Tracing Condition Status

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Dynamic Analysis of Belt Conveyor

Pankaj Dheer

Technische Univ ersi tei t Del ft

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Tracing Condition Status

Dynamic Analysis of Belt Conveyor

by

Pankaj Dheer

Master of Science

in Mechanical Engineering

at the Delft University of Technology.

Student number: 4518527 Report Number: 2016.TEL.8066.

Project duration: August 15, 2016 – October 31, 2016 Supervisor: Dr. ir. Xiaoli. Jiang

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Preface

The purpose of this analysis is to study the effect of long hauling belt conveyor systems and to help designer’s in predicting the behavior of such a system so that necessary steps can be taken to optimize the design. The main component of belt conveyor under this study is the pulley shaft. The stresses acting on the component under dynamic operation of belt conveyor would be analyzed with the help of ADAMS and ANSYS.

Designing of Long belt conveyor systems has always been difficult, partly because of limited data avail-ability in standards. To counter the effect of dynamics, the standard advices to design using safety factors which are essentially based on experience. To help designers attain maximum efficiency with available data, this research would attempt to understand the behavior of belt conveyor system using software utilizing multi-body dynamics. Multi-body dynamics (MBD) have been proven to be helpful in studying the interaction between various bodies in a system thereby providing the effects of their interaction for further study. There are few MBD software’s which are capable to analyze a belt con-veyor system, as these are quite complicated. Out of these software’s the oldest and most reliable is ADAMS, which will be used in this research.

The research involves modeling of a belt conveyor system as per guidelines suggested in standard DIN22101. Then this model will be used as a reference to find the dynamic forces acting on the sys-tem with the help of ADAMS. The static strength analysis will be done on ANSYS using the forces from the calculations. This would provide us with the critical sections in the system which are prone to failures, in our case the shaft of pulley.

The dynamic analysis in ADAMS would lay the foundation of fatigue analysis in ANSYS, where the static and dynamic analysis conducted on pulley would be compared. This comparison would be beneficial in determining the actual diameters of pulley shafts to be utilized for the system. Findings of this research would help in developing a parametric model which can be used for any configuration of belt conveyor system. Coupling a multi-body dynamic software like ADAMS with a finite element method software like ANSYS should provide the necessary means to understand the critical areas of the system. The report will start of with the introduction of the system in Chapter 1. Then we will move forward with stating the research proposal in Chapter 2. In this chapter we will be talking about the problem description in Section2.1and the proposed solution in Section2.2. The modelling of the current system with available data and assumption will be discussed in Chapter3. The force analysis of the conveyor system is given in Chapter 4. The structure analysis is shown in Chapter5. The observation and the results are discussed in Chapter6. Finally we conclude with recommendations provided to improve on this current research in Chapter7.

Pankaj Dheer Delft, October 2016

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List of Figures

1.1 Examples of Belt Conveyor and related failures . . . 1

3.1 Area of material on the belt [1]. . . 8

3.2 Belt width [1] . . . 9

3.3 Roller assembly - Carry Side [2] . . . 10

3.4 Roller assembly - Return Side [2]. . . 10

3.5 Layout of the belt conveyor system under study. . . 14

3.6 3D model of Idler support structure . . . 14

3.7 3D model of pulleys . . . 15

3.8 3D model of conveyor system . . . 15

4.1 Conveyor model in ADAMS . . . 17

4.2 Broken segments in ADAMS. . . 18

4.3 Pulley and Support creation in ADAMS . . . 19

4.4 Step 1 in belt creation in ADAMS . . . 19

4.7 Strain in 25 m belt. . . 21

4.8 Torque versus Time graph of actuator . . . 23

4.9 Simulation parameters . . . 24

4.10 Post processing window in ADAMS . . . 24

4.11 Variation of Tension in Segment 6 . . . 25

5.1 Loading on pulley shaft in Ansys . . . 29

5.2 Results of Static analysis - Coarse Mesh . . . 29

5.3 Stress in the shaft - Coarse Mesh. . . 30

5.4 Results of Static analysis - Fine Mesh . . . 30

5.5 Stress in the shaft - Fine Mesh . . . 31

5.6 Loading of shaft for Transient analysis . . . 32

5.7 Stress in Shaft . . . 32

5.8 Deformation of Shaft . . . 33

5.9 S-N Curve for Steel . . . 33

5.10 Rainflow counting method [3] . . . 36

5.11 Steps involved in Rainflow counting method [4] . . . 37

5.12 User interface of J-Rain . . . 37

A.1 Detailed Timeline of the Research . . . 45

A.2 Flowchart of Research. . . 46

B.1 Coefficient ’C’ with respect to length of belt [5] . . . 47

C.1 Initial Tensions in a 25 m conveyor system . . . 49

C.2 Initial Tensions in a 50 m conveyor system . . . 49

D.1 Plot of values on S-N Curve . . . 56

D.2 Plot of values on S-N Curve for Rainflow counting. . . 57

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List of Tables

3.1 Assumption for Belt width selection . . . 7

3.2 Parameters of Roller - Carry side . . . 10

3.3 Parameters of Roller - Return side . . . 10

3.4 Parameters of the Steel cord Belt. . . 11

3.5 Pulley dimensions . . . 13

4.1 Parameters of Small conveyors . . . 17

4.2 Pulley co-ordinates . . . 18

4.3 Parameters for total resistance force on 25 m belt . . . 21

4.4 Parameters for total resistance force on 50 m belt . . . 22

4.5 Power and Torque for smaller conveyor belt . . . 22

4.6 Theoretical and Analytical values of tension . . . 23

5.1 Parameters for Shaft diameter . . . 27

5.2 Shaft Material Properties . . . 28

5.3 Life of Shaft in terms of number of cycles . . . 34

5.4 J-Rain result . . . 38

6.1 Summary of Fatigue assessment . . . 39

C.1 Result from ADAMS . . . 50

D.1 Ansys Results . . . 53

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1

Introduction

(a) Belt conveyor system [6] (b) Example of spillage at the site of conveyor

Figure 1.1: Examples of Belt Conveyor and related failures

Belt conveyors are considered to be the most important and complicated electromechanical systems developed. Belt conveyor systems are mainly used for transferring and/or transporting materials from source to destination. Such an important and expensive system should have an optimized design with respect to its structural stability and expense spent. Companies designing/selling these systems have been applying static analysis to design belt conveyors and to counter the effects of dynamic forces are using high values of safety factors which are specified by standard [7]. As these safety factors are empirical values based on experience of designer and the people involved in writing the standard, it may lead to over design of the system involving much higher investments. This could also lead to under-design of the system which will have catastrophic effects. The idea behind this research is to help them understand their system so that design is optimized.

The dynamic forces on the system also have an ill effect on the shafts of pulley and idler roller, which are a part of the conveyor system. These shaft diameters are calculated using theories like equivalent bending moment and/or equivalent torque methods. This might lead to over or under compensation of material quality to be used. This research will also help in understanding the actual forces acting on pulley shaft and correspondingly help in selecting appropriate diameter and/or material.

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2

Research Proposal

2.1. Problem Description

Designing a belt conveyor system broadly involves two types of analysis, static and dynamic. For shorter conveyor lengths static calculation and safety factors defined under DIN-22101 are suitable as the belt properties have very little effect on the performance of the system. But if this procedure or method is utilized to design conveyor belt for longer distance it may lead to an improper design of the system. One of the major reasons behind this can be inaccurate consideration of starting and stopping forces acting on the belt. Designers and experts in this area are aware that during starting and stopping the force exerted on the belt is much higher than during normal operation. Starting and stopping of conveyor exerts tremendous forces on the belt, pulley and its supporting structure. To counter these forces, the belt and the supporting structure are strengthened using high values of safety factors. Moreover a continuous monitoring of the belt conveyor system is also placed to prevent catastrophic failures like failure of idler shafts, pulley shaft or in worst case the supporting structures. Preventive maintenance is an expensive solution to incorporate in such a system as the run time for a typical belt conveyor system is usually in years. Dynamic analysis of a conveyor system will help in an optimized and robust design helping designers reduce uncertainties while coming up with a solution for new variants of belt conveyor systems. Optimizing the belt conveyor system means to balance the productivity of the system and the investment that needs to be made. This will hopefully help in developing a safe, reliable and economical system which will have benefits for both management and people.

