyors. The slope resistance can be calculated with the following formula:

St G

F



q

 

H g

(3.13)

The height is taken as positive for ascending conveyors and negative for declining conveyors.

3.4.6 General calculation of peripheral driving force

The main resistance 𝐹𝐻 can be calculated in a simplified manner by using an artificial friction

coefficient 𝑓. By applying Coulomb’s friction law the main resistance is equal to the product of the artificial coefficient 𝑓, the conveyor length L, and the sum of the vertical forces per linear metre resulting from all the moving masses; therefore, by substituting 𝐹𝐻 in equation (x), the

following equation is obtained:

(17)

16 Where the conveyor load 𝑞𝐺 can be calculated as follows:

𝑞𝐺=

𝐼_𝑣∙ 𝑄

𝑣 (3.15)

(18)

17

3.5 DIN 22101

The next section will cover the content of DIN 22101 (DIN 22101: Gurtförderer für Schüttgut – Grundlagen für die Berechnung und Auslegung (Belt conveyors for bulkmaterials –

Fundamentals for calculation and design), 1982) and all the mentioned formulas originate from this document.

The main resistance force mentioned earlier can be split up in different aspects, namely: 1. Main resistances (𝐹𝐻)

2. Secondary resistances (𝐹𝑁)

3. Slope resistances (𝐹𝑠𝑡) 4. Special resistances (𝐹𝑠)

The total resistance is the sum of those four resistance forces:

𝐹 = 𝐹_ℎ+ 𝐹_𝑛+ 𝐹_𝑠𝑡+ 𝐹_𝑠 (3.16)

In the next few sections takes a closer look to each of these resistance forces.

3.5.1 Main resistances (FH)

Instead of focussing on the different aspects of the main resistance, DIN 22101 (DIN 22101: Gurtförderer für Schüttgut – Grundlagen für die Berechnung und Auslegung (Belt conveyors for bulkmaterials – Fundamentals for calculation and design), 1982) focuses on a general formula to calculate the main resistance.

𝐹_ℎ = 𝑓 ∙ 𝐿 ∙ 𝑔 ∙ [𝑚_𝑅′ _{+ (2𝑚} 𝐵 ′ _{+ 𝑚}

𝐿

′_{) ∙ 𝑐𝑜𝑠𝛿]} _(3.17)

In case of an installation inclination degree of ≤ 15°, it is allowed to use 𝑐𝑜𝑠𝛿 = 1 in this formula.

3.5.2 On friction coefficient

In the case of belt conveyor installations with filling ratios 𝜑 in the range from 0,7 to 1,1, and with a relative belt sag ℎ𝑟𝑒𝑙 of ≤ 1% , and equipped with carrying idlers mounted on antifriction

bearings and fitted with labyrinth seals, the value of 𝑓 will be situated in the range from 0,012 to 0,035, depending on the operating and installation conditions.

3.5.3 Secondary resistances (FN)

For belt conveyors longer than 80 meters the secondary resistances will be calculated as a fraction of the main resistances. This is used a rule of thumb instead of actually calculating the secondary resistances.

For shorter belt conveyors, the secondary resistances will be much larger compared to the main resistances and will therefore be calculated separately.

3.5.4 Smaller secondary resistance forces

(19)

18 𝐶 =𝐹𝑁

𝐹_𝐻 (3.18)

In case of filling ratios 𝜑 in the range from 0,7 to 1,1 and of a relatively low percentage of the secondary resistance in relation to the total resistance, the coefficient C can be taken from the following table:

Table 1: Standard values for coefficient C for belt conveyor installations with filling ratios in the range of 0,7 to 1,1

3.5.5 Larger secondary resistance forces

If the secondary resistances represent a large percentage of the total resistance, e.g. in the case of installation lengths L < 80 m, and of installations with more than one feeder point, it will be necessary to determine the secondary resistances individually, or the coefficient C respectively. In this case the secondary resistance forces FN consists of the following components:

a) Inertia resistance 𝐹𝐴𝑢𝑓

b) Frictional resistance between the material conveyed and the lateral chutes 𝐹𝑆𝑐ℎ𝑏

c) Frictional resistance caused by belt cleaner 𝐹𝐺𝑟

d) Resistance to bending 𝐹𝐺𝑏

e) Pulley bearing resistance 𝐹𝑇𝑑

The total secondary resistance can be written as follows:

𝐹𝑁 = 𝐹𝐴𝑢𝑓+ 𝐹𝑆𝑐ℎ𝑏+ 𝐹𝐺𝑟+ 𝐹𝐺𝑏+ 𝐹𝑇𝑑 (3.19)

a) Inertia resistance and frictional resistance between the material conveyed and the belt in the zone of a feeder point



0



Auf m

F



I

 

v v

(3.20)

b) Frictional resistance between the material conveyed and the lateral chutes within the acceleration zone of a feeder point

2 2 2 2 0 2 m b Schb Schb Rank Sch I g l F C C l v v





             (3.21) Where 𝑙𝑏 > 𝑙𝑏,𝑚𝑖𝑛 =𝑣 2_−𝑣 02 2∙𝑔∙𝜇1

For belt conveyer installations of conventional type we can write: 𝐶𝑆𝑐ℎ𝑏∙ 𝐶𝑅𝑎𝑛𝑘 = 1.

(20)

19 approx. 0,5 to 0,7.

c) Frictional resistance caused by belt cleaner: 4

Gr Gr Gr

F







p



A

(3.22)

As a general rule, the parameter 𝑝_𝐺𝑟 is situated in the range from approx. 0,03 to 0,1 𝑁/𝑚𝑚2, and the friction coefficient 𝜇4 is situated in the range from approx. 0,6

to 0,7.

d) Belt resistance to bending 𝐹𝐺𝑏 on its passage over the pulleys and the pulley bearing

resistance 𝐹𝑇𝑑 of the idler pulleys. These resistance forces are in nearly every instance

negligible in comparison to the first three resistances mentioned. Coefficient 𝐶 can now be calculated as follows:

𝐶 = 1 +𝐹𝐴𝑢𝑓+ 𝐹𝑆𝑐ℎ𝑏+ 𝐹𝐺𝑟+ 𝐹𝐺𝑏+ 𝐹𝑇𝑑

𝐹_𝑁 (3.23)

3.5.6 Slope resistances (Fst)

Slope resistance 𝐹𝑆𝑡 is resistance due to lifting or lowering of the material on inclined conveyors.

This resistance can be negative for declining conveyors. The slope resistance can be calculated with the following formula:

'

St L

F H g m  (3.24)

The height is taken as positive for ascending conveyors and negative for declining conveyors.

3.5.7 Special resistances (Fs1)

The special main resistances occur along the length of belt conveyor, which consists of the following:

a) Camber resistance 𝐹𝑅𝑠𝑡

b) Frictional resistance between the material conveyed and the lateral chutes outside the feeder points

c) Resistances of devices for the delivery of goods along the conveying path d) Camber resistance

The camber resistance which arises at an individual side carrying idler will depend on its normal force, on the friction coefficient 𝜇3 between the belt and the carrying idler, and

also on the angle of tilt 𝜀.

The camber resistance 𝐹𝑅𝑠𝑡 which arises at an individual belt strand of the installation

will, therefore amount to the values below obtained from the total of the individual resistances, and taking the the angel of inclination 𝛿 of the installation into

(21)

20 Upper strand:



' '



3 Rsto Rsto Rsto G L Ro Z F L c sin cos g m m Z







         (3.25) Lower strand: ' 3 Rstu Rsto Rstu G Ru Z F L c sin cos g m Z







        (3.26)

The friction coefficient 𝜇3 is, as a general rule, situated in the range from approx. 0,5 to

0,7. In the above relationships, the parameters 𝑐𝑅𝑠𝑡 are dependent on the carrying idler

arrangement, and in the case of the upper strand, the parameter is dependent in addition on the geometry of the bulk material. in the case of three piece carrying idler arrangements with carrying idlers of equal length in the upper strand, and with filling ratios 𝜑 in the range from 0,7 to 1,1 we have

𝑐_{𝑅𝑠𝑡𝑜} = 0,4 for 𝑙𝑎𝑚𝑏𝑑𝑎 = 30° 𝑐_{𝑅𝑠𝑡𝑜} = 0,5 for 𝑙𝑎𝑚𝑏𝑑𝑎 = 45°

In the case of two-piece troughed carrying idlers in the (unloaded) lower strand, we have:

𝑐_{𝑅𝑠𝑡𝑜} = 𝑐𝑜𝑠𝛿

e) Frictional resistance between the material conveyed and the lateral chutes outside the feeder points: 2 2 2 2 m Sch Sch Rank Sch I g l F c v b





      (3.27)

In the above relationship, 𝑐𝑅𝑎𝑛𝑘 = 𝑡𝑎𝑛2(45° − 𝛽𝑑𝑦𝑛

2 ) ; the friction coefficient 𝜇2 is, as a

general rule, situated in the range of approximately 0,5 to 0,7.

f) Resistances of devices for the delivery of goods along the conveying path

In certain special cases where a side delivery of goods takes place along the conveying path, e.g. by means of stripping or scraping devices, the forces which are generated thereby must be taken into account in the form of additional special resistances.

3.5.8 Total friction in steady state

The total friction in steady state amounts now to:

H st s

F

 

C F



F



F





' ' ' ' 2 R B L L s F     C L f g _m  m m cos



_  H g m F (3.28)

In case of a uniformly loaded belt conveyor installation with filling ratios 𝜑 in the range from 0,7 to 1,1. In case of angles of inclination of the installation 𝛿 ≤ 15°, we can enter 𝑐𝑜𝑠𝛿 = 1 in the above equation.

(22)

21

3.6 Comparison between ISO 5048 and DIN 22101

General ISO DIN

Main FH FH Idler bearings and seals Belt advancement resistance due to belt flexing Secondary FN FN

Inertial Inertial and friction of material - loading area FbA Inertia resistance Fauf Skirtplates acceleration area

Side walls of the chute – loading area Ff Frictional resistance at feeder point Fschb

Pulley bearing Pulley bearing resistance

Ft Pulley bearing resistance

Ftd

Wrap resistance Wrapping of the belt on pulleys F1 - Belt resistance to bending FGb Special Fs FS FS1

Idler tilting Tilt of the idler Fe Camber resistance FRst Skirtplates general Friction against chute flaps or skirtplates – full length of belt Fgl Friction material with lateral chutes outside the feeder points Fsch FS2 Resistance due to belt cleaner?

Belt and pulley cleaners

(23)

22 Friction against chute flaps or skirtplates - locally - - Reversion of the return strand of the belt - - Discharge ploughs Discharge ploughs Fa - Trippers - Resistances of devices for the delivery of goods along the conveying path - Gradient Gradient Fst Gradient Fst

(24)

23

3.7 CEMA

The next section will cover the content of Conveyor Equipment Manufacturers Association, Belt conveyors for Bulk Materials, fifth edition, 2002 (CEMA: Belt Conveyors for Bulk Materials, 2002) and all the mentioned formulas originate from this document.

For the CEMA standard (CEMA: Belt Conveyors for Bulk Materials, 2002) 𝑇𝑒 is the final

summation of the belt tension forces produced. These are produced as the following 1. The gravitational load to lift or lower the material being transported.

2. The frictional resistance of the conveyor components, drive, and all accessories while operating at design capacity

3. The frictional resistance of the material as it is being conveyed

4. The force required to accelerate the material continuously as it is fed onto the conveyor by a chute or a feeder

The basic formula for calculating the effective tension 𝑇𝑒 is:



0.0015







e t x y b b m y p am ac

T LK K K W  W W  LK H T T T (3.29)

The following symbols will be used to assist in the identification and evaluation of the individual forces that cumulatively contribute to 𝑇𝑒 and that are therefore components of the total

propelling belt tension required at the drive pulley:

𝐴_𝑖= Belt tension, or force, required to overcome frictional resistance and rotate idlers, lbs 𝐶_𝑙 = Friction modification factor for regenerative conveyor

𝐻 = Vertical distance that material is lifted or lowered, ft 𝐾_𝑡 = Ambient temperature correction factor

𝐾_𝑥 = Factor used to calculate the frictional resistance of the idlers and the siding resistance between the belt and the idler rolls, lbs per ft

𝐾_𝑦= Carrying run factor used to calculate the combination of the resistance of the belt and the resistance of the load to flexure as the belt and load move over the idlers. For return run constant 0.015 in place if 𝐾𝑦. See 𝑇𝑦𝑟.

