Designing Energy Saving Test Rig for Belt Conveyors; Ontwerpen van een testopstelling voor transportbanden

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 61 pages and 3 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: 2016.TEL.8062

Title:

Designing Energy Saving Test Rig

for Belt Conveyors

Author:

F.J. Reijnders

Title (in Dutch) Ontwerpen van een testopstelling voor transportbanden

Assignment: Design Assignment

Confidential: No

Initiator (TU Delft): Dr.ir. Y. Pang Supervisor(s): Dr.ir. Y. Pang

Daijie He

TUDelft

Delft University of Tecfinoiogy Department of Marine and Transport Technology

Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax -1-31 (0)15-2781397 www.mtt.tudel1t.nl Student: Supervisor(s): Specialization: Creditpoints (EC): Fedde Reijnders Yusong Pang, Daijie He TEL 15 Assignment type: Report number: Confidential: Design 2016.TEL.8062 No

Subject: Designing Energy Saving Test Rig for Belt Conveyors

Belt conveyors have been proven to be a cost-effective way to continuously transport large amount of bulk materials. They are used in many industries and implemented all over the wodd. Previous research has shown that the power consumption of a belt conveyor is in fact speed dependent. This opens up the possibilities of energy savings by regulating the operation speed of belt conveyors under the variance of material feeding rate. This is known as the speed control of belt conveyor systems. In practice, the adjustment and regulation of the belt speed encounter many challenges before a proper control system can be implemented. Therefore, test facilities are needed to verify the algorithms of speed control and the performance of relatively controlled belt conveyor systems.

Together with the section Transport Engineering and Logistics (TEL) of Delft University ofTechnology (TUD), Taiyuan University ofTechnology (TUT) has acquired a joint project in China and will establish a laboratory to validate the energy savings of speed controlled belt conveyor systems. This research assignment will focus on the design of the test rig of the laboratory, which should cover the following:

• To survey the principles and approaches of belt conveyor speed control;

• To clarify the functions of the test rig based on defined speed control scenarios;

• To formulate the design scope and design requirements regarding specified test facilities; • To propose and compare different design concepts and solutions;

• To make detailed design with respect to mechanical (and control in necessary) aspects. The final research 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 repod: should comply with the guidelines of the section. Details can be found on the website.

Considering the facts that this assignment is under the cooperation, the involvement and the supervision of two universities and further the design outputs will be potentially applied to establish the hereinabove mentioned laboratory, the agreement among the two universities and the student to fully share the copyright of the final research report and the intellectual properties of the design works will apply on the purposes of future scientific research.

List of Symbols

Symbol Description Unit

𝛼 Angle of pulley belt wrap rad

𝛽 Surcharge angle ∘

𝛿 Inclination angle ∘

𝜂 Transmission efficiency

-𝜆 Trough angle of the conveyor belt ∘

𝜌 Bulk material density kg/m

𝜑 Filling ratio

-𝐴 , Partial cross section above water fill m

𝐴 , Partial cross section below water fill m

𝐴 Cross section of fill m

𝐵 Belt width mm

𝑏 Usable belt width mm

𝑏 Part of belt lying on a side idler on 2- or 3-roller idler sets mm

𝑐 ̈ Transition length coefficient

-𝑐 Pulley diameter coefficient

-𝑑 Belt tension member thickness mm

𝐷 Idler diameter mm

𝐷 Pulley diameter mm

𝑓 Hypothetical friction coefficient

-𝐹 Primary resistance N

𝐹 Secondary resistance N

𝐹 Special resistance N

𝐹 Gradient resistance N

𝐹 Belt tension N

𝐹 Belt tension of the belt running onto a pulley N

𝐹 Belt tension of the belt running off a pulley N

𝐹 Pulley peripheral force N

𝐹 Total motion resistance N

𝑔 Gravitational acceleration = 9.81 m/s

ℎ Height difference m

ℎ Distance from the belt edge to the deepest level of the trough mm v

Symbol Description Unit ℎ Distance from the belt edge to the pulley surface level mm

ℎ Relative belt sag

-ℎ Pulley lift mm

𝑖 Transmission gear ratio

-𝐼 Mass flow kg/s

𝐼 Volume flow m /s

𝑘 Nominal belt breaking strength N/mm

𝐿 Belt length axis to axis m

𝑙 ̈ Transition length m

𝑙 Length of central roller in a 3-roller idler set mm

𝑙 Idler pitch m

𝑚 Belt line load kg/m

𝑚 Material line load kg/m

𝑚 Roller line load kg/m

𝑛 Idler rotation speed rpm

𝑃 Required motor power kW

𝑃 Nominal motor power kW

𝑃 Drive pulley power kW

𝑄 Conveyor capacity MTPH

List of Figures

1.1 Maximizing the filling ratio𝜑 by using speed control. . . 2

2.1 Horizontal belt conveyor side view. . . 5

2.2 The horizontal belt conveyor already present in the laboratory. . . 6

2.3 Horizontal belt conveyor front view. . . 6

2.4 Potential cross section of fill for 3-roller idler set. Source:DIN22101. . . 7

2.5 Different loading principles . . . 8

2.6 Resistance contribution. Source: DIN22101. . . 9

2.7 Load position options. . . 9

2.8 Load set-up. . . 10

2.9 Different actuation principles. . . 10

2.10 Linear actuator example. Source:www.progressiveautomations.com . . . 11

2.11 Screw jack actuator example. Source:www.wholesalesupplier-db.net. . . 11

2.12 Two concepts for different loading devices. . . 11

2.13 Load roller suspension. . . 12

2.14 Linear guide model example. Source: www.skf.com. . . 12

2.15 Linear guides in LD. . . 12

2.16 Load cell example. Source: www.directindustry.com . . . 13

2.17 Load cell connection.. . . 13

2.18 Horizontal belt conveyor with two different loading devices. . . 13

3.1 Calculating the transition length. Source: DIN22101 . . . 18

3.2 Exploded view of the frame. . . 23

3.3 Screw take-up device. . . 23

3.4 Impressions of the inclined belt conveyor. . . 24

3.5 Impressions of the system of belt conveyors. . . 25

4.1 Discretized load profile distributed along the belt sections . . . 27

4.2 Load condition at𝑡 = 𝑥. . . 28

4.3 Load condition at𝑡 = 𝑥 + 1 . . . 28

4.4 Discretized load profile distributed along the belt sections . . . 29

List of Tables

2.2 Mass and load calculations. . . 7

3.1 Inclined belt conveyor requirements. . . 15

3.2 Standard belt speeds in m/s. Source: Dunlop-Enerka. . . 15

3.3 Standard roller lengths in mm. Source: Dunlop-Enerka. . . 16

3.4 Inclined belt conveyor mass flow. . . 16

3.5 Belt properties. Source: http://www.huaxiarubber.cn/. . . 17

3.6 Transition length. . . 18

3.7 Standard pulley diameters in mm. Source: DIN22101 . . . 19

3.8 Standard idler diameters in mm. Source: Dunlop-Enerka. . . 19

3.9 Estimation of idler mass in kg. Source: Dunlop Enerka. . . 20

3.10 Friction coefficient𝑓. Source: DIN22101. . . 20

3.11 Inclined belt conveyor mass flow. . . 21

3.12 Transmission efficiency. Source: Dunlop-Enerka. . . 22

Contents

List of Figures vii

List of Tables vii

1 Introduction 1

1.1 General introduction . . . 1

1.2 Speed control for belt conveyor systems . . . 1

1.3 Former research . . . 2

1.4 Goal of the assignment. . . 3

1.5 Design scope. . . 3

1.6 Report structure . . . 4

2 Loading device 5 2.1 Design preparations . . . 5

2.1.1 Belt conveyor specifications . . . 5

2.1.2 Design requirements and assumptions . . . 6

2.1.3 Design calculations. . . 6 2.2 Mechanical design . . . 8 2.2.1 Loading principle. . . 8 2.2.2 Loading position . . . 8 2.2.3 Actuation principle . . . 10 2.2.4 Actuator selection . . . 10 2.2.5 Structural design . . . 11