2.1.1. State of the Art

For the static calculation, according to research papers [8] and lectures at TU Delft (Using standards like DIN22101), assumptions are made on the elastic properties and load distribution on belt while calculating the belt power requirement. The static calculations provided are preliminary and can only to be used for basic understanding of the system for example which gearbox to be used and what should be the speed of operation. Power calculations done using these methods may be regarded as preliminary analysis. As said before, large safety factors are considered for analysis leading to over-design of systems by the use of these standards as talked in the paper by Lodewijks [7].

The dynamic analysis of belt conveyors has improved a lot since the introduction of simulation soft-ware’s which can perform complex calculations very quickly. Various mathematical models have been developed since 1950’s as explained by Lodewijks in [7]. The first objective was to determine the development of axial stress waves in the belt and their effect on the belt tension and the drive force. The first mathematical models that were implemented for this purpose were the electrical analogue models. But as discussed in the paper by Funke [9] these were not practical and can be considered

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4 2.Research Proposal

to be very rudimentary. The second phase started in 1975 with Nordell and Ciozda which included time dependent drive force, motion resistances and visco-elastic behavior of the material [10]. The only problem with these models were they can be used to study the dynamic behavior of a conveyor belt in the axial or longitudinal direction and not in the transverse direction [7] . Lodewijks briefly discusses this in his paper [7] that the main reason behind considering transverse direction is belt sag, which effects in long belt conveyors. Lodewijks further comments that to consider effect in transverse direction it is essential to build a model using multi-body dynamics. Lodewijks provides a unique way in [11] and [12] which will be helpful to our research problem to design a model considering axial, lateral and transverse direction effects on belt conveyors.

Research has also been done to understand and study the effects of forces on pulley and idler roller shaft. Studies have shown some signs where the strength analysis gives a more clear picture on the material requirement of the shaft for pulley and idler rolls as shown in [13]. The report performs an analysis of a relatively shorter belt conveyor system modeled in Creo. The strength analysis is done using ANSYS workbench to find the force exerted on the shafts of pulley and idler roller. Though the analysis provides important information, it can be considered as a simple analysis as it uses only static forces due to weight of the material on belt.

Commercial software companies have managed to develop software’s which can help companies in designing long belt conveyor systems providing an optimized solution for their problems. Software companies like Helix technologies in Australia and Conveyor Dynamic Inc. in Washington have de-veloped a software which can help in tracking belt conveyor performance in both static and dynamic conditions. These software packages can calculate every detail of the conveyor system and can be very useful to companies designing what belt conveyors system to be used. Another concern maybe that these software provide a certain black box situation for the operator where he/she is unaware on what the actual process considers. There is no transparency in the process on how the software actually works and it can be said to be expensive. For more information on the software one can refer to website in [14] and [15].

2.2. Proposed Solution

To understand the dynamic behavior of belt conveyor system having multiple bodies a software is needed which can create the same scenario of the system in real life or as close to it as possible. Luckily, due to advancement in software a multi-body analysis software is available to us. ADAMS can be used to analyze dynamic behavior of long belt conveyor system to provide the designer insights on critical sections of the design. Moreover, it can help achieve the optimized design using design of experiments (DOE). The output of ADAMS in the form of force versus time graph can be used for analysis of its support structure. These force-time graph can be introduced into ANSYS as an input to analyze the structural strength of pulley shaft.

2.2.1. Scientific Steps involved

The research will be conducted in four phases and their finding will be discussed. Details regarding each phase is explained below.

1. Modeling of Belt Conveyor in “PTC Creo”: Conceptualizing a proper belt system for analysis is also an important part of this research. For this particular research problem, the modeling software we will be using is PTC Creo Parametric. The model will be developed in detail to facilitate accurate strength analysis in ANSYS. For the purpose of keeping the model a bit simple, devices like motor, brakes and gearbox will not be modeled. The power from the motor will be assumed to be given to the pulley. The tension given by the take up system will be calculated and will be applied in ADAMS for further analysis.

2. Force analysis using “ADAMS”: The model will be refined in ADAMS with the sole purpose to reduce analysis time. To achieve this, model will be made in ADAMS without the support structure, idler roller system and take up system. The output expected form ADAMS is in the form

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2.2.Proposed Solution 5

of a force-time graph plotting the effects of operating forces on pulley and its shaft. Also tensions in belt will be analyzed and compared to specification of belt provided by its manufactured. This check should be performed to determine whether the chosen belt can be used for this particular system or a stronger belt should be chosen. Also to verify the model, speed of stress wave will be compared with the expected theoretical value.

3. Verification of Model: Verification of the ADAMS model is important to establish the authenticity of our model. This will help in proving the credibility of the forces that will be calculated in ADAMS. This is important as these forces will be used to analyze the structural strength of the supporting system. For our model we thought of using stress wave propagation to establish the authenticity of the force calculated in ADAMS. The speed of the stress wave in the longitudinal direction can be calculated using the formula provided in [16].

𝑐 = √(𝐸 × 𝐴

́

𝑚 ) (2.1)

Where𝐸 = Elastic modulus of the belt, 𝐴 = Cross section and ́𝑚 = total mass per unit length. This total mass includes mass of the belt per unit length, mass of the roller per unit length and mass of the material per unit length.

This speed will be calculated in ADAMS to compare the values with theoretical values obtained from above equation to verify the model.

4. Structural analysis using “ANSYS”: As the nature of force is transient, there are peaks during an operation of conveyor. These peak forces over a short time period induces high stresses on the support structure. These transient stresses can lead to fatigue and formation of crack which eventually result failure of structures. Care should be taken during designing that the structure is also safe to operate under fatigue conditions. Forces determined through ADAMS will help us analyze the structural strength of pulley shaft under operation. The static analysis will also be carried out using the forces found during modelling of the system. Dynamic analysis will be done using S-N curve and J-Rain method to find the fatigue strength of the shaft. Both the static and dynamic analysis will eventually be compared to find out the optimized value of diameter of pulley shaft.

Analyzing the system with this framework would lead to better design of the pulley shafts and provide a deeper understanding about the system. Better systems would eventually lead to a faster progress in the field of transportation. Still, the analysis is the first step towards finding out the abnormalities in a belt conveyor system and an attempt to optimize it with respect to cost and design. Conducting this research will help us mark the first steps towards gaining further knowledge about belt conveyor system through multi-body dynamic simulation and ADAMS maybe the software to help us achieve it.

2.2.2. Deliverables

The research will have following two main deliverables: 1. An executable program.

2. Report containing all the technical aspects of the research and the reasons behind them.

2.2.3. Timeline

The project will start from 15th April and end around 15th September. This is involve working part time from 15th April to 30th June and then full time in the months of July and August to complete all the laid out activities. A buffer period of 10 days to be provided for completion of report. A more detailed time-line is available in the excel sheet attached. If scope of research needs to expand then coordination to be done in presence of Prof. Xiaoli Jiang. The main highlights of the time-line are provided below and detailed time-line is provided in the SectionA.1.

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6 2.Research Proposal

1. Final Design of all three models by third week of May. 2. Selection on the final model for analysis by the end of June.

3. Force calculations on this model using ADAMS by first week of August.

4. Using ANSYS to calculate the structural strength of the model and DOE by second week of Septem-ber.

5. A report with all the laid out foundations on how the procedure of finding out the optimal conveyor system was conducted by the third week of September.

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3

Modelling - PTC Creo

Modelling of the belt conveyor system can be broadly divided into two main sections:

1. The calculations of parameters of belt and its corresponding support structure. This is done in Section3.1.

2. The 3D model that is made in Creo is explained in Section3.2

3.1. Calculation of parameters

This section will talk about calculation of different parameter which are needed to design the belt conveyor system in regard with the material that will be transported. The first and foremost calculation is related to the selection of belt width. This depends upon the type of material being carried, capacity required on the system and the approximate velocity the belt will move. Table3.1gives the values of this parameters for the belt conveyor system.