𝐿 = Length of conveyor, ft

𝑄 = Tons per hou conveyed, tph, short tons of 2,000 lbs 𝑇𝑎𝑐= Total of the tensions from convetor accessories, lbs:

(25)

24 𝑇_𝑎𝑚= Tension resulting from the force to accelerate the material continuously as it is fed onto

the belts, lbs.

𝑇𝑏 = Tension resulting from the force needed to lift or the lower the belt, lbs

𝑇_𝑏 = ∓𝐻 × 𝑊_𝑏 (3.31)

𝑇_𝑏𝑐 = Tension resulting from belt pull required for belt-cleaning devices such as belt scrapers, lbs

𝑇_𝑒 = Effective belt tension at drive, lbs

𝑇_𝑚= Tension resulting from the force need to lift or lower the conveyed material, lbs

𝑇_𝑚 = ∓𝐻 × 𝑊_𝑚 (3.32)

𝑇𝑝 = Tension resulting from resistance of belt to flexure around pulleys and the resistance of

pulleys to rotation on their bearings, total for all pulleys, lbs 𝑇_𝑝𝑙 = Tension resulting from the frictional resistance of plows, lbs

𝑇𝑠𝑏 = Tension resulting from the force to overcome skirtboard friction, lbs

𝑇_𝑡𝑓= Tension resulting from the additional frictional resistance of the pulleys and the flexure of the belt over units such as trippers, lbs

𝑇_𝑥= Tension resulting from the frictional resistance of the carrying and return idlers, lbs

𝑇_𝑥 = 𝐿 × 𝐾_𝑥× 𝐾_𝑡 (3.33)

𝑇𝑦𝑏 = Total of the tensions resulting from the resistance of the belt to flexure as it rides over

beoth the carrying and return idlers, lbs

𝑇𝑦𝑏 = 𝑇𝑦𝑐+ 𝑇𝑦𝑟 (3.34)

𝑇_𝑦𝑐= Tension resulting from the resistance of the belt to flexure as it rides over the carrying idlers, lbs

yc y b t

T  L K W K (3.35)

𝑇𝑦𝑚= Tension resulting from the resistance of the material to flexure as it rides with the belt

over the carrying idlers, lbs

ym y m

(26)

25 𝑇𝑦𝑟= Tension resulting from the resistance of the belt to flexure as it rides over the return

idlers, lbs

0.015

yr b t

T  L W K (3.37)

𝑉 = Design belt speed, fpm

𝑇𝑏 = Weight of belt in pounds per foot of belt length. When the exact weight of the belt is not

known, use average estimated belt weight. 𝑊_𝑚 = Weight of material, lbs per foot of belt length:

2, 000 33,33 60 m Q Q W V V      (3.38)

Three multiplying factors 𝐾𝑡, 𝐾𝑥 and 𝐾𝑦, are used in calculations of three of the components of

the effective belt tensions, 𝑇𝑒.

3.7.1 𝑲𝒕− Ambient Temperature Correction Factor

Idler rotational resistance and the flexing resistance of the belt increase in cold weather operation. In extremely cold weather the proper lubricant for idlers must be used to prevent excessive resistance to idler rotation. 𝐾𝑡 is a multiplying factor that will increase the calculated

value of belt tensions to allow for the increased resistances that can be expected due to low temperatures.

3.7.2 𝑲𝒙− Idler Friction factor

The frictional resistance of idler rolls to rotation and sliding resistance between the belt and the idler rolls can be calculated by using the multiplying factor 𝐾𝑥 . 𝐾𝑥 is a force in lbs/ft of conveyor

length to rotate the idler rolls, carrying and return, and to cover the sliding resistance of the belt on the idler rolls. The 𝐾𝑥 value required to rotate the idlers is calculated using the following

equation.