2.2.6 Load roller suspension. . . 12

2.2.7 Guiding selection. . . 12

2.2.8 Load cell and actuator connection. . . 12

2.2.9 Final design. . . 13

3 Inclined belt conveyor 15 3.1 Design preparations . . . 15

3.1.1 Design requirements and assumptions . . . 15

3.1.2 Design calculations. . . 16 3.2 Mechanical design . . . 22 3.2.1 Frame. . . 22 3.2.2 Take-up device . . . 22 3.2.3 Final design. . . 22 4 Control system 27 5 Conclusion and recommendations 31 5.1 Conclusions. . . 31

5.2 Recommendations. . . 32

A LD-A 33

B LD-B 43

C Inclined belt conveyor 49

References 61

1

Introduction

This report will start with a general introduction to the assignment in Section1.1. In Section1.2the principles and approaches of belt conveyor speed control will be examined and the general idea behind speed control for belt conveyor systems will be covered. Then some former research on the topic will be discussed in Section1.3. After that, in Section1.4, the goal of this project will be discussed. The design scope of this project will be described in Section 1.5. Finally, the structure of the rest of this report is presented in Section1.6.

1.1.

General introduction

Belt conveyors have proven to be a relatively simple and very cost-effective way of transporting bulk materials over relatively short distances. For this reason, belt conveyor systems are widely used in bulk handling environments, such as mines and dry bulk terminals. The use of belt conveyors in bulk handling is so extended that the energy consumption of belt conveyor systems is estimated to account for 50-70% of the total dry bulk handling energy consumption [5]. A reduction in energy usage of these systems can therefore have a significant impact on operating costs of dry bulk handling.

For maintenance considerations, belt conveyor systems are often designed as systems with belt con-veyors that are all the same size, and thus have all the same nominal capacity. This nominal capacity corresponds with the maximum capacity that is needed for peak operation on the most heavily used sections of the system. Consequently, most of the conveyor belts in the system are over-designed and their capacity is not fully utilized. Also, belt conveyors usually run at their nominal belt speed. This implicates that during non-peak hours belt conveyor capacity is also not fully utilized.

Former research has indicated that the design calculations in the DIN22101 standard for belt conveyors suggest that speed reduction will lead to a reduced energy consumption. This finding creates a pos-sibility to save significant amounts of energy by controlling the belt speed of individual belt conveyors, and thus making sure that the belts are completely filled. This is called speed control for belt conveyor systems, and shows great potential to reduce dry bulk operating costs and make the industry more durable.

1.2.

Speed control for belt conveyor systems

To prevent spillage or bulk material build-up, belt conveyors are designed to deal with peak flows in dry bulk terminals or mines. These belt conveyors are generally running at a fixed speed, which is usually their nominal belt speed. Because peak flows only rarely occur, most of the times the belts are only partly filled, i.e. the filling ratio𝜑 < 1. This means that belt capacity is wasted, and also energy that is needed to keep these belts running at maximum speed is wasted. By lowering the belt speed during non-peak operation, it is possible to maximize the filling ratio. By using variable-speed control on a belt conveyor system, it is possible to convert a varying material load at maximum speed, into a maximum material load at varying speed. This can be seen in Figure1.1.

Two different types of speed control can be distinguished: passive speed control and active speed 1

vmax, ϕ’ v’, ϕmax

(a) Cross sectional view

(b) Side view

Figure 1.1: Maximizing the filling ratio by using speed control.

control. With passive speed control the belt speed is fixed prior to operation and is based on the expected material flow. In practice, this still means that the utilization of the belt capacity is sub-optimal, because the belt speed is not adjusted for relatively small material flow variations, and is therefore never completely filled. With active speed control, the belt speed is adjusted continuously by a control system to match the belt capacity with the actual material flow, and thereby maximizing the filling ratio of the belt. These systems involve complex closed loop control systems and are therefore more expensive compared to passive speed control systems.

When designing a belt conveyor, the DIN22101 standard is used to predict the motion resistances to calculate the required motor power. According to DIN22101, a lower belt speed reduces the motion resistance and will therefore require less motor power, thus saving power consumption. On the other hand, a lower belt speed maximizes the load on the belt and will thus in turn the load that needs to be transported. These two effects are working against each other. However, it is expected that the reduction of motion resistances is larger than the increase in material load, so per balance a lower belt speed will lead to energy savings.

1.3.

Former research

The idea that energy savings could be realized by controlling the speed of belt conveyor systems has already been around for several decades. Already in 1998 Siemens reported about a project in the Nochten Opencast mine in Germany in 1997 [7], where one of the main focusses was to achieve en-ergy savings by using variable-speed belt conveyors. They justly noted that most of the workings in the mine were greatly oversized, and decided to apply converter-controlled drives to the new belt conveyor system. Although they made several different improvements to the conveyor system, including auto-mated stacking and reclaiming, a new process control system, and a new maintenance management sytems, in the end they stated that electrical power consumption savings between 15% and 38% are considered possible for converter-controlled belt plants compared to conventional plants.

In 2000, ABB Process Industries described how they for the first time implemented grid frequency con-verters to create a variable-speed drive belt conveyor system [1]. A laser scanner was used to monitor the cross section of the load on the belt. This value was then used to calculate all the reference values for downstream conveyors. The main advantages of the use of frequency converters that were found include an optimal loading of the belts by controlling the belt speed, a reduction of gear and belt wear, elimination of belt slip at the driving drums, even torque distribution on drive drums, and control of speed differences between motors on one drive drum.

Not everyone has been enthusiastic about the possibilities of speed control for belt conveyor systems. Lauhoff [6], for example, shows some criticism toward this theory. Lauhoff states that the fictitious

1.4.Goal of the assignment 3

motion resistance is more dependent of the filling ratio𝜙 than on the belt speed 𝑣. Especially the in-dentation resistance of the belt turns out to have a major share in the motion resistances, and rises progressively with the load on the idlers. According to Lauhoff, this cancels out the potential benefits of lower belt speeds, since it is demonstrated that speed control for the purpose of energy savings is inappropriate at traditional filling levels in the range between 60% and 100%.

As part of his MSc Thesis in 2008, Hiltermann performed speed control measurements at dry bulk terminal EMO in Rotterdam, the Netherlands [4]. He states that predictions of energy savings are inac-curate due to a lack of extensive generic motional resistance models, and that only the physical power consumption can reasonably determine the possible speed control savings. He concludes that there still is a lack of knowledge on speed control, and that development of more accurate generic models is needed to make better predictions of speed control energy savings. He also recommends additional measurements on different belt conveyors to gain insight into the possibilities of applying speed control. In 2011, Hiltermann continues his research by presenting a methodology to predict the speed control energy savings by using calibrated calculations based on DIN22101 [5]. He chooses to use discrete speed control. Discrete speed control is able to avoid belt speeds at which detrimental vibrations occur, and it reduces stressful continuous acceleration and deceleration of the belt. His calculations suggest that speed control reduces the overall power consumption by 23%, and he concludes that speed control promises considerable energy savings in annual power consumption of belt conveyors.

1.4.