Table 3.1: Assumption for Belt width selection

Property Value Unit Material Handled Coal

-Bulk Density 850 𝑘𝑔/𝑚 Angle of repose 40 𝑑𝑒𝑔𝑟𝑒𝑠𝑠 Capacity of the system 4000 𝑀𝑇𝑃𝐻

Velocity of bet 5.2 𝑚/𝑠 Trough Angle 35 𝑑𝑒𝑔𝑟𝑒𝑠𝑠 Belt Surcharge Angle 15 𝑑𝑒𝑔𝑟𝑒𝑠𝑠 Length of the conveyor 20 𝑘𝑚

Coal is used here as the material as belt conveyors are extensively used to transfer it from coal mines to factories for various purposes. The density of coal is chosen from selection chart [17]. Bulk density of Coal in form of granules is selected. The capacity of the system is assumed as the length of the conveyor is very long. Trough angle and surcharge angle is also assumed as per application. Speed of the belt is decided as mentioned in [1]. A standardized speed of 5.2𝑚/𝑠 is selected for our belt. The calculation of various parameters of the belt will be covered in this section based on assumptions made in Table3.1. The selection of belt width will be discussed in Subsection3.1.1. Then idler roller for carry and return side will be selected in Subsection 3.1.2, then we will move on to selection of the Belt in Subsection3.1.3. Power consumption, motor selection and gearbox selection will be done in Subsection 3.1.4. Pulley selection will be done in Subsection 3.1.5and subsequent calculation of tensile forces will be done in Subsection 3.1.6. Based on above calculation, the layout of the belt

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8 3.Modelling - PTC Creo

conveyor system will be decided and discussed in Subsection 3.1.7. This would eventually conclude this particular section and move on to 3D modelling of the system.

3.1.1. Belt width Selection

The belt width is selected according to the capacity of the conveyor and the bulk density of the carried material. As per [1] the belt width can be selected from trough angle and belt surcharge angle if we know the appropriate value of𝐴 which is the effective area of material on the belt. Figure3.1gives more clarification on the area of material.

Figure 3.1: Area of material on the belt [1]

𝐴 is equal to addition of 𝐴 and 𝐴 . This can be calculated using the capacity of belt in MPTH and bulk density of the material. Equation3.1[1] gives the value of𝑚 which the mass of material peŕ length. This can be used to calculate𝐴 using Equation3.2[1].

́

𝑚 = 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦

3.6 ∗ 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (3.1)

The values can be taken from Table3.1to find the value of mass per unit length.

́

𝑚 = 213.67 𝑘𝑔/𝑚

𝐴 = 𝑚́

𝑑𝑒𝑛𝑠𝑖𝑡𝑦 = 0.2513 𝑚 (3.2)

This value of 𝐴 can be used with the help of graphs to find the appropriate width of belt of our system. From Figure 3.2for trough angle of35 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 and surcharge angle of 15 𝑑𝑒𝑔𝑟𝑒𝑒 the belt width selected is 1600 mm.

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3.1.Calculation of parameters 9

Figure 3.2: Belt width [1]

We will be using steel cord reinforced belt which has many advantages over elastic polymer belt which are listed below [18]:

1. Belts reinforced with Steel Cords deliver extremely high strengths. 2. Steel Cord Conveyor Belts have a long life expectancy.

3. Large Centre Distances can be planned. 4. Low Pulley Diameters can be used. 5. Low Elongation, high impact resistance. 6. Excellent Trough-ability.

7. Long Splice Life and Strength.

8. Easily Reconditioned and Rejuvenated.

3.1.2. Idler Roller selection

As the capacity of the conveyor is high, so will the forces acting on the belt. These forces are trans-ferred to the support structure containing the idler rollers. For our system the number of rollers on carry side considered is 3 and on return side 1. The important parameter is the distance between the idler supports on the carry as well on the return side. There are guidelines available for selecting this distance. As stated in the IS:4776 Table 2 [19] the distance between idlers on carry side for a belt width of 1600 mm should be 1 m. This is true for rollers having density between 400-1200𝑘𝑔/𝑚 . Similarly the distance between idler on return side is 3 m. But due to the length of the conveyor and to save material for supporting, the distance between idlers have been reconsidered. The new distance between idlers on the carry side is 4 m and that on the return side is 8 m. To counter the effect of belt sag due to increase in idlers spacing, suitable take-up system would be applied.

There are two main important objectives while selecting an idler roller. The main assumptions made here is that impact idlers are not considered which would be used in practical situations. For our system the idler roller selected from Sandvik Idler catalogue [2]. Figure3.3shows the assembly of idlers and Table3.2shows the value of dimensions.

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Figure 3.3: Roller assembly - Carry Side [2]

Table 3.2: Parameters of Roller - Carry side

Parameter Value Unit

Roller diameter 159 𝑚𝑚 Bearing Number 6309 -Code Number 55113-1600-00 -A 569 𝑚𝑚 B 2000 𝑚𝑚 C 615 𝑚𝑚 D 1528 𝑚𝑚 E 240 𝑚𝑚 F 285 𝑚𝑚

Total Mass of Roller (𝑚 ) 105.1 𝑘𝑔

Similarly, the dimensions for return side roller given in Figure3.4and Table3.3

Figure 3.4: Roller assembly - Return Side [2]

Table 3.3: Parameters of Roller - Return side

Parameter Value Unit

Roller diameter 159 𝑚𝑚 Bearing Number 6309 -Code Number 55161-1600-00 -A 1852 𝑚𝑚 B 2000 𝑚𝑚 E 60 𝑚𝑚 F 38 𝑚𝑚

Total Mass of Roller (𝑚 ) 61.7 𝑘𝑔

3.1.3. Belt Selection

Steel cord belts are divided as per the minimum breaking strength of the belt itself. It is based on the diameter of steel cords used and the thickness of the covers. An additional cover maybe introduced to

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increase this strength. This breaking strength can be roughly calculated with the help of mass per unit length (𝑚). The main stress on the belt can be said to be induced when the belt passes between twó idler support. Depending upon the pitch between idlers, the weight on the belt because of the mass of material imparts tension on the belt.

Spacing between idlers is 1 m as selected from 3.1.2. Then the mass of material between two idler support is:

𝑀𝑎𝑠𝑠 = ́𝑚 ∗ 𝑠𝑝𝑎𝑐𝑖𝑛𝑔 = 213.67 𝑘𝑔𝑠 = 2136.7 𝑁

Now the belt should have this strength per millimeter to avoid any breakage. So we select a belt from Phoenix Conveyor belt [20], the specification provided are listed below in Table3.4:

Table 3.4: Parameters of the Steel cord Belt

Property Value Unit

Belt Type Steel Cord

-ST Number 2500

-Mini. Breaking Strength 2500 𝑁/𝑚𝑚

Belt Thickness 25 𝑚𝑚

Thickness of Top cover 10 𝑚𝑚 Thickness of Bottom cover 8 𝑚𝑚 Mass of carcass 38.5 𝑘𝑔/𝑚

3.1.4. Power Calculation

The total power requirement for the belt conveyor system can be calculated using ISO 5048 [5].

𝐹 = 𝐹 + 𝐹 + 𝐹 + 𝐹 (3.3)

Where𝐹 is the primary resistance force due to mass of the belt and mass of material on the belt. The secondary resistance force is due to the length of the conveyor. The third term is due to the elevation of the conveyor. As seen in Figure 3.5, there is no inclination of the conveyor so this term can be neglected. The fourth term is related to the special resistances that act on the belt conveyor like belt cleaner and skirts plates which is also neglected in this case.