0.00068 i x b m i A K W W S    (3.39)

In lbs per foot of belt length

𝐴_𝑖=1.5 for 6” diameter idlers rolls, CEMA C5, D6 𝐴_𝑖=1.8 for 5” diameter idlers rolls, CEMA B5, C5, D6 𝐴_𝑖=2.3 for 4” diameter idlers rolls, CEMA B4, C4 𝐴𝑖=2.4 for 7” diameter idlers rolls, CEMA E7

𝐴𝑖=2.8 for 6” diameter idlers rolls, CEMA E6

(27)

26

Table 3: Estimated average belt weight, multiple- and reduced-ply belts, lbs/ft

3.7.3 𝑲𝒚− Factor for Calculating the Force of Belt and Load Flexure over the Idlers

Both the resistance of the belt to flexure as it moves over idlers and the resistance of the load flexure as it rides the belt over the idlers develop belt-tension forces. 𝐾𝑦 is a multiplying factor

(28)

27

(29)

28

Table 5: and B values for equation Ky

After estimating the average belt conveyor tension and selecting an idlers spacing, refer to table 3 to obtain values for 𝐴 and 𝐵 for use in the following equation:





4 2

10

y m b

K



W



W

 

A



 

B

 (3.40)

Using this equation, an initial value for 𝐾𝑦 can be determined and an initial average belt tension

can be subsequently calculated. The comparison of this calculated average belt tension with the original tentative value will determine the need to select another assumed belt tension.

Recalculate 𝐾𝑦 and calculate a second value for the average belt tension. The process should be

repeated until there is a reasonable agreement between the estimated and final calculated average belt tensions.

There are no tabulated 𝐾𝑦 values or mathematical equations to determine a 𝐾𝑦 for conveyors

having an average belt tension exceeding 16,000 lbs. A reasonably accurate value that can be used for calculations is 𝐾𝑦 equals 0.016. lt is suggested that this value for 𝐾𝑦 be considered a

(30)

29

Table 6: Corrected factor Ky values when other than tabular carrying idler spacings are used

(31)

30

3.7.4 Compilation of Components of 𝑻𝒆

The procedure for calculating the belt tension components are in the following order: 1. 𝑇𝑥

2. 𝑇𝑦𝑏 3. 𝑇𝑦𝑚 4. 𝑇𝑚 5. 𝑇𝑝

1. 𝑇𝑥 – From the frictional resistance of the carrying and return idlers, lbs

x x t

T

 

L K



K

(3.41)

2. 𝑇𝑦𝑏 – Summation of belt flexure of the belt flexure as it moves over the carrying and the

return idlers

𝑇_𝑦𝑐− For carrying idlers: 𝑇𝑦𝑐= 𝐿 × 𝐾𝑦× 𝑊𝑏× 𝐾𝑡

𝑇𝑦𝑟− For carrying idlers: 𝑇𝑡𝑦= 𝐿 × 0.015 × 𝑤𝑏× 𝐾𝑡

𝑇_𝑦𝑏= 𝑇𝑦𝑐+ 𝑇𝑦𝑟 0.015 yb y b t b t T  L K W K  L w K



0.015



yb b t y T  L W K K  (3.42)

3. 𝑇𝑦𝑚 – From resistance of the material to flexure as it rids the belt over the idlers, lbs

ym y m

T  L K W (3.43)

4. 𝑇𝑚− From force needed to lift or lower the load

m m

T



m

H W



(3.44)

5. 𝑇𝑝− From resistance of belt to flexure around pulleys and the resistance of pullets to

rotate on their bearings, lbs. This is the total of the belt tension required to rotate each of the pulleys on the conveyor.

Pulley friction arises from two sources. One source is the resistance of the belt to flexure over the pulleys, which is a function of the pulley diameter and the belt stiffness. The belt stiffness depends upon the ambient temperature and the belt construction. The other source of pulley friction is the resistance of the pulley to rotate, which is a function of pillow block bearing friction, lubricant, and seal friction. The pillow block bearing friction depends upon the load on the bearings, but the lubricant and seal frictions generally are independent of load.

(32)

31

Table 7: Belt tension to rotate pulleys

6. 𝑇𝑎𝑚− From force to accelerate the material continuously as it is fed onto the belt When

material is discharged from chutes or feeders to a belt conveyor, it cannot be assumed that the material is moving in the direction of belt travel, at belt speed, although this may be the case in some instances. Normally, the material loaded onto the belt is traveling at a speed considerably lower than belt speed. The direction of material flow may not be fully in the direction of belt travel. Therefore, the material must be

accelerated to the speed of the belt in the direction of belt travel, and this acceleration requires additional effective tension.