Goal of the assignment

Despite the fact that already quite some research has been done on speed control for belt conveyors, it has never been empirically proven that it is possible to save energy with speed control. To make the next step in this improvement on belt conveyor systems, testing facilities are required to verify the theories and models that have been developed in former research.

In pursuing this goal, the section of Transport Engineering and Logistics (TEL) from Delft University of Technology (DUT) and the Taiyuan University of Technology (TYUT) have started a joint project to establish a new laboratory to enable research on energy savings for belt conveyor systems by means of speed control. As part of this larger joint project, this assignment will focus on designing a new test rig for the laboratory. The goals of the assignment are as follows:

• To survey the principles and approaches of belt conveyor speed control; • To clarify the functions of the test rig based on defined speed control scenarios;

• To formulate the design scope and design requirements regarding specified test facilities; • To propose and compare different design concepts and solutions;

• To make detailed design with respect to mechanical, electronic and electrical/control aspects.

1.5.

Design scope

This project aims to design new testing facilities to make it possible to verify the methods and theories on belt conveyor speed control that have emerged from former research, as mentioned above. One of the key steps to be taken in designing new testing facilities for belt conveyor speed control, is to find a way to simulate a variable load on the conveyor belt so the power consumption can be measured for different loading cases. This design project will focus on that aspect.

Currently the laboratory at TYUT already possesses a simple belt conveyor for testing purposes. The specifications of this conveyor will be listed in section 2.1.1. Because of the presence of this belt conveyor it was decided to split the design part of this project into two separate steps. The first step will be to design some sort of modular loading device that can be attached to the already existing belt conveyor. This loading device will be controlled by a control system, and will enable variable load simulation on the belt to measure power consumption of different loading scenarios. The second step will be to design a second belt conveyor to take part in the ‘system of belt conveyors’. With a cascade of belt conveyors and loading devices the concept of individual belt speed control can be tested. First, this report will focus on the mechanical design of the loading device and the new belt conveyor. For this, the DIN22101 belt conveyor designing standard [2] will mainly be used as a guideline. The

Dunlop-Enerka Conveyor Belt Technique Design and Calculation manual [3] will be used for additional reference. Detailed construction drawings will be presented. Second, a basis for a possible control system will be proposed to show how the designed equipment, i.e. the loading device and the combined belt conveyors, can be used in practice.

1.6.

Report structure

Chapter2is about the main part of this project. A modular loading device will be designed, and two different concepts for a loading device are proposed. In chapter 3 a completely new inclined belt conveyor is designed to take part in the system of belt conveyors, needed for speed control energy saving research. In chapter4a possible control system for the system of belt conveyors is discussed. Finally, in Chapter5the assignment goals will be evaluated and some recommendations are given.

2

Loading device

The first and main part of this project is about designing a loading device to simulate a load on a belt conveyor test rig. Since the laboratory already features a belt conveyor test setup, the loading device will be designed as a separate module that can be attached to the existing belt conveyor.

2.1.

Design preparations

Before we can start the design of the loading device, the belt conveyor specifications, design require-ments, design assumptions and the design calculations will be discussed.

2.1.1.

Belt conveyor specifications

Table 2.1: Horizontal belt conveyor specifications.

Name Value Unit

Conveyor length 4.5 m Conveyor speed 2.0 m/s Trough angle 20 ∘ Belt type ST800 Belt width 800 mm Belt thickness 13 mm Motor voltage 220 V Motor power 2.2 kW Gear ratio 20 Pulley dimensions 500x950 mm Idler dimensions 108x950 mm

In order to successfully design a loading device for the existing belt conveyor, the conveyor specifications are needed. The current belt conveyor is a 4.5 meter long horizontal test setup. The conveyor has a 3-roller carrying idler configuration, and the belt has a trough angle of approximately 20 degrees. One of the two pulleys is driven by a 2.2 kW motor, which allows for an estimated maximum belt speed of 2.0 m/s. The other pulley is equipped with a fixed take-up system. Two long bolts, one on each side of the pulley, are installed to tension the belt. The belt itself is a steel-cord belt with rubber cover layers of type ST800, which means that the nominal belt breaking strength 𝑘 is 800 N/mm. The belt has a width of 800 mm and a thickness of 13 mm. 5200 4500 950 500 108 440 1125 1125 1125 scale units author benaming date

format drawing no. remarks

A2

TU Delft

mm

<<names & student numbers>> <<group>> 1:1

Flat Belt Conveyor

18-7-2016 <<remarks>> <<drawing no.>> grams 0 weight group

SolidWorks Student Edition. For Academic Use Only.

Figure 2.1: Horizontal belt conveyor side view.

The conveyor belt testing setup is has so far mainly be used for optical detection of longitudinal tear of the belt. Tears have been applied manually to the rubber belt. Therefore the belt is heavily damaged and it is running off-center due to unbalanced stress distributions. The actual belt conveyor is shown in figure2.2. A construction drawing of the conveyor can be seen in figure2.1. The most important conveyor specifications are listed in table2.1.

Figure 2.2: The horizontal belt conveyor already present in the laboratory.

2.1.2.

Design requirements and assumptions

As mentioned before the loading device is going to be used to simulate a variable load on the con-veyor belt to measure different power consumptions. One of the main requirements is therefore that the loading device is capable of simulating a load that corresponds as closely as possible to a real-time situation of bulk material transportation. Also, since the loading device is to be designed as an attach-able module to the existing belt conveyor, it must fit the conveyor frame. The loading device shape and location have still to be decided, but it is safe to say that the device’s width will have to correspond with the conveyor frame width. A section cut of the horizontal belt conveyor is shown in figure2.3.

Design assumptions 5200 4500 950 500 108 440 1125 1125 1125 1080 1280 950 280 440 scale units author benaming date

format drawing no. remarks

A2

TU

Delft

Industrial Design Engineering

<<names & student numbers>> <<group>>

1:1

Flat Belt Conveyor

5-8-2016 <<remarks>> <<drawing no.>> grams 0 weight group

SOLIDWORKS Student Edition.

For Academic Use Only.

Figure 2.3: Horizontal belt conveyor front view. Before the calculations can be started on the

de-sign, a few assumptions have to be made about the theoretical conveying properties. Most of the research being done in the laboratory is focused on coal mining operations. The loading device will therefore be designed for coal bulk material. Two parameters are of importance for the de-sign calculations: the coal bulk density𝜌 and the dynamic angle of repose, or surcharge angle𝛽. From literature we can find that the average coal bulk density can be assumed to be𝜌 = 850 kg/m and the surcharge angle𝛽 = 25∘_.

2.1.3.

Design calculations

The design calculations for the loading device are used to determine the load that is required for re-alistic load simulation. The calculations will be based on the DIN22101 standard for belt con-veyor design [2].

2.1.Design preparations 7

Theoretical mass and load

The loading device will be able to apply a load to the belt conveyor, varying between 0 N and a certain maximum load. This maximum load corresponds with the maximum amount of bulk solid material that can theoretically be present on the belt conveyor. In order to determine this maximum load, the theoretical maximum volume and mass flow will be calculated. According to DIN22101 the maximum

DIN 22101:2011-12

12

a Non-steady operation (start-up, braking) eff Effective

erf Required

i Running index for belt strand sections

j Running index for belt deflection points (at pulleys) inst Installed m Centre idler max Maximum min Minimum o Upper strand s Side idler th Theoretical u Bottom strand zul Allowable

* Index for identifying operating conditions

5 Volume flow and mass flow

The maximum volume flow and mass flow of a belt conveyor is determined by the potential cross section of fill, which is dependent on the dynamic angle of slope of the material conveyed and on the feeding conditions, among other factors.