Primary Resistance force:

To calculate the primary resistance force𝐹 it is essential to calculate the load of material, belt and roller per unit length as specified in ISO 5048 [5]. The total roller weight per unit length can be calculated using Equation3.4below:

𝑀𝑎𝑠𝑠 𝑜𝑓 𝑟𝑜𝑙𝑙𝑒𝑟/𝑙𝑒𝑛𝑔𝑡ℎ(𝑚 ) = 𝑀𝑎𝑠𝑠 𝑜𝑓 𝑟𝑜𝑙𝑙𝑒𝑟, 𝑐𝑎𝑟𝑟𝑦 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑟𝑜𝑙𝑙𝑒𝑟+

𝑀𝑎𝑠𝑠 𝑜𝑓 𝑟𝑜𝑙𝑙𝑒𝑟, 𝑟𝑒𝑡𝑢𝑟𝑛

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑟𝑜𝑙𝑙𝑒𝑟 (3.4) Substituting the values from Subsection3.1.2and Table3.2and3.3the value of𝑚 is found to be

𝑚 = 33.9875 𝑘𝑔/𝑚

As stated in [11] the mass of roller that should be added to while calulating the power for belt conveyor should be 90% of this mass. Thus mass of roller should be𝑚 = 30.58 𝑘𝑔/𝑚. Mass of belt is calculated based on the [1] given by Equation3.5

𝑀𝑎𝑠𝑠 𝑜𝑓 𝐵𝑒𝑙𝑡/𝑙𝑒𝑛𝑔𝑡ℎ(𝑚 ) = 𝐵𝑒𝑙𝑡 𝑊𝑖𝑑𝑡ℎ ∗ (𝑀𝑎𝑠𝑠 𝑜𝑓 𝑐𝑎𝑟𝑐𝑎𝑠𝑠 + (𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑐𝑜𝑣𝑒𝑟 ∗

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Belt width is calculated in Subsection3.1.1and other values can be found in Table3.4to find the Mass of belt/length

𝑚 = 94.72 𝑘𝑔/𝑚

There also exist an friction coefficient called as the artificial coefficient of friction [5]. This value is generally equal to 0.012 as stated in DIN 22101 [21]. But there are certain additional friction acting on a long travelling conveyor belt system as explained by Lodewijks in [22]. Its is suggested to add these values to the artificial coefficient of friction while calculating the power requirement of a particular conveyor system.

As suggested in [22], there are three types of resistances, the indentation rolling resistance, rotation inertia of rolls and resistance of bearing of rolls. These three values are calculated for our system.

Secondary Resistance force:

The secondary resistance force is related to the length of the conveyor which introduces a factor ’C’ which is called as coefficient [5]. The value of ’C’ can be found from the graph in FigureB.1. As it can be seen from the graph the value of ’C’ approaches to 1 as the length of the conveyor belt increase. As for length of the conveyor above 5000 m are not available in the graph the value of ’C’ is assumed to be ’1’. The total resistance force is calculated using the Equation3.6[1].

𝐹 = 𝐶 ∗ 𝐿 ∗ 𝑔 ∗ 𝑓 ∗ ( ́𝑚 + 2 ∗ 𝑚 + 𝑚 ) (3.6) Where𝐶 is the coefficient, 𝑓 is the overall frictional coefficient, 𝐿 is the length of the belt from Table 3.1and𝑔 is acceleration due to gravity. If these are values are substituted in Equation3.6the value of𝐹 is:

𝐹 = 1008772.613 𝑁 = 1.021 𝑀𝑁

The power required for a motor efficiency of (𝜂) 95% is given by the Equation3.7

𝑃 = 𝐹 ∗ 𝑣

𝜂 (3.7)

where𝑣 is the velocity of the belt. Substituting these values in Equation3.7the power requirement is found to be

𝑃 = 5589247.982 𝑊 = 5.59 𝑀𝑊

Now this power is very high and would be rather impossible for a single drive to achieve this, hence multi-drive is selected. More on the position of drives will be discussed in Subsection3.1.7.

3.1.5. Pulley Selection

The diameter of pulley is selected using the standard DIN 22101 [23]. A factor𝐷 is calculated using the thickness of the belt and a coefficient𝑐 based on the type of belt. In standard DIN 22101 [23], the factor𝑐 for steel cord belt is 145 and thickness of belt is given in Table3.4. Using these values the factor𝐷 is equal to 1015. Using table provided in standard, Table3.5gives the value of drive, tail and snub pulley for our system.

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Table 3.5: Pulley dimensions

Property Value Unit Drive pulley 1000 𝑚𝑚 Tail Pulley 1000 𝑚𝑚 Snub pulley 800 𝑚𝑚

As these values are without any consideration of lagging’s, a12 𝑚𝑚 thick lagging is suggested in [8] which effectively increases the diameter of pulley by 24 𝑚𝑚. So the overall diameter of pulley with lagging is1024 𝑚𝑚. The length of the pulley is based on the length of belt calculated in Subsection 3.1.1. The length of the pulley should be 200 mm more than the length of belt which makes pulley length of1800 𝑚𝑚.

3.1.6. Tensile forces

The tensions in the system are calculated using DIN 22101 [21] in the following manner. The belt tensions are calculated using two principles, first is the equation of forces on the pulley and other is using maximum allowable belt sag. Both methods will be discussed and tensions will be calculated. As per DIN 22101 section 8.1.1 [21],

𝑇 − 𝑇 = 𝐹 (3.8)

where 𝑇 is the maximum tension in the belt and 𝑇 is the minimum tension. 𝐹 is the maximum resistance force calculated in Equation3.6. Also as per DIN 22101

𝑇 /𝑇 ≤ 𝑒 ∗ _(3.9)

where 𝜇 is the co-efficient of friction between belt and pulley. As per Table 6 in [21], the value of𝜇 for rubber friction pulley under wet conditions is0.35 and 𝛼 is the total wrap angle in radians. As per layout in Figure 3.5, total wrap angle is 180 + 135 + 164.5 = 497.5 𝑑𝑒𝑔𝑟𝑒𝑒𝑠. Substituting all the values in Equations3.8and3.9we get the values of𝑇 and 𝑇 .

𝑇 = 1080866.67 𝑁 = 1.08 𝑀𝑁 & 𝑇 = 51752.04 𝑁 = 51.72 𝐾𝑁

As per DIN 22101 section 8.1.2 [21] using minimum allowable belt sag, tensions in the belt can also be calculated using Equation3.10and3.11.

𝑇 =𝑔 ∗ ( ́𝑚 + ́𝑚 ) ∗ 𝑙

8 ∗ ℎ (3.10)

𝑇 = 𝑔 ∗ ́𝑚 ∗ 𝑙

8 ∗ ℎ (3.11)

where𝑇 and 𝑇 are the minimum tensions in carry and return side. 𝑙 and 𝑙 are the spacing between two idler sets on carry and return side. ℎ is the maximum allowable belt sag on carry and return side. As per IS standard [24], the maximum allowable belt sag is 2% of the distance between the idler sets on each side. As per idler set spacing suggested in Subsection3.1.2, the maximum allowable belt sag is0.08 𝑚 on carry side and 0.16 𝑚 on return side. Using these values we find the respective tensions.

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3.1.7. Belt Layout

The layout of the belt is clearly shown in Figure3.5.

Figure 3.5: Layout of the belt conveyor system under study

The system consist of four (04) pulleys, three (03) of them are driving pulley and one is the like a snub pulley. The drive pulley on the left will have a motor having power 1.2𝑀𝑊 and the other two pulleys will be two motors each having combined power of 2.4𝑀𝑊 per drive. This is done to prevent huge tensions on the respective pulleys [25].

3.2. 3D model in Creo

The 3D model was made in PTC Creo 3.0 Parametric. The belt was designed as per its specification keeping in mind the layout of the system. The idler roller system is modelled as per dimensions and design provided in [2]. The pulley are designed as per specifications obtained in Table3.5. Its diameter of shaft is selected using equivalent bending moment and equivalent torque methods. We will look at the method of shaft diameter selection in Chapter 5. On basis of shaft diameter, suitable bearing is selected from the catalogue of SKF bearings. The selected bearings are cylindrical bearings to sustain high stresses that would act on the them during the operation of conveyor. Below some images will be provided of the various components which are modelled.

(a) 3D model of Idler support structure - Carry side

(b) 3D model of Idler support structure - Return side

Figure 3.6: 3D model of Idler support structure

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3.2.3D model in Creo 15

the idler assembly on carry side and Figure3.6bshows the return side assembly. The carry side idler are arranged at any angle which is called as trough provided in Table3.1.

(a) 3D model of main driving pulley

(b) 3D model of support pulley

Figure 3.7: 3D model of pulleys

Figures3.7aand3.7bshows 3D model of the main and support pulleys respectively. The dimensions provided in Table 3.5is used. A pulley support structure is shown in Figure3.7b. It should be noted that this is selected as arbitrary as this research does not focus on the support structure of the pulley but on the shaft diameter of the pulley. Full 3D model is shown in Figure3.8

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4

Force Calculation - Adams

Adams will be used to analyze the dynamic behavior of the conveyor system under consideration. As a 20 km long conveyor system cannot be analyzed in ADAMS, a small equivalent system will be implemented in ADAMS which would imitate similar conditions. As the model has to be verified, two small models will be used of length 25 m and 50 m. These models are selected based on the solver capability and simplicity of the model. The calculations for these models are conducted as specified in Chapter3. Table4.1provides a rough summary on the major parameters of the conveyor systems.