The belt tension can be derived from the equation: 𝐹 = 𝑚 ∙ 𝑎 = 𝑀𝑉𝑐

Note that the term 𝑉𝑐 is the velocity change and 𝑀 is the mass of material accelerated

per second

The weight of the material 𝑀 is can be calculated as follows:

2000 3600 Q W   (3.45) lbs/sec 𝑄 = tph 𝑔 = 32.2 ft/sec2

2000

3600 32.2

W

Q

M

g







(3.46) 𝑉_𝑐 = Velocity change, fps =𝑉−𝑉0 60

𝑉 = Design belt speed, fpm

𝑉₀= Initial velocity of material as it is fed onto belt, fpm





4 0 0 2000 2.8755 10 3600 32.2 60 am V V Q T         Q VV  (3.47)

(33)

32 8. 𝑇𝑡𝑓− From trippers and stackers

9. 𝑇𝑝𝑙− From frictional resistance of plows

10. 𝑇𝑏𝑐− From belt-cleaning devices

11. 𝑇𝑠𝑏− From skirtboard friction

Table 8: Skirtboard friction factor, Cs

𝑇_𝑠𝑏= 𝑇 + 2𝐿_𝑏× 3 = 𝐶_𝑠𝐿_𝑏ℎ_𝑠2_{+ 2𝐿}

𝑏× 3 =

𝑇_𝑠𝑏= 𝐿_𝑏(𝐶_𝑠ℎ_𝑠2_{+ 6)}

3.7.5 Summary of Components

1. Idler friction 𝑇𝑥

2. Belt flexure, carrying idlers 𝑇𝑦𝑐

3. Belt flexure, return idlers 𝑇𝑦𝑟

4. Material flexure 𝑇𝑦𝑚 5. Lift or lower 𝑇𝑚 6. Pulley resistance 𝑇𝑝 7. Accelerated material 𝑇𝑎𝑚 8. Accessories 𝑇𝑎𝑐 e x yc yr ym m p am ac T T T T T T T T T (3.48)

(34)

33

3.8 Friction coefficient and different standards

In this section comprises of the different approaches the different standards have towards the friction coefficient 𝑓. In different standards this friction coefficient is actually a composition of different frictions. This coefficient is important in calculating the total energy needed. It will become clear that this constant is dependent different variables and is not constant. This section 3.8 will consider multiple source on how to estimate the right friction coefficient 𝑓.

3.8.1 ISO 5048

For ISO 𝑓 comprises of the rolling resistance of the carrying idlers and belt advancement resistance, and has been calculated at 0,02 as a basic value for a moving belt, based on the result of a broad series of tests.

For fixed and properly aligned installations, with easily rolling idlers and also for low internal friction materials, this value can be lower by about 20%, dropping to 0,016, whereas for poorly aligned belt conveyors with badly rolling idlers and high internal friction materials, values exceeding the basic value about 50%, ranging up to 0,03, may result.

The value of 0,02 is strictly only applicable under the following conditions:

- Used around 70% to 110% of its nominal capacity This could impact passive speed control as it is possible

- Conveying products with an average internal friction coefficient - Equipped with three-roll carrying idlers for the upper side of the belt; - With a 30° side through angel

- Operating at belt speeds of about 𝟓 m/s

This could impact both forms of speed control as the speed could change considerably from this value.

- Operating temperatures of about 20 °𝐶

- With 108mm to 159mm diameter carrying idlers with labyrinth grease seals, together with idler spacing of 1, to 1,5, for the upper strand (or carrying side) of the belt and of around 3m for the lower strand (or return side) of the belt.

The value of 𝑓 may, for instance, increase above the basic value 0,02 up to 0,03 in the following cases:

a. For handled materials with a high internal friction coefficient b. For throughing angles of over 30°

c. For belt speeds over 5m/s

This again could impact both forms of speed control as the speed could change

considerably from this value. It is not clear however how much the basic value needs to be increased as a function the speed.

d. For carrying idler diameters lower than those mentioned above e. For ambient temperatures of less than 20°

(35)

34 f. For a decrease in belt tension

g. For flexible carcass belts and those with thick and flexible covers h. For poorly aligned installations

i. When operating conditions are dusty and wet and/or sticky

j. For idler spacing or markedly more than 1,5m for the upper strand (or carrying side) of the belt and of around 3m for the lower strand (or return side) of the belt.

The artificial friction coefficient 𝑓, may decrease under the basic value of 0,02 if the influences listed above in a) to j) are reversed.

