A Test-Bed Design Characterization of Tidal

Turbine Flows

Eric M Martin Jacob Folz

Patrick Bates Richard Peale Russell Dunn Scott Lessard

MEE 487 Final Report May 6, 2008

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Executive Summary Maine is in an excellent position to leverage one of its defining characteristics, high tidal

fluctuations in narrow channels for alternative energy research and economic growth.

Tidal turbines act in a similar fashion to wind turbines, creating rotational movement

from axial flow. Across the globe numerous companies have developed proprietary

turbines. It was the goal of the University of Maine Mechanical Engineering Department

to create a Tidal Turbine Test Bed that could be used to quantify the performance of tidal

turbines for public use.

The apparatus produced resulted from careful consideration of multiple possible designs.

The final design was mounted in the University of Maine Aquaculture Research Center

Tow Tank. The design used a six-axis dynamometer and upper data collection drive line

to collect the quantities of drag, rotational speed, and torque. A streamlined strut and

nacelle were used to submerge the lower driveline that attached to the turbine being

tested. A chain drive running through the struts links the upper and lower drivelines. A

data acquisition system was used to collect the data, which was processed using

LabView. The final constructed apparatus was a fully integrated mechanical, electrical,

and data acquiring system.

A sample 3-D printed tidal turbine was used for system evaluation. Final results of

testing produced non-dimensionalized power curves that collapsed to a single

performance curve, validating the effectiveness of the system.

The design, constructing, and testing of the Tidal Turbine Test Bed was a success,

meeting all defined criteria. In continuation of the project, the first generation design

should be improved in numerous areas. Though the improvements needed vary greatly,

friction and vibrational losses as well as overall setup organization were identified as

major barriers to system precision, accuracy, and longevity.

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Table of Contents I. Introduction: Problem Definition

a. Global Opportunity b. A prospect for Maine c. Research Need d. University of Maine e. Key Challenges f. Target Specifications & Design Requirements g. Product Satisfaction h. Background Engineering Theory / Relevant Equations

II. Design Selection a. Design Matrix of Bevel Gear Apparatus b. Design Matrix of In Line Motor Apparatus c. Design Matrix of Chain Assembly d. Design Matrix Comparison

III. Design Description a. Mechanical Design

i. Dynamometer and Upper Driveline ii. Struts & Lower Driveline

iii. Fabricated Parts and Bill of Materials iv. Assembly

b. Electronic & DAQ Design i. Data Requirements

ii. Data Collecting Equipment iii. Data Processing iv. Hardware Specifics v. Electronic/Mechanical Integration

vi. Wiring vii. System Function

IV. Design Evaluation a. Shaft Dynamic Load Analysis b. Shaft Sizing c. Test Procedures d. Calibration e. Results f. Discussion

V. Conclusion& Recommendations a. Assessment of Design: Mechanical

i. Strengths ii. Weaknesses

b. Assessment of Design: Electronic & DAQ i. Strengths

ii. Weakness c. Mechanical Improvements d. Electrical Improvements e. Conclusion

VI. References VII. Appendices

a. Dimensioned Drawings of Custom Fabricated Parts b. Bill of Materials c. Singularity Functions & M Files d. Shaft Diameter Calculations

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Contributions For Paper: Eric M Martin – Introduction, Design Selection Sections Jacob Folz – Design Description – Electronic & DAQ Design Section Patrick Bates – Design Evaluation, Conclusions & Recommendations Sections Richard Peale – Design Description – Mechanical Design, Design Selection Sections Russell Dunn - Design Description – Electronic & DAQ Design Section

For Project:

Eric M Martin Web Design Original Website Designer

Fabrication CNC Milling and Manual Milling Operator

Technical Writer Organized Final Paper

Oral Presenter SNAME

Carriage Drive train Redesign Design, Fabricate support for drive drum and carriage encoder

Design Role in design matrix

Jacob Folz

Data Acquisition System Developed LabView Progam to interface with instrumentation

Instrumentation Setup Assisted in wiring instrumentation

Fabrication Instrumentation housings, storage fixture for test bed

Design Role in design matrix

Catalog Engineer Ordered instrumentation

Patrick Bates

Design Role in design matrix

Numerical Analysis Shaft diameter sizing, singularity functions

Fabrication Assisted in CNC Milling and CNC Lathe Fabrication, Manual Milling Operator

Richard Peale

Design Role in design matrix

3D SolidWorks Modeling Created and controlled 3D models

Dimensioned Drawings Created and controlled drawings for fabricating custom parts

Catalog Engineer Ordered material and instrumentation

Assembly of Test Bed Lead in assembly of test bed apparatus

Fabrication Manual Lathe and Manual Milling Operator

Russell Dunn

Instrumentation Setup Wiring of instrumentation

Numerical Analysis Assisted in Analysis

Scott Lessard

Fabrication Master Machinist on CNC Milling, CNC Lathe, Manual Lathe, and Manual Milling

Design Role in design Matrix

Web Design Final Web Designer

Custom Machining Designed, and fabricated custom tooling for troubleshooting and assembly of test bed

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Introduction: Problem Definition Global Opportunity Today we exist in an age of both rapid technological development and even more rapid

population growth. The total number of people functioning in a high energy demand

lifestyle is increasing in parallel with the energy demand increase per capita. Scientific

evidence on global climate change has indicated that industrialization and the releasing of

greenhouse gases into the atmosphere have likely affected weather and temperature

patterns worldwide. There is not only a demand for increased energy production; there is

a demand for increased energy production from sources that produce decreased quantities

of carbon dioxide and other greenhouse gasses. As global natural resource supplies

dwindle and energy costs increase, we quickly approach an age were alternative sources

of energy become not only necessary, but economically viable.

A Prospect for Maine Though many other alternative or renewable energy sources could be explored in Maine,

tidal energy has a specific and somewhat unique niche in this state. The Maine coastline,

a series of narrow and deep bays, presents an ideal geography for the harnessing of tidal

energy. The large tide variations at Maine’s high latitude produce significant velocities

in these narrow channels as water flows in and out. In-Stream tidal turbines

mechanically extract energy from the movement of a tidal flow, as opposed to the

traditional tidal barrage dam, which utilizes a head rise created by a dam for the energy

source. Tidal In-Stream systems would resemble wind farms, using an array of turbines

located within high velocity tidal flow channels.

Research Need Over the past decade there has been intense development realized for In-Stream Tidal

power generation. As more and more research is completed, these tidal energy systems

are being viewed as a viable, sustainable, and renewable energy source. Though much

public attention is being given to this new industry as it develops, much work needs to be

done to establish the technology as both environmentally and economically feasible.

Many companies have been developing tidal turbine systems in the recent past.

Competition is growing and most company designs are proprietary. Very little published

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data exists on key quantitative information that defines In-Stream tidal turbine flows,

including basic performance characteristics, wake flow patterns, turbine array interaction

effects and surface profile effects. Today there is no baseline data for designing turbines

placed in a confined channel.

University of Maine This paper presents the development of a test platform for efficiently characterizing the

performance and flow patterns of scale model tidal turbine designs. The University of

Maine and Maine Maritime Academy created this testing capability as part of a larger

effort, which aims to achieve the following:

- Develop a rapid design/build/test sequence for rapid development of turbine

designs

- Create a series of Baseline turbine designs using this rapid development process

- Generate detailed performance and flow field data for this design, which is

publicly available.

- Provide these resources to the public and turbine development community

Key Challenges In order to meet the goals of the senior design groups section of the above described

design loop, key challenges had to be overcome on an individual and team basis. Though

many resources were available to the group in order to assist the completion of the

project, numerous tasks were completed to prepare the group and hardware for

integration into a successful project:

- The group required training in safety procedures associated with work in confined

spaces, and in working on electrical equipment near, and submerged in, a water

environment

- The Aquaculture Research Center Wave Tank needed attention in cleaning the

workspace as well as the control center for the drive system

- The Wave Tank Drive system was in disrepair and did not produce continuous,

smooth motion

- The Wave Tank Carriage was in disrepair as well with numerous damaged and

rusted parts

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- No previous research was completed at University of Maine on the theory behind

the functioning of submerged tidal turbine systems

- No previous physical effort was produced at University of Maine in relation to the

design and construction of a tidal turbine testing platform

- Group members had little knowledge of data acquisition systems, electronics, and

the appropriate design process

Target Specifications & Design Requirements Along with the complete design and fabrication of a tidal turbine test bed, the team

determined specific deliverables that the device should fulfill. In general, it was required

that the test bed best put to use the area of the tow tank and control spaces available for

the research. A functional system integrated into the infrastructure of the Aquaculture

Research Center Tow Tank area was paramount in the design process. In the area of

direct data acquisition, it was determined that the test bed should produce reliable values

of torque produced by the turbine, axial force induced by the turbine during full flow, and

rotational speed of the turbine during motion. Along with these specific production

values, it was determined that the device should maintain the highest degree of usability,

maintainability, manufacturability, survivability, and sensitivity while reducing the cost

of the process as much as possible. All of these aspects were considered as the design

developed and specific selections of method and hardware were chosen.

Product Satisfaction

The final tidal turbine testing apparatus exists as a fully integrated mechanical, electrical,

and data collection system. All mechanical components of the completed design were

modeled and fabricated with specific dimensions and materials quantified. All electrical

and data collection systems were mapped and specified in detail. The overall system

produces and collects information on a given tidal turbine being tested in an accurate and

readable manner. Uncertainties and losses due to friction do exist in the rotational speed,

torque, and axial thrust quantities; these undesirable factors are however, quantifiable and

explicitly discussed. The system was designed in a manner that allows for easy

replacement of worn or broken components. The test bed system is flooded, but was

designed to allow for simple improvements that will one day be conducive to a dry and

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closed data collection system. The current setup does not significantly effect data

collection, nor does it maintain conditions that expedite the expiration of expensive parts.

Background Engineering Theory / Relevant Equations

To obtain a clear understanding of the theory behind tidal turbine performance an

examination of hydrodynamic theory and associated equations was performed. A list of

assumptions concerning physical conditions under which a tidal turbine would be tested

was created.

To explicitly quantify the performance of a tested turbine, four vital relationships were

used. The turbine performance data was non-dimensionalized using the following

relations. Each is explained to include the details of its meaning and its usefulness in

describing the turbine quantitatively.

The power coefficient or coefficient of performance was calculated by dividing the power

produced by the testing apparatus by the total power available in the flow. Total power

in the flow is represented by one half multiplied by the product of the density of water,

the velocity cubed, and the cross sectional area. This term captures the overall

effectiveness of the turbine’s design.