Table 4.1: Parameters of Small conveyors

Parameter Conveyor Length - 25m Conveyor Length - 50m

Capacity 4000𝑀𝑇𝑃𝐻 4000𝑀𝑇𝑃𝐻

Speed 5.2𝑚/𝑠 5.2𝑚/𝑠

Pulley diameter 1𝑚 1𝑚

Power required 11.4𝑘𝑊 23.36𝑘𝑊

Pulley shaft diameter 0.11𝑚 0.11𝑚

Figure4.1shows the conveyor system modelled in ADAMS.

Figure 4.1: Conveyor model in ADAMS

There are two main tasks carried out using ADAMS and those will be explained in this chapter. They are as follows:

1. Verify the equivalent ADAMS model. This is essential as the output of ADAMS will be utilized in ANSYS to carry out further structural analysis on the pulley shaft. It is of utmost importance that the forces acting on the pulley are correct which would prove the correctness of the ANSYS analysis.

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18 4.Force Calculation - Adams

2. To calculate the forces acting on the pulley and pulley shaft like joint forces and tension. Using the ADAMS ’Dynamic’ solver, the model will be analyzed and appropriate output will be used for further analysis in ADAMS.

The output of ADAMS as discussed in the research proposal include the effect of material mass on the belt which would have an effect on the pulley shaft. But, as the research moved along there were a couple of problems implementing effect of material mass on belt. These are as follows:

1. At first the problem faced during simulation was that the belt segments broke down due to a glitch in the software. Due to this it was impossible to simulate the effect of material mass on belt segments. While simulation, the belt segments would start to break off and when the material mass had to fall down, there would be no belt segments left to support the fallen mass.

Figure 4.2: Broken segments in ADAMS

2. Once the problem of belt segment falling was rectified, the displacement of belt segments were huge of the orders of hundreds of mm which could not be rectified.

Because of the problems faced during the simulation and lack of software help, the problem definition had to be cut short to exclude the dynamic effect of belt conveyor due to material mass. Now we will discuss about the approach used to solve the small conveyor models of 25 m and 50 m in ADAMS and their verification. The approach for both the models are similar but as discussed earlier for verification it was decided to use two separate model differing in conveyor length.

Both the models were setup in ADAMS 2013.2 version. The model is divided into three main parts namely pulley, additional supports and the belt. Each of these parts has to be modelled by providing the necessary parameters specified in the software. For modelling belt conveyor system a special belt module under machinery module is provided in ADAMS. Pulleys and belts can be directly modelled inserting the necessary parameters. Supports are modelled along with pulleys under ’Create Pulley’ and belt is modelled using ’Create Belt’. Also an important part of belt conveyor system is the motor which is used to rotate the pulley putting the overall system under motion. This is called ’Actuator’ in ADAMS and can be created using ’Belt Actuation Input’. All these features of the belt module are explained below with respect to 25 m conveyor system.

Pulley creation:

The pulley dimensions were selected in Chapter3, these remain same for shorter conveyor as it is for the longer conveyor system. The pulley selected is a smooth pulley, most popularly used in conveyor systems. The supports provided are like the idler rollers provided on an actual belt conveyor system. The diameter of pulley and idlers can be found in Chapter3Tables3.5and3.2respectively. Table4.2 shows the co-ordinate of pulleys 1 and 2 for different conveyor lengths.

Table 4.2: Pulley co-ordinates

Conveyor Length Pulley - 1 Pulley -2 25 m (-12.5,0,0) (12.5,0,0) 50 m (-25,0,0) (25,0,0)

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19

Figure 4.3: Pulley and Support creation in ADAMS

Two idlers are are placed in either side of each pulley as seen in Figure 4.3to increase the wrapping angle of the belt on the pulley to decrease the overall power consumption. Also the figure shows the positions of idlers on the conveyor system.

Belt creation:

The belt is created after pulley creation as belt needs to be assigned to a particular pulley set. Figures 4.4,4.5and4.5highlights the important parameters that should be provided to the software for creating belt. We will discuss each of the parameters in the figures separately providing information on why these values are chosen.

Figure 4.4: Step 1 in belt creation in ADAMS

In this figure the important parameter is the belt segment length. It should be noted that the units used in this analysis is MKS. The segment length is selected considering the computational capacity and accuracy needed for the analysis. It should also be noted that belt segments wrap around the pulley

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surface, so the segment length should be small enough to properly wrap around the pulley. Selection of segment length also influences the tension in the belt, so trial and error method can be used while deciding the segment length.

Belt height is the thickness of belt selected using calculations in Chapter3. Belt width is also selected from the same calculation. The segment area is calculated based on the segment length and thickness of belt. Calculation of Young’s modulus will be discussed later.

Belt segment mass is entered along with the mass moment of inertia in all directions which are𝐼 , 𝐼 and 𝐼 . For this calculations, PTC creo software was used. The segment was modelled in Creo and mass properties were found out using an inbuilt tool called as ’Mass properties’. The stiffness of the contact was increased from initial value of 1.0E+007 to 1.0E+012 as the mass of the belt segment is on the higher side and sufficient stiffness is required to keep rigid contact between belt segments. To improve the contact, damping value is also increased from 3.0E+004 to 3.0E+005.

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21

Next step is provide the contact friction values between the belt segment and pulley surface. These are static and dynamic friction coefficients and are selected from DIN 22101 based on the pulley lining material and belt carcass. Transition velocity is the velocity of belt selected in Chapter3.

After this the wrapping order of the belt is to be selected. An important thing to note here is that while providing the wrapping order of the belt, the pulleys and support should be selected in clockwise direction with respect to the movement of the belt. In simple terms this means that if we start from Pulley-1 then we should include all the supports from Pulley-1 to Pulley-2 on the carry side and end the wrapping order with the support near Pulley-1 on the return side. Once this is done the software provides the initial tension and strain in the belt. This strain is used to calculate the Young’s modulus of the belt.

We are going to calculate the Young’s modulus of belt for conveyor length 25 m, similar procedure can be followed to calculate for 50 m belt. Figure 4.7provides details of the strain value in the belt while creating belt in ADAMS.

Figure 4.7: Strain in 25 m belt

Simple mechanical calculation is used to find out the value of Young’s modulus. As per definition, Young’s or Elastic modulus is defined as stress divided by strain. Stress on the belt can be found out using the force on the belt segment divided by cross-sectional area of belt segment. The force is calculated from Equation3.6in Chapter3. If we remove the𝑚 from the equation and modify it for 25́ m we get a new value for resistance force on the belt without mass on the conveyor. Table4.3shows the change in values of parameters for 25 m conveyor length.

Table 4.3: Parameters for total resistance force on 25 m belt

Sr. No. Parameter Value Unit 1 Length Coefficient (C) 2.9 -2 Length of Conveyor (L) 25 m 3 Mass of Belt (𝑚 ) 35.52 kg/m 4 Mass of Rollers (𝑚 ) 24.47 kg/m

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𝐹 = 𝐶 ∗ 𝐿 ∗ 𝑔 ∗ 𝑓 ∗ (2 ∗ 𝑚 + 𝑚 ) = 815.51 𝑁 (4.1) Using this we can find the Young’s modulus of the belt. Equation4.2gives the value of Young’s modulus (E) of the belt.

𝐸 = 𝐹𝑜𝑟𝑐𝑒

𝐴𝑟𝑒𝑎 ∗ 𝑠𝑡𝑟𝑎𝑖𝑛 = 2.71𝐸 + 007 𝑁/𝑚 (4.2) Similarly, the result can be obtained for 50 m conveyor system. Table4.4provides the details of the parameters and the resistance force without mass and also gives the Young’s modulus of the belt.

