DESIGN OF FISH FEEDING MECHANISM

FOR RECIRCULATION AQUACULTURE

SYSTEM (RAS)

NITHIN SIVAKUMAR

Master of Science Thesis TRITA-ITM-EX 2019:523

KTH Industrial Engineering and Management

Machine Design

SE-100 44 STOCKHOLM

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Examensarbete TRITA-ITM-EX 2019:523

Utformning av fiskmatningsmekanism för återcirkulation av vattenbrukssystem

Nithin Sivakumar

Godkänt

2020-09-22

Examinator

Ulf Sellgren

Handledare

Stefan Björklund

Uppdragsgivare

{Namn}

Kontaktperson

{Namn}

Sammanfattning

Fiskodling eller vattenbruk är en växande livsmedelsproducerande industri för att odla fisk i

konstgjorda tankar. Ett stort antal fiskar uppföds i tankar i 100-150 dagar och producerar mat för

befolkningen. Med ökande befolkning och minskande världsfångstfiske uppfattas vattenbruk som

en potentiell teknik för att möta den ständigt växande efterfrågan på livsmedel utan att skada

vattenlevande livsmedelskedjan. Emellertid hämmar problem som tas upp i nuvarande system som

mänsklig intervention och oanvänt foderråvara produktions hastigheten. Denna avhandling ger

metoder och riktlinjer för att lösa utmaningarna och förenkla de mekaniska designaspekterna av

lagring, transport och kontroll av utmatning processen, vilket i slutändan gynnar småskaliga

producenter och entreprenörer. Lagring och distribution av fiskfoder längs vätskeflödet innebär att

man överväger tvärvetenskapliga tekniska beräkningar. Den grundläggande kunskapen om

fluidmekanik, diskreta element egenskaper och mekanisk design har visat sig vara en effektiv

lösning för sådana utmaningar. Resultaten av detta arbete ger information om utformningen av

fiskmatning mekanismen som innehåller vätskeflöde partikeldosering och utvärdering av

komponenter som finns i systemet. Examensarbetet tillhandahåller lösningar som fungerar som

utgångspunkt för lågkostnads konstruktion, validering och automatisering av komponenter i en

utfodringsmekanism för vattenbruksindustrin.

Nyckelord: Vattenbruk, Hopper, Diskreta element, Mekanisk design.

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Master of Science Thesis TRITA-ITM-EX 2019:523

Design of fish feeding mechanism for Recirculation Aquaculture System (RAS)

Nithin Sivakumar

Approved

2020-09-22

Examiner

Ulf Sellgren

Supervisor

Stefan Björklund

Commissioner

{Name}

Contact person

{Name}

Abstract

Fish farming or Aquaculture is a growing food-producing industry to culture the fish in artificially

constructed tanks. A large number of fishes are reared in tanks for 100-150 days and produce food

for the population. With increasing population and declining worldwide capture fishery,

Aquaculture is perceived as a potential technique to meet the ever-expanding food demand without

tarnishing the aquatic food chain. However, problems which are addressed in current systems like

human intervention and unused feed material inhibit the production rate. This thesis provides

methods and guidelines to resolve the challenges and simplify the mechanical design aspects of

storage, transportation, and control of the dispensing process, which ultimately benefits the small-

scale producers and entrepreneurs. Storing and distributing the fish feed along the fluid stream

involves in considering multi-disciplinary engineering calculations. The fundamental knowledge

of fluid mechanics, discrete element properties and mechanical design have been found to be an

effective solution for such challenges. The results of this work provide information on designing

the fish feeding mechanism incorporating fluid stream particle dispensing and evaluation of

components present in the system. The thesis work provides solutions that serve as a starting point

for low-cost design, validation and automation of components in a feeding mechanism for

aquaculture industries.

Keywords: Aquaculture, Hopper, Discrete elements, Mechanical design.

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FOREWORD

Firstly, I would like to thank my parents for their endless support from India and sacrifices over

the years to help get me where I am. I am eternally grateful to Sherjeel Ton, CEO at Cross-

Disciplinary Engineering, for all the support, practical help, and patience throughout this project.

Sincere thanks to Cross-Disciplinary Engineering for supporting me in this project. I want to thank

Associate Professor, Stefan Björklund, at KTH Royal Institute of Technology for all his frequent

and vital advice, ideas, and encouragement. I would also like to thank Håkan Karlsson, Technical

Manager at MAFA for his tireless assistance on both theoretical and practical matters.

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NOMENCLATURE

Notations

Symbol Description

𝑑𝑠 𝑆𝑐𝑟𝑒𝑤 𝑎𝑢𝑔𝑒𝑟 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 (𝑚𝑚)

𝑑𝑐 𝑆ℎ𝑎𝑓𝑡 𝑜𝑢𝑡𝑒𝑟 𝑑𝑖𝑎𝑚𝑡𝑒𝑟 (𝑚𝑚)

𝑟𝑝 𝑅𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑝ℎ𝑒𝑟𝑖𝑐𝑎𝑙 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 (𝑚𝑚)

𝐶𝐹1 𝑆𝑝𝑒𝑐𝑖𝑎𝑙 𝑠𝑐𝑟𝑒𝑤 𝑝𝑖𝑡𝑐ℎ 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟

𝐶𝐹2 𝑆𝑝𝑒𝑐𝑖𝑎𝑙 𝑠𝑐𝑟𝑒𝑤 𝑓𝑙𝑖𝑔ℎ𝑡 𝑚𝑜𝑑𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟

𝐶𝐹3 𝑆𝑝𝑒𝑐𝑖𝑎𝑙 𝑠𝑐𝑟𝑒𝑤 𝑚𝑖𝑥𝑖𝑛𝑔 𝑝𝑎𝑑𝑑𝑙𝑒 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟

𝜌𝑏 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑎𝑠 𝑐𝑜𝑛𝑣𝑒𝑦𝑒𝑑 (𝑘𝑔/𝑚3)

𝐹0 𝑂𝑣𝑒𝑟𝑙𝑜𝑎𝑑 𝐻𝑃 𝑓𝑎𝑐𝑡𝑜𝑟

𝐿 𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑐𝑟𝑒𝑤 𝑎𝑢𝑔𝑒𝑟 (𝑚)

𝑒 𝐷𝑟𝑖𝑣𝑒 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦

𝐹𝑚 𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝐹𝑎𝑐𝑡𝑜𝑟

𝐹𝑓 𝐹𝑙𝑖𝑔ℎ𝑡 𝑚𝑜𝑑𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝐻𝑃 𝑓𝑎𝑐𝑡𝑜𝑟

𝐹𝑝 𝑃𝑎𝑑𝑑𝑙𝑒 𝐻𝑃 𝑓𝑎𝑐𝑡𝑜𝑟

𝐹𝑑 𝐶𝑜𝑛𝑣𝑒𝑦𝑜𝑟 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝐻𝑃 𝑓𝑎𝑐𝑡𝑜𝑟

𝐹𝑏 𝐻𝑎𝑛𝑔𝑒𝑟 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 𝐻𝑃 𝑓𝑎𝑐𝑡𝑜𝑟

𝑁 𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑐𝑟𝑒𝑤 𝑐𝑜𝑛𝑣𝑒𝑦𝑜𝑟

𝐻𝑃𝑡𝑜𝑡𝑎𝑙 𝑇𝑜𝑡𝑎𝑙 𝐻𝑜𝑟𝑠𝑒𝑝𝑜𝑤𝑒𝑟 (kW)

𝐻𝑃𝑓 Frictional Horsepower (kW)

𝐻𝑃𝑚 Material Horsepower (kW)

𝑃2 Pressure of water at the Pipe junction (Pa)

𝑃3 Pressure of water at the tank surface (Pa)

𝑉2 Velocity of water at the Pipe junction (m/s)

𝑉3 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑎𝑡 𝑡ℎ𝑒 𝑡𝑎𝑛𝑘 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 (m/s)

𝜌 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 (𝑘𝑔/𝑚3)

𝑔 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑢𝑒 𝑡𝑜 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 (9.8 𝑚/𝑠2)

𝑉ℎ𝑜𝑝𝑝𝑒𝑟 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 ℎ𝑜𝑝𝑝𝑒𝑟 (𝑚3)

𝑉𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑝ℎ𝑒𝑟𝑖𝑐𝑎𝑙 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 (𝑚3)

𝑀𝑝 Mass of single-feed particle (grams)

𝑁𝑝ℎ Total number of particles that can be accommodated inside the hopper

𝑀𝑝ℎ Total mass of the particles accommodated inside the hopper (kg)

x

𝑁𝑝𝑝 Number of particles that can be accommodated between one pitch of

the screw conveyor

𝑀𝑝𝑝 Total mass of the particles accommodated between one pitch of the

the screw conveyor

𝑊𝑝𝑒 Total weight of pellets in conveying tube (kg)

𝐿𝐴𝑔 Length of flexible screw auger (m)

𝑊𝐴𝑔 weight per unit length of flexible screw auger (kg/m)

𝑃𝑑 𝑃𝑎𝑐𝑘𝑖𝑛𝑔 𝑑𝑒𝑛𝑠𝑖𝑡𝑦

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Abbreviations

AISI American Iron and Steel Institute

ASTM American Society for Testing and Materials

CAD Computer Aided Design

CEN European Committee for Standardization

DN Diameter Nominal

FCR Food Conversion Rate

PVC Poly Vinyl Chloride

SS316 Stainless steel AISI 316

RAS Recirculation Aquaculture System

SMS Sveriges Mekanförbunds Standardcentral

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Table of contents

SAMMANFATTNING ............................................................................................................................................... III

ABSTRACT ................................................................................................................................................................ V

FOREWORD ........................................................................................................................................................... VII

NOMENCLATURE .................................................................................................................................................... IX

TABLE OF CONTENTS ..................................................................................................................................... XII

1 INTRODUCTION .................................................................................................................................................1