Power Coefficient: AV

WC p

∗∗∗=

•

3

21 ρ

The tip speed ratio was calculated by dividing the tangential speed of the turbine tip by

the velocity of the water. The tangential speed is represented by the product of pi, the

rotational speed, and the diameter of the turbine. This term captures the effect of blade

pitch on the speed of the turbine.

Tip Speed Ratio: V

DNTR ∗∗=π

The torque coefficient was calculated by dividing the torque produced by the turbine by

the total work available in the flow. Total work in the flow is represented by one half

multiplied by the product of the density of water, the velocity squared, and the cross

sectional area. This term represents the percentage of work that was converted into

torque on the shaft of the turbine.

8

Torque Coefficient: AV

QCq

∗∗∗=

2

21 ρ

The thrust coefficient was calculated by dividing the thrust produced by the turbine by

the total work available in the flow. This term represents the percentage of work that was

converted into axial thrust on the shaft of the turbine.

Thrust Coefficient: AV

TCT ∗∗= 2ρ

For the design of the testing apparatus, estimated values of specific key quantities were

determined based on assumptions made about the testing apparatus as well as the turbine

performance. These quantities included but were not limited to speed of tow, coefficient

of performance, tip speed ratio, and rotor radius. Known values such as density of water

and the Betz Limit were used as well.

From these assumptions, the maximum torque produced by the test turbines as well as the

maximum thrust generated was calculated. These values were to be the driving constraint

on the Turbine Testing Apparatus Design. The maximum torque determined the shaft

diameter on the turbine drive, the selection of sprockets and chain drive, the sizing of the

resistance motor, and bearings on both the submerged and motor shafts. The maximum

thrust on the turbine was used to calculate thrust bearing size in the drive shaft, the

moment on the test apparatus supports, and the approximate motion that will be seen on

the dynamometer.

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Design Selection:

The objective of the design selection was to design and fabricate an accurate and precise

testing apparatus for tidal turbine testing process. To do so, many different designs were

examined and compared in a quantitative manner.

The following three comparisons represent designs that were examined and researched on

a preliminary basis. No modeling or calculations were completed on the designs.

Evaluations of the designs have been made on generalized research of drive systems.

The method of comparison began with a definition of the qualities that each specific drive

system possessed. Drawings were examined secondarily.

The designs were compared on the following comparative attributes:

• Ease of Mounting to Dynamometer

• Sensitivity in Shaft – Reduction of Frictional Losses

• Hydrodynamics of Apparatus – Turbine Mounted behind Keel

• Strength of Keel

• Vibrational Resistance of Keel

• Collects Power Data

• Collects Drag Data

• Accessibility of components

• Survivability

• Manufacturability

• Cost

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Design Matrix of Bevel Gear Apparatus

The Bevel Gear Drive Design (Table 1) contained the following attributes: PRO CON

Ease of Mounting to Dyno

Machine dyno to attach keel

Sensitivity in Shaft Frictional Losses in gear, high tolerances in alignment of shafts

Hydrodynamics of Apparatus

Can create streamline housing

Strength of Keel Dual Keel System Vibrational Resistance Dual Keel System Collects Power Data Instruments stay dry Collects Drag Data Connected to Dyno

Accessibility Instrumentation above water Unbolt dyno/keel to access

Survivability Instrumentation above water Grinding of gears if out of alignment

Manufacturability High Tolerances in Alignment of Shafts

Cost Material Cost down

The preliminary designs were combined to create a final design for the bevel gear drive

system (Figure 1). This apparatus utilized a double keel system to keep the apparatus

rigid. The shaft ran vertically between the instrumentation housing and the dynamometer

with two bearings for maintaining shaft position and reducing vibrational loses in the

vertical shaft. The front of the keel was covered with sheet metal to deflect flow around

the rotating shaft.

Figure 1: Preliminary Bevel Gear Design

Table 1: Bevel Gear Drive Matrix

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Design Matrix of In-Line Motor Apparatus

The In-Line Motor Drive Design (Table 2) contained the following attributes: PRO CON Ease of Mounting to Dyno

Bolts directly to dyno

Sensitivity in Shaft We can not quantify the frictional losses in the seal Hydrodynamics of Apparatus

Large House (10” x 6” Minimum)

Strength of Keel 1 Keel

Vibrational Resistance 1 Keel, less resistance to moment of shaft

Collects Power Data No transfer of energy Risky of instrumentation Collects Drag Data Connected to Dyno Accessibility Underwater, lots of bolts Survivability Water Leakage

Manufacturability High tolerances of seal, machine housing

Cost Material, instrumentation

AC Electric Motor

Couplings

Torque / Speed Sensor Bearing

Marine Bellows Seal

Figure 2: In Line Motor Component Drawing

Table 2: In-Line Motor Drive Matrix

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The AC electric motor would be calibrated to provide a known torque to the shaft at a

given input current (Figure 2). This would be coupled to a torque sensor to double check

calibration and increase accuracy, while obtaining the shafts speed. The shaft would stay

aligned with a bearing and a water tight seal around the shaft with a marine bellows seal

system.

This apparatus was considered so that the instrumentation would run inline with the

turbines shaft and not have any frictional losses of gears or chains. Along with the milled

out housing a pipe was also considered. We chose the milled out housing for its greater

stream line shape potential and the support it would provide close to the turbine (Figure

3). The big concerns of this design were the seal on the shaft and making the housing

watertight with a gasket. Using a plate gasket between the flat surfaces of the two halves

Figure 3: Front and Top View of Housing

Components attached to plate sit in air space

Front View

Top View

Stream Line Body

Tapped ¼” – 20 Holes

Gasket for Seal

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of the housing would seal the air space within the housing. For sealing the rotational

shaft, two things were accounted for. The seal must work when the shaft is not rotating

and have low frictional losses when rotating at speeds between 50 rpm and 3000 rpm

(preliminary calculations of shaft speed). The seal chosen was for a marine prop for a

motorized water craft. The manufacturer assured that the seal would be reliable at speeds

between 0 and 6000 rpm; however they were unable to give a resistance torque or

frictional loss metric for the seal.

Design Matrix of Chain Apparatus

The Chain Drive Design (Table 3) contained the following comparative attributes: PRO CON Ease of Mounting to Dyno

Machine Dyno to connect keel Sensitivity in Shaft Smallest Frictional Losses in

Energy Transfer

Hydrodynamics of Apparatus

Smallest Housing, less effect on flow

Strength of Keel 2 Keels Vibrational Resistance 2 Keels to counteract moment

of shaft

Collects Power Data Less risk for instrumentation, experience less vibration

Collects Drag Data Connected to Dyno Accessibility Instrumentation above water Covering of sprocket, bearings,

and shaft Survivability Instrumentation above water Lubrication of Chain Manufacturability Simple Components, less

material/machining Alignment of Sprockets

Cost Material

Table 3: Chain Drive Matrix

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A chain drive was examined for its high efficiency (91-94%) in transferring energy from

one rotational shaft to another. This allows for the electrical components to be above the

water along with not having high tolerances in aligning the sprockets on the shafts

(Figure 4). A 1:1 gear ratio was chosen preliminarily, however if the speeds of the

turbine is different from the expected calculations a resized sprocket will be used to

optimize the speed of the shaft for the instrumentation. The turbine was also downstream

of the keels due to the change in the flow’s velocity profile as the water passes through

Figure 4: Underwater Housing of Chain Drive

Bearings

Tapped Hole to secure Turbine

Bondo for Steam Lining Housing

15

Impo

rtan

ce

Bevel

Gear

In-Line Motor

Chain D

rive

Ease of Mounting to Dynamometer 5 4 5 3

Sensitivity in Shaft 3 3 4 4

Hydrodynamics of Apparatus 5 3 2 4

Strength of Keel 4 4 3 4

Vibrational Resistance 3 3 3 4

Collects Power Data 5 3 3 4

Collects Drag Data 5 X X X

Accesabilty 4 3 2 4

Survivability 5 3 1 4

Manufacturability 4 2 3 4

Cost 3 4 3 4

131 117 159Totals

the blades of the turbine. This would reduce vibration from irregular flow passing over

the keel, enable the capture of the velocity profile after the turbine, along with allow the

setup of a series of turbine apparatuses.

Design Matrix Comparison

The Final Matrix (Table 4) contained the following comparative attributes:

Table 4: Final Drive Selection Matrix

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Based on the design criteria set forth in the design selection, a final design selection

matrix was created as a tool to make the decision on which drive system to use (Table 4).

A relative importance scale was set based on overall performance implications and used

as a multiplier to the values indicated below each design for each category. Based

significantly on its hydrodynamics, accessibility, survivability, and manufacturability, the

chain drive was selected as the best choice.

The drive system was the main aspect of the design that was under debate. The group

was provided with a complete dynamometer. Other aspects including the design of the

upper and lower drivelines were constrained by their need for simplicity and

functionality. After making the selection of the chain drive, all other pieces followed suit

to meet the requirements set forth explicitly by the drive system. Later changes were

made from the above sketches to make improvements for simplicity and ease of

construction on the final design.

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Design Description:

The final design was a synthesis of mechanical, electrical, and data acquisition

components.

Mechanical Design

The tidal turbine test bed was engineered to test the performance of tidal turbine designs

in an overhead carriage tow tank. Design matrices were used to develop the final design

of a chain driven system with an open water lower driveline, a streamline housing, and a

dry upper driveline on a moveable platform connected to a dynamometer as seen in

Figure # 4. The chain drive was chosen after much analysis for its efficiency in energy

transfer, resistance to the test-environment and ease of fabrication. The system was

wired with instruments to read torsional load, rotational velocity, and frontal drag force

on the turbine. The test bed was broken up into four major assemblies:

• The dynamometer,

• Upper driveline assembly

• Streamline struts

• Lower driveline with streamline housing.

FIGURE # 4: Fully Assembled Test Bed in Tow Tank

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FIGURE # 5: 3D Model of Dynamometer without movable plate

Dynamometer

The dynamometer used was a 6-Axis direct force dynamometer. The system was

designed and built by Matt Zeh of MMA [1]. Figure 5 shows a 3D model of the

dynamometer used in the experiment.

The dynamometer works by using the slender rod theory. By attaching necked, long

slender rods to a plate from the dynamometer’s frame, the horizontal forces experienced

in the rods are negligible. This results in complete axial loading on each of the rods. Due

to this axial load, a load cell may be placed inline with the slender rod to obtain the axial

force the rod is experiencing. Combining the readings of multiple load cells, the

dynamometer can produce accurate readings of applied forces on 6 axes.