Table 4.4: Parameters for total resistance force on 50 m belt

Sr. No. Parameter Value Unit

1 Length Coefficient (C) 2.3 -2 Length of Conveyor (L) 50 m 3 Mass of Belt (𝑚 ) 35.52 kg/m 4 Mass of Rollers (𝑚 ) 30.58 kg/m 5 Total resistance without mass 1375.8 N 6 Young’s modulus (E) 8.9E+007 𝑁/𝑚

Now that the all the parameters are made, next part of the model is to put actuation to one of the pulleys. In this case, Pulley - 2 will act as the actuation. Torque is applied to the pulley according to the power consumption given in Equation3.7. For smaller conveyor lengths used in ADAMS Table4.5 gives the power and torque values.

Table 4.5: Power and Torque for smaller conveyor belt

Conveyor Length Required Power (kW) Torque (Nm)

25 m 14.4 711.09

50 m 23.36 1150.25

Torque is applied to pulley in a step wise manner because in reality a sudden increase in torque from zero to its maximum value is not suitable. To increase torque in a step wise manner, a function is available in ADAMS called as ’STEP’ function. So the torque applied to Pulley-2 is given by the following equation for 25 m conveyor belt system.

step(time,0,0,0.5,88.89)+step(time,0.5,88.89,1,177.77)+step(time,1,177.77,1.5,355.55)+ step(time,1.5,355.55,2,533.45)+step(time,2,533.45,2.5,711.09)

The ’STEP’ function allows a smooth curve between two points, thus allowing a smooth increase in torque for the actuator (Pulley-2). The terms inside the brackets are defined arbitrarily by dividing the maximum torque value into five different time steps. The first term inside the bracket is ’time’, which tells the software that the torque will be plotted with respect to time. The next term is the first point in ’x’ coordinate which is time. The term next to it is the first point on ’y’ coordinate which is torque. So the second and third term together plots the first point on graph. Similarly. the fourth and fifth terms plot the second point on the graph creating a smooth curve between these points. The addition of these equation provides the smooth curve of torque. Equation of actuator for Pulley-2 will graphically represent as in Figure4.8.

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23

Figure 4.8: Torque versus Time graph of actuator

Verification of Model:

As stated earlier the belt segments were getting disconnected from each other and falling off, the verification of the model could not be done as described in Chapter 2Subsection2.2.1. An alternate method is utilized to verify the model using the initial overall tension in the belt. In simpler words the resultant tension in the belt at t = 0 seconds is calculated using DIN 22101 which is also the resistance force of the system. This resistance force is the equivalent tension in the system at t = 0 seconds. This resultant tension is calculated in ADAMS when the belt is created. If these two values are equal or within certain error limits, the model made in ADAMS could be considered to represent the system which is designed in Chapter3.

Table 4.6 provides the results of tension calculated theoretically and through ADAMS along with the difference in these values.

Table 4.6: Theoretical and Analytical values of tension

Sr. No. Conveyor Length Theoretical force (N) Force from ADAMS (N) Error (%)

1 25 m 815.15 815.02 0.01

2 50 m 1375.82 1376.58 0.05

From the table it is quite evident that the tension values obtained from ADAMS are the same as that calculated using DIN 22101. For more clarification FiguresC.1andC.2can be referred. So we can say that the model in ADAMS resembles to the actual system considered in this research. The output of ADAMS is achieved in the form of force time graph of the forces acting on the pulley.

As the effect of material mass is neglected, the simulation should not have to run for a longer time. As discussed in Chapter2the highest force acts at the start of conveyor motion. So the simulation will run from 0.5 second with 100 steps to plot a smooth curve of Force versus time. Figure4.9shows the parameters assigned while running the simulation.

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Figure 4.9: Simulation parameters

Once the simulation is completed the results can be seen in the post processing window as shown in Figure4.10.

Figure 4.10: Post processing window in ADAMS

As it can be seen in the figure, belt-1 represents the results of each of the segments of the belt. Each segment provides tension, axial contact force and normal contact force as results. The result we are interested in is the tension, specifically tension in the segments near to the pulley. The pulley under consideration is Pulley - 1. The maximum tension is in ’Segment-6’ around Pulley - 1. The results of segment-6 is shown in Figure4.11. A graph is plotted showing the variation of tension during the operation of belt conveyor.

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25

Figure 4.11: Variation of Tension in Segment 6

As it can be seen from the graph above, at the start of the conveyor the tension in the belt near the pulley is very high when compared to the creation of belt. This tension force comes down quickly as the belt begins to move and if the simulation ran for a while, then the force will stabilize. To make sure that the pulley shaft is able to handle the initial starting forces of the belt, the simulation is ran only for half a second. As said in Chapter2the shaft has to withstand the initial forces exerted by the belt on the pulley.

The data points are exported in a table format and these values are then utilized to conduct structural analysis on the pulley shaft. This simulation was conducted for 25 m conveyor belt system. Similar method can be applied to find the tension in segments for 50 m conveyor system. As the methodology is the same, it is decided that the structural analysis will only be done for 25 m conveyor to optimize the diameter of pulley shaft.

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5

Analysis - Ansys Workbench

The main objective of this research is the analysis of pulley shaft under static loading condition and dynamic loading condition. This chapter will cover the analysis of pulley shaft in static loading in Section 5.1and dynamic loading in Section5.2. The analysis is done using Ansys Workbench version 16.1.

5.1. Static Analysis

The static analysis begins with calculating the diameter of the pulley based on the load acting on the pulleys. The important thing to note here is that the pulley under consideration is the drive pulley. The diameter of the pulley is calculated using the tensions on the drive pulley along with the weight of the pulley. The load on the pulley shaft is calculated as below:

The tension on the pulley is calculated Section 3.1.6. Horizontal forces is sum of maximum and min-imum tension on the pulley. Vertical force is the weight of the pulley on the shaft. The main forces, distances and service factors are given in Table5.1

Table 5.1: Parameters for Shaft diameter

Sr. No. Parameter Value Unit

1 Total Horizontal Force 1123811.88 𝑁 2 Total Vertical Force 10826.66 𝑁

3 Length of Pulley 1.8 𝑚

4 Distance of support 1.1365 𝑚 5 Bending service factor(𝑘 ) 1.5 -6 Torque service factor(𝑘 ) 1.2

-As the total force is applied on the center of the shaft and the shaft is supported at the two ends like a simple support structure. Diameter of shaft is calculated as follows:

𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑜𝑛 𝑠ℎ𝑎𝑓𝑡 = 𝑇𝑜𝑡𝑎𝑙 ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 / 2 = 561905.94 𝑁 (5.1)

𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑜𝑛 𝑠ℎ𝑎𝑓𝑡 = 𝑇𝑜𝑡𝑎𝑙 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 / 2 = 5413.33 𝑁 (5.2) Moment is calculated using the force and distance of support using following equations.

𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑚𝑜𝑚𝑒𝑛𝑡 𝑜𝑛 𝑠ℎ𝑎𝑓𝑡 = 𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑜𝑛 𝑠ℎ𝑎𝑓𝑡 ∗ 1.1365 = 301462.53 𝑁 (5.3) 27

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28 5.Analysis - Ansys Workbench

𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑚𝑜𝑚𝑒𝑛𝑡 𝑜𝑛 𝑠ℎ𝑎𝑓𝑡 = 𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑜𝑛 𝑠ℎ𝑎𝑓𝑡 ∗ 1.1365 = 2904.25 𝑁 (5.4) Resultant moment is given in Equation5.5

𝑅𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 𝑚𝑜𝑚𝑒𝑛𝑡 = √(𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑜𝑛 𝑠ℎ𝑎𝑓𝑡) + (𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑜𝑛 𝑠ℎ𝑎𝑓𝑡) = 301476.52 𝑁 (5.5) Properties of shaft material is given in Table5.2below:

Table 5.2: Shaft Material Properties

Property Value Unit Length of shaft 2.48 𝑚

Yield Strength 250 𝑀𝑃𝑎 Ultimate Tensile Strength 460 𝑀𝑃𝑎

Factor of Safety 2 -Allowable bending stress(𝜎 ) 90 𝑀𝑃𝑎

Allowable shear stress(𝜏 ) 45 𝑀𝑃𝑎

From above data and using equations of equivalent bending moment and equivalent torque, the di-ameter of shaft can be calculated. The didi-ameter of shaft is then compared and the highest of the two values is selected as the final diameter of shaft.