To calculate the maximum volume and mass flow a simple equivalent geometrical cross section needs to be found. This theoretical cross section Ath is calculated from the shape of the conveyor belt on the carrying idlers

and from the shape of the slope formed by the material conveyed. Figure 1 shows this cross section for a belt supported by a 3 roller idler set, which is commonly used.

Figure 1 — Theoretical cross section of fill in the case of horizontal conveyance and a 3 roller idler set

Figure 2.4: Potential cross section of fill for 3-roller idler set. Source:DIN22101.

volume flow can be determined by the potential cross section of fill𝐴 . For a belt conveyor with a 3-roller idler set,𝐴 is the sum of the two partial cross sections𝐴 , and𝐴 , , as shown in figure2.4.

The cross section of fill and the partial cross sections can be calculated with

𝐴 = 𝐴 , + 𝐴 , (2.1) 𝐴 _, = [𝑙 + (𝑏 − 𝑙 ) ⋅ cos 𝜆] ⋅tan 𝛽 4 (2.2) 𝐴 , = [𝑙 + 𝑏 − 𝑙 2 ⋅ cos 𝜆] ⋅ 𝑏 − 𝑙 2 ⋅ sin 𝜆 (2.3)

In these equations𝑙 is the length of the central roller of the 3-roller idler set, 𝑏 is the usable belt width and𝜆 is the trough angle. For belts smaller than 2 000 mm the usable belt width 𝑏 can be calculated with

𝑏 = 0.9 ⋅ 𝐵 − 50𝑚𝑚 (2.4)

Table 2.2: Mass and load calculations.

Name Value Unit

Coal density 850 kg/m

Coal surcharge angle 25 ∘

Central roller length 280 mm

Usable belt width 670 mm

Partial cross section , 0.049 m

Partial cross section , 0.031 m

Cross section 0.080 m

Material line load ’ 67.7 kg/m

Total coal mass 304.5 kg

Total coal load 2.99 kN

For a belt width of 800 mm this means the usable belt width will be 670 mm. When we fill in these equa-tions we find that for this belt conveyor𝐴 is 0.08 m . By multiplication of this cross sectional area with the coal density, we can find the material line load𝑚’ . In our case the material line load is 68 kg/m. With a to-tal conveyor length of 4.5 meter, this means that the maximum theoretical mass on our belt conveyor is ap-proximately 300 kilograms, which corresponds with a maximum theoretical load of 3.0 kN. We should bear in mind that in reality this is of course an evenly dis-tributed load, but we will come back to that later. All calculated values are listed in table2.2.

2.2.

Mechanical design

The most important parameters are now known, so the loading device can be designed. First the loading principle will be chosen, and with that it can also be decided where the loading device is going to be placed on the belt conveyor. After that, the actuation principle and the corresponding actuator can be selected. Finally the device’s structure can be designed and other components can be selected.

Pulley pendulum Pulley break

Load roller

Figure 2.5: Different loading principles

2.2.1.

Loading principle

Now we know the theoretical maximum load that can be exerted to the belt, it needs to be decided in what way the 3kN load is going to be simulated. Three different options are illustrated in figure2.5.

1) Press the belt with a roller

Pressing the belt with a load roller is probably the simplest way to exert a load to the belt. A load roller cannot simulate the bulk material inertia, but by pressing the belt we can increase the belt tension (in case of a fixed take-up), and thus increase the motion resistance.

2) Press the pulley with a break

It is also possible to slow down one of the pulleys with some sort of brake. By breaking down the rotational speed of one of the pulleys the conveyor motor experiences it as if there was a load on the conveyor belt. This way a load simulation could be performed. However, it is difficult to determine what breaking force corresponds with a certain bulk material load on the belt.

3) Slow down the pulley with a double pendulum

Finally, one of the pulleys could be slowed down by use of some sort of double pendulum. By pushing the weights of the pendulum outwards, the rotational resistance on the motor increases, thus simulat-ing a load on the conveyor. Again, with this technique it is difficult to determine what position of the pendulum weights corresponds with what particular conveyor load.

Since we are trying to make the load simulation as realistic as possible, option 1 was chosen for our loading device. A load rollers will be used to press the conveyor belt with a force of approximately 3kN to simulate the presence of bulk material.

Justification

At this point the question arises whether it is correct to translate the theoretical distributed load of the bulk material to one or more loading points. To answer this we will take a closer look to what DIN22101 says about the motion resistance of belt conveyors. According to DIN22101 the portions of motion resistance are distributed as in figure2.6. In case of a horizontal belt conveyor, around 60% of the motion resistance comes from the indentation rolling resistance. This resistance arises when the rubber conveyor belt indents on the idlers under the weight of the bulk material. Using load rollers to simulate the bulk material also causes this indentation rolling resistance. Therefore it is believed that this way of load simulation is realistic enough for our goal.

2.2.2.

Loading position

Next, it needs to be decided where this load roller is going to press the belt. Six different options will be evaluated, which are: carry side between idlers, carry side on idlers, return side between idlers, return side on idlers, and on the pulley. All cases are illustrated in figure2.7. Again, we are searching for the

2.2.Mechanical design 9

DIN 22101:2011-12

48

Here the values ca and cb vary depending on the measured function of the relevant indentation rolling

resistance.

The indentation rolling resistance FE,3 acting on each idler of a 3-roller idler set is determined by integrating

the locally varying value of F'E along the contact line bR under consideration of the local line load. For the total

indentation rolling resistance acting on the idler set the following numeric equation applies [20]:

b b s R, s n, b s R, a m R, m R, m n, a E,3 2 ₁ 2 c c b F c b c b b F c F _       ⋅ ⋅ + ⋅ ⋅ + ⋅         ⋅ = (A.2)

In order to demonstrate the importance of the indentation rolling resistance for a safe dimensioning while at the same time minimizing investments and operating costs, Figure A.2 can be used as it shows examples of the distribution of parts of motion resistances for long belt conveyors:

 Left column: belt conveyor installation with horizontal layout

 Right column: belt conveyor installation with approx. 5 % inclination

It should be borne in mind that, especially as regards the interpretation of the left column, in the future an increasing use of energy-optimized belts will accordingly reduce the portion of the indentation rolling resistance in the total resistance to motion. Furthermore, the information shown in Figure A.2 should not be taken as basis for the design of conveyors, in view of the dependence of the single parts of the resistance to motion on the operational and design-related parameters of the conveyor.

Key

Gradient resistances Special resistances Secondary resistances Flexing resistance of the belt Flexing resistance of the bulk material Idler running resistance

Indentation rolling resistance

Figure A.2 — Comparison of the portions of resistance of two long belt conveyor installations of identical design, with different inclinations

Figure 2.6: Resistance contribution. Source: DIN22101.

Carry Side

Return Side

Drive Pulley/ Tail Pulley

Between Idlers On Idler Loading Device

most realistic way to simulate the load. When the conveyor belt would be loaded with bulk material, belt sag is created between the idlers. We consider this as realistic belt behavior. Therefore the options where the load roller presses on the idlers, and the option where the load roller presses on the pulley are ruled out. That leaves us with two possible options: between the carry idlers or between the return idlers. Between the carry idlers would of course be the most optimal solution, since in real cases that is where the bulk material will be. However, as stated before in section2.1.1the belt is already heavily damaged and is running off-center over the 3-roller idler sets. Also, the fact that the belt has a trough on the carry side makes it far more complex to design a loading device, because the load rollers would have to be in a trough shape. For these two reasons it was chosen to place the loading device between the return idlers. For a more realistic solution, two loading devices will be installed between the three present return idlers. Both loading devices will be capable of exerting a load of approximately 1.5 kN. This is shown graphically in figure2.8. Since some spare return idlers (𝜙108*950 mm) were already present in the laboratory, it was decided to use those as our load rollers.