For the test bed, only one of the six axes was used. The axis which ran parallel to the

velocity vector of the tow tank carriage was connected through a 100 lbs. S-Type Load

Cell to the upper driveline platform and was used to measure the frontal drag force on the

turbine. Figure 6 shows the dynamometer, the driveline platform, the S-Type load cell,

and the direction of the flow.

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FLOW

The frame of the dynamometer was used to bolt the entire test bed assembly to the tow

tank carriage so that tests could be performed. By attaching the frame of the

dynamometer to the underbody of the carriage, both drivelines and the streamlined struts

could only transfer force parallel to the flow through the 100 lbs. load cell.

Upper Driveline Platform

The upper driveline assembly was the heart of the test bed as shown in Figure 7. This

system coupled together all the instrumentation needed for data acquisition to the upper

shaft, while keeping it out of the water.

FIGURE # 6: 3D Model of Dynamometer with driveline plate, load cell, and flow direction

FIGURE # 7: 3D Model of Dynamometer with upper driveline assembly

20

The upper driveline begins with the 0.500” OD stainless steel shaft being supported by

two .500” ID Rylon Linear Bearings. The bearings sit in aluminum pillow blocks and

rest on risers to align the shaft off of the driveline plate. These bearings allowed the

upper shaft to self align the chain drive system to the lower driveline. Figure 8 shows the

SS shaft, bearings, and risers connected to the driveline plate.

On the right end of the shaft, a 100 pulse/sec Rotary Incremental Encoder fixed to the

upper plate by a right angled mount was coupled to the shaft with an aluminum coupling

that compensated for misalignment up to 5o. The encoder was used to get the rotational

velocity of the upper shaft. On the left end of the shaft, a DC stepper motor was

connected inline with the upper shaft to provide rotational resistance to the turbine. The

rotational resistance was varied with a fixed (24 volt, 15 amp) Power Source and a

Variable Resistor shown in Figure 10. The motor was connected by a stainless steel solid

coupling and set screws. A third Rylon Linear Bearing supported the other end of the

motor through the motors rear output shaft and suspended the motor over a slot in the

driveline plate. This allowed the body of the motor to rotate freely. Figure 9 depicts the

setup of the encoder and motor assemblies.

FIGURE # 8: 3D Model of Upper driveline with upper shaft, bearings, and risers

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FIGURE # 9: 3D Model of Upper driveline with upper shaft, bearings, risers, encoder, and motor assemblies

A gimble device was then bolted to the upper plate and connected to the motor through a

50 lbs. S-Type Load Cell by ¼”-28 threaded rods and ¼” OD pin supports on the plate

and on the outer fringe of the motor. The gimble was used to obtain torque readings from

the reactant force on the rotating motor. Due to fixing the motor’s housing to a pin with

the inline load cell, the force read by the load cell was then processed into a torque by

using the force experienced by the load cell and the distance from the center of the

motor’s shaft to where the gimble connected to the motor. Figure 11 shows the addition

of the gimble to the assembly.

FIGURE # 10: Picture of Power Source, Variable Resistor, and DC Stepper Motor

Power Supply

DC Stepper Motor

Variable Resistor

22

To transfer power between the lower and upper drivelines an ANSI #25 Stainless Steel

Roller-Less Chain was used in conjunction with a 30 tooth, 2.53” OD Nylon Sprocket for

the ANSI #25 chain. The sprocket was bored out to fit our 0.500” OD shaft where it was

secured by a ¼”-20 Socket Head Set Screw. Figure 12 shows the complete upper

driveline on the driveline platform.

The upper plate was connected to the dynamometer housing by long, necked-down,

slender rods so that all of the upper and lower assemblies were essentially free to move

and the forces could be measured by the dynamometer load cells. For our experiment, as

earlier stated, the frontal drag force on the turbine was the only load recorded. Figure 13

shows the assembled upper driveline and the dynamometer.

FIGURE # 12: 3D Model of Upper driveline assembly

FIGURE # 11: 3D Model of Upper driveline with upper shaft, bearings, risers, encoder and motor assemblies, and gimble

23

FIGURE # 14: 3D Model of front view of struts FIGURE # 15: 3D Model of tensioner plate, struts, and lower driveline housing

Struts & Nacelle

Two side by side streamline aluminum airfoil struts connected the upper driveline plate to

the lower driveline. These struts were extruded in the shape of a streamlined airfoil and

were purchased from Aircraft Spruce. The bottom ends of the struts were machined to

match the 3.00” OD profile of the lower driveline housing. This allowed for a seamless

connection when welding the two together. The top ends of the struts were squared off

and welded to the chain-tensioner plate. The chain tensioner plate was bolted onto the

driveline plate to connect the struts and lower driveline to the upper assembly. Figure 14

through 16 shows a 3D model of the struts, strut assembly, and photograph of welded

assembly.

FIGURE # 13: Picture of Dynamometer and Upper Driveline Assembly without gimble

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The use of twin side-by-side struts allowed for the chain to run up through the center of

one of these struts and back down through the other while minimizing drag on the system

as it moved through the water. Nylon tubing lined the walls of the strut to minimize

friction from contact between the chain and the side wall of the strut.

Lower Driveline and Housing

The lower driveline was an open water system as shown in Figure 17. Its body consisted

of a 3.50” OD by 12.00” long aluminum pipe. This pipe was machined with internal

threads on both ends to allow two matching threaded UHMW Polyethylene bearing

inserts, which housed the unsealed stainless steel ball bearings, to be screwed into

position. Two .825” holes were drilled in the top of the cylinder to allow for the chain to

pass through.

FIGURE # 16: Picture of struts welded to tensioner plate and lower driveline housing

Welds

25

These inserts can be easily turned into the body and removed for occasional bearing

maintenance. The two threaded inserts had a tapered 45 degree back edge that mated with

a matching taper inside the pipe housing to center the inserts. The driveline housing was

streamlined with a fabricated UHMW front nose cone that threaded into the cylinder.

The curve of the front nose connected the 1.875” OD of the turbine hub and the 3.50” OD

of the cylinder, as seen in Figure 18. The rear of the housing had a similar machined

UHMW cone that was designed to streamline the cylinder from 3.50” OD to the center

axis of the housing. These cones were constructed to minimize separation in the flow so

the assembly would smoothly cut through the water creating as little disruption to the

flow. This aspect of the design is geared towards the future when multiple test beds will

be set up in an array to develop the understanding of the interaction between multiple

turbines inline with each other.

FIGURE # 18: 3D Model of exterior of lower driveline housing

FIGURE # 17: 3D Model of partial lower driveline and housing

26

The lower drive shaft consisted of a 0.500” OD Stainless Steel Shaft. This rode on the

ball bearings within the housing. To transfer the axial thrust and drag forces, the SS shaft

was machined with a round nose to contact the flat face of the Rear Nose Cone, as seen in

Figure 19. The front end of the shaft was machined with a 3/8”-16 thread .500” down the

shaft to connect the turbine nose cone. A matching sprocket (30 tooth, 2.53” OD, ANSI

#25 Nylon Sprocket) was attached to the shaft by a matching set screw. This allowed the

power and rotational motion to be transmitted from the lower shaft to the upper shaft by

the stainless steel self lubricating chain which ran up through the housing and through the

struts.

Part Fabrication

Through designing the test bed, certain parts could not be purchased out of a catalog.

SolidWorks was used to 3D model the entire test bed and create drawings for parts the

group fabricated. Figure 20 and 21 shows pictures of many of the parts that the group

machined.

FIGURE # 19: 3D Model of complete lower driveline and housing

27

FIGURE # 21: Picture of fabricated custom tap for cylinder threads and assembly tool

FIGURE # 20: Picture of Various fabricated parts

Cylinder with Internal Thread

Custom Tool to Turn in Bearing

Inserts

Bearing Insert

Driveline plate

Machined 3D Printed Turbine

Front Nose Cone

Rear Nose Cone

Struts welded to Cylinder and

Tensioner plate

28

Fabricated Parts List and Bill of Materials

Refer to Appendix A for drawings of fabricated parts: Pay special attention to notes in drawings.

Refer to Appendix B for complete list of Bill of Materials

Bearing Disk Insert

Cylinder Housing

Dynamometer Attachment Plate

Front Nose Cone

Gimble Mount

Gimble Threaded End Connector

Linear Bearing Spacer

Lower Shaft

Motor Support Bracket

Rear Nose Cone

Right Strut

Upper Shaft

Welding Assembly

Assembly

The assembly of the test bed is relatively simple, though it looks complex, as seen in

Figure 22. The key to any assembly is the order the parts are installed. This especially

holds true for the test bed. The construction of the entire test bed is broken up into three

divisions:

Upper Driveline and Dynamometer

Lower Driveline and Struts

Connection of Test Bed to carriage

29

#6 -32 SS Socket Head

Screws

#6 -32 SS Nuts ¼”-20 SS Nuts

¼”-20 SS Hex Cap Screw

Right Angle Dyno

Attachments

Driveline Plate

Gimble Mount

FIGURE # 23: Exploded View of 1st step in assembly of the Upper Driveline and Dynamometer

Assembly of Upper Driveline and Dynamometer For the assembly of the upper driveline and dynamometer, follow the sequence in this

step by step process (Figures 23 – 34).

Step 1:

FIGURE # 22: Exploded View of Upper Driveline Assembly

30

Step 2: NOTE: Very loosely tighten the #6-socket head screws to account for the

misalignment in the motor.

FIGURE # 24: Diametric View of 1st step in assembly of the Upper Driveline and Dynamometer

FIGURE # 25: Exploded View of 2nd step in assembly of the Upper Driveline and Dynamometer

Rylon Linear Bearing and Pillow Block

Housing

#5 -40 SS Socket Head

Screws

ANSI #25 Nylon Sprocket with ¼”-

20 Set Screw

Linear Bearing Spacers

Encoder Mount

Encoder Coupling

0.500” OD SS Upper Shaft

#6 -32 SS Socket Head

Screws

31

#6-32 SS Socket Head Screws

Rylon Bearing

Linear Bearing Spacer

DC Stepper Motor

SS Coupling with SS Set Screws

Step 3: NOTE: For this step, attach the coupling to the right side of the motor’s shaft.

Next place the left side of the motor’s shaft in the Rylon coupling and attach the coupling

to the left side of the upper shaft. Very loosely tighten the nuts on the #6-32 Socket head

nuts to account for the misalignment in the motor.