Equivalent Torque method

Equivalent torque is given by Equation5.6

𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑡𝑜𝑟𝑞𝑢𝑒 = √(𝐵𝑒𝑛𝑑𝑖𝑛𝑔 𝑚𝑜𝑚𝑒𝑛𝑡 ∗ 𝑘 ) + (𝑇𝑜𝑟𝑞𝑢𝑒 ∗ 𝑘 ) = 559935.11 𝑁𝑚 (5.6) Diameter of shaft is given by Equation5.7

√16 ∗ 𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑡𝑜𝑟𝑞𝑢𝑒

𝜏 ∗ 𝜋 ∗ 10 = 0.399 𝑚 (5.7)

Equivalent Bending moment method

Equivalent Bending moment is given by Equation5.8

𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝐵𝑒𝑛𝑑𝑖𝑛𝑔 𝑚𝑜𝑚𝑒𝑛𝑡 = √(𝐵𝑒𝑛𝑑𝑖𝑛𝑔 𝑚𝑜𝑚𝑒𝑛𝑡 ∗ 𝑘 ) + 𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑡𝑜𝑟𝑞𝑢𝑒 = 506074.95 𝑁𝑚 (5.8) Diameter of shaft is given by Equation5.9

√32 ∗ 𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝐵𝑒𝑛𝑑𝑖𝑛𝑔 𝑚𝑜𝑚𝑒𝑛𝑡

𝜎 ∗ 𝜋 ∗ 10 = 0.385 𝑚 (5.9)

As both the values are the same, the diameter of shaft for the drive pulley is calculated to be400 𝑚𝑚. Similar analysis was done to evaluate the shaft diameter of smaller conveyor belt. The shafts of smaller belt conveyor system are given in Chapter4Table4.1. The fatigue analysis on the shaft will be done in Ansys workbench for the smaller conveyor as the dynamic analysis is only present for smaller conveyor. Static structure analysis is conducted in workbench version 16.1. The shaft is made in ansys using the geometry module and loading is done on the shaft as shown in Figure5.1.

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5.1.Static Analysis 29

Figure 5.1: Loading on pulley shaft in Ansys

As shown in Figure5.1the loading pattern is clearly visible. The analysis is done in two stages, one with a coarse mesh shown in Figure5.2and other with a much finer mesh shown in Figure5.4. Loading pattern is static and majority of load is applied on region under the pulley. The blue region represents the fixed location of the shaft on the pulleys.

(a) Coarse Meshing (b) Deformation of Shaft

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Figure 5.3: Stress in the shaft - Coarse Mesh

The coarse mesh is shown in Figure 5.2 has 3522 nodes and 660 elements. The element used is 4 node quadrilateral to have good values of equivalent stress along the length of the shaft. As seen in Figure5.3the equivalent stress under fatigue conditions is 22.24 MPa. It can be seen from Table5.2 the allowable stress is 125 MPa which gives an safety factor of 5.62 which is quite large. It can be seen here that such a large safety value is used to compensate the dynamic effect, but still it is quite high.

(a) Fine Meshing (b) Deformation of Shaft

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5.2.Dynamic Analysis 31

Figure 5.5: Stress in the shaft - Fine Mesh

The coarse mesh is shown in Figure 5.4 has 6446 nodes and 3949 elements. The element used is triangular elements, refined near the fixed location to have excellent values of equivalent stress. As seen in Figure5.5 the equivalent stress under fatigue conditions is 35.28 MPa. It can be seen from Table 5.2the allowable stress is 125 MPa which gives an safety factor of 3.54, which is quite large. It can be seen here that such a large safety value is used to compensate the dynamic effect.

5.2. Dynamic Analysis

The transient structural analysis is conducted in Ansys Workbench 16.1. The variation of stress on the shaft with respect to time is found from this analysis. This stress variation is used to find the life of the shaft for each in every value of stress, which can be calculated from S-N curve of the material. This is used to find life of the shaft using Miner’s rule. Another method to find life in terms of number of cycles is using rainflow method instead of S-N curve to find the life for each of the stresses found from Ansys. Then using software’s like J-Rain, the stress ranges and corresponding life of shaft can be found out. Shaft will be analyzed using both these methods and a comparison will be made based on the values of number of life cycles.

Before that, it is essential to find the variation of stress using Ansys workbench. The boundary condi-tion of the shaft is same as in the static analysis. The forces that act on the shaft are different. The tension and joint forces acting on the pulley are evaluated from ADAMS. These forces will act in an time domain analysis on the shaft and the shaft will be analyzed to find out effects of these forces. Figure5.6shows how the shaft is loaded in Ansys for transient analysis. Total number of steps used for this analysis is 100. The results from ADAMS is exported in such a way that the system is analyzed in 100 sub-steps. This information is feed to Ansys to calculate the stress variation and provide details with respect to the maximum stress value acting on the shaft. The complete the analysis the total deformation of the shaft is also calculated.

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Figure 5.6: Loading of shaft for Transient analysis

To save time only fine mesh is analyzed in this analysis. On simulating the analysis, the stress and deformation of shaft with respect to time is found out and these are shown in Figures 5.7 and 5.8 below respectively.

Figure 5.7: Stress in Shaft

The maximum value of stress is 207.75 MPa at time t = 0.01 seconds, which is at just the start of the system. This is very to the maximum yield limit of the shaft. Therefore, it can be concluded that the as far as the design of shaft with respect to stress is considered, the shaft has minimal factor of safety and should not be used.

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Figure 5.8: Deformation of Shaft

The maximum value of deformation is 2.86 mm at time t = 0.01 seconds. This value can be considered to be under safety limits, but suitable stiffness should be provided to minimize this value and to protect the shaft from unbalancing.

Now we will calculate the life of shaft in terms of number of cycles before failure using S-N curve and rainflow counting methods.

5.2.1. S-N Curve

The stress result obtained from Ansys is used to find the life of the shaft in terms of number of cycles. One of the method to find life of shaft is the use of S-N curve. The stress values obtained from Ansys are used to find the corresponding life using S-N Curve of the material. The material used here is Steel, more specifically structural steel with a Yield limit of 250 MPa and ultimate strength of 360 MPa. A S-N curve is given by Ansys workbench which is taken in a semi-log format. This means that the stress is represented in normal coordinated and the N (number of cycles) is represented in a logarithmic format as shown in Figure5.9below.

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To get the number of cycles corresponding to the stress values obtained from Ansys, Matlab is utilized. The code used to obtain the values of number of cycles is given in AppendixD.2.1. As you can see in the code, a soothing curve is used to create the S-N curve and find the values of number of cycles in logarithmic terms. These values are taken from Matlab in excel format and are analyzed further using Miner’s rule.

Miner’s rule or cumulative damage rule is the most prominent method to determine the damage to a model. The expression is given below [26]:

Σ 𝑛

𝑁 = 𝐶 (5.10)

Miner’s rule is the simplest cumulative damage model available. It simply states that if there are ’k’ different stress levels acting on the model and the number of cycles to failure at 𝑆 is 𝑁 and ’C’ represents the damage factor. If the value of ’C’ is 1 for a particular model, it is said that the model fails. The values of stress obtained from Ansys as given in Table D.1 is used in Matlab to obtain the value of number of cycles (𝑁 ) for a particular stress. Table 5.3 shows the life of shaft corresponding to particular stress cycle. Also, the table shows the