1.5kN 1.5kN

Figure 2.8: Load set-up.

2.2.3.

Actuation principle

To move the load roller up and down, two different actuation principles are being investigated: a dual spindle concept, and a single linear actuation concept. Both concepts are shown in figure2.9. The dual spindle concept can be designed very compact, which is an advantage because there is limited space between the carry and return side of the conveyor belt. However, two individual spindles need either two individual motors, which requires a complex control system to keep them synchronized, or a mechanical coupling. Also, it makes it far more difficult to create a force feedback for the control system. The single linear actuation concept is a little less compact, but only requires one motor and is therefore cheaper and less complex. This makes the single linear actuation concept the preferred way of driving the load roller.

Figure 2.9: Different actuation principles.

2.2.4.

Actuator selection

The actuator needed for the loading device is going to be a linear actuator. As calculated in section 2.1.3, the total force required is at least 3 kN, but as discussed in section2.2.2this will be divided over two loading devices, so each actuator needs to be able to exert a dynamic force of at least 1.5 kN. Also, there is limited space available, so the linear actuator needs to be as compact as possible. The height between the upper and lower idler beams is 440 mm, so the frame size is limited to this dimension. However, at the center of the belt some extra space is available for the actuator, as long as we stay

2.2.Mechanical design 11

clear of the carry side of the belt itself.

Figure 2.10: Linear actuator example. Source:www.progressiveautomations.com

Figure 2.11: Screw jack actuator example. Source:www.wholesalesupplier-db.net.

When the belt is pressed with a load, it will of course stretch, which means the linear actuator will have to reach further to exert the desired load. However, since the conveyor is equipped with a steel-cord belt the stretch is expected to be minimal. Therefore it is assumed that an actuator stroke of around 100 mm will suffice. The most simple linear actuator that meets these requirements is a DC electric motor driven linear actuator, as shown in Figure2.10. A model with a maximum dynamic load of 2 kN and a stroke of 100 mm was selected.

At this point it was decided that also one concept should be designed with more power than the calcu-lated 1.5 kN per loading device. It was desired to have a loading device that could exert a maximum load of 3.0 kN per loading device, which would add up to a total of 6 kN on the belt conveyor. For this concept a screw jack in combination with an AC electric motor was chosen. As can be seen in Figure 2.11. In the figure the screw jack is pointed upwards, but this concept can be turned around so that the screw jack will press down.

This means that two concepts for a loading device will be further developed. One with a screw jack driven by an AC electrical motor for higher loads, from now on referred to as LD-A. And one with a build-in DC motor linear actuator, from now on referred to as LD-B.

2.2.5.

Structural design

Because two different concepts will be elaborated, two different structures have to be designed. How-ever, both concepts will be quite similar, only with minor differences, of which the most significant will be the height difference. In both cases the structure is going to be a bridge-like frame with the same width as the conveyor frame. The structure can be installed to the return idler support beams of the conveyor. For LD-A the frame will be lower because the actuator will be placed on top of the structure. The actuator in LD-B will hang underneath the structure, so the frame will be higher. The two different concepts are illustrated in figure2.12.

Load cell

Linear actuator Linear guiding

Electric motor Screw jack

(a) Conceptual design for LD-A

Load cell

Linear actuator Linear guiding

Electric motor Screw jack

(b) Conceptual design for LD-B

Both concepts will consist of the same basic components, i.e.:

• Roller cage: the roller cage carries the load roller and is placed inside the frame.

• Frame: the frame embodies the complete loading device and is placed on the return idler beams of the belt conveyor.

• Linear actuator: the linear actuator will press the load roller on the conveyor belt.

• Linear guiding: the linear guiding will keep the load roller in place and ensures a straight motion. • Load cell: the load cell provides the control system with force feedback.

2.2.6.

Load roller suspension

For installation purposes the load roller suspension will be designed as to enable easy attachment and detachment of the roller. The beams can be shoved inside each other and pinned with a normal bolt and nut or a clevis pin, as can be seen in figure2.13.

Figure 2.13: Load roller suspension.

2.2.7.

Guiding selection

To keep the load roller steady and the loading motion linear, guiding is needed. A simple and solid solution for this is a linear guiding rail that can easily be bought. In our case a linear guiding rail, as can be seen in figure2.14, was selected. Four guiding rails, two on each side, will support the linear motion. See figure2.15.

Figure 2.14: Linear guide model example. Source:

www.skf.com. Figure 2.15: Linear guides in LD.

2.2.8.

Load cell and actuator connection

The load cell needs to be as compact as possible and it needs to be able to handle and measure tension and compression. This is because in some cases we want to lift the load roller off the belt, so the load cell will be carrying the weight of the roller. For our loading devices a threaded button type load cell was chosen, as shown in figure2.16.

2.2.Mechanical design 13

Figure 2.16: Load cell example. Source:

www.directindustry.com Figure 2.17: Load cell connection.

The advantage of this threaded type of load cell is that it can easily be installed. On the bottom it can be connected to the roller cage with a nut on the inside of the cage beam. On the top we can install a clevis bracket. This clevis bracket provides a simple but effective way to connect the load cell to the actuator screw jack. This can be seen in figure2.17. For LD-A we will use a 10 kN load cell, and for LD-B a 3 kN load cell will be installed.

2.2.9.

Final design

The final designs of LD-A and LD-B can be seen in appendicesAandBrespectively. An impression of the final result when both concepts are installed on the belt conveyor can be seen in figure2.18.

3

Inclined belt conveyor

To be able to test the possible energy savings by means of speed control for belt conveyors, a system of belt conveyors is needed. A second belt conveyor is to be designed to work in series with the belt conveyor that is already present in the laboratory. This chapter covers the design of this newly designed belt conveyor.

3.1.

Design preparations

First the design requirements, design assumptions and the design calculations will be discussed.

3.1.1.

Design requirements and assumptions

Table 3.1: Inclined belt conveyor requirements.

Name Value Unit

Belt length 4.5 m

Belt speed 4.19 m/s

Belt width 800 mm

Trough angle 30 ∘

Inclination angle 15 ∘

The new belt conveyor should have realistic dimensions, and therefore have a minimal theoretical capacity of 850 MTPH (metric tons per hour), which is a common capacity in mining operations. The belt width should be the same as the existing conveyor and with a trough, so the width will be 𝐵 = 800 mm and the trough angle will be 𝜆 = 30∘_{. Also the}

belt length should be around the same length as the existing conveyor. The belt length𝐿 is set to be 4.5 meter. A special request from the laboratory was that the new belt conveyor would have an inclination of 10∘ ≤ 𝛿 ≤ 20∘, and a higher

belt speed than the existing conveyor. The inclination is set at𝛿 = 15∘. The belt speed is chosen from the standard conveyor belt speeds by Dunlop (see Table3.2) and is set to be𝑣 = 4.19 m/s, which is also a common belt speed in coal mining operations. Also, since this belt conveyor is going to be a

Table 3.2: Standard belt speeds in m/s. Source: Dunlop-Enerka.

11.1

Design

Main Data Values

Speed V

Standard Values

Recommended Velocity (m/s)

After establishing the duty of the operation and the type of belt conveyor, the main data may be determined.

Belt Speed v (m/s)

Belt Width B (m) or (mm)

Carrying Idler Arrangement

Cross Sectional area of Load Stream A (m2₎

Conveyor Capacity Q (t/h)

The belt or Conveying Speed V (m/s) must be appropriate for the material composition and operation conditions.