FIGURE # 27: Exploded View of 3rd step in assembly of the Upper Driveline and Dynamometer

FIGURE # 26: Diametric View of 2nd step in assembly of the Upper Driveline and Dynamometer

32

Step 4:

FIGURE # 29: Exploded View of 4th step in assembly of the Upper Driveline and Dynamometer

FIGURE # 28: Diametric View of 3rd step in assembly of the Upper Driveline and Dynamometer

Motor Support Bracket

¼”-20 SS Machine Screws, 3.50” Long

¼”-20 Machine Screws, 1.00” Long

Large SS Washers

¼”-20 Machine Screws, 1.00” Long

Washers with ¼” Jam Nuts

ABS Skate Wheels

Washers with ¼” Jam Nuts

33

¼”-20 Threaded Rod

¼”-20 Jam Nuts

¼”-20 Jam Nuts

Dynamometer Assembly

Step 5:

FIGURE # 31: Exploded View of 5th step in assembly of the Upper Driveline and Dynamometer

FIGURE # 30: Diametric View of 4th step in assembly of the Upper Driveline and Dynamometer

34

¼”-20 Threaded Rod

¼”-20 SS Hex Nuts

100 lbs. S-Type Load Cell

¼”-28 Threaded Rod

50 lbs. S-Type Load Cell

¼” Pin and ¼”-28 Threaded Rod

Gimble Threaded End Connectors

Step 6:

FIGURE # 33: Exploded View of 6th step in assembly of the Upper Driveline and Dynamometer

FIGURE # 32: Diametric View of 5th step in assembly of the Upper Driveline and Dynamometer

35

¼”-20 SS Hex Screws, 2.00”

¼”-20 Jam Nuts

Wing Attachment Plate Welded to

Assembly of Lower Driveline and Struts For the assembly of the lower driveline and struts, follow the sequence in this step by

step process (Figures 35 – 42).

Step 1:

FIGURE # 35: Exploded View of 1st step in assembly of the Lower Driveline and Struts

FIGURE # 34: Completed Assembly of Upper Driveline and Dynamometer

36

Threaded Read End Cap

.500” SS Ball Bearing

Threaded Rear Bearing Insert

Internally Threaded Cylinder Welded to Struts

Step 2: NOTE: Screw the bearing insert into the cylinder with the custom tool.

FIGURE # 37: Exploded View of 2nd step in assembly of the Lower Driveline and Struts

FIGURE # 36: Diametric View of 1st step in assembly of the Lower Driveline and Struts

37

ANSI #25 Nylon Sprocket with ¼”-

20 Set Screw

Threaded Front Bearing Insert

.500” SS Ball Bearing

.500” OD SS Lower Shaft

Step 3: NOTE: First, feed the #25 Pitch SS Chain down one strut. Using a bent close

hanger, reach down the other strut and hook a chain link and pull the chain up through the

strut. Attach the sprocket with the set screw on the shaft and position the shaft through

the rear bearing. While adjusting the tension in the chain, move the lower shaft and

sprocket to hook the chain on the sprocket. After the chain is secured to the lower

sprocket, connect the chain link, and adjust the tensioner plate to fit the chain on the

upper sprocket. Continue to install the front bearing insert and bearing with the custom

tool.

FIGURE # 39: Exploded View of 3rd step in assembly of the Lower Driveline and Struts

FIGURE # 38: Diametric View of 2nd step in assembly of the Lower Driveline and Struts

38

Threaded Front End Cap

Tidal Turbine

Threaded Turbine Nose Cone

Step 4:

FIGURE # 41: Exploded View of 4th step in assembly of the Lower Driveline and Struts

FIGURE # 40: Diametric View of 3rd step in assembly of the Lower Driveline and Struts

39

Assembly of Lower Driveline and Struts For the assembly of the lower driveline and struts, follow the sequence in this step by

step process (Figure 43 – 49).

Step 1: NOTE: Bring assembled test bed apparatus to tow tank.

FIGURE # 43: Picture of Tow Tank

FIGURE # 42: Complete Assembly of Lower Driveline and Struts

40

¼”-20 Threaded Rods, or 1.50” Long Hex

Screws on bolt pattern (See Figure 45)

Tow Tank Carriage

Test Bed

Upside down ¼-20 Hex bolts, 1.50” Long

¼”-20 Threaded Rods, or 1.50” Long

Hex Screws

Upside down ¼-20 Hex bolts, 1.50” Long

Step 1:

FIGURE # 45: Top View of Test Bed that depicts bolt pattern to connect test bed to carriage

FIGURE # 44: Exploded View of 2nd step in assembly of the Test Bed to the Carriage

41

FIGURE # 47: Section View of underneath carriage in 2nd step in assembly of the Test Bed to the Carriage

FIGURE # 46: Exploded View of underneath carriage in 2nd step in assembly of the Test Bed to the Carriage

Drilled .375” holes in Carriage for Test

Bed to bolt into

42

FIGURE # 49: Photograph of actual Test Bed connected to Tow Tank Carriage

FIGURE # 48: Completed Assembly of connecting the Test Bed to the Tow Tank Carriage

43

Electronic & DAQ Design

Required outputs included power data, this was determined from the rotational velocity

of the shaft and the torque on the shaft. Other values to be determined included the

velocity of the carriage, to determine the flow rate, i.e. the velocity of the fluid flow.

Lastly the drag of the system was to be found as a comparable design factor.

Data Requirements

As explained earlier, the most important information needed to evaluate the performance

of a turbine was the flow velocity and the power generated by the flow. The actual power

generated by a turbine was known to be a function of the flow velocity, the density of the

fluid, the swept area, and a coefficient of performance which essentially indicates the

quality of the turbine design. Determining the coefficient of performance, a non-

dimensional quantity, would allow for easy comparison of turbine designs.

In this case, the flow velocity was simply equivalent to the speed at which the carriage

(with the test apparatus attached) moved down the tow tank. To determine the power

generated, the team decided to measure two related quantities, the angular velocity of the

shaft and the torque in the shaft. Power is equal to the torque times the angular velocity;

this was not a difficult calculation after gathering the data.

The last quantity needing measurement was the drag force created by pulling the turbine

through the water. For a stationary turbine, this would be equivalent to the frontal force

experienced on the turbine as the moving water tries to push it backwards. This was a

secondary consideration compared to the power generated and the efficiency of the

turbine, but still an important factor to consider when designing the support structure for

the turbine.

Data Collecting Equipment

Knowing the quantities of interest, the next step was to decide what type of instruments

would be needed to measure the data. In the end, the velocity of the carriage was

determined by marking out a fixed distance where the carriage was up to speed, then

using a stopwatch to measure the time it took to traverse this know distance. Originally,

an encoder was to be attached to the drive shaft of the tow tank carriage. However, due

to the data acquisition location, this was not an easily obtainable option. The torque in

44

the shaft was determined using an S type load cell as part of the gimble/motor system

discussed in the mechanical design section. The angular velocity of the shaft was

measured using an in-line rotary encoder connected to the upper shaft. Finally, the drag

force was measured by tensioning a second S type load cell with one end connected to a

fixed point and the other connected to the free-floating upper plate of the turbine

apparatus.

Data Processing

Converting the raw data from the instruments into a useful form on a computer was a

process which involved several intermediate devices. The load cells have one output that

is on the order of tens of milivolts, whereas the encoder provides an output that is a

frequency (alternating values of fixed voltage output which switch back and forth at a

speed which is related to the rate at which the encoder shaft is rotating). The team

decided to normalize these different output signals using signal conditioners (connected

to an isolation module mounting rack) so that all of them were between 0 and 5 V. This

voltage range matched that of an available data acquisition system (DAQ) used this as an

acceptable range for its incoming signals. The DAQ is able to handle up to eight analog

and eight digital channels in real time, making only one USB connection to a computer

necessary to transfer over all of the data. For the project only three analog channels were

used, but the extra channels allow for the possibility of more data signals in the future,

perhaps if array effects are studied.

With useful signals reaching the computer, a computer program called LabVIEW was

used to interface with the DAQ. The program was developed using modular blocks that

represent the functions needed to import, convert, and generate tables of data. The

collection of blocks into a coherent program was a VI or virtual instrument. Figuring out

how to develop a block diagram that would take the analog signals from the DAQ and

write them to a specific file proved complex. The first version of the program was as

basic as possible. It allowed for multiple analog inputs from different channels. Once

imported, the data was routed through functions that returned the form to volts. This

allowed for the data to be either preprocessed into standard units: pounds, foot pounds,

revolutions per minute, etc, or to be left in terms of volts and processed later. With the

45

assistance of a graduate student the second version of the program was over developed.

This complication made LabVIEW unwieldy and difficult to debug. In the end even after

the weeks used to develop the second version it was scrapped in favor of the first. The

following image show the actual block diagram used in the tests. The diagram flows

from left to right showing how the input ports through the blocks which are wired

together in a progression (Figure 50). The data flow from the input to several LabVIEW

sub-VI of subprograms which process the data into voltages. Following this there are

spaces where the conditioning or calibration information could be input allowing for

preprocessing, this function was not used in this application. From here the data was put

into an array allowing for multiple sources of data to be graphically represented as on

figure on the front screen. The data was also diverted to the “write to file” portion of the

VI from here. This application allowed for the streaming data to be written to a specified

file as the data is reported to the LabVIEW program from the DAQ.

Figure 50: LabVIEW block diagram used for data collection file construction

46

Hardware Specifics

The major piece of electronic hardware used was the DAQ PMD 1608-FS, which allowed

for 16 total channels of information to be input and a tremendous sampling rate, allowing

for very accurate readings. This was used by a former project allowing us to save money

by not purchasing new DAQ. The voltage signals read by the DAQ were from a voltage

conditioning source known as an isolation module mounting rack. The model used was

an ISO-Rack08, which could hold up to 8 cartridges. The conditioner used was a

frequency to voltage card with a range of 0 to 1000 Hz and an output of 0 to 5 V. The

other two conditioners were for the load cells and had an input of +/-100mV and +/-

30mV, with an output range of 0 to 5 V. The encoder was a TRD-N100-RZWD (Totem

pole), and the load cells were Massload S type ML-0200’s of 100 and 50 lb capacity. A

sealable hard plastic box protects much of the wiring and more sensitive equipment from

the harsh water environment of the tow tank facility. The components inside the box

were attached to a Plexiglas board to keep them from moving. The box was mounted on

a wooden frame that was bolted to the carriage. This setup ensured a water-tight and

secure environment for the vital electronic equipment. Further specifications for the

equipment can be seen below in Table 5 through 7 and Figure 51. Signal conditioning

cards were manufactured by Dataforth Corporation and DATAQ Instruments

Frequency input module

Input Output Error

1SCM5B45-02 0 to 1kHz 0 to 5 V +/-.05% span Analog Voltage Input Module

Input Output Error

2DI-5B38-02 +/-30mV 0 to 5 V +/-.08% span 1SCM5B40-06 +/-100mV 0 to 5 V +/-.03% span

Table 5: Signal Conditioning Card Specifications

47

Massload S-type Load Cells ML-0220 capacity 50 and 100 lb

Encoder TRD-N100-RZWD (Totem pole)

Safe Overload 150 % Operating Voltage 4.75-30 VDC Full Scale Output 3 mV/v + or - 0.25% Allowable Ripple 3%rms Maximum Excitation 15 volts DC Current Consumption 60mA max Non- Linearity < 0.03 % FS Hystersis < 0.02 % FS Non Repeatability < 0.01 % FS

H-10mA L-30mA H-2.5 V L-.4 V 35VCD max

Thermal Sensitivity Shift 0.0008% of reading /deg. F Thermal Zero Shift 0.0015% FS/deg. F

Input: Signal Wave

Barometric Effect NIL Max Response Frequency: 100kHz Bridge Resistance 350 ohms

Iso-Rack08 Details Analog Input Specs. Module types: Provides 8 isolated channels Channels: 8 Voltage input 5B modules provide a wide variety of signal conditioning

Module isolation: 1500Vrms

High speed voltage input (10 KHz)

Sensor/module types may be mixed on a single board

Input filtering: 4Hz (standard module), 10kHz (high speed)

Current input

DAS-8 and DAS-16 compatible Thermocouple input RTD input Strain gauge input Frequency input

Table 6: Iso-Rack08 Specs.