Table 5.3: Life of Shaft in terms of number of cycles

Sr. No. Results from Matlab (𝑁 ) 𝑛 /𝑁

Life in terms of Log Life in terms of Number of Cycles

1 5.267952242 1.85E+05 5.40E-06 2 4.377445854 2.38E+04 4.19E-05 3 5.254017449 1.79E+05 5.57E-06 4 5.096238557 1.25E+05 8.01E-06 5 4.565039861 3.67E+04 2.72E-05 6 5.137811634 1.37E+05 7.28E-06 7 5.015892726 1.04E+05 9.64E-06 8 4.684276223 4.83E+04 2.07E-05 9 5.071487371 1.18E+05 8.48E-06 10 4.962112209 9.16E+04 1.09E-05 11 4.772256869 5.92E+04 1.69E-05 12 5.017562884 1.04E+05 9.60E-06 13 4.939132378 8.69E+04 1.15E-05 14 4.825159943 6.69E+04 1.50E-05 15 4.984728277 9.65E+04 1.04E-05 16 4.925429135 8.42E+04 1.19E-05 17 4.860015437 7.24E+04 1.38E-05 18 4.961762353 9.16E+04 1.09E-05 19 4.918779523 8.29E+04 1.21E-05 20 4.882097846 7.62E+04 1.31E-05 21 4.946072258 8.83E+04 1.13E-05 22 4.916262269 8.25E+04 1.21E-05 23 4.895316636 7.86E+04 1.27E-05 24 4.936131489 8.63E+04 1.16E-05 25 4.914890383 8.22E+04 1.22E-05 26 4.903831038 8.01E+04 1.25E-05 27 4.929221095 8.50E+04 1.18E-05 28 4.914776096 8.22E+04 1.22E-05 29 4.90895501 8.11E+04 1.23E-05 30 4.924855137 8.41E+04 1.19E-05

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31 4.914890383 8.22E+04 1.22E-05 32 4.912034919 8.17E+04 1.22E-05 33 4.921872647 8.35E+04 1.20E-05 34 4.915233278 8.23E+04 1.22E-05 35 4.913976248 8.20E+04 1.22E-05 36 4.920039183 8.32E+04 1.20E-05 37 4.915576224 8.23E+04 1.21E-05 38 4.915004676 8.22E+04 1.22E-05 39 4.918779523 8.29E+04 1.21E-05 40 4.915804883 8.24E+04 1.21E-05 41 4.91569055 8.24E+04 1.21E-05 42 4.91797828 8.28E+04 1.21E-05 43 4.916033565 8.24E+04 1.21E-05 44 4.916033565 8.24E+04 1.21E-05 45 4.917520552 8.27E+04 1.21E-05 46 4.916147914 8.24E+04 1.21E-05 47 4.916262269 8.25E+04 1.21E-05 48 4.917177315 8.26E+04 1.21E-05 49 4.91637663 8.25E+04 1.21E-05 50 4.916490997 8.25E+04 1.21E-05 51 4.91694852 8.26E+04 1.21E-05 52 4.91637663 8.25E+04 1.21E-05 53 4.916490997 8.25E+04 1.21E-05 54 4.91683413 8.26E+04 1.21E-05 55 4.916490997 8.25E+04 1.21E-05 56 4.916605369 8.25E+04 1.21E-05 57 4.916719747 8.26E+04 1.21E-05 58 4.916490997 8.25E+04 1.21E-05 59 4.916605369 8.25E+04 1.21E-05 60 4.916719747 8.26E+04 1.21E-05 61 4.916605369 8.25E+04 1.21E-05 62 4.916605369 8.25E+04 1.21E-05 63 4.916605369 8.25E+04 1.21E-05 64 4.916605369 8.25E+04 1.21E-05 65 4.916605369 8.25E+04 1.21E-05 66 4.916605369 8.25E+04 1.21E-05 67 4.916605369 8.25E+04 1.21E-05 68 4.916605369 8.25E+04 1.21E-05 69 4.916605369 8.25E+04 1.21E-05 70 4.916605369 8.25E+04 1.21E-05 71 4.916605369 8.25E+04 1.21E-05 72 4.916605369 8.25E+04 1.21E-05 73 4.916605369 8.25E+04 1.21E-05 74 4.916605369 8.25E+04 1.21E-05 75 4.916605369 8.25E+04 1.21E-05 76 4.916605369 8.25E+04 1.21E-05 77 4.916605369 8.25E+04 1.21E-05 78 4.916605369 8.25E+04 1.21E-05 79 4.916605369 8.25E+04 1.21E-05 80 4.916605369 8.25E+04 1.21E-05 81 4.916605369 8.25E+04 1.21E-05 82 4.916605369 8.25E+04 1.21E-05 83 4.916605369 8.25E+04 1.21E-05 84 4.916605369 8.25E+04 1.21E-05 85 4.916605369 8.25E+04 1.21E-05

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86 4.916605369 8.25E+04 1.21E-05 87 4.916605369 8.25E+04 1.21E-05 88 4.916605369 8.25E+04 1.21E-05 89 4.916605369 8.25E+04 1.21E-05 90 4.916605369 8.25E+04 1.21E-05 91 4.916605369 8.25E+04 1.21E-05 92 4.916605369 8.25E+04 1.21E-05 93 4.916605369 8.25E+04 1.21E-05 94 4.916605369 8.25E+04 1.21E-05 95 4.916605369 8.25E+04 1.21E-05 96 4.916605369 8.25E+04 1.21E-05 97 4.916605369 8.25E+04 1.21E-05 98 4.916605369 8.25E+04 1.21E-05 99 4.916605369 8.25E+04 1.21E-05 100 4.916605369 8.25E+04 1.21E-05

According to miner’s rule using Equation5.10the damage ’C’ can be calculated which is found to be 1.24E-03. This implies that the pulley shaft is not in immediate danger of damage but does not clears say about the remaining life of the shaft under this transient stress. To find this out we simply inverse the value of ’C’ for a particular model. For the pulley shaft in this research, the life in terms of number of cycle is 807 cycles. This is not a lot for system of this importance, as the shaft will fail when its exposed to808 stress cycle. Thus it is imperative to design a much more suitable shaft which will have required strength to operate effectively under static and dynamic conditions.

5.2.2. RainFlow Counting

The rainflow counting method is used analysis fatigue load data on a model to reduce the complex spectrum of varying stress to cycles of simple stress reversals. Figure 5.10 shows how the rainflow counting method helps in reducing the complex transient stress variation into a simple blocks of similar stresses.

Figure 5.10: Rainflow counting method [3]

As we know that rainflow counting can be done either in time domain or frequency domain. The counting method used here is based on time domain. Figure5.11gives a pictorial representation of all the steps involved in evaluating life of model.

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Figure 5.11: Steps involved in Rainflow counting method [4]

We will be using J-Rain to covert the complicated load cycle into blocks of simple stress cycles. A text file containing all the load data is used as an input and a text file output is selected. The user interface of J-Rain software can be seen in Figure5.12below.

Figure 5.12: User interface of J-Rain

The output file from J-Rain consists of maximum value of stress along with the minimum value. These values are used to find out the range. This range will be then implemented in Maltab to find the corresponding number of cycles based on S-N curve. The code D.2.2 is used find out the points relating to the stress ranges found from J-Rain. Then Miner’s rule is applied to find the cumulative damage and then number of life cycles of the shaft. Table5.4provide details on the procedure. According to miner’s rule using Equation5.10the damage ’C’ can be calculated which is found to be 1.86E-03. This implies that the pulley shaft is not in immediate danger of damage but does not clears say about the remaining life of the shaft under this transient stress. To find this out we simply inverse the value of ’C’ for a particular model. For the pulley shaft in this research, the life in terms of number of cycle is 537 cycles. This is not a lot for system of this importance, as the shaft will fail when its exposed to538 stress cycle. Compared to the value obtained from S-N curve, this value is much less and thus, it is imperative to design a much more suitable shaft which will have required strength to operate effectively under static and dynamic conditions considering rainflow counting method.

Tracing Condition Status - Dynamic Analysis of Belt Conveyor

Tracing Condition Status

Dynamic Analysis of Belt Conveyor

Pankaj Dheer

Tracing Condition Status

Dynamic Analysis of Belt Conveyor

Pankaj Dheer

Preface

Contents

List of Figures

List of Tables

1

Introduction

2

Research Proposal

2.1.

Problem Description

2.1.1.

State of the Art

2.2.

Proposed Solution

2.2.1.

Scientific Steps involved

2.2.2.

Deliverables

2.2.3.

Timeline

3

Modelling - PTC Creo

3.1.

Calculation of parameters

3.1.1.

Belt width Selection

3.1.2.

Idler Roller selection

3.1.3.

Belt Selection

3.1.4.

Power Calculation

3.1.5.

Pulley Selection

3.1.6.

Tensile forces

3.1.7.

Belt Layout

3.2.

3D model in Creo

4

Force Calculation - Adams

5

Analysis - Ansys Workbench

5.1.

Static Analysis

5.2.

Dynamic Analysis

5.2.1.

S-N Curve

5.2.2.

RainFlow Counting