High Speed - Narrower belt widths

Lower belt tension Greater wear and tear

Low Speed - Greater belt widths

Higher belt tension Less wear and tear

The most economical installation is that having the highest belt speed consis-tent with the type of material and operating conditions.

Speeds V (m/s)

0.42 - 0.52 - 0.66 - 0.84 - 1.05 - 1.31 - 1.68 2.09 - 2.62 - 3.35 - 4.19 - 5.20 - 6.60 - 8.40

Duty v (m/s)

Unit Loads, Assembly Lines

_≤

Mobile Conveyors 0.52 - 1.68

Very dusty loads such as Flour, Cement

_≤

Ash and Refuse

≤

Grain, Crushed Limestone 1.05 - 2.09

Gravel, Sand Readymix Ores, Bituminous Coal, Sinter

Storage and transhipment, Power Stations 1.31 - 3.35

Long distance conveying, overburden 2.62 - 6.60

Brown coal

Thrower belts

_≥

Steep gradient belts 0.84 - 2.62

Type CHEVRON and HIGH CHEVRON

part of the belt conveyor system for speed control, it needs loading devices to simulate a fluctuating load on the belt. The loading devices are already designed (see Chapter2), so the dimensions will be chosen in such a way that the loading devices also fit this inclined belt conveyor. This means that the return idler support beams will be 1,100 mm apart, and that the normal distance between the carry and return beams will be at least 350 mm.

Design assumptions

For the design of the inclined belt conveyor the same assumptions will be made as for the loading device. Again we assume the conveyor system will be used for bulk coal, so the material density used

16 3.Inclined belt conveyor

for calculations is𝜌 = 850 kg/m and the surcharge angle is 𝛽 = 25∘_{. All values are listed in Table3.1.}

3.1.2.

Design calculations

The calculations for designing the belt conveyor will be based on the DIN22101 [2] standard and the Conveyor Belt Technique Design and Calculation guide by Dunlop-Enerka [3].

Theoretical volume and mass flow

The theoretical mass flow calculations are almost identical to the ones done before in Section2.1.3. Again, equations (2.1), (2.2), (2.3) and (2.4) are used. The central roller length is selected from Table 3.3from Dunlop-Enerka, and is 315 mm. The usable belt width stays the same at 670 mm, but the

Table 3.3: Standard roller lengths in mm. Source: Dunlop-Enerka.

11.3 Idler rotation should not be greater than approximately 650 r.p.m.

The length of the middle idler roll determines the cross sectional area of the load and thus the conveying capacity.

The gap d between 2 adjacent rolls should not be greater than 10mm, with belt widths B > 2000mm d = 15mm refer to DIN22107, carrying idler arrange-ments.

Values for Idler Spacing

Idler Rotation

Standard

Idler Diameter (mm)

Carrying Side

l_o= 0.5 à 1.0 m Small installation or high impact

l_o= app. 1.2 m Normal installation

l_o= 1.4 à 4.0 m High tension installation

Return Side l_{u= (2-3)*lo} Maximum approx 6 m n_{R= 60 * v (r.p.m. )}  DR D_R ( m ) Roll diameter v ( m/s ) Belt speed Carrying Idlers 51 63.5 88.9 108 133 159 193.7 219 Impact Idlers 156 180 215 250 290 Return Run Support Discs 120 138 150 180 215 250 290

Standard length L (mm) of rollers

Belt Troughing Type

Width Flat 2 roll 3 roll Deeptrough Garland

B (mm) 300 380 200 - - -400 500 250 160 - -500 600 315 200 - -600 700 340 250 - -650 750 380 250 - -800 950 465 315 200 165 1000 1150 600 380 250 205 1200 1400 700 465 315 250 1400 1600 800 530 380 290 1600 1800 900 600 465 340 1800 2000 1000 670 530 380 2000 2200 1100 750 600 420 2200 2500 1250 800 640 460 l B l d d l d l l _d

different trough angle of 30∘gives a different result for the cross section. The cross section for this belt configuration is 0.087 m . By multiplication with the belt speed we find that the theoretical volume flow 𝐼 is 0.36 m /s. The volume flow can be multiplied with the coal density to calculate the theoretical mass flow𝐼 , which is around 300 kg/s. This means our theoretical capacity is approximately 1,100 MTPH, which is well above the minimal requirement of 850 MTHP. The material line load𝑚’ is 73.7 kg/m. All calculated values are listed in Table3.4

Table 3.4: Inclined belt conveyor mass flow.

Name Value Unit

Coal density 850 kg/m

Coal surcharge angle 25 ∘

Central roller length 315 mm

Usable belt width 670 mm

Partial cross section , 0.045 m

Partial cross section , 0.042 m

Cross section 0.087 m

Volume flow 0.36 m /s

Mass flow 309 kg/s

3.1.Design preparations 17

Belt selection

The belt for the inclined conveyor is going to be provided by Huaxia Rubber1_{, and it is going to be}

a steel cord belt. Since the conveyor is only for testing purposes, a simple ST630 belt will be strong enough, i.e. a conveyor belt with a belt breaking strength of 630 N/mm. As can be seen in Table3.5, the belt has a cord diameter of 3 mm, top and bottom covers of 5 mm thickness, and a specific mass of 18 kg/m , which means that the belt line load𝑚’ for a 800 mm wide belt is 14.4 kg/m.

Table 3.5: Belt properties. Source: http://www.huaxiarubber.cn/.

Transition length

The transition length 𝑙 _{̈ ,} depends on the type of belt being used, and is calculated according to DIN22101. For 3-roller idler sets the minimum transition length𝑙 _{̈ ,} is calculated with

𝑙 _{̈ ,} = 𝑐 ̈ ⋅ ℎ (3.1)

, where the transition length coefficient 𝑐 ̈ = 14 for steel cord belts. ℎ is the distance from the belt

edge to the pulley surface level, and can be calculated with

ℎ = ℎ − ℎ (3.2)

ℎ is the distance from the belt edge to the deepest level of the trough, andℎ is the pulley lift, as can be seen in Figure3.1. ℎ can be calculated with

ℎ = 𝑏 ⋅ sin 𝜆 (3.3)

𝑏 = 𝐵 − 𝑙

2 (3.4)

Pulley lift can be useful to decrease the minimum transition length. Since we have limited space for our conveyor belt we use maximum pulley lift. According to DIN22101 the standard value for maximum pulley lift isℎ , = 1/3 ⋅ ℎ . In our caseℎ = 0.12 m, soℎ , = 0.04 m andℎ = 0.08 m. This

gives𝑙 _{̈ ,} = 1.13 m.𝑙 ̈ is set at 1.25 m, and the idler pitch at 1.0 m, so the total belt length becomes

2 ⋅ 1.25 + 2 ⋅ 1 = 4.5 m.

DIN 22101:2011-12

33

Figure 7 — Transition length without pulley elevation (above) and with pulley elevation (below)

With the tension difference ∆k between the belt edge and the central zone of the belt according to Figure 8,

the width-related belt tension is calculated as follows:

Central zone of the belt:

(63)

with

(64)

Belt edge

(65)

To avoid compression of the conveyor belt, the following applies:

k

≥ 0

(66)

The length of the belt edge l

is the decisive parameter for the magnitude of the occurring belt tensions (see

Figure 7).

(67)

k

B

b

k

k

=

−

⋅

∆

2

B

l

b

=

−

k

k

k

=

+

∆

(

sin

λ

cos

λ

)

2

2

+

+

⋅

−

⋅

⋅

⋅

+

⋅

=

l

h

b

b

h

b

l

Figure 3.1: Calculating the transition length. Source: DIN22101

Table 3.6: Transition length.