If the installation is running under no-load conditions, the value of 𝑓 can be either lower or higher than under full-load operating conditions, depending on the mass of the moving parts and on the tension of the conveyor belt.

Downhill conveyors which require to be braked by brakemotor, shall as a safety measure, be calculated with a value lower by 40% than used for the calculation of driven belt conveyors: the result of this basic value of 𝑓 = 0.012.

3.8.2 DIN 22101

The main value of 𝑓 will be situated in the range from 0,012 to 0,035 depending on the operating and installation conditions. No truly reliable values for 𝑓 are available for unloaded belt conveyor installations; these values can be either lesser or greater than those applying to the nominal loading range.

The next able features values of the coefficient 𝑓 for installations with filling ratios 𝝋 in the range from 0,7 to 1,1 in function of the operating conditions and of the design characteristics.

Horizontal installations, also installations conveying uphill and down gentle inclines (with electric motor drives)

- Favourable operating conditions, e.g. good belt alignment, easy running carrying idlers and material conveyed at low speeds, with low internal friction

0,017

- Installations constructed and operated in normal (standard) manner 0,020 - Adverse operating conditions, e.g. dust laden atmosphere, low

temperatures, material conveyed exhibiting a very high internal friction, overloading, high speeds

0,023 to 0,027

- Extremely low temperatures, but otherwise normally operated and conventionally constructed installations

Up to 0,035

Installations conveying downhill at a steed incline 1_{) (drives operating as} dynamos

0,012 to 0,016 1_{) In the case of installations conveying downhill at a steep incline – drives operating as} dynamos – the adoption of a somewhat lower value for 𝑓 will result in a higher degree of

(36)

35 safety in the design; in other cases – where the drives operate as motors – an enhanced

safety of design is attained by adopting a higher value for 𝑓.

Again these filling ratios could affect passive speed or any case in which the influx of material is lower that the nominal value while the belt speeds runs at its nominal value.

3.8.3 Impact of DIN 22101

The paper “Impact of the german standard DIN 22101 on Belt conveyor design” by Alles and Keller (Alles & Keller, The Impact of the German Standard DIN 22101 on Belt Conveyor Design, 2004) provides a table to determine the friction factor based on classification of the belt.

Figure 2:Determination of friction factor f

3.8.4 Contitech Model of the fiction coefficient

Alles (Alles, Conveyor Belt System Design, 1994) states that the friction coefficient provides by the DIN22101 standard is not constant with varying load or speed, and is therefore not a reliable source for calculating the required power for operating a belt conveyor. Contitech provided the data in order to establish a resistance model dependent on both belt load and belt speed. Belt load

Alles has provided a graph for the corrector factor based on the relative belt load. This correction factor should then be applied to the friction coefficient provided by DIN22101. The relative belt load is determined as the ratio between the weight of the belt [kg/m] and that of the belt and rollers of the carrying belt side combined:





' ' ' 1 10 L B RO m belt load ratio

m m

 

 (3.49)

So if the belt load is ten times the weight of the belt and rollers of the carrying belt side, the belt load ratio is 1.0. For most belts this ratio is much lower. From the graph below one part of the correction factor can be determined.

(37)

36

Figure 3: Resistance coefficient Figure 4: Guiding values for f+

However it must be noted that this graph is empirically determined. Belt speed

Along with the belt load, the belt speed has also an influence on the coefficient of friction. Alles provides a Guiding values for the friction factor based on the speed, presented in Figure 4.

3.8.5 Calculation of Artificial friction coefficient f, and a comparison between ISO and CEMA – Ish G. Mulani

In this paper of Ish G. Mulani (Mulani) compares the friction coefficients of ISO and CEMA. Mulani researches on which factors the coefficient of friction is dependent on. Among many variables an increment/decrement for belt speed is also considered. It is stated that:

The conveying friction coefficient value 𝑓 = 0.02 can be decreased for conveyor speed lesser than

5.0 𝑚/𝑠. These reduction factors with respect to speed are beased on a ContiTech germany publication (slightly changed here for safety in design)

10% reduction on 0.02 for 2.75 mps < v < 3.75 m/s. 15% reduction on 0.02 for 2.0 mps < v < 2.75 m/s. 17.5 reduction on 0.02 for v <= 2.0 m/s.