Table 7: Load Cell and Encoder Specs.

Figure 51: Timing Chart

48

Electronic/Mechanical Integration

Connecting all of the electrical components together correctly took much trial and error.

The resulting system is imaged below in Figures 52 with Table 8 and Figure 53.

Component(s) Label

Description

A The laptop, which has LabView and is connected to the DAQ B The motor power source with rheostat attached

C The electronics box housing the ISO Rack08, signal conditioners, and DAQ, along with the terminal blocks that distribute power to the devices and connect the instruments to the ISO Rack08

D The primary power source, providing 5 V and 12 V to the system E Upper shaft system, including the motor, encoder, and 2 load cells

F The whole apparatus under the carriage; the interaction of mechanical and electrical components can be visualized with all the components in view

Figure 52: Components of the test apparatus data collection system (1)

Table 8: Key of components in Figures 52& 53

49

It isn’t possible to accurately model the wiring of the system with actual pictures. The

wiring diagram for the data collection system is shown in Figure 54.

Figure 53: Components of the test apparatus data collection system (2)

50

Wiring

Full explanation of all the fine points of the wiring scheme would be a confusing process.

The key points are described here, and details (such as how wire colors match up) are

covered in the wiring diagram. The specification sheets for the equipment were used to

plan how all the pieces would come together. The input power provided to each device

was of vital importance. An input of 5 V of power was a common possibility for all of

the equipment in the system. This was used for everything except the load cells. Both

load cells were powered at 12 V because the higher the excitation voltage on the load

cell, the higher their output for a given load (3mV/V of excitation is the full scale output

of the load cells). Increasing the possible range of output in this way increased the

accuracy of the readings. While 15 V excitation was the maximum for the load cells, 12

V was the highest fixed voltage terminal on the Elenco Precision XP-580, the main

power source. There was a variable voltage terminal that could have provided 15 V, but

Figure 54: Wiring Diagram for the data collection system

51

this introduced the risk of someone turning the knob by mistake and causing damage to

the load cells.

The load cell output connections into the ISO-Rack08 were straightforward; low matched

to low and high matched to high. The encoder connection was not as intuitive, and a few

attempts were made before careful examination of the signal conditioner specification

sheet determined that the TTL configuration was required. Only output A was used on

the encoder, outputs B and Z do not connect to anything.

The signal conditioner cards only fit into the ISO-Rack08 one way, so inserting them

correctly was not difficult. The circuitry on the backside of the ISO-Rack08 connected

the signal conditioners to the 37 connector pins used to send the signals to the DAQ.

Table 9 summarizes the color code of the wires going from the ISO-Rack08 to the DAQ

for any future use of additional channels. The first color was the solid wire color and the

2nd and 3rd colors were the dashed colors. Terminal 10 was arbitrarily chosen to carry the

analog ground signal from the power source.

Pin number

Pin assignments on ISO-Rack08

Our Use Wire color in cable

1 Terminal 1 Not Used Black 2 Terminal 2 Not Used White 3 Terminal 3 Not Used Red 4 Terminal 4 Not Used Green 5 Terminal 5 Not Used Orange 6 Terminal 6 Not Used Blue 7 Terminal 7 Not Used White/Black 8 Terminal 8 Not Used Red/Black 9 Terminal 9 Not Used Green/Black 10 Terminal 10 Analog Ground Orange/Black 11 No Connect Not Used Blue/Black 12 NC Not Used Black/White 13 NC Not Used Red/White 14 NC Not Used Green/White 15 NC Not Used Blue/White 16 NC Not Used Black/Red 17 NC Not Used White/Red 18 DAS08 LLGND Not Used Orange/Red 19 DAS16 LLGND Not Used Blue/Red 20 Terminal 20 Not Used Red/Green 21 Terminal 21 Not Used Orange/Green 22 Terminal 22 Not Used Black/Red/White

52

23 Terminal 23 Not Used White/Red/Black 24 Terminal 24 Not Used Red/White/Black 25 Terminal 25 Not Used Green/Black/White 26 Terminal 26 Not Used Orange/Black/White 27 Terminal 27 Not Used Blue/Black/White 28 Terminal 28 Not Used Black/Red/Green 29 Terminal 29 Not Used White/Red/Green 30 Ch7 Module7 Not Used Red/Black/Green 31 Ch6 Module6 Not Used Green/Orange/Black 32 Ch5 Module5 Not Used Orange/Green/Black 33 Ch4 Module4 Not Used Blue/Orange/White 34 Ch3 Module3 Not Used Black/Orange/White 35 Ch2 Module2 Ch2 Output White/Red/Orange 36 Ch1 Module1 Ch1 Output Orange/Blue/White 37 Ch0 Module0 Ch0 Output White/Blue/Red

The DAQ used the USB connection with the computer for both communication and

power. Each channel on the DAQ corresponded to two neighboring terminals (1 and 2

for Ch0, 3 and 4 for Ch1, etc.), one for the conditioned signal from the instruments and

one for ground. The DAQ was connected to the ISO-Rack08 as shown in the wiring

diagram to receive signals from all three instruments. The analog channels not being

used were connected to ground, since this was recommended in the DAQ’s User’s Guide

(which also contains extensive details of the PMD 1608-FS specifications).

As noted in the wiring diagram, a second power source was connected to a rheostat which

was then connected to the motor in the apparatus. The rheostat was adjusted back and

forth to change the rate at which the motor rotates. The wires can be easily switched so

that the motor spins in the opposite direction, allowing the motor to aid or hinder the

natural rotation caused by the turbine moving through the water.

System Function

After some trial and error in the early stages, the data collection process worked very well

and provided the necessary information from the instruments. The data could be seen in

real time on the laptop as the test was conducted to make sure everything was working

properly, and then once the program was stopped, the data was written to file which can

be opened in Microsoft Excel for data processing. Once the data was processed,

meaningful and expected results were obtained, indicating that the system was likely

Table 9: ISO-Rack08 pin and cable color code

53

effective in its required tasks. This quality was further examined in the design

examination.

In the secondary system with the power source, rheostat and motor, the rheostat proved to

be somewhat inconsistent in use. It was difficult to slide the connection back and forth

and the same settings could not be duplicated with much accuracy. Additionally, there

was no easy way to quantify what the different settings actually meant.

54

Design Evaluation:

The test apparatus drive train consists of two ½” rotary shafts connected by a highly

efficient chain. Upon initial design the shafts were sized using Von Misses design

equation for an ideal torque of 22.2 lb-ft, which was based upon ideal dynamic theory of

potential fluid energy. The Von Mises equation also takes into account the bending

moment in the rotary shafts. It was idealized that there would be no bending moment.

After completion of the testing apparatus and running multiple tests at different speeds

and resistances it was found that a high amount of friction was occurring internally. In an

attempt to quantify where this might be occurring along the shaft. A dynamic load

analysis was completed to better understand the stresses occurring.

Shaft Dynamic Load Analysis

The loading analysis on both upper and lower shaft was completed using singularity

functions. These take into account discrete loading collections such as point loads and

segmented distributed loads. Integrating these functions and applying boundary

conditions will yield the shear force, moment, slope, and deflection of the shaft. See

Appendix C for Matlab Scripts and/or Machine Design by Norton for a more in depth

explanation of how these functions work.

Upper Shaft

The upper shaft, Figure 55 consists of three linear bearings supporting the pancake motor

and a spur gear.

K2K1

K3

T1

Figure 55: External Forces on Upper Shaft

55

W2 W4 W1

wb

R2

W3

wb

R3

The linear bearings are denoted in red and the chain tension in blue. It should be noted

that three degrees of freedom (3 unknowns) exist. Linear bearings do not act like ball

bearings where the boundary conditions of no moment and deflection are present. So the

moments about these reactions can not be used to solve for the 3 D.O.F. Therefore this

was an indeterminate loading case and only finite element analysis could estimate the

loading of this shaft.

In order to make this a determinate problem the shaft was cut at the center of the linear

bearings and they were treated as point forces. This conservatively idealized the loading

case present. Figure 56 shows the right and left side of the upper shaft and the loading

case analyzed.

The reactions of the spur gear and motor, R2 and R3 respectively were found from free-

body diagrams conducted on those parts. Wb is the distributed load caused by the weight

of the rod per unit length. The singularity loading functions were then created and

integrated four times. They yielded the following four graphs of shear, moment, slope,

and deflection for both the right and left upper shaft in Figure 57:

Figure 56: Idealized Upper Shaft Loading

56

Top Right Shaft Shear & Moment

-6

-4

-2

0

2

4

6

8

10

12

14

0 0.5 1 1.5 2 2.5 3 3.5 4

Position (in.)

Shear Force (lbs) Moment (in-lbs)

Top Left Shaft Shear & Moment

-3

-2

-1

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3 3.5 4

Position (in.)

Shear Force (lbs) Moment (in-lbs)

Top Left Shaft Slope & Deflection

-0.00008

-0.00007

-0.00006

-0.00005

-0.00004

-0.00003

-0.00002

-0.00001

00 0.5 1 1.5 2 2.5 3 3.5 4

Position (in.)

Slope Deflection (in.)