1.1 BACKGROUND ...............................................................................................................................................1 1.2 PURPOSE .......................................................................................................................................................2 1.3 DELIMITATIONS ..............................................................................................................................................2 1.4 RESEARCH QUESTIONS ................................................................................................................................ 2

2 FRAME OF REFERENCE .................................................................................................................................3

2.1 RECIRCULATION AQUACULTURE SYSTEM (RAS) ..........................................................................................3 2.1.1 Relevant theory .......................................................................................................................................3 2.1.2 Feed pellets .............................................................................................................................................4 2.1.3 Hopper ....................................................................................................................................................5 2.1.4 Screw conveyors ......................................................................................................................................7 2.1.5 Pipeline system .......................................................................................................................................8 2.1.6 Control system ........................................................................................................................................9 2.1.7 Bulk solid flow sensor ............................................................................................................................10

3 IMPLEMENTATION .........................................................................................................................................11

3.1 METHODOLOGY ...........................................................................................................................................11 3.1.1 Hopper selection ...................................................................................................................................11 3.1.2 Hopper evaluation .................................................................................................................................11 3.1.3 Selection and assessment of conveyor system .......................................................................................14 3.1.4 Calculation of power and torque requirements......................................................................................14 3.1.5 Control system ......................................................................................................................................16

4 RESULTS ..........................................................................................................................................................18

4.1 EXPERIMENTAL RESULTS .............................................................................................................................18 4.1.1 Hopper selection ...................................................................................................................................18 4.1.2 Hopper structural analysis .....................................................................................................................19

4.2 SELECTION OF CONVEYOR SYSTEM .............................................................................................................20 4.3 FEED CONVEYING SYSTEM DESIGN ..............................................................................................................25

4.3.1 Driven shaft system design ....................................................................................................................25 4.3.2 Driving shaft system design ...................................................................................................................27

4.4 DETAILED DESIGN OF COMPONENTS ...........................................................................................................29 4.4.1 Key/keyway ...........................................................................................................................................29 4.4.2 Bearings ................................................................................................................................................29 4.4.3 Flanged housings ..................................................................................................................................31 4.4.4 Locating lid............................................................................................................................................31

4.5 PIPELINE LIFT HEIGHT ..................................................................................................................................32 4.6 CONTROL OF MASS FLOW RATE ...................................................................................................................33

5 DISCUSSION AND CONCLUSIONS ............................................................................................................35

5.1 DISCUSSION .................................................................................................................................................35 5.1.1 Hopper evaluation .................................................................................................................................35 5.1.2 Pipeline design ......................................................................................................................................35 5.1.3 Auger evaluation ...................................................................................................................................35 5.1.4 System control ......................................................................................................................................36

5.2 CONCLUSIONS .............................................................................................................................................36

6 RECOMMENDATIONS AND FUTURE WORK .............................................................................................37

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6.1 RECOMMENDATIONS ....................................................................................................................................37 6.2 FUTURE WORK .............................................................................................................................................37

7 REFERENCES ..................................................................................................................................................38

APPENDIX A: SCREW CONVEYOR DESIGN MANUAL ..............................................................................41

APPENDIX B: KEY DESIGN CALCULATOR ..................................................................................................53

APPENDIX C: BEARING LIFE CALCULATION .............................................................................................54

APPENDIX D: VOLUME AND LOAD CALCULATION USING 3D CAD SOFTWARE ..............................56

APPENDIX E: SYSTEM CONTROL – SIMULINK MODEL ............................................................................57

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1 INTRODUCTION

This report focuses on the design and evaluation of storage, transportation and dispensing

components present in the fish feed mechanism for Recirculation Aquaculture System (RAS).

1.1 Background

Recirculation Aquaculture System is an emerging technology in the field of Aquaculture systems

to meet the demand for seafood in the market. The ever-expanding seafood demand is depleting

the resources in the ocean. Recirculating aquaculture systems offer sustainable solutions for

meeting such requirements by using closed-loop water treatment and circulation [1]. One of the

essential subsystems in a RAS is the grow-out tank. Thousands of fishes are raised in these grow-

out tanks for 100-150 days depending on the species. A process diagram indicating the working

of a RAS system is shown in Figure 1.

Figure 1 Recirculation Aquaculture System

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Bio-Filtration

(ammonia removal)

Feeding

mechanism

Fish wastes and uneaten feed

Mechanical filter 2

Solids Removal

1

Grow-out Tank

Bio- Filter

4

Dissolved gas Control

(Oxygenation)

Aeration Unit

Recirculated

water “in”

Recirc

ula

ted

water “

ou

t”

2

1.2 Purpose

Meeting the food demand for the culture of the fishes in the aquaculture system is a critical process

as they incorporate a regular feeding schedule. There are several working models for dispensing

the fish feed on the water surface in culture tanks [2], but there is no existing design which

incorporates feed dispense with the fluid stream. In the fluid stream dispensing method, the feed

particles are not allowed to settle down due to water current, which significantly reduces the

amount of uneaten fish feed. In addition to this, surface dispensing results in bloating of fish and

eventually reduces its life. The thesis work gives information on designing of a feeding mechanism

for Recirculation Aquaculture System (RAS) and evaluation of the storage, transportation and

dispensing components present in the fish feeding mechanism. The feeding mechanism

incorporates fluid stream fish feed dispensing and control of feed rate (kg/hr) to maximize the feed

conversion rate (FCR) or to minimize the amount of uneaten feed.

1.3 Delimitations

The thesis work was carried out with assumptions in places where there is a lack of experimental

data. The assumptions made are closely associated with the real-time situation. The delimitations

that exist in this work are presented below

The Hopper deformation was simulated by assuming the Bulk material as a liquid which

exerts pressure equally in all the directions. The behaviour of the discrete elements was not

taken into consideration in the static structural simulation.

The forces exerted by the discrete element particles on the components of the driving shaft

and driven shaft sub-assembly are assumed with a conservative factor of safety.

The sensor signals used for simulating the closed-loop control model developed in

Simulink were generated manually to check the feasibility of the control algorithm. No

experiments were conducted to extract the data for the simulation.

1.4 Research questions

The various research questions that were addressed and answered in this thesis are,

Is it possible to facilitate fluid stream dispensing of feed particles ?

How far can material intensive design be elimated in the feeding mechanism ?

To what extent can the human intervention be reduced in the feeding process?

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2 FRAME OF REFERENCE

2.1 Recirculation Aquaculture System (RAS)

In a recirculation aquaculture system, the feeding mechanism plays a significant role in deciding

the overall efficiency, i.e. the Feed Conversion Rate (FCR). The feeding device in this thesis

consists of four specific parts, namely the feed pellets, hopper to store the feed pellets, screw auger

for feed transportation and a dispensing approach.

2.1.1 Relevant theory The basic definitions and the technical terms used throughout the report are consolidated and

elaborated in this subsection.

Bulk density of a powder contained in a known volume is the ratio of the Mass of the Powder to

the Volumetric capacity of the container, including the inter-particle void volume. Bulk density is

expressed in kg/m3. Bulk density depends on the spatial arrangement of the particles in all the

layers of the powder bed. A powder contained in a known volume can have a range of Bulk density

depending on its preparation, treatment, and storage.

Packing density (Pd) is a parameter that defines how efficiently you arrange particles in a given

volume with minimum void space between the particles in 3D dimensional space. For perfectly

ordered and closely packed spheres, the packing density is found to be 0.74 according to [3] and

decrease till 0.54 for random packing and different encapsulated volumes [4] (see Figure 2 [5]).

Untapped Bulk Density is defined as the Bulk density of the powder as it is stored. Even the

slightest tap of the container rearranges the spatial arrangement of the powder layers to fill in the

interparticle voids.

Figure 2 Random packing (left) and perfect packing (right) of dice in a cylinder

4

The Powder's Effective Angle of Internal Friction is the measure of friction within the adjacent

particles when its sheared internally. The effective angle of internal friction is stated in degrees.

The Hopper Wall Angle (𝜽) in Figure 3 represents the angle in degrees of the conical hopper wall

measured from a line drawn vertically along the axis of the hopper.

The Powder's Wall Friction Angle expressed in degrees is the measure of the sliding friction at

the powder-wall interface. In this study, the powder is the fish feed pellets.

Feed Conversion Rate (FCR) also called the Aquaculture production efficiency, is the ratio of kg

of feed dispensed in the culture tank to the kg of fish produced.

𝐹𝐶𝑅 =𝑘𝑔 𝑜𝑓 𝑓𝑒𝑒𝑑 𝑑𝑖𝑠𝑝𝑒𝑛𝑠𝑒𝑑

𝑘𝑔 𝑜𝑓 𝑓𝑖𝑠ℎ 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑

2.1.2 Feed pellets

The feed pellets shown in Figure 4 are to be stored and transported to the culture tank. The size

of the fish food (Feed) dispensed in the pipeline system varies from time to time. For the first 51

days, 4.5 mm diameter spherical pellets are dispensed in the culture tank. With growing fish size,

6.5 mm pellets are distributed in the tank for the next 51 days. Throughout this report, the

calculations are done for the larger 6.5 mm pellets since they occupy more volume inside a hopper

for a specified weight (for example, 3000 kg). The image of the 6.5 mm feed pellets is shown in

Figure 4. The constituents of the feed pellets are Crude protein, Crude fat, Carbohydrates, Fibre,

Ash and Phosphorus at different Proportions.

Figure 3 Hopper wall angle

Figure 4 Feed pellets

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2.1.3 Hopper

The picture illustrated in Figure 5 represents a hopper which is a cylindrical tank-like structure

used to store granular materials. It consists of conical bottom part attached to one or more

cylindrical sections placed on top of each other. The hopper is constructed by bending and rolling

of steel sheets ranging from 1 mm to 6 mm thickness into a hollow cylindrical structure and held

together with the help of rivets. Support structures are provided to the hopper to prevent it from

collapsing. The Hopper material changes from one manufacturer to another based on their

structural requirements. In general, the thickness of the sheet metal in the hopper varies along its

vertical dimension, i.e. the bottom cone part has a comparatively higher material thickness to

withstand the weight of particle layers above it.

Though the flow of particles inside the hopper seems easy, it involves in the calculation of several

parameters like powder's wall friction angle, semi-included angle, interparticle friction etc. These

parameters are required to determine the type of flow inside the hopper. There are two different

types of flow inside a Hopper, namely mass flow, and funnel flow (see Figure 6).

Conical

Bottom

Outlet

Cylindrical

tank

Figure 5 Schematic representation of hopper for storing granular materials

a) b)

Figure 6 a) Funnel Flow b) Mass flow

6

In mass flow during discharge as depicted in Figure 7, the first portion of the granular material

entering the silo is the first to exit through the hopper outlet, i.e. it provides first-in, first-out flow

with all the particles in motion during discharge. Figure 8 shows the funnel flow, where the central

portion of material forms a channel and flows out first leaving behind stagnant zones inside the

hopper. The mass flow has several advantages over the funnel flow. It can be observed from Figure

7; the motion of the particles is uniform and steady [6]. The Bulk density of the powder discharged

remains constant and is independent of the height of the Hopper/Silo. As a result, the particle layers

remain non-cohesive throughout the discharge operation taking place inside the hopper.

However, the interparticle friction and wall friction due to the continuous flow of powders erodes

the hopper wall in the long run. In such cases, funnel flow or core flow is used. The funnel flow

shown in Figure 8 has a predominant flow of particle stream through the central channel compared

to a nearly stagnant flow at the hopper walls [6]. Note that a hopper giving mass flow with one

type of particle necessarily does not provide mass flow with different particle. According to [7]

the flow of the particles inside the hopper depends on

Semi-included angle

Wall friction angle

Effective angle of internal friction

Powder's flow function

Untapped Bulk density

In general, the material used for the hopper construction changes from one manufacturer to another

depending on the requirements. These requirements are drafted based on the type of material to be

stored in the hopper, its abrasiveness, and the maximum weight of the Bulk material it can hold.

The RAS system discussed in this report requires a durable hopper which is environment friendly

and has zero adverse effects on the fish feed particles. On extensive research, two materials,

namely Stainless steel AISI 316 [8] and Mild Steel coated with Aluzinc (DX51D+AZ) [9], were

identified to be commonly used in the food industries for the transporting bulk materials. These

Figure 8 Funnel Flow of discrete elements in a hopper

Figure 7 Mass Flow of discrete elements in a hopper

7

two materials are environment friendly with good corrosion resistance and mechanical properties.

The latter part of the report gives a detailed explanation of the tests carried out for evaluating the

mechanical properties of the hopper material.

2.1.4 Screw conveyors

The Screw conveyor system transports the particles from inlet to outlet with the help of a screw

auger. It consists of multiple hollow shafts supported at the ends and connected using a solid shaft

with fastening elements. A motor drives the auger through the power transmission components.

To construct the screw auger, the inner diameter of the spiral helix is welded onto the outer

diameter of the hollow shaft (see Figure 9 [10]). This auger setup is enclosed by a trough to move

the materials in a predefined path. The helix face of the screw auger provides the necessary

thrusting force to drive the feed pellets towards the outlet. The particles are sheared and tumbled

continuously by rotary, and linear motion exerted on them by the screw auger. Each rotation of the

screw auger transports the feed material present between screw auger pitch through continuous

tumbling and shearing action.

There are distinct augers which are shaftless throughout its length except for end cap and the motor.

These screw augers provide comparatively higher mass flow rate due to larger volumetric space

available between the conveying tube and the screw auger. The two ends of the shaft are supported

by bearings to avoid eccentric turning. One of the significant advantages which can be observed

from Figure 10 of shaftless screw augers is that they provide flexibility with length [11], enabling

them to fit into pipes having a certain radius of curvature.

Figure 10 Flexible Screw Conveyor

Conveying tube

Motor

End cap

Figure 9 Conventional screw conveyor for transporting Bulk materials

8

2.1.5 Pipeline system

The pipeline system integrates the hopper-screw conveyor system with the culture tank. Figure

11 shows the mainline pipe connecting the feeder system split into three sections, namely the

pump end, junction end, and the tank/nozzle end. All three parts use the pipework components

based on the DN150 nominal size. The water is pumped to the culture tank at a specified pressure

and velocity. This portion of piping until the screw auger system is called the pump section. The

T-junction is connected to the screw conveyor to dispense the particles into the fluid stream by

gravity. The final portion of pipeline extending from junction end till the nozzle at the tank is

called the tank section. The pipe material used here is PVC, and the pipe standard followed is

CEN/TC 155 [12]. Using the available pipeline parameters such as the density of the fluid,

velocity of the fluid and the vertical height of fluid level from the ground, the minimum pressure

required to pump the water to a defined head (in metres) can be calculated using Bernoulli's

theorem [13]. The details of the pipe dimensions are provided in Table 1 and its visual

representation in Figure 12.

Table 1 Pipe Dimensions according to CEN Standard

Pipe Specification: DN 150

Material PVC

Inside Diameter (ID) 154.08 mm

Outside Diameter (OD) 168.3 mm

Pipe Wall Thickness (t) 7.11 mm

Surface roughness, Ra 1.5 µm

Figure 11 Pipeline layout in RAS system

Pum

p e

nd

Junction end

Water from pump

Culture tank

T-Junction

Integration with delivery

tube of the conveyor

Tank section

Nozzle

9

Figure 12 Dimensions of DN150 based on CEN Standards

2.1.6 Control system A control system directs and edits the parameters of a continuous time-variant system in such a

way that the desired output is produced [14]. The two significant attributes of a control system are

its stability and its ability to retain the desired output. The two types of control systems are

Open-loop and

Closed-loop control systems

An open-loop control system takes in the time-variant input given and gives the results as

produced. There is no control over the value of the output produced irrespective of the desired

value of the result. There are no external or internal disturbances encountered that affects the

system. The components of an open-loop control system are shown in Figure 13.

In a closed-loop control system, as depicted in Figure 14, feedback control is incorporated that

adjusts the parameters of the system to get the desired output. The difference between ideal value

and measured value from the sensor is taken as an error and added as feedback. A closed-loop

system minimizes the error between what is measured and what is desired iteratively. As a result,

the desired result is obtained and maintained for successive cycles.

Figure 14 Process flow diagram of a Closed-Loop control system

Figure 13 Process flow diagram of an Open-Loop control system

OD

ID t

10

A control system has different components like Reference or setpoint, Controller, Actuator, and

Plant. The components are sequenced as illustrated in process flow diagrams. An actuator is a

component that does the work to obtain the desired output. The object whose output must be

controlled is called the plant. The reference or set point is the desired output to be produced from

the system. The output signal measured using the sensor is compared with the desired output. The

difference in value is termed as an error in the signal. The controller acts based on the computed

error and sends the command to the actuator to correct its parameters to get the desired output. If

the data from previously installed sensors for an intended application are not available, a logical

solution is to model the sensor values as Gaussian distribution [15].

2.1.7 Bulk solid flow sensor

A Bulk solid flow sensor shown in Figure 15 is used for measuring the mass flow rate of Bulk

solid flow inside an Open or closed channel [16] [17]. It accurately predicts the number of particles

or the weight of the Bulk material flowing through channels. Bulk solid flow sensor works under

the principle of physical doppler effect [18]. According to this principle, the sensor generates a

uniform electromagnetic field in microwave frequency, and it calculates the number of particles

passing through the field. Every particle passing through this electromagnetic field reflects the

microwaves to the sensor's receiver. The main advantage of this sensor is that it can be integrated

into the existing systems having a vertical channel or a horizontal channel effortlessly.

Figure 15 Bulk solid flow sensor application

Particle flow

Bulk solid

flow sensor

Open Channel

Sensor

Closed Channel

Sensor

11

3 IMPLEMENTATION

3.1 Methodology

3.1.1 Hopper selection

For selecting the Hopper, maximum weight/load to be stored is first determined. Then a safety

factor is considered since the mass to be stored may vary. The commercially available hoppers are

explored, and the number of particles that can be held within the given volume (𝑁𝑝ℎ) is calculated

using equation (1) where 𝑉ℎ𝑜𝑝𝑝𝑒𝑟 indicates the volume of the selected hopper and 𝑉𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

indicates the volume of the feed particle. The total mass of all the particles that can be filled (𝑀𝑝ℎ)

is calculated using equation (2). For the mass experiment, 15 trials were conducted by measuring

the mass of a single particle ( mp) in a 25 ml container, as shown in Figure 16. The experimental

observations are provided in under section 4.1.1.

𝑁𝑝ℎ = (𝑉ℎ𝑜𝑝𝑝𝑒𝑟

𝑉𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 ) 𝑃𝑑

(1)

𝑀𝑝ℎ = 𝑁𝑝ℎ𝑚𝑝 (2)

3.1.2 Hopper evaluation

The selected Hopper is evaluated for structural integrity to ensure that it does not collapse during

its service time. The Hopper evaluation that was carried out in ANSYS® Workbench™ and is

explained in detail.

The steps involved in the Hopper design analysis are,

Create and import a simplified CAD model in ANSYS

Definition of material properties

Discretizing the 3D model

Setting up boundary conditions

Defining the loads

Simulation and Extraction of results (Stress and strain)

Parametric analysis

Figure 16 Particles used for mass measurement

12

Figure 17 Translation of engineering drawing to 3D CAD model

Figure 18 Defining the fixed support for static structural analysis

The first step involved in the analysis is to transform the engineering drawing of the Hopper and

Hopper bottom given by the supplier MAFA AB to 3D CAD model using Autodesk Inventor

Professional 2020. From the dimensions given in the engineering drawing, the hopper assembly

was reconstructed into a simplified model, as shown in Figure 17. The two components were then

assembled and imported as a single rigid body in ANSYS to perform the structural analysis.

Hopper

Hopper

bottom

Fixed support

13

In the Main window of ANSYS Workbench, Static structural analysis is selected from the toolbox.

Since two materials are used, namely Mild Steel and SS316, the analysis is first performed using

SS316 as hopper material. Then the entire setup, including the parametric study, is replicated for

Mild Steel. The properties of Mild Steel and SS316 are not available in the material library of

ANSYS, so the physical properties of the material were imported from Outokumpu product

catalogue [8]. After setting up the material properties, the simplified 3D CAD assembly of the

Hopper was imported as a Step file.

In the Workbench editor menu, the material for the Hopper and the Hopper's bottom is assigned

as SS316. All the components in the model are then meshed using an adaptive size meshing. The

meshed model of the hopper assembly is shown in Figure 19. After meshing, the next step is to

define the loads and boundary conditions. From the drawing shown in Figure 17Figure 18, it is

evident that the entire load of fish pellets that is to be carried by the Hopper is supported at the

base by horizontal structural members and cylindrical body using vertical structural members. The

two surfaces highlighted in blue colour shown in Figure 18 were defined as fixed support.

Figure 19 Discretization of the imported CAD model in ANSYS

Figure 20 Hydrostatic pressure acting on inner walls of hopper

Liquid level

Hydrostatic pressure

exerted throughout the

hopper length

Hopper inner walls

14

Since ANSYS does not support discrete element simulations, a major assumption is made in this

step by considering the discrete elements as a fluid of equivalent Bulk density. The approximated

fluid is modelled as a hydrostatic pressure acting on the inner walls of the hopper assembly, having

the density equal to the Bulk density of the feed pellets (see Figure 20). A factor of safety has

been implemented, and the analysis is repeated for liquid with density 1000 kg/m3 (density of

water). The analysis is made simpler by parameterizing the study (see Figure 21) with a density as

the Design variable, and the results were consolidated based on maximum von-mises stress acting

on the hopper walls for both the materials.

3.1.3 Selection and assessment of conveyor system From the literature study, two system concepts were selected for the conveying system, namely

the Conventional Screw Auger and Shaftless Screw Auger. Both have their advantages and

disadvantages. In section 4.2, a Pugh’s evaluation matrix [19] is constructed for conventional

screw conveyor and shaftless screw conveyor based on the following factors.

Material requirement

Design complexity

Conveying efficiency

Maintenance and service

3.1.4 Calculation of power and torque requirements The screw conveyor system connects the Hopper with the pipeline system. The particles from the

Hopper are transported to the pipeline system via the screw auger. Irrespective of the type of auger,

the motor power is calculated for the equivalent commercially available auger with shafts (refer

Figure 9 and Figure 27). This is a conservative approach as the Power required for driving the

conventional screw conveyors is comparatively more than shaftless screw conveyors. From the

conveyor manual referred (see appendix A), the calculation of power and torque requirements is

done for the auger having the following dimensions as specified in Table 2.

Table 2 Dimensions of the screw auger from CEMC screw conveyor manual

Screw Auger specifications

Diameter of the Screw, 𝑑𝑠 152.4 mm

Diameter of the shaft, 𝑑𝑐 25.4 mm

Pitch distance 152.4 mm

Radius of the feed particle, 𝑟𝑝 3.25 mm

Figure 21 Parametrizing the design variables for simulation

15

The number of particles to be dispensed per pitch of the conventional screw auger is determined

by the following formula,

𝑁𝑝𝑝 =

𝜋4

(𝑑𝑠2−𝑑𝑐

2)

43

𝜋𝑟𝑝3

(𝑃𝑑) (3)

Where,

𝑑𝑠 − 𝑆𝑐𝑟𝑒𝑤 𝑎𝑢𝑔𝑒𝑟 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟

𝑑𝑐 − 𝑆ℎ𝑎𝑓𝑡 𝑜𝑢𝑡𝑒𝑟 𝑑𝑖𝑎𝑚𝑡𝑒𝑟

𝑟𝑝 − 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑝ℎ𝑒𝑟𝑖𝑐𝑎𝑙 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

The packing density of the sphere in a cylindrical volume for random loose packing is 0.54 [4]

Based on the number of particles per pitch ( Npp), mass per pitch (Mpp) can be determined by

multiplying the weight of a single particle ( mp).

Mpp = Nppmp (4)

The single-particle mass used is the average mass of 15 particles. The experimental data for finding

the single-particle weight is given in section 4.1.1. This approach to finding the number of particles

in the volumetric space between the pitch is for the general purpose only. Actual experimentation

must be done by filling the space with particles experimentally or by using the discrete element

simulations to find out the mass occupied in that space. The performance of screw auger depends

on numerous factors such as percentage of conveyor loading, bearing factor, friction horsepower,

material horsepower etc. The formulas governing screw auger calculations according to [20] are

given below.

𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 =𝑚𝑎𝑠𝑠 𝑡𝑜 𝑏𝑒 𝑐𝑜𝑛𝑣𝑒𝑦𝑒𝑑 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟

𝑏𝑢𝑙𝑘 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 (5)

𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 (𝑓𝑡3

ℎ𝑟⁄ ) = (𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦)𝐶𝐹1𝐶𝐹2𝐶𝐹3 (6)

Where,

𝐶𝐹1 − 𝑆𝑝𝑒𝑐𝑖𝑎𝑙 𝑠𝑐𝑟𝑒𝑤 𝑝𝑖𝑡𝑐ℎ 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟

𝐶𝐹2 − 𝑆𝑝𝑒𝑐𝑖𝑎𝑙 𝑠𝑐𝑟𝑒𝑤 𝑓𝑙𝑖𝑔ℎ𝑡 𝑚𝑜𝑑𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟

𝐶𝐹3 − 𝑆𝑝𝑒𝑐𝑖𝑎𝑙 𝑠𝑐𝑟𝑒𝑤 𝑚𝑖𝑥𝑖𝑛𝑔 𝑝𝑎𝑑𝑑𝑙𝑒 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟

The capacity per rpm is selected from the screw conveyor design manual. The total power required

by the motor to drive the screw auger is the sum of power needed to overcome friction (𝐻𝑃𝑓) and

power required to transport the material multiplied (𝐻𝑃𝑚) by overloading factor (𝐹0).

𝐻𝑃𝑡𝑜𝑡𝑎𝑙 =(𝐻𝑃𝑚+𝐻𝑃𝑓)𝐹𝑜

𝑒 (7)

𝐻𝑃𝑚 =𝐿𝑁𝐹𝑑𝐹𝑏

106 (8)

𝐻𝑃𝑓 =𝐶𝐿𝜌𝑏𝐹𝑚𝐹𝑓𝐹𝑝

106 (9)

16

𝐶 − 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝜌𝑏 − 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑎𝑠 𝑐𝑜𝑛𝑣𝑒𝑦𝑒𝑑

𝐹𝑚 − 𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝐹𝑎𝑐𝑡𝑜𝑟 𝐹𝑓 − 𝐹𝑙𝑖𝑔ℎ𝑡 𝑚𝑜𝑑𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝐻𝑝 𝑓𝑎𝑐𝑡𝑜𝑟

𝐹𝑝 − 𝑃𝑎𝑑𝑑𝑙𝑒 𝐻𝑃 𝑓𝑎𝑐𝑡𝑜𝑟 𝐹𝑑 − 𝐶𝑜𝑛𝑣𝑒𝑦𝑜𝑟 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝐻𝑃 𝑓𝑎𝑐𝑡𝑜𝑟

𝐹𝑏 − 𝐻𝑎𝑛𝑔𝑒𝑟 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 𝐻𝑃 𝑓𝑎𝑐𝑡𝑜𝑟 𝐹0 − 𝑂𝑣𝑒𝑟𝑙𝑜𝑎𝑑 𝐻𝑃 𝑓𝑎𝑐𝑡𝑜𝑟

𝑒 − 𝐷𝑟𝑖𝑣𝑒 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 𝐿 − 𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑐𝑟𝑒𝑤 𝑎𝑢𝑔𝑒𝑟

𝑁 − 𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑐𝑟𝑒𝑤 𝑐𝑜𝑛𝑣𝑒𝑦𝑜𝑟

Detailed information on the different factors and the instructions for selecting them are mentioned

in the screw conveyor design manual and the Matlab code in Appendix A.

3.1.5 Control system

The control system for the feedback control is modelled in Simulink® plugin in Matlab [21]. The

primary objective of the control loop in this application is to maintain a constant mass flow rate

by tweaking the rpm of the motor. The entire structure of the control system modelled in Simulink

is shown in Figure 22. Figure 23 illustrates that the bulk solid flow sensor is fit through a hole on

the surface of the vertical pipe. The sensor setup acts as a closed channel bulk flow sensor, and it

estimates the mass flow rate of the discrete particles falling through the pipe. For getting a clear

view of how the closed-loop control works, the mass flow rate is assumed to be 5000 kg/hr. A

simple relation is defined to state the relation between the rps (revolutions per second) of the motor

and the amount of fish feed dispensed for a single revolution of the motor shaft connected to the

auger. From the assumption, 1.39 kg of feed must be dispensed every second (See Appendix E).

This is a proportional model wherein the mass dispensed is directly proportional to the number of

revolutions of the motor. The feedback gain used in closed-loop feedback control is to converge

the results and to stabilize the overall system. The value of the gain can be tuned for quicker

convergence of the results.

Figure 22 Simulink Model of Closed-Loop control system

17

The bulk solid flow sensor data is modelled as white Gaussian noise with the mean value equal to

the ideal mass flow of feed dispensed per revolution of screw auger for 1 hour[15]. The sensor

value mimicked is brought close to the real-time situation. The command used for generating the

sensor data and the histogram plot is given in Figure 24. The difference in the desired output value

and the sensor value is computed and sent through the feedback controller, which converts the

deducted mass flow rate back into rps (revolutions per second). The value is then added as

feedback to the motor controller and will either add or reduces the speed of the motor shaft to get

the desired mass flow rate in kg/s.

Figure 24 Histogram of simulated sensor data

Figure 23 Mass flow rate control setup

Vertical pipe

Motor feedback

controller

Data generated by bulk

solid flow sensor

Sensor fitted

through drilled

hole

Conveying tube

18

4 RESULTS

4.1 Experimental results

4.1.1 Hopper selection

In the case of the fish feeder, the maximum weight of pellets to be stored is 2520 kg for 51 days.

Since the weight may vary, a safety factor with 20% excess load has been considered, and the

hopper is selected for holding a maximum weight of 3000 kg. The lab-scale experiment was set

up to find individual particle mass is shown in Figure 25. The results of the experiment conducted

according to section 3.1.1, are consolidated in Table 3.

Table 3 Bulk mass measurements for 6.5 mm diameter spherical pellets

Mass experiment

Trial Number Mass with the

glass container

×10-3(kg)

Mass of the

empty container

×10-3(kg)

Mass of individual

Particle ×10-3(kg)

Density of single

particle

(kg/m3)

1 36.86 20.38 0.16 1113

2 36.5 20.38 0.18 1252

3 37.6 20.38 0.19 1321

4 37.42 20.38 0.16 1113

5 37.57 20.38 0.15 1043

6 37.79 20.38 0.17 1182

7 37.54 20.38 0.18 1252

8 37.87 20.38 0.2 1391

9 36.52 20.38 0.18 1252

10 36.3 20.38 0.2 1391

11 36.19 20.38 0.17 1182

12 37.68 20.38 0.17 1182

13 37.35 20.38 0.18 1252

14 37.05 20.38 0.2 1391

15 37.76 20.38 0.17 1182

Average = 0.18 1233

Standard Deviation = 0.015 110

Figure 25 Lab-Scale Bulk mass measurement setup

19

The smallest commercially available hopper provided by MAFA AB, which was previously used

for the aquaculture application had a minimum volume of 6.3 m3. The specifications of the selected

hopper are shown in Table 4.

Table 4 Specifications of the commercially available hopper

Hopper specifications

Manufacturer MAFA AB

Type UNS-6

Material Mild Steel coated with Aluzinc

Semi included angle 210

Volume 6.3 m3

Height 5.33 m

Diameter 1.88 m

Weight of hopper 380 kg

The maximum weight of feed pellets that can be stored in the 6.3 m3 volume is calculated using

equation (2). The maximum weight of feed pellets which can be stored in the 6.3 m3 volume hopper

was found to be 4260 kg.

4.1.2 Hopper structural analysis

As discussed in section 3.1.2, the results of the parametric structural study on the hopper carried

out in ANSYS® Workbench™ using two different Mild Steel and SS316. The deformation plot

for Stainless Steel AISI 316 (SS316) hopper with a hydrostatic pressure exerted by a liquid having

a density of 700kg/m3 is shown in Figure 26. The results of the similarly performed simulations

are summarized in Table 5.

Figure 26 ANSYS result showing total deformation in mm along the hopper bottom

20

Table 5 Results of the parametric analysis on hopper deformation

Material Yield strength

(Ys) of the

material

(Mpa)

Density of

approximated

feed pellets

(kg/m3)

Approximate

weight of fluid

in 6.3 m3

hopper (kg)

Maximum

Equivalent

stress

(Mpa)

Maximum

deformation

(mm)

Mild Steel

coated with

Aluzinc

370 700 4410 168 2.77

1000 (water) 6300 240 3.96

Stainless

Steel AISI

316

270 700 4410 173 2.73

1000 6300 247.24 3.90

4.2 Selection of conveyor system

Based on existing literature [22], two design choices were available for integration of the screw

auger with the hopper bottom: 1) the conventional screw auger based on design manual (see Figure

27) and 2) the shaftless screw auger (see Figure 28). The evaluation matrix for selecting the screw

auger is shown in Table 6.

Table 6 Pugh's Evaluation matrix for selection of conveyor system

Pugh's Evaluation matrix

Parameters Weight (0-5) Points

Design method 1 Design method 2

Material requirement 5 4 2

Design complexity 4 4 3

Conveying efficiency 4 2 3

Maintenance & Service

requirement

3 4 3

∑(𝑤𝑒𝑖𝑔ℎ𝑡𝑎𝑔𝑒 × 𝑝𝑜𝑖𝑛𝑡𝑠) 56 43

The power required to drive the conventional screw auger is larger than the shaftless auger due to

rotational inertia of components. The power and torque requirements are calculated according to

equations (3) to (8). These equations are based on the screw conveyor manual [20]. A Matlab code

attached in Appendix A provides the calculation for relatively larger auger, whose results are

provided in Table 7. The units of the calculation are converted from customary units to SI units.

21

Figure 27 Conventional screw auger setup for Bulk material transport

Figure 28 Shaftless Screw auger setup for Bulk material transport

Delivery

tube

Delivery

tube

22

Table 7 Calculated Drive requirements

Calculated Screw auger parameters

Diameter of the Screw 152.4 mm

Diameter of the shaft 19 mm

Speed of the motor 1200 rpm

Length of the Auger 2400 mm

Efficiency (spur gear drive) 0.88

Total power required 0.5 Hp

Total torque required 41 Nm

The specifications of the selected motor for the driveshaft, calculated using equations (3) to (9) is

presented in Table 8. The motor selection is made based on the torque demand to move the material

through the conveying tube. The calculations for the torque and the horsepower required is

provided in Appendix A.

Table 8 Specifications of the geared motor attached to the driving shaft

Motor Specifications

Manufacturer Nord drive systems AB

Designation Standard Line Gearmotor SK 01XZ - 80SH/4

TF

Motor type 3-phase Asynchronous

Power 0.55 kW

Rated speed 1420 rpm

Supply frequency 50 Hz

Number of poles 4

Gear ratio 11.6:1

Max speed at the output shaft 123 rpm

Max torque at the output shaft 43 Nm

23

The motor designated for conventional screw auger is used for driving the shaftless screw auger

as a conservative approach. The dimensions of shaftless screw auger corresponding to design

method 2 are illustrated in Figure 29. The specifications of the screw auger are provided in Table

9.

Table 9 Specifications of MAFLEX-skruv 90/75

Shaftless Screw auger Specifications

Manufacturer MAFA AB

Designation Maflex-skruv 90/75

Inside diameter (ID) 41.4 mm

Outside diameter (OD) 60.45 mm

Pitch, mm 41.4 mm

Figure 30 Dimensions of the conveying tube

The product “Maflex – Skruv 90/75” provides a set of standard screw auger and the conveying

tubes compatible with the Hopper's bottom and the stainless-steel tube (refer Figure 32). The cross-

sectional image of the conveying tube is displayed in Figure 30, and its specifications are provided

in Table 10.

Table 10 Specifications of the conveying tube for MAFLEX skruv 90/75

Conveying tube Specifications

Manufacturer MAFA AB

Outside diameter, A 96.1 mm

Inside diameter, B 89.3 mm

Inside diameter, C 82.2 mm

Outside diameter, D 89.0 mm

ID OD

Pitch

Figure 29 Dimensions of Shaftless Screw auger

24

The flexible screw auger runs from the hopper’s bottom (driven end) to the motor shaft (driving

end) inside the conveying tube which is fixed to the stainless-steel delivery tube (a standard

component provided by MAFA AB). The stainless-steel delivery tube connects the motor

assembly to the right with the help of fasteners, and the conveying tubes to the left with the help

of pipe clamps. The location lid and flanged housing design are adapted to the stainless-steel tube

(see Figure 31).

Once the hopper, auger and motor have been selected, the next step is to design the integrating

subsystems like driving shaft assembly and driven shaft assembly that connects the components

mentioned above to complete the feeding conveying system.

Figure 31 Cross section of delivery tube integrated with location lid and flanged

housing

Stainless steel Delivery tube Location lid

Flanged housing Connection for

conveying tubes

25

4.3 Feed conveying system design

In this subsection, the design of integrating components between the hopper and the conveyor is

carried out. The integrating components are split into two parts, one for the hopper and driven

shaft integration and the other for the motor assembly. The hopper assembly consists of the hopper

body and hopper bottom fastened together. The driven shaft sub-assembly is attached to the hopper

via a flanged housing. The other end of the hopper is connected to the stainless-steel delivery tube

via plastic pipes. The 3D CAD of the finalized fish feeding mechanism modelled in Autodesk®

Inventor Professional 2021 is shown in Figure 32.

4.3.1 Driven shaft system design The screw auger is fitted to the hopper bottom with a flanged housing. This housing accommodates

the driven shaft, ball bearing (SKF 61906) and two oil seals. The seals used in the system are

located inside the bore with an interference fit with outside diameter. The driven shaft (see Figure

33 and Figure 34) is connected to the screw auger at one end and is resting against the bearing’s

inner ring on the other end. The outer diameter of the sleeve provides a sliding fit with auger’s

inner diameter. The auger is held tightly in place with two hook screws (or hook bolts) and nut

setup passing through the hole drilled in the shaft and sleeve surface. The hook screws present in

Figure 34 is just a representation to realize its function in the assembly. The ball bearing in the

flanged housing supports the stepped diameter of the driven shaft and is sealed from the

atmosphere using a radial seal. The ball bearing is locked axially against the housing using a snap

Figure 32 3D-CAD model of the Fish feeding system

Driving shaft

Assembly

Driven shaft

Assembly

PVC- Conveying

tubes

Hopper/Silo

Hopper

Bottom

Direction

of feed

dispense

Delivery tube

26

ring. The axial locking of the shaft is taken care of by the snap ring present on the shaft groove.

When the conveyor is in action, the feed pellets get accommodated between the screw auger and

the conveying tube. As a result, the pellets support the driven shaft from overhanging and keeps

the bearing misalignment within acceptable limits. All the components in the system are standard

parts except for the flanged housing and the cap.

Hook Screws + Nut Setup

Screw

auger

Shaft seals

Snap ring

Shaft Sleeve

Deep Groove Ball

bearing

Housing

cap

Driven shaft

Figure 34 Cross sectional view of driven shaft Sub-Assembly

Figure 33 Driven shaft assembly integrated with hopper bottom

Hopper Bottom

Shaft Shoulder

Deep groove ball bearing

27

4.3.2 Driving shaft system design

Motor Shaft

Key/Keyway

Oil seals

Location Lid

Locknut

Coupling Shaft

(Driven shaft)

Adapter Plate

Geared Motor

Deep Groove Ball bearing

Figure 35 Components of the Motor Sub-Assembly

Figure 36 Detailed cross sectional view of the Motor Sub-Assembly

Delivery tube

28

The motor assembly is connected to hopper bottom by a series of plastic pipes which is supported

at various points from the roof using clamps. Figure 35 and Figure 36 shows the delivery tube

carrying the entire weight of the motor sub-assembly. The opening at the bottom of the stainless-

steel tube is integrated into the plastic T-junction of the main pipeline using pipework components.

In the motor assembly, one end of the driving shaft act as a coupling with an open keyway to

transmit the motor torque. The sliding fit provided at the interface of the key/keyway prevents the

dragging of the motor shaft due to auger weight and pellet load. At the same time, the other end of

the coupling shaft is connected to the screw auger using a shaft sleeve with hook screws and

counter locking nuts. The geared motor is fastened to the double-flanged housing with an

intermediate adapter plate. The housing accommodates the deep groove ball bearing (SKF

W6007), driveshaft, locknut, and a lid. Table 8 gives the specification of the motor used to drive

the shaft and the screw auger. The flanged housing and lid locate the outer ring of the ball bearing,

whereas the inner ring is located against the shaft step using a locknut (SKF KMFE 7 L35). This

sub-Assembly inherently prevents the shaft from moving in the axial direction away from the

motor. Radial seals are provided in the housing on either end for sealing the lubrication.

29

4.4 Detailed Design of components

4.4.1 Key/keyway The key/keyway is used for transmitting the torque from the motor to the screw auger via the

driven shaft. The dimensions of key/keyway are selected from the standards SMS 2305 [23], and

SMS 2306 [24] is shown in Figure 37.

With the input parameters such as shaft diameter and torque to be transmitted, the key dimensions

are calculated using according to Appendix B is presented in Table 11

Table 11 Calculated key dimensions based on SMS 2305

Key design parameters

Shaft diameter, D 20 mm

Material for key AISI 1020 CD Steel

Maximum shaft torque 60 Nm

Width of the key, B 6 mm

Depth of the key, H 6 mm

Minimum key length 12 mm

Depth of key on shaft, C1 3.5 mm

Depth of key on the hub, C2 2.8 mm

4.4.2 Bearings There are two deep groove ball bearings present in the system, one at the hopper side and the other

at the motor side. These bearings are selected based on the radial and axial loads, amount of space

available for packaging of components and life of the bearing. As a conservative estimation, it is

assumed that both the bearings (driven shaft and driving shaft) are assumed to carry the load of

the auger and the pellets in the axial direction. In the radial direction, only the shaft weight is

carried by the bearings in static conditions. During conveying operation, the feed pellets occupy

the volumetric space between the auger and conveying tube. The flexibility of the shaftless auger

makes the pellets present inside the conveying tube to share the radial load. Stainless steel shafts

were used as shaft material [25]. The weight of the auger per meter length, 𝑊𝐴𝑔 is 1.4 kg

considering Mild Steel as material. The total length of the auger 𝐿𝐴𝑔 passing through the conveying

tube is approximately 4.15 m. The pellet loads are calculated by assuming the entire conveying

tube filled with homogeneous Bulk material of density 700kg/m3 (𝑤𝑝𝑐). The volume of the Bulk

Figure 37 Reference key dimensions based on SMS 2305

30

material and required auger length was found using features available in 3D CAD software. The

mass of the heaviest shaft (𝑊𝑠ℎ𝑎𝑓𝑡) (2.2 kg assuming stainless Steel as material) is taken as the

radial load for both the bearings. For further clarification on determining the radial and axial load,

see appendix D. Figure 38 depicts load acting on the motor shaft bearing in radial and axial

direction.

𝑇𝑜𝑡𝑎𝑙 𝑎𝑥𝑖𝑎𝑙 𝑙𝑜𝑎𝑑 (𝑇𝐴𝐿) = (𝑤𝐴𝑔 × 𝐿𝐴𝑔 + 𝑤𝑝𝑐)

𝑇𝑜𝑡𝑎𝑙 𝑟𝑎𝑑𝑖𝑎𝑙 𝑙𝑜𝑎𝑑 (𝑇𝑅𝐿) = 𝑊𝑠ℎ𝑎𝑓𝑡

The load parameters (displayed in Table 12) are kept constant for both bearings for bearing life

computation. Assuming to be grease lubricated and temperature not exceeding 700C, the bearing

life was calculated using the SKF bearing calculator, which is based on the rolling bearing

catalogue [26]. A factor of safety of 2 has been implemented for both radial and axial loads. Small

internal clearance is assumed between two bearings races to reduce the radial play.

Table 12 Bearing life Calculation results by SKF online bearing life calculator

Bearing life calculation

Total Axial Load (𝑇𝐴𝐿) 540 N

Total Radial load (𝑇𝑅𝐿) 440 N

Lubrication Grease SKF: LGFP2 (Food compatible)

Internal Clearance Normal

Equivalent dynamic load, N 990

SKF W6007 Deep groove ball bearing (Motor side)

Dimensions (ID×OD×Width), mm 35×62×14

L10h, (hours) >2×105

SKF W61906 Deep groove ball bearing (Hopper side)

Dimensions (ID×OD×Width), mm 30×47×9

L10h, (hours) 33500

Deep groove

ball bearing

Axial load

(Weight of the pellets)

(Radial Load)

Weight of Shaft

Keyway

Double

flanged

housing

Screw auger

Driving shaft

Figure 38 Loads acting on the Motor shaft bearing

31

4.4.3 Flanged housings The housings present in the motor end and the hopper end accommodates all the packaging

components present in the system like the bearings, shafts, seals, locknuts, and snap rings. The

flanged housings are designed to pack components mentioned above within the sub-assembly

tightly. The images of the housings used in the system are attached in Figure 34 and Figure 36.

4.4.4 Locating lid The function of the locating-lid is to push the outer ring of the bearing against the double-flanged

housing. The inner bore of the lid acts as a housing for holding the oil seal via an interference fit.

Sliding direction Gap(𝑔1)

Oil seal

Driving Shaft

Location lid

Figure 39 Gap (g1) provided by locating lid for axial sliding

Figure 40 Gap (g2) provided between housing and snap ring for axial sliding

Gap(𝑔2) between

snap ring and housing

Hopper Bottom

Snap ring

Flanged housing

32

From Figure 39 and Figure 40 and, the sum of two gaps 𝑔1 (Between the lid and outer ring of the

bearing) and 𝑔2 (Between snap ring and housing) is set to be less than 1 mm. The gap provides

sliding motion between two shaft assemblies to prevent the driveshaft pulling motor shaft directly

with the weight of auger and pellets.

4.5 Pipeline lift height

The following calculations based on Bernoulli's equation discussed in section 2.1.5 give a good

understanding of how the theory is implemented in the system. The inner pipe diameter is constant

throughout the pipeline system (refer to Table 1), which indicates that the velocity of the water is

constant. The pipe calculations are done by assuming that the pipe’s inner surface is smooth, and

there is no frictional head loss throughout the pipeline.

𝑃1 +1

2𝜌𝑉1

2 + 𝜌𝑔ℎ1 = 𝑃2 +1

2𝜌𝑉2

2 + 𝜌𝑔ℎ2

Due to data confidentiality, the velocity of water flowing through the pipe is not disclosed in this

report. As a result, when point A is raised to height h2 (= 2 meters), the level of water in the pipe

equalizes with the water in the tank. The feed particles, when dispensed at this time, will directly

fall into the fluid stream without stagnating on the sides of the T- junction pipe.

Applying Bernoulli's principle between 1 & 2,

𝑃1 = 𝑃2 + 𝜌𝑔ℎ2

By applying the Bernoulli principle (see Figure 41) and reverse calculating the pressure 𝑃1 at the

pump end to maintain the water head of 2 meters in the culture tank is found to be 0.2 bar without

considering the losses due to friction and pipe bends.

Figure 41 Schematic representation of Pipeline layout

T - Junction

ℎ1 = 0

3

h2= 2 m

Water from pump

Culture tank

1

2

A B

𝑃1

𝑃2 = 1 𝑎𝑡𝑚

𝜌 = 1000 𝑘𝑔/𝑚3

𝑔 = 9.81 𝑚/𝑠2

33

4.6 Control of mass flow rate

From the feedback control loop discussed in section 3.1.5, input parameters were initialized, and

graphs from the system model indicating the flow control and motor speed control are plotted in

Figure 42 and Figure 43. The reference mass flow rate shown in Figure 42 was calculated to be

1.39 kg/s.

Figure 42 Change in mass dispensed per second

Figure 43 Corrected RPS to achieve targeted mass flow rate

Ideal revolutions per second (15 rps)

15

Ideal mass dispensed per second (1.39 kg/s)

34

35

5 DISCUSSION AND CONCLUSIONS

5.1 Discussion

5.1.1 Hopper evaluation The hopper provided by MAFA AB for the storing of the fish feed has a semi included angle of

210. The company has tested for the flow of the fish feed supplied by Biomar AB with pellet size

ranging from 4.5 mm to 8.5 mm. This gives an assurance that the hopper selected suits the

application.

The results consolidated in Table 5 indicates that both materials, Mild Steel and SS316, have a

very less significant difference in the total deformation. The above results can be backed up by the

fact that the young’s modulus of the Mild Steel and Stainless steel 316 is 210 Gpa and 205 Gpa

respectively. The maximum stress experienced by the hopper walls is less than the yield strength

of the 2 materials (i.e. Factor of safety =1). For the deformation analysis, the data in Table 5 can

be used as a benchmark for comparing similarly sized hoppers with different materials which are

commercially available.

It is observed from Table 5 that the hopper exhibited similar deformation behaviour for both

materials. The maximum deformation is calculated for the hopper to hold about 6300 kg, i.e. the

entire volume of hopper filled with water up to the brim. But the maximum possible weight that

could be acting considering random packing of particles is 4259 kg. However, the actual weight

of the particles that are stored never exceeds 3000 kg.

The conservative approach of taking the pressure exerted by water assumes that the hopper is

structurally capable as it handled two times the actual force exerted by the particles. Thus, it can

be established that both materials qualify as an eco-friendly and structurally capable for hopper

construction. But incorporating a custom material SS316 for constructing the hopper increases the

initial investment and manufacturing costs. Thus, Mild Steel coated with Aluzinc is the better

choice among the two food-grade materials due to its economic feasibility, structural and

functional capability.

5.1.2 Pipeline design From the values of the height and pressure calculated (refer section 4.5), the pipeline in the junction

end should be raised to a height of 2 m from the ground to equalize its water level with respect to

the tank. Also from Table 3, it is clear that the single-particle density is higher than the density of

water (1000 kg/m3), and it prevents it from stagnating at the junction, thereby ensuring smooth

transportation of pellets along the fluid stream.

5.1.3 Auger evaluation The evaluation matrix in Table 6 states that the parameter material requirement has more

weightage over others, such as design complexity, conveying efficiency, and maintenance. Since

the end-user/customer are farmers, material investment and maintenance is the primary concern.

From Table 6, it is clear that the design method 1 has high figures in every evaluation parameter

compared to design method 2.

Design method 1 can be implemented if material cost and the total weight is not of primary

importance. Raising the screw auger from the ground according to design method 1 increases the

number of intermediate elements. This complicates the design process as we require auger

couplings, intermediate hanger bearings and trough material. Further, the addition of intermediate

components inside the trough disrupts the flow of the particles inside the channel/trough.

In contrast, the design method 2, the shaftless screw auger can be cut to the required length, which

is an excellent way to reduce the material costs. This helps in avoiding the use of intermediate

36

elements that disrupt the particle flow. Thus, design method 2 proves its functionality over the

previous one with replaceable plastic conveying tube, low maintenance and service cost.

The design concept created according to design method 2 accounts for the sliding of the driving

shaft and driven shaft assembly in the axial direction. This prevents the driven shaft pulling the

motor shaft due to the weight of auger and pellets. A possibility for reverse rotation of the motor

is provided to clean the residual material present inside the screw conveyor. To prevent the pellets

forming aggregates, a limited angular rotation in the clockwise and counterclockwise rotation is

provided to loosen up the particles in the conveying tube.

5.1.4 System control The fluctuating mass flow graph, according to Figure 42, is since the sensor values generated are

in Gaussian distribution. The mass flow rate graph is fluctuating about the ideal value (1.39 kg/s)

as the average value. The rps feedback graph in Figure 43 illustrates that it is the mirror image of

the rps graph in Figure 42. The system control algorithm, according to the proportional math

model, shows promising results. However, by implementing the transfer functions for the actuator

(motor), a more accurate working model of the complete feeding control can be obtained. In

addition to that, when implementing an actual system, the ideal value must be calculated by

experiments rather than a mathematical model.

5.2 Conclusions

From the simulation results, the Hopper material (Mild Steel coated with Aluzinc) was found to

be structurally capable which was validated by comparing the strength characteristics with a

similar material (SS316) used in Agricultural industries. The material showed its structural

capability by withstanding the maximum possible load condition without demonstrating abnormal

deformations. Further, a benchmark study was created based on the parametric analysis carried out

in ANSYS to compare different hopper materials for research purposes. The conveying system

designed is less material-intensive compared to conventional ones. This reduces the material usage

and in turn, the material costs. The mass experiment conducted indicated that the individual

particle density is higher than the density of water, which validates the possibility of fluid stream particle dispensing. The conveying system with flexible screw conveyor was found to be less

material-intensive compared to conventional screw conveyors. This reduces the material usage

and in turn, the material costs. The driving and the driven shaft assemblies of the feeding system

attached to hopper were made as compact as possible. The number of custom components with

motor and hopper sub-assembly were reduced, keeping economic feasibility and material

requirements as a priority. A preliminary Closed-loop control system was created as a first step

towards automating the feeding mechanism. The algorithm to control the motor rpm showed

promising results towards the mass flow control, which reduces the amount of excess or uneaten

feed ultimately.

37

6 RECOMMENDATIONS AND FUTURE WORK

6.1 Recommendations

The hopper to store the materials can be designed according to European standards, and a

parametric study on the hopper wall thickness along its length can be conducted. This

parametric analysis gives an optimized hopper volume.

The sensor used for the bulk mass flow measurement can be made from scratch with simple

electronic components so that its functionality can be altered suiting the requirements.

6.2 Future work

Improvisation of the friction model using dedicated triaxial shear testing apparatus to find

an accurate angle for wall and inter-particle friction, which can be applied to optimize

hopper parameters.

Particle interactions can be modelled using ANSYS-EDEM Plugin for studying the

behaviour of particle flow in different mediums like water and air.

Comparison of volumetric efficiency obtained from experiments and the simulation model

built in EDEM for optimization of the overall system performance.

A new mathematical model linking motor rotation with the mass flow rate can be derived

based on data logged from the experiments to get the accurate mean value of the feed to be

dispensed.

The closed-loop control system can be refined by incorporating the voltage-rpm correlation

into the Simulink model.

38

7 REFERENCES

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[18] H. and Resnick, Fundamentals of Physics Halliday & resnick 10ed. 2007.

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[20] Conveyor Engineering and Manufacturing Co., “Screw Conveyor components & design,”

vol. 2.20, p. 25, 2012.

[21] MATLAB-Simulink. 2006.

[22] J. Kold and C. Silverman, “Conveyors Used in the Food Industry,” in Handbook of

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Hygiene Control in the Food Industry: Second Edition, 2016.

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2/12/2020,” 2020.

[24] Fastställd, “Svensk Standard,” pp. 2017–2028, 2019.

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[26] “Rolling bearings SKF mobile apps.”

40

41

APPENDIX A: SCREW CONVEYOR DESIGN MANUAL

42

43

44

45

46

47

48

Matlab Code clear all

%screw pitch calculations

L=2.4; %length of screw auger (m)

r_p=6.5e-3; % radius of one particle (m)

p=6*0.0254; %pitch in m

pckden=0.74;

rc=(1.5/2)*0.0254; %radius of core shaft (m)

rs=6*0.0254; %radius of outer screw (m)

m_p=(0.18e-3); %average mass of particle in kg

pitch_perm=L/p;%pitches per meter

%particles per pitch

V_btw_p=pi*p*(rs^2 - rc^2); %vol between two pitches m^3

vff= 4/3 * pi * (r_p)^3;% volume of one particle in m^3

npartperpitch_approx = (V_btw_p/vff)*pckden; % approximate

number of particles accomodated between pitch

mass_per_pitch= npartperpitch_approx * m_p;

p_req = (56)./mass_per_pitch; %number of pitches required to

dispense the mass of 56kg (one run)

% since it is similar to a single start thread, pitch=lead

% rotations required by the motor for dispensing of feed

lead=(p*pi)/tand(90-17.6568); %lead of the screw auger, tand -

angle of inclinaion of screw helix with respect to vertical

ppl=lead/p; % pitches for lead

mass_per_lead=mass_per_pitch*ppl; %mass per lead / mass per rpm

n_rot_req=(56)./mass_per_lead;% no of rotations required for

dispensing mass

fprintf("vol.btw.p \t vol.p \t part.per.p \t

mass.per.p\t p.req.Q\t");

fprintf("\n");

fprintf("%0.1d\t\t\t %0.1d\t\t %.0f\t\t\t %.1f\t\t\t

%.2f\t",V_btw_p,vff,npartperpitch_approx,mass_per_pitch,p_req);

fprintf("\n");

fprintf("\n");

% volume of silo

r_c_c=1.88/2; %radius of Cone/clinder (m)

max_w=2520;%maximum amount of feed filled in silo(kg)

vol_fos=1.2; % volume fos

vol=1:0.2:55; %capcity of silo in m3

rho_p=m_p/vff; %density of particle

csa=pi*(r_c_c)^2;% cross sectional area

h=vol/(csa*3/4);% height of the silo (cone part)

no_p_sl=(vol/vff)*pckden;% number of spheres of radius r_c_c

mass_oc=no_p_sl*m_p;% total mass inside the silo in kg

vol_tab=[vol; no_p_sl; mass_oc]';

% amount of sheet metal required to cover the volume

t_s=8e-3; %sheet thickness m

sa_s=(2*pi*r_c_c*h) + pi*r_c_c*(h/sind(30));%surface area m2

49

sa_sr=(2*pi*r_c_c*h)+ 2*(r_c_c+1)*(r_c_c+1); %material surface

area required m2

%for i=1:length(vol_table)

fprintf("vol.silo\t no of particles\t mass.feed\t

surf.area\t surf.req\t tot.mat.vol\n");

fprintf("m3\t\t\t\t\t n\t\t\t\t kg\t \t\t m2\t\t\t m2\t

\t\tm3\n");

ii=find (vol_tab(:,1)<50);

for i=1:length(ii)

fprintf('%f \t %f \t %f \t %f \t %f\t

%f',vol_tab(i,1),vol_tab(i,2),vol_tab(i,3),sa_s(i),sa_sr(i),sa_s

r(i)*t_s);

fprintf('\n');

end

% Fish meal

% Material class code = 38C45HP

% Conveyor loading = 30A

% Component Group= 1A 1B 1C

e=0.85; %cut tooth spur gears, enclosed, for each reduction

rho_b=700;%kg/m3

req_C=7/rho_b; %m3/hr

C_prpm=4.7*0.028; %capacity per rpm m3/hr assuming 95% of

conveyor loading

%cfproduct=[1,1.95000000000000,0,1.04000000000000;1.500000000000

00,2.92500000000000,0,1.56000000000000;2,3.90000000000000,0,2.08

000000000000;0.670000000000000,1.30650000000000,0,0.696800000000

000;1,1.57000000000000,3.75000000000000,1.37000000000000;1.50000

000000000,2.35500000000000,5.62500000000000,2.05500000000000;2,3

.14000000000000,7.50000000000000,2.74000000000000;0.670000000000

000,1.05190000000000,2.51250000000000,0.917900000000000;1,1.4300

0000000000,2.54000000000000,1.62000000000000;1.50000000000000,2.

14500000000000,3.81000000000000,2.43000000000000;2,2.86000000000

000,5.08000000000000,3.24000000000000;0.670000000000000,0.958100

000000000,1.70180000000000,1.08540000000000];

%screw morphohological factors

cf1=[1 1.5 2 0.67]';

cf3=1;

cf21=[1 1.04]; %15 percent conveyor loading (standard and ribbon

flight)

cf22=[1 1.37]; %30 percent conveyor loading (standard and ribbon

flight)

cf23=[1 1.62]; %45 percent conveyor loading (standard and ribbon

flight)

cfp= [cf1*cf21*cf3; cf1*cf22*cf3; cf1*cf23*cf3];

%verification of cfp

% fprintf("15 percent loading")

% fprintf("\nstd.flight ribbon.flight")

50

% fprintf("\n")

% disp(cfp(1:4,1:2))

% fprintf("30 percent loading")

% fprintf("\nstd.flight ribbon.flight")

% fprintf("\n")

% disp(cfp(5:8,1:2))

% fprintf("45 percent loading")

% fprintf("\nstd.flight ribbon.flight")

% fprintf("\n")

% disp(cfp(8:12,1:2))

%screw hp factors

fm=1;

fp=1.00; %std paddles se at 45deg reverse pitch

ff=1.0;

fb=1.7; %hanger bearing hp factor

fd=18.0; %diameter hp factor

F0=2.3;

roh_water=1000;%kg/m3

%conveyor speed

eqv_C=req_C*cfp;

eqv_c1=max(eqv_C(:));

%N =ceil((eqv_c1/C_prpm));

N=1200;

hpf=(L*3.28*N*fd*fb/10^6); %friction horse power

hpm=(eqv_C.*L*rho_b*ff*fm*fp/10^6);% material horse power

cum_hp=hpf+max(hpm(:));

total_hp=((hpf+hpm)*F0)/e;

disp('maximum HP required');

disp(max(total_hp(1,:)));

disp('maximum Torque required');

torque=63025*total_hp/N;

disp(max(torque(1,:)));

%output to be displayed

disp("horse power and torque for loading conditions");

fprintf("\n");

fprintf("15 percent loading");

fprintf("\n[std.flight - HP1,T1] [ribbon.flight - HP2,T2]");

fprintf("\n");

fprintf("\n HP1 HP2\t T1\t T2\n");

disp([total_hp(1:4,1:2),torque(1:4,1:2) ]);

fprintf("30 percent loading");

fprintf("\n");

fprintf("\n HP1 HP2\t T1\t T2\n");

disp([total_hp(5:8,1:2),torque(5:8,1:2)]);

fprintf("45 percent loading");

fprintf("\n");

fprintf("\n HP1 HP2\t T1\t T2\n");

disp([total_hp(8:12,1:2),torque(8:12,1:2)]);

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%Shaft calculations

%Support Reactions

b = 3*p;%Length of udl in meter

W =3000/b; %Uniformly distributed load in N/m

cg =L/4 %'position of center' of udl from left end of the beam

in meter

a = (cg-b/2);

c = L-a-b;

R1 = W*b*(b+2*c)/(2*L); %Left Support Reaction.

R2 = W*b*(b+2*a)/(2*L); %Right Support Reaction.

% Discretization of x axis.

n = 1000; %Number of discretization of x axis.

del_x = L/n; %discretization of x axis.

x = (0:del_x:L)';

Vx= zeros(size(x, 1), 1); %Shear force as function of x.

Mx= zeros(size(x, 1), 1); %Bending moment as function of x.

fos=1;

Ys=29e6;

E=1500e6;

% Material factors

for i = 1:n+1

% for 0 < x < a

if x(i) < a

Vx(i) = R1;

Mx(i) = R1*x(i);

elseif a <= x(i) && x(i)< a+b

% for a < x < a+b

Vx(i) = R1-W*(x(i)-a);

Mx(i) = R1*x(i)-W*((x(i)-a)^2)/2;

elseif x(i) >= (a+b)

% for a+b < x < L

Vx(i) = -R2;

Mx(i) = R2*(L-x(i));

end

end

xx=[x,Mx];

[B,I] = maxk(xx,1);

xi=xx(I(2));

x1 = a+R1/W; %a+R1/W

Mmax = W*b*(b+2*c)*(4*a*L+2*b*c+b^2)/(8*L^2);

Tmax=ceil(max(torque)); %from the 45% loading

disp (['Left support Reaction' '=' num2str(R1) '' ' N']);

disp (['Right support Reaction' '=' num2str(R2) '' ' N']);

disp (['Maximum bending moment' '=' num2str(Mmax) '' ' Nm']);

%assuming the core shaft to be a soid shaft of diameter ds

const=(32*fos/(pi*Ys));

eqvstr=sqrt((Mmax).^2 + (3/4)* Tmax.^2);

ds=max((const*eqvstr).^(1/3));

52

disp (['Minimum shaft diamter' '=' num2str(ds) '' ' m']);

I=(pi/64)*((2.*rc).^4);

del_D=(max_w*vol_fos*((L-cg))*xi)*((L.^2-((L-cg).^2).^2-xi.^2));

del_d=6*L*E*I;

del_max=(del_D/del_d);

disp (['Maximum Shaft Deflection' '=' num2str(del_max) '' '

m']);

%cheking for conformity

if rc>ds

fprintf("\n core shaft dia %f is greater than min safe dia

%f",rc,ds);

else

fprintf("\n increase the core shaft dia \n");

end

%eqivalent hollow shaft

figure(1)

plot(x, Vx, 'r','linewidth',1.5);

line([x(1) x(end)],[0 0],'Color','k');

line([0 0],[0 Vx(1)],'Color','b','linewidth',1.5);

line([x(end) x(end)],[0 -R2],'Color','b','linewidth',1.5);

title('Shear Force Diagram')

axis off

figure(2)

plot(x, Mx, 'r','linewidth',1.5);

line([x(1) x(end)],[0 0],'Color','b');

line([x1 x1],[0 Mmax],'LineStyle','--','Color','b');

title('Bending Moment Diagram')

axis off

53

APPENDIX B: KEY DESIGN CALCULATOR

Key/Keyway calculation

Key calculator from tribology-abc.com

54

APPENDIX C: BEARING LIFE CALCULATION

The online SKF bearing calculator was used in calculating the basic bearing life. The parameters

that have been selected are presented in the images below.

55

56

APPENDIX D: VOLUME AND LOAD CALCULATION USING 3D CAD SOFTWARE

The span of the conveying tube indicated in blue arrows

Volume of conveying tube = 0.0303 m3

Density of bulk material = 700 kg/m3

The total mass of material that is assumed as a single homogeneous solid = 212.1 N

Ground

57

APPENDIX E: SYSTEM CONTROL – SIMULINK MODEL

System Control % matlab initialization file for Simulink model

clear;

clc;

time = 0;

counter = 0;

for i=1:3599

time = [time; counter + 1];

counter = counter + 1;

end

%In Meters

dsc = 0.0683;

dsh = 0.0445;

pitch = 0.058;

rp = 0.0065; %Particle Radius

mp = 0.17e-3; % In kilograms - assumption

%Packing Density

pckden = 0.74;

%Mass per Rotation 0.1071 Kg/rot

mass = (1)*(0.25*pi*(0.082.^2)*pitch*pckden)/(4/3*pi*rp.^3)*mp;

tot_mass=5000; %total mass/session in kg for 1 hour

% 1.38 Kgs in 1 second (1 session = 3600 seconds)

ses_req = tot_mass/3600;

rpm = (ses_req/mass)/60;

n_rot_tot=tot_mass/mass; %no of rotations in 1 hour

rps = n_rot_tot/3600; %no of rotations in 1 sec

58

rps_list = [];

for i2=1:3600

rps_list = [rps_list; rps];

end

mu = ses_req;

sigma = 0.1;

% sensor_data = normrnd(mu,sigma,3599,1);

sensor_data = normrnd(mu,sigma,3500,1);

histogram(sensor_data,3599);

xlabel('Mass flow kg/s per revolution for a period of 1 hour')

ylabel('Frequency');

sensor_data = [linspace(0,1.3889,100)'; sensor_data];

sensor = zeros(3600,1);

Matlab Function 1

% Function for determination of set value

function m_a_dot = fcn(rps)

mass_per_rotation = 0.0335; %Kg/rot

% theoritical model must be calculated for every session

requirement,

% it is also the ideal value to be constantly maintained over

time

% see the main program for details

% 5000 Kgs in 1 hour (1 session) Assumption --> 5000/3600 =1.39

kg/s

%rps is based on no of rotations totally required to dispense

5000 kg divided by mass/rotation (see main program)

m_a_dot = 0.0335*rps;

Matlab Function 2

%Function for converting mass flow rate back to rps

function rpsfn = fcn(massdiff)

rps = massdiff/0.0355;

rpsfn = rps;