(38)

37

3.9 Calculating the coefficient of friction from measurements based on DIN22101

So far only this paper has only provided a theoretical model to calculate the coefficient of friction for the ISO or DIN standard. But as stated before the calculation based on standards can differ from the actual values of the coefficient of friction. Usually the coefficient based on the calculations are higher than one that is derived from experimental work.

This section will provide a brief calculation method to experimentally determine the coefficient of friction. It will also provide an example where this method is used.

Calculation method

This method is based on the DIN22101 and the paper by G. Lodewijks, D. L. Schott, Y. Pang (Lodewijks, Schott, & Pang, Energy Savings At Belt Conveyors By Speed Control). The standard uses formula (3.28), where it leaves out the special resistance:





' ' ' ' cos

2

R B L L F CfLg_

_m



_{m m}





_

_m

gH

The factors that are based on the belt load are those that are not can be split up. As such the formula can be rewritten as a function of the belt load 𝑚𝐿′:





' ' ' ' 1 2

cos

2

R B L L

F



CfLg



_

_m



_m



_





CfLg





gH

_m



_{C C m}



(3.50)

It is assumed that the fictive coefficient of friction is also independent of the reduced belt load. From equation (3.50) an expression can be derived for the coefficient of friction:









' ' ' ' cos

2

e mech freq motor L R B L P gH v f CLg

m

m m

  



    (3.51)

This equation can be used to determine the fictive coefficient of friction from experimental results.

Physical measurements

This section will be entirely based on the work done in the paper (Lodewijks, Schott, & Pang, Energy Savings At Belt Conveyors By Speed Control). A belt conveyor with a length of 660m is used to investigate the coefficient of friction and its dependency on the belt load. Data on the specifics of the belt conveyor are given below:

L [m] H [m] v [m/s] Qm [MTPH] m’B [kg/m] m’R [kg/m] C (DIN)

ηmech ηfreq ηmotor 660 16.1 4.5 6,000 48.6 55.8 1.17 0.960 0.961 0.984

Table 9: Belt conveyor data

The electrical power consumption of the belt conveyor was measured with a digital clam meter around the power supply lines of the belt conveyor’s frequency converter. This frequency converter was used to control the belt speed.

(39)

38 The load on the belt was controlled by a speed-controlled apron feeder underneath the hopper. Three different bulk solid materials were transported with the belt conveyor at different speeds and capacities (Daijie He, 2016).

The following results are based on the equation of (3.51).

Figure 5: Derived friction coefficient

The average value for the derived friction coefficient 𝑓 is about 0,022 (Lodewijks, Schott, & Pang, Energy Savings At Belt Conveyors By Speed Control).

The paper states that: “The variance which arises due to measurements with different dry bulk materials and operating conditions is larger than the variation of f itself (see Figure 5). Therefore the assumption that the DIN f factor is independent of the reduced material load of the belt, and thus the capacity of the conveyor is justified.” At 0 MTPH one would expect a converging coefficient of friction. However this is not the case due to the electrical efficiency at different belt speeds, as the power was determined electronically and not mechanically.

(40)

39

3.10 Single resistance method

So far the energy calculation methods discussed are all based on a single coefficient of friction for all masses. The primary resistances can actually be split up into different resistances. This is called the single resistance method. The DIN/ISO method of a single coefficient of friction is however a more convenient way to quickly estimate the total friction of a belt conveyor. In general the primary resistances can be subdivided as follows:

- Running resistance of Idlers U’ - Flexure resistances U’’

o Indentation resistance of the belt 𝑈𝐸′′

o Belt flexure resistance 𝑈𝐺′′

o Transport load flexure resistance 𝑈𝐿′′

There have been multiple researchers trying to formulate a general calculation model based on the single resistance method. Hilterman (Hilterman, 2008) has made an overview of these studies, considering their analytical relationships and general application. This overview is shown below:

Figure 6: Resistance based models, overview by Hilterman, 2005

Hilterman (Hilterman, 2008) states in agreement with (Spaans, 1991) that “There is a lack of complete fundamental methods for determining the total primary motional resistance of troughed belt conveyors [..] Only DIN22101 and the Contitech models can be used to calculate the motional resistance of generic belt conveyors.”

Even though these models lack completeness or generic application, this chapter will still take a look at single resistance based models. This will be done based on the paper of Lauhoff (Lauhoff, 2005).