Top Right Shaft Slope & Deflection

-0.00018

-0.00016

-0.00014

-0.00012

-0.0001

-0.00008

-0.00006

-0.00004

-0.00002

00 0.5 1 1.5 2 2.5 3 3.5 4

Position (in.)

Slope Deflection (in.)

Lower Shaft

The lower shaft consisted of a simple loading scheme. There are two deep-groove ball

bearings with a spur gear in the middle. The end of the shaft was fitted with a turbine that

collected the energy from the flow. The lower shaft external forces can be seen in Figure

58.

K4 K5 T2

Figure 57: Upper Shaft Shear Force, Moment, Slope, and Deflection.

Figure 58: External Forces on Lower Shaft

57

R3

W5 W6

wb

The deep groove-ball bearing reactions are in red and the tension force blue. The tension

force was the same, but opposite direction as the tension force on the upper shaft. Note

that the turbine causes no reaction bending force on the shaft. It creates only a constant

torque in the shaft from the turbine to the spur gear.

Only the section between the two bearings was analyzed because the rest of the shaft was

free hanging and will have only the weight of the shaft causing any small moment. The

loading profile for the lower shaft can be seen in Figure 59 below:

This loading profile was determinate therefore the singularity functions were derived and

the shear force, moment, slope, and deflection of the shaft was calculated and was

presented in graphical form in Figure 60.

Figure 59: Idealized Lower Shaft Loading

58

Lower Shaft Shear & Momen

-5

-4

-3

-2

-1

0

1

2

3

0 0.5 1 1.5 2 2.5 3 3.5 4

Position (in.)

Shear Force (lbs) Moment (in-lbs)

Bottom Shaft Slope & Deflection

0

0.0000002

0.0000004

0.0000006

0.0000008

0.000001

0.0000012

0.0000014

0.0000016

0.0000018

0 0.5 1 1.5 2 2.5 3 3.5 4

Position (in)

Slope Deflection (in.)

There were two main factors important to analyze and should be noted from the loading

analysis of both the upper and lower shaft. The most important was the deflection of the

shaft. In both cases of the upper and lower shaft the maximum deflection occurred at the

motor. The deflection was so small at these points along the shaft that it could be

determined to not be a source of high friction in the system.

The other factor to be considered was the bending moment created in the shaft. The point

of greatest moment occurs in the same spot as the maximum deflection. The maximum

moment was taken into account in making sure our initial shaft size was large enough and

would not cause failure of our material. See Shaft Sizing section to see how the

maximum moment calculated in this section is incorporated into shaft sizing.

Figure 60: Lower Shaft Shear Force, Moment, Slope, and Deflection

59

Csize .869 ditr .097−⋅:=

Shaft Sizing

Initial Constraints and Factors

The shaft is made of 316 stainless steel with material constants as follows:

Von Mises uses problem dependent safety coefficients that are multiplied by the yield

strength (Sf) of the material to make sure the shaft will stand up to the conditions that it

will be used in [2].

• Loading Factor: The shafts will only be loaded axially.

Cload = 0.7

• Size Factor: The shaft will be less than 3 inches in diameter (ditr).

• Surface Factor: The shaft is cold-rolled so a = 2.7 and b =-.265

• Reliability Factor: The apparatus is needed for many tests over many years.

Crelib.=0.814

• Temperature Factor: The temp will not have extreme changes.

Ctemp=1

Csurf a Sut b:=

Sf Cload Csize⋅ Csurf⋅ Ctemp⋅ Creliab⋅ Sfprime⋅:=

E 27.5 106⋅ psi⋅:= σy 40 103⋅ psi⋅:= σut 110 103⋅ psi⋅:= Sfprime 50 103⋅ psi⋅:=

60

Moment and Torque:

The shaft experienced both constant and alternating torque caused by the propeller

stopping and starting. This torque was constant in the shaft between the turbine and spur

gear on the lower shaft; spur gear and motor on the upper shaft. The bending moments

were minuscule in the test apparatus but should be incorporated in Von Mises. The

maximum torque that was recorded in the shaft for our testing is:

Von Mises Equation:

Where:

Factor of Safety: Nf =2

Keyway Factors: Kf, Kfs, Kfm, Kfsm = 1 (Due to no keyways being used.)

Yield Strength: Sf

Shaft Over Sizing:

Von Mises equation yielded a shaft diameter of 0.135 inches for the point of maximum

moment and torsion in the test bed. This showed that the ½” shaft used for this test bed

was oversized and therefore added rigidity, not causing any internal friction due to a

bending moment or torsion. The ½” shaft had a factor of safety of about five compared to

its minimal design requirement. See Appendix D for shaft sizing worksheet.

d32 Nf⋅

π

kf Ma⋅( )2 .75 kfs Ta⋅( )2⋅+

Sfkfm Mm⋅( )2 .75 kfsm Tm⋅( )2+

σut+

⎡⎢⎣

⎤⎥⎦

1

3

:=

TmTmax Tmin−

2:= Ta

Tmax Tmin−

2:=

Tmax 4.26 lbf in⋅:=

Tmin 0lbf in:=

Mmax 11.756 lbf in⋅:=

Mmin 0lbf in:=Mm

Tmax Tmin−2

:= MaTmax Tmin−

2:=

61

Test Procedures

The wave tank located in the Aquaculture Center at the University of Maine is where all

testing was carried out. The wave tank was used to create a laminar flow through a

scaled model of a tidal turbine by attaching the Turbine Test Bed to a carriage, which

traveled down the length of the wave tank at a controllable speed. From these short time

intervals, data was produced which showed turbine characteristics.

• Multiple data runs were performed for speeds ranging from 1 to 2 m/s;

possible flow rates for different tidal sites along Maine’s coast. The speed of

the carriage was recorded using two stopwatches and dividing the recorded

time by the distance the carriage covered once steady state speed had been

reached.

• Data was gathered at three different test speeds of 3.00, 4.53, and 6.00 feet per

second. For each speed six runs were conducted at preloaded torsional

resistances. The pancake motor created the pre-load using a variable resistor

connected to a power supply, which varied voltage and therefore torsional

resistance in the test bed. The torsional resistance was varied to develop the

optimum torque in the shaft in order to achieve the maximum power produced

by the turbine.

• During each data run shaft torque, thrust, and rpm were measured several

times a second using a reaction-torque load-cell, load-cell on shaft axis, and

encoder respectively. An encoder based carriage velocity sensor was

designed into the test bed system however, was not used for this study. A lab-

view program then stored the data collected by the various measuring

instruments. The data from each data run was then converted into a useful

data point by taking an average of the steady state data from the middle of the

run. Non-dimensional analysis was then performed to create operating

characteristic charts for the tested turbine

62

Calibration

The calibration of both load cells was conducted on the same day testing was preformed.

Note the importance of calibration for each test session due to the harsh environment the

tow tank is subjected too.

Calibration of the frontal load cell was preformed by running thin rope attached to one

end of the load cell over a low friction sleeve covering a bracket to a vertical weight

hanger. The gimble load cell was calibrated by hanging a thin rope perpendicular to the

motor from the same radius the load cell was connected to the motor. This is better

depicted in Figure 61:

The calibration range for both load cells was zero to five pounds. The weights were

calibrated on a digital scale for accuracy. Figure 62 shows the frontal load cell calibration

curve for converting load cell output (micro strains) into force:

Frontal Load Cell

Gimble Load Cell

Weights Weights

Figure 61: Frontal & Gimble Calibration Setup

63

Calibration Curve Frontal Load Cell

Load = -0.0601*(Output) + 0.1351

0

1

2

3

4

5

6

-90 -80 -70 -60 -50 -40 -30 -20 -10 0

Output (MircoStrain)

MicroStrain Linear (MicroStrain)

The gimble load cell calibration curve and equation is shown in Figure 63. This curve

depicts the applied torque for the shaft as a function of load cell output.

Gimble Calibration Curve

Applied Torque= 20.024*(Output) + 1.0698

0

1

2

3

4

5

6

-0.1 -0.05 0 0.05 0.1 0.15 0.2

Output (Mirco Strain)

Calibration Data Linear (Calibration Data)

Figure 62: Frontal Force Calibration Curve

Figure 63: Gimble Calibration Curve

64

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25

Time (s)-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Encoder (V) Torque (V) RUN # 022608C2

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00RPM

Vo = 1.38 m/s Vo = .914 m/s Vo = 1.831 m/s

Results

Raw Data

Figure 64 shows the raw data from a single tow tank run, showing the RPM and torques

signals. The RPM data was used to determine steady state speed. The data over this

steady region was averaged to get the mean rotational speed and torque for each data run.

Dimensional Analysis

Figure 65 shows the dimensional performance data curves for each of the three test

speeds. The mean torque, rpm and carriage velocity data for all runs are depicted.

Figure 64: Raw Data Trace of RPM and Torque for a typical tow tank run

Figure 65: Dimensional performance of the test turbine at three speeds

65

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 0.5 1 1.5 2 2.5 3 3.5Tip Speed Ratio

Vo = 1.38 m/s Vo = .914 m/s Vo = 1.83 m/s

Non-Dimensional Analysis

The turbine performance data was non-dimensionalized using the following relations:

Power Coefficient: AV

WC p

∗∗∗=

•

3

21 ρ

Tip Speed Ratio: V

NTR ∗=π

Torque Coefficient: AV

QCq

∗∗∗=

2

21 ρ

Thrust Coefficient: AV

TCT ∗∗= 2ρ

Figure 66 shows the non-dimensional performance of the turbine at the three test speeds.

Note that the curves collapse to a single curve for the middle and higher speeds,

indicating that the test apparatus was properly measuring the turbine performance. The

lower speed data may have suffered from the lower measurement forces due to the low

speed, but the number of data points collected was insufficient to make any concrete

conclusions. The data showed that the loading resolution of the device at higher

preloaded torques needs to be improved to capture the lower speed, higher load region of

the power curve.

Figure 65: Non-dimensional performance of the test turbine at three test speeds

66

Discussion

A test bed for the testing of scale model tidal turbines was developed and implemented in

the University of Maine tow tank. A sample turbine was tested which successfully

demonstrated the test beds measurement capabilities. Data was collected over a range of

three speeds and it was shown that the non-dimensionalized power curves collapsed to a

single performance curve as expected. The uncertainty in the power, power coefficient,

and tip speed ratio is 3.01%, +/- 3.8, and 3.8% respectively. The power coefficient had an

uncertainty of plus or minus 3.8 directly. No percentage of actual value need be found.

This percentage represents a direct value of turbine efficiency. These values were used to

validate the performance of the test bed measurement system.

67

Conclusions & Recommendations This project fully created and established performance curves for a tidal turbine. Though

the task was completed, there was room for numerous changes and improvements.

Below are evaluated the mechanical and electrical designs and components thereof.

Assessment of Design: Mechanical

Strengths

The strengths of this design greatly outweighed its weaknesses. All established tasks and

milestones were completed. The main strengths are listed below:

• Effectively collects high speed flow rate data

• Able to collect preliminary data

• Overall Mechanical System Integration

• Flexibility for Array Setup and Turbine Type

• Streamlined Design

Weaknesses

The weaknesses of the mechanical system inhibited certain performance characteristics.

The weaknesses summarized indicate the major impacting factors on data collection and

system functionality. The main weaknesses are listed below:

• Ineffectively collects speed flow rate data

• High friction losses within system

• Misalignment

• Torque Data Skew from Motor Asymmetry

• Motor to Upper Shaft Coupling

• Fabrication

o Welds on Struts to Cylinder

o Cylinder Distortion

o Inner Threading of Pipe

68

Assessment of Design: Electrical & DAQ

Strengths

The strengths of this design greatly outweighed its weaknesses. All established tasks and

milestones were completed. The main strengths are listed below:

• Effectively collects Torque, Rotational Speed, and Frontal Force data

• Overall Electronic System Integration

• User Friendly Interface with LabView Program

• System Organization

Weaknesses

The weaknesses of the electrical and data acquisition systems inhibited certain

performance characteristics. The weaknesses summarized indicate the major impacting

factors on data collection and system functionality. The main weaknesses are listed

below:

• Lack of Power Supply and Rheostat Reproducibility

• Wiring Short and Instrumentation Overload

o Communication Failure

o Equipment Mislabeling

• Multi-voltage Power Supplies to Instrumentation

• Exposure to High Humidity Environment

o Wiring Containment Box not Watertight

• Power Supply Not Connected to Carriage

• Over Sizing of Load Cells

69

Product Cost Overall mechanical system costs were very low for a first generation test bed that

produced viable data. Custom fabrication and the use of university facilities lowered

production costs, eliminating expenditure on fabrication labor. Instrumentation and

signal conditioning modules were moderately priced, however wire shortages and group

miscommunication resulted in the need for multiple replacements. Product cost was

minimal due to the use of generic equipment and materials. This yielded a high

performance turbine testing system.

Future Improvements

Mechanical Improvements

Despite the successful operation of the mechanical system, there were numerous

opportunities for improvement. The upper and lower drivelines contained significant

friction. This was largely due to misalignment in the motor, linear bearings, and motor

coupling. To fix the problem, the upper driveline bearings could be replaced with deep

groove ball bearings or better aligned. The coupling on the motor could be redesigned to

reduce motor run out.

The gimble contained a significant amount of play between the motor and the load cell

joint. This could be reduced with a plastic insert to reduce vibration and yield more

defined torque results.

The carriage movement on the tracks is not uniform. This results in high variation in all

data types. To improve this, open linear roller bearings could be installed as a

replacement track. The drive system could also be redesigned as to not torque the

carriage to one side.

The drive system on the tow tank, consisting of a 7.5 hp electric motor, variable

frequency drive (VFD) does not function. After the first collection of data, the drive

system failed. This situation should be rectified by fixing/replacing the motor and/or

VFD.

The mechanical motion produced by the turbine was translated to the upper driveline via

a chain. Though efficient, this extra step in the data collection process induces

70

uncertainty in the form of vibrational and frictional losses. To overcome this issue, the

housing of the lower driveline could be sealed. This sealed housing would contain inline

torques sensor and slip ring.

As long term goals, the following could be done. For further flow analysis, multiple

turbine arrays and particle velocimetry should be integrated into the tow tank.

Electrical Improvements

Despite the successful operation of the data acquisition system, improvements could be

made in several areas. Using a stopwatch to measure the velocity of carriage produced

consistent results during testing, however the team originally planned on using a second

encoder mounted on the carriage drive system to measure the velocity of the carriage.

Knowing the diameter and angular velocity of the drum would make it easy to calculate

how quickly the cable connected to the carriage was moving, producing the carriage

velocity. This hasn’t yet been implemented due to the signal degradation that would

likely occur attempting to connect the moving parts on the carriage and the stationary

drive train encoder to the same DAQ. A system already exists to run cables to the

moving carriage, and a plan is in progress for keeping the laptop in the control room

(rather than on the carriage) and running an Ethernet cable from the DAQ to the laptop.

With the laptop now in the control room, connecting the drive train encoder would be a

simple matter.

Another area of concern was the electronics box. The team has improved accessibility to

the electronics in the box by building a tilted stand, but due to the wires coming out of the

box, it cannot be fully sealed and protected. This problem could be solved by drilling a

hole or two in the wall of the box for the wires to exit, then using quick connects to

sealing up the extra space.

Both of the power sources simply sat on top of the carriage, which could potentially be

dangerous. There was little chance of them sliding into the water, but it was possible.

Ideally, it would be best to have power sources that fit into the box with the other

electronics. Steps should be taken to ensure they are securely attached to the carriage.

71

The rheostat which controlled the motor was far from desirable. An investment in some

type of electronic controller for the motor would likely improve that part of the system

considerably.

While the instruments and signal conditioning cards selected successfully measured the

desired data, accuracy might be improved by scaling down a little. The load cells

especially seemed to register readings well below the full scale values. On the positive

side, with the current instrumentation, turbines of more than ten inches in diameter (the

size of the turbine tested) could be evaluated without having to change the electronic and

data acquisitions systems.

Conclusion

Overall, the tidal turbine test bed met or exceeded the milestone requirements set. The

system precisely models dimensional and non-dimensional turbine performance in areas

of torque, rotational speed, and drag force data. The test bed acts as a tool for accurately

determining tidal turbine performance via a scaled model system.

References

[1] Zeh,M.: Development of a Six Axis Dynamometer for Tow Tank Testing;

Undergraduate Capstone Project, April 2006 Maine Maritime Academy, Castine Me.

[2] Norton, Robert L. 2006, Machine Design: An Integrated Approach, Pearson Prentice

Hall, Upper Saddle River, NJ.

72

Appendix A – Dimensioned Drawings of Custom Fabricated Parts

73

74

75

76

77

78

79

Appendix B – Bill of Materials Part Description Model # Dist. Qnty Price Test Bed BOM Dynamometer 6-Axis Measuring

Tool - - 1 -

Upper Driveline Plate

6061 Aluminum, .375" Thick, 6" Wide, 18" Long

975K214 McMaster 1 $23.95

Rotary Encoder

Light Duty Incremental Encoder, Standard Shaft, 100PPR

TRD-N100-RZWD Automation Direct 1 $112.00

Encoder Coupling

Aluminum Coupling for Encoder

MCGL20-8-952 Automation Direct 1 $25.00

Encoder Mounting Bracket

- JT-350D Automation Direct 1 $9.50

Linear Bearing Spacers

6061 Aluminum, .70" thick - - 3 -

Gimble Mount 6061Aluminum, .70" thick - - 1 -

Pillow Block Linear Bearing Mount

Aluminum Pillow-Block Housing for Linear Bearing

9804K3 McMaster 3 $89.37

Rylon Lined Bearings

Rylon Lined, SS Linear Bearing Closed, 1/2" ID

6676K62 McMaster 3 $57.33

Wing Attachment (Tensioner Plate)

6061 Aluminum, .375" Thick, 6" Wide, 6" Long

975K214 McMaster 1 $7.98

#6-32 Socket Head Screw

SS Socket Head Cap Screw #6-32, 1 3/4" Length

92196A158 McMaster 14 $5.26

#6-32 Machine Screw Nut

SS Machine Screw Nut #6-32, 5/16" Width (100)

90257A007 McMaster 14 $10.44

Lock Washer for #6 Screw

SS Spring Lock Washer for #6 Screw (100)

98437A104 McMaster 14 $2.53

#5-40 Socket Head Screw

SS Socket Head Cap Screw #5-40, 1" Length (50)

92196A129 McMaster 4 $12.53

#5 Machine Screw Nut

SS Machine Screw Nut #5-40, 5/16" Width (100)

91841A006 McMaster 4 $6.21

80

Lock Washer for #5 Screw

SS Spring Lock Washer for #5 Screw (100)

92146A535 McMaster 4 $2.28

1/4"-20 Hex Head Cap Screw, 2" Long

SS Hex Head Cap Screw 1/4"-20, 2" Length (10)

93190A550 McMaster 10 $9.34

1/4"-20 Lock Nut

SS Hex Nylon-Insert Locknut 1/4"-20 Screw Size, 7/16" Width, 5/16" Height (50)

90715A125 McMaster 26 $11.84

Struts (Right and Left)

Air Foil Fins, 6ft Long 03-40000 Aircraft Spruce 1 $109.85

Cylinder Housing

Alloy 6061 Aluminum Round Tube, 3.5" OD, 3" ID, 12" Length

9056K241 McMaster 1 $38.25

Front Bearing Disk

Polyethylene (UHMW) Rod, 3.5" OD

8701K57 McMaster 1 - 1.5" Long

Rear Bearing Disk

Polyethylene (UHMW) Rod, 3.5" OD

8701K58 McMaster 1 - 1.5" Long

Rear Bearing Disk

Polyethylene (UHMW) Rod, 3.5" OD

8701K59 McMaster 1 - 8" Long

Rear End Cap Polyethylene (UHMW) Rod, 3.5" OD

8701K60 McMaster 1 - 6" Long $67.92

Motor Support Bracket

6061 Aluminum, .70" thick - - 1 -

1/4"-20 Hex Head Cap Screw, 1" Long

SS Hex Head Cap Screw 1/4"-20, 1" Length (25)

93190A542 McMaster 4 $12.09

1/4"-20 Hex Head Cap Screw, 3.5" Long

SS Hex Head Cap Screw 1/4"-20, 1" Length (25)