Name Value Unit

Pulley lift 0.04 m

Distance belt edge-trough level 0.12 m

Distance belt edge-pulley level 0.08 m

Transition coefficient ̈ 14

-Minimal transition length ̈ , 1.13 m

3.1.Design preparations 19

Pulley diameter

The minimum pulley diameter 𝐷 , also depends on the belt type and is calculated according to

DIN22101 with

𝐷 , = 𝑐 ⋅ 𝑑

= 145 ⋅ 3 = 435 mm

(3.5)

The pulley diameter coefficient𝑐 for steel cord belts is selected from Table3.7from DIN22101. Table 3.7: Standard pulley diameters in mm. Source: DIN22101

DIN 22101:2011-12

42

Table 13 — Parameter cTr for the determination of the minimum pulley diameter Dtr Material of longitudinal tension member cTr B (cotton) P (polyamide) E (polyester) St (steel cords) 80 90 108 145

Each diameter determined for Group A pulleys in accordance with the above description shall be rounded up to the next standard value indicated in Table 14. The minimum diameters of Group B and C pulleys shall be chosen in relation to the pulley load factor from Table 14 that is relevant for Group A.

Table 14 — Minimum diameter of Group A, B and C pulleys in relation to the utilization of the maximum pulley load factor in the steady operating condition

Minimum diameter in mm (without lagging)

D_Tr

as per Pulley load factor N ⋅8 ⋅100%

max k k _a Equation (80) A B C A B C A B C A B C 100 125 100 100 125 160 125 100 125 100 100 160 200 160 125 160 125 100 125 100 100 100 200 250 200 160 200 160 125 160 125 100 125 125 100 250 315 250 200 250 200 160 200 160 125 160 160 125 315 400 315 250 315 250 200 250 200 160 200 200 160 400 500 400 315 400 315 250 315 250 200 250 250 200 500 630 500 400 500 400 315 400 315 250 315 315 250 630 800 630 500 630 500 400 500 400 315 400 400 315 800 1 000 800 630 800 630 500 630 500 400 500 500 400 1 000 1 250 1 000 800 1 000 800 630 800 630 500 630 630 500 1 250 1 400 1 250 1 000 1 250 1 000 800 1 000 800 630 800 800 630 1 400 1 600 1 400 1 000 1 400 1 250 1 000 1 250 1 000 800 1 000 1 000 800 1 600 1 800 1 600 1 250 1 600 1 250 1 000 1 250 1 000 800 1 000 1 000 800 1 800 2 000 1 800 1 250 1 800 1 400 1 250 1 600 1 250 1 000 1 250 1 250 1 000 2 000 2 200 2 000 1 400 2 000 1 600 1 250 1 600 1 250 1 000 1 250 1 250 1 000

a _{kmax is the mean width-related tension at the point of maximum belt tension in the zone of Group A pulleys in the steady operating}

condition.

12 Design and layout of transition curves and vertical curve radii

12.1 General

Clause 9 deals with the calculation of belt tensions distributed across the belt width proceeding from the specified design of transition curves or convex curves for the subsequent design and layout of the conveyor belt. This clause deals with the calculation of suitable transitions and vertical curves suitable for a specified belt type.

over 100 % over 60 % to 100 % over 30 % up to 60 % up to 30 % Pulley group Pulley group Pulley group Pulley group The thickness of the tension member𝑑 was already mentioned in Section3.1.2and is 3 mm for the selected belt. This results in a minimum pulley diameter𝐷 _, = 435 mm, so theoretically a pulley diameter of 500 mm would suffice. However, to create enough space between the carry and return side of the conveyor for our loading devices to fit, a standard pulley diameter of𝐷 = 630 mm was chosen.

Idler diameter

The minimum idler diameter𝐷 , is mostly dependent on the belt speed. According to Dunlop-Enerka

the maximum idler rotation𝑛 , should not exceed 650 rpm. Therefore we can calculate the minimum

idler diameter with

𝐷 _, = 60 ⋅ 𝑣

𝜋 ⋅ 𝑛 (3.6)

This gives𝐷 _, = 123.1 mm. From Table3.8from Dunlop-Enerka we can select the idler diameter of 𝐷 = 133 mm.

Table 3.8: Standard idler diameters in mm. Source: Dunlop-Enerka.

11.3

Design

Idler rotation should not be greater than approximately 650 r.p.m.

The length of the middle idler roll determines the cross sectional area of the load and thus the conveying capacity.

The gap d between 2 adjacent rolls should not be greater than 10mm, with belt widths B > 2000mm d = 15mm refer to DIN22107, carrying idler arrange-ments.

Values for Idler Spacing

Idler Rotation

Standard

Idler Diameter (mm)

Carrying Side

l_o= 0.5 à 1.0 m Small installation or high impact

l_o= app. 1.2 m Normal installation

l_o= 1.4 à 4.0 m High tension installation

Return Side l_{u= (2-3)*lo} Maximum approx 6 m n_{R= 60 * v (r.p.m. )}  DR DR ( m ) Roll diameter v ( m/s ) Belt speed Carrying Idlers 51 63.5 88.9 108 133 159 193.7 219 Impact Idlers 156 180 215 250 290 Return Run Support Discs 120 138 150 180 215 250 290

Standard length L (mm) of rollers

Belt Troughing Type

Width Flat 2 roll 3 roll Deeptrough Garland

B (mm) 300 380 200 - - -400 500 250 160 - -500 600 315 200 - -600 700 340 250 - -650 750 380 250 - -800 950 465 315 200 165 1000 1150 600 380 250 205 1200 1400 700 465 315 250 1400 1600 800 530 380 290 1600 1800 900 600 465 340 1800 2000 1000 670 530 380 2000 2200 1100 750 600 420 2200 2500 1250 800 640 460 l B l d _d l d l l d

From Table3.9from Dunlop-Enerka we can find an indication of the idler mass. For a belt width of 800 mm we find that the mass for a flat (or return) idler is 13.3 kg, and for a 3-roller idler set 15.6 kg. Since the idler pitch𝑙 is 1.0 m, the combined roller line load 𝑚’ = 28.9 kg/m.

Belt sag criterion

With the belt sag criterion we can calculate the minimum belt tension to avoid too much relative belt sag, which can cause unnecessary energy losses. According to DIN22101 the maximum relative belt sagℎ should not exceed 1.0%. The minimum belt tension𝐹_, can be calculated with

𝐹, =

𝑔 ⋅ (𝑚 + 𝑚 ) ⋅ 𝑙

8 ⋅ ℎ (3.7)

When we fill in equation (3.7) we find𝐹, = 10.8 kN. We will use this value later on for the belt tension

20 3.Inclined belt conveyor

Table 3.9: Estimation of idler mass in kg. Source: Dunlop Enerka.