- Parks Hardware 2 $0.75

DC Stepper Motor - - Rich Kimbal 1 -

Gimble Threaded Ends

Stainless Steel - - 2 -

1/4"-28 Threaded Rod

Steel, .75" Length - - 2 -

Skate Wheel 1 7/8" OD, 11/16" Thick ABS Skate Wheel w/ 1/4" Axle

2290T31 McMaster 2 $4.38

81

SS Washer SS 3/8" Bore Flat Washer - Parks Hardware 8 $2.45

Upper Driveline Shaft

Unhardened Precision Type 316 SS Drive Shaft 1/2" OD, 36" Length

6493K5 McMaster 1 - 8" Length

Lower Driveline Shaft

Unhardened Precision Type 316 SS Drive Shaft 1/2" OD, 36" Length

6493K6 McMaster 1 - 18" Length $48.74

Motor Coupling

SS One-Piece Set-Screw Coupling 1/2" Bore, 1-1/2" Length, 1" OD, Without Keyway

6099K24 McMaster 1 $15.51

ANSI #25 Nylon Sprocket

Nylon Machinable Bore Sprocket for #25 Chain, 1/4" Pitch, 30 Teeth, 2.53" OD

60425K174 McMaster 2 $36.22

1/4"-20 Socket Head Set Screw

- - - 2 -

ANSI #25 SS Chain

SS ANSI #25 Chain, 1/4" Pitch, Rollerless,8ft Length

6264K218 McMaster 1 $137.76

.500" ID SS Ball Bearings

ABEC 1, 1/2" R8 Stainless Steel Ball Bearing

6138K15 McMaster 2 $31.46

3D Printed Scaled Tidal Turbine

- - Rich Kimball 1 -

Power Supply 120V input, 24 V 15 Amp Output - Mick Peterson 1 -

Variable Resistor

Variable Tube Resistor - Stig Callahan 1 -

TEST BED B.O.M. PRICE TOTAL $890.94

Instrumentation BOM S-type load cells 50 lb & 100 lb

ML-200 Massload Inc 1 $125.00

Modular conditioning Rack

ISO-Rack08 Measurement Computing 1 $149.00

Signal Conditioning cards

SCM5B40-06 Measurement Computing 1 $149.00

82

SCM5B45-02 Measurement Computing 1 $179.00

SCM5B38-02 Measurement Computing 1 $149.00

DAQ PMD1608-FS Measurement Computing 1 $399.00

Encoder TRD-N100-RZWD Automationdirect.com 1 $112.00

INSTRUMENTATION B.O.M. PRICE TOTAL $1,262.00

COMPLETE SYSTEM PRICE TOTAL $2,152.94

Appendix C: Singularity Functions & M-Files %************************************************* % Save this file as InitalBotShaft.m % Initial Bottom Shaft Parameters F3=5; % Tangental Motor Force (lbs) F2=0; % Spur Gear Relationship F1=F3; % Spur Gear Relationship Wm=8.25; % Weight of Motor wb=.0533; % Weight of Shaft Per Unit Length E=29E6; % Youngs Modulus (316 SS) % Upper Shaft Length Parameters (inches) r=.25; % Radius of Shaft rm=2.369; % Radius of Motor rs=1.75; % Radius of Spur Gear lb=18; % Length of Shaft f=1.75; % Spur Gear 1 Position g=4; % Bearing 6 Position % Reactions & Moment Relationships Ib=(1/12)*(((wb*lb)/32.2)*((3*r^2)+(lb^2))); % Moment of Interia R2=(F3*cos((pi/180)*45)*(rm/rs)); % Reaction at Top Spur Gear R3=(Wm+F3*cos((pi/180)*45)); % Reaction at Motor R1=R2; % Reaction at Bottom Spur Gear %****************************************************************** % Save this file as InitialTopShaft.m % Initial Top Shaft Parameters F3=5; % Tangental Motor Force (lbs)

83

F2=0; % Spur Gear Relationship F1=F3; % Spur Gear Relationship Wm=8.25; % Weight of Motor wb=.05375; % Weight of Shaft Per Unit Length E=29E6; % Youngs Modulus (316 SS) % Upper Shaft Length Parameters (inches) r=.25; % Radius of Shaft rm=2.369; % Radius of Motor rs=1.75; % Radius of Spur Gear lup=8; % Length of Shaft b=2; % Spur Gear 2 Position c=4; % Bearing 2 Position d=1.5; % Motor Position e=4; % Bearing 4 Position % Reactions & Moment Relationships I=(1/12)*(((wb*lup)/32.2)*((3*r^2)+((lup/2)^2))); % Moment of Interia R2=(F3*cos((pi/180)*45)*(rm/rs)); % Reaction at Top Spur Gear R3=(Wm+F3*cos((pi/180)*45)); % Reaction at Motor %*************************************************************** % Save this file as Print.m % When run this assigns values of Singularity Functions at each point along the % shaft to array D, K, and X and outputs excel files for each array. format short e D = []; for x = (0:0.05:4); B = [x Vtr(x) Mtr(x) Otr(x) Ytr(x)]; D = [D;B]; end K = []; for x = (0:0.05:4); L = [x Vtl(x) Mtl(x) Otl(x) Ytl(x)]; K = [K;L]; end X = []; for x = (0:0.05:4); Z = [x Vb(x) Mb(x) Ob(x) Yb(x)]; X = [X;Z]; end

84

xlswrite('TopRight.xls', D) xlswrite('Topleft.xls', K) xlswrite('Bottom.xls', X) %*************************************************************** function v =s(x,a,n) %------ Definition of singularity function ----------- %This function will return the value of the singularity function <x-a>^n. if x<a v = 0; else v = (x-a)^n; end %*************************************************************** % Save this file as Vtr.m % Shear Singularity Function for top right shaft function val = Vtr(x); InitialTopShaft; W3=((R3*(e-d))+wb*(e^2))/e; % Reaction Force 3 W4=(wb*e)-W3+R3; % Reaction Force 4 C3=(wb*(e^4)-W4*(e^3)+R3*((e-d)^3))/e; % Integration Constant C4=0; % Integration Constant val = -wb*s(x,0,1)+W3*s(x,0,0)-R3*s(x,d,0)+W4*s(x,e,0); %*************************************************************** % Save this file as Vtl.m % Shear Singularity Function for top left shaft function val = Vtl(x); InitialTopShaft; W1=((R2*(c-b))+wb*(c^2))/c; % Reaction Force 1 W2=(wb*c)-W1+R2; % Reaction Force 2 C3=(wb*(c^4)-W1*(c^3)+R2*((c-b)^3))/c; % Integration Constant C4=0; % Integration Constant val = -wb*s(x,0,1)+W1*s(x,0,0)-R2*s(x,b,0)+W2*s(x,c,0); %*************************************************************** % Save this file as Vb.m % Shear Singularity Function for bottom shaft function val = Vb(x) InitialBotShaft;

85

W5=((R1*(g-f))-wb*(g^2))/g; % Reaction Force 5 W6=(-wb*g)-W5+R1; % Reaction Force 6 C3=(wb*(g^4)+W5*(g^3)-R1*((g-f)^3))/g; % Integration Constant C4=0; % Integration Constant val = -wb*s(x,0,1)-W5*s(x,0,0)+R1*s(x,f,0)-W6*s(x,g,0); %*************************************************************** % Save this file as Mtr.m % Moment Singularity Function for top right shaft function val = Mtr(x); InitialTopShaft; W3=((R3*(e-d))+wb*(e^2))/e; % Reaction Force 3 W4=(wb*e)-W3+R3; % Reaction Force 4 C3=(wb*(e^4)-W3*(e^3)+R3*((e-d)^3))/e; % Integration Constant C4=0; % Integration Constant val = -wb*s(x,0,2)+W3*s(x,0,1)-R3*s(x,d,1)+W4*s(x,e,1); %*************************************************************** % Save this file as Mtl.m % Moment Singularity Function for top left shaft function val = Mtl(x); InitialTopShaft; W1=((R2*(c-b))+wb*(c^2))/c; % Reaction Force 1 W2=(wb*c)-W1+R2; % Reaction Force 2 C3=(wb*(c^4)-W1*(c^3)+R2*((c-b)^3))/c; % Integration Constant C4=0; % Integration Constant val = -wb*s(x,0,2)+W1*s(x,0,1)-R2*s(x,b,1)+W2*s(x,c,1); %*************************************************************** % Save this file as Mb.m % Moment Singularity Function for bottom shaft function val = Mb(x) InitialBotShaft; W5=((R1*(g-f))-wb*(g^2))/g; % Reaction Force 5 W6=(-wb*g)-W5+R1; % Reaction Force 6 C3=(wb*(g^4)+W5*(g^3)-R1*((g-f)^3))/g; % Integration Constant C4=0; % Integration Constant val = -wb*s(x,0,2)-W5*s(x,0,1)+R1*s(x,f,1)-W6*s(x,g,1); %****************************************************************

86

% Save this file as Otr.m % Theta Singularity Function for Top Right Shaft function val = Otr(x); InitialTopShaft; W3=((R3*(e-d))+wb*(e^2))/e; % Reaction Force 3 W4=(wb*e)-W3+R3; % Reaction Force 4 C3=(wb*(e^4)-W3*(e^3)+R3*((e-d)^3))/e; % Integration Constant C4=0; % Integration Constant val = (1/(E*I))*(-wb*s(x,0,3)+W3*s(x,0,2)-R3*s(x,d,2)+W4*s(x,e,2)+C3); %**************************************************************** %Theta Singularity Function for Top Left Shaft function val = Otl(x); InitialTopShaft; W1=((R2*(c-b))+wb*(c^2))/c; % Reaction Force 1 W2=(wb*c)-W1+R2; % Reaction Force 2 C3=(wb*(c^4)-W1*(c^3)+R2*((c-b)^3))/c; % Integration Constant C4=0; % Integration Constant val = (1/(E*I))*(-wb*s(x,0,3)+W1*s(x,0,2)-R2*s(x,b,2)+W2*s(x,c,2)+C3); %**************************************************************** % Save this file as Ob.m %Theta Singularity Function for Bottom Shaft function val = Ob(x) InitialBotShaft; W5=((R1*(g-f))-wb*(g^2))/g; % Reaction Force 5 W6=(-wb*g)-W5+R1; % Reaction Force 6 C3=(wb*(g^4)+W5*(g^3)-R1*((g-f)^3))/g; % Integration Constant C4=0; % Integration Constant val = (1/(E*Ib))*(-wb*s(x,0,3)-W5*s(x,0,2)+R1*s(x,f,2)-W6*s(x,g,2)+C3); %**************************************************************** % Save this file as Ytr.m % Deflection Singularity Function for Top Right Shaft function val = Ytr(x); InitialTopShaft; W3=((R3*(e-d))+wb*(e^2))/e; % Reaction Force 3 W4=(wb*e)-W3+R3; % Reaction Force 4

87

C3=(wb*(e^4)-W3*(e^3)+R3*((e-d)^3))/e; % Integration Constant C4=0; % Integration Constant val = (1/(E*I))*(-wb*s(x,0,4)+W3*s(x,0,3)-R3*s(x,d,3)+W4*s(x,e,3)+C3*x); %**************************************************************** % Save this file as Ytl.m % Deflection Singularity Function for Top Left