B.1

Mass m’_R(kg)

Idler Rollers Carrying and Return

Belt width B Idler Rollers Idler Roller Diameter

(mm) 51 63.5 88.9 108 133 159 193.7 219.1 300 flat 1.6 2.2 3.2 2 part 2.3 3.4 4.1 flat 2.0 2.7 3.9 5.6 400 2 part 2.6 3.7 4.7 6.6 3 part 2.9 4.4 5.4 7.3 flat 2.2 3.2 4.5 6.6 500 2 part 2.8 4.1 5.5 7.8 3 part 3.2 4.6 6.1 8.4 flat 4.0 5.5 8.0 10.8 650 2 part 4.7 6.3 9.0 12.1 3 part 5.4 7.0 9.8 13.1 800 flat 4.7 6.7 9.8 13.3 2 part 5.6 7.4 10.6 14.2 3 part 6.5 8.3 11.6 15.6 5 part 9.0 12.4 16.3 1000 flat 9.4 11.7 15.9 21.9 2 part 11.3 13.2 17.8 24.7 3 part 13.0 13.6 18.2 26.3 5 part 13.8 14.2 18.9 28.0 1200 flat 14.2 19.3 26.1 2 part 15.0 20.5 28.0 3 part 16.3 22.3 24.5 5 part 17.2 21.7 31.9 1400 flat 21.8 29.3 2 part 23.3 31.6 3 part 25.0 35.5 5 part 24.3 35.0 1600 flat 25.1 33.4 2 part 26.5 35.0 3 part 28.0 38.7 5 part 28.5 39.3 1800 flat 27.6 37.8 2 part 29.1 39.5 3 part 30.7 42.4 5 part 31.5 42.5 2000 flat 30.2 40.2 69.1 2 part 31.8 43.3 76.4 3 part 33.3 47.0 80.1 5 part 33.8 46.5 89.5 2200 flat 46.5 77.8 88.0 2 part 49.0 82.6 97.1 3 part 50.1 93.2 111.0 5 part 51.0 95.5 111.8

Carrying Side Rollers

Flat Belt

Return Idlers

Box Section Belt

2 Part Idlers

3 Part Idlers

5 Part Garland Idlers

Motion resistance

The motion resistance𝐹 is needed to determine the required power at the drive pulley 𝑃 , and thus the required motor power𝑃 . According to DIN22101 [2]𝐹 can be calculated with the following formula:

𝐹 = 𝐹 + 𝐹 + 𝐹 + 𝐹 (3.8)

It consists of four separate resistances; the primary resistance𝐹 , the secondary resistance 𝐹 , the gradient resistance𝐹 and the special resistance 𝐹 .

Primary resistance

The primary resistance𝐹 can be calculated with

𝐹 = 𝐿 ⋅ 𝑓 ⋅ 𝑔 ⋅ [𝑚 + (2 ⋅ 𝑚 + 𝑚 ) ⋅ cos 𝛿] (3.9) The hypothetical friction coefficient for the approximate calculation of the total primary resistance to motion𝑓 can be selected from Table3.10from DIN22101. The standard value of𝑓 = 0.02 will be used. According to Dunlop-Enerka we can assume cos 𝛿 = 1 for 𝛿 ≤ 18∘.

Table 3.10: Friction coefficient . Source: DIN22101

DIN 22101:2011-12

17 If there are no values which have been obtained by measurement or on the basis of experience, or if only an approximate dimensioning is intended, standard values for the hypothetical friction coefficient f can be selected from Table 4 for estimating the total primary resistance of the upper and lower strands on the basis of the operating conditions and design features (see also Annex A). These values are based on numerous combined upper and lower strand measurements and for the following limiting conditions:

 3 roller fixed idler sets in the top run

 carrying idlers with antifriction bearings and labyrinth seals  values of relative belt sag hrel≤ 0,01

 filling ratio ϕ within a range from 0,7 to 1,1

Table 4 — Standard values for the hypothetical friction coefficient f for estimating the total primary resistance in the upper and lower strands of conveyors

with a filling ratio ϕ within the range 0,7 to 1,1

Characteristic Values for characteristic

Internal friction of material to be conveyed medium low high

Belt conveyor alignment medium good bad

Belt tension medium high low

Operating conditions (dusty, sticky) medium good bad

Idler diameter 108 to 159 > 159 < 108

Spacing of upper strand idlers in m 1,0 to 1,5 < 1,0 > 1,5 Spacing of lower strand idlers in m 2,5 to 3,5 < 2,5 > 3,5

Belt speed in m/s 4 to 6 < 4 > 6 Troughing angle in ° 25 to 35 < 25 > 35 Ambient temperature in °C 15 to 25 > 25 < 15 Standard value ≈ 0,020 causes

Friction coefficient f reduction of increase of friction coefficient f

to

0,010 0,040

When the drives function as generators, an assumed smaller friction coefficient f leads to greater safety with regard to the dimensioning; for drives functioning as motors this effect will be achieved by assuming a larger friction coefficient f.

The application of these friction coefficients f in the calculation of primary resistances according to Equation (14) is acceptable only if the calculation does not need to be very accurate.

6.3 Secondary resistances

6.3.1 General

Secondary resistances include friction resistances and inertia resistances arising only in some places on the conveyor. Secondary resistances are calculated from several individual resistances.

The secondary resistances in the upper strand FN,o,i and in the lower strand FN,u,i are required for the calculation of the belt tensions (see 8.3).

When we fill in equation (3.9) we find that the primary resistance𝐹 = 116 N. This is rather low, but it is not surprising for a belt conveyor with a length of only 4.5 m.

3.1.Design preparations 21 Table 3.11: Inclined belt conveyor mass flow.

Name Value Unit

Belt line load 14.4 kg/m

Material line load 73.7 kg/m

Roller line load 28.9 kg/m

Friction coefficient 0.020 -Height difference 1.16 m Primary resistance 116 N Secondary resistance 0 N Gradient resistance 843 N Special resistance 0 N Motion resistance 959 N Secondary resistance

The secondary resistance𝐹 is the summation of the inertia resistance of material conveyed and fric-tional resistance between material conveyed and belt at the feeding point𝐹 , the friction resistance between material conveyed and lateral chutes within the acceleration zone of a feeding point 𝐹 , and the friction resistance caused by belt cleaners𝐹 . However, none of these resistances apply to our test rig. Therefore, the secondary resistance will be treated as𝐹 = 0 N.

Gradient resistance

The gradient resistance𝐹 is a little bit difficult in our case. It is the resistance as result of height differ-ences in the conveyor. As was already shown in Figure2.6, the gradient resistance contributes by far the largest part to the total motion resistance for inclined conveyors. But our test rig is not really going to lift any material. Also, the loading devices are not really capable of simulating the lift of material, other than pressing the belt harder to increase the indentation resistance. The gradient resistance is therefore purely theoretical. However, for designing purposes the gradient resistance will be fully taken into account. The gradient resistance is calculated with

𝐹 = ℎ ⋅ 𝑔 ⋅ 𝑚’ (3.10)

Here,ℎ is the height difference of the belt conveyor, which is equal to 𝐿 ⋅ sin 𝛿 = 1.16 m. When we fill in equation (3.10) we find that𝐹 = 843 N.

Special resistance

The special resistance𝐹 is the summation of the camber resistance 𝐹 , the friction resistance be-tween material conveyed and lateral chutes outside the acceleration zone of feeding points𝐹 , and the resistances of material transfer devices arranged along the belt conveyor path 𝐹 . In our case none of these resistances apply to the test rig belt conveyor. The special resistances will therefore be treated as𝐹 = 0 N.

For our belt conveyor, the total motion resistance becomes𝐹 = 116 + 0 + 843 + 0 = 959 N. This value is equal to the pulley peripheral force𝐹 . All calculated values are listed in Table3.11.

Motor power

Now we know the motion resistance we can calculate the required motor at the drive pulley𝑃 with formula

𝑃 = 𝐹 ∗ 𝑣 (3.11)

This give us𝑃 = 4.0 kW. To find the required motor power 𝑃 we need to estimate the transmission efficiency𝜂. 𝜂 can be found in Table3.12for a geared transmission, so𝜂 = 0.75 was selected. 𝑃 can be calculated with

𝑃 = 𝑃

𝜂 (3.12)

which gives𝑃 = 4.0/0.75 = 5.4 kW. Now we can select the nominal motor power 𝑃 from Table3.13 from Dunlop-Enerka. As can be seen we have to choose𝑃 = 5.5 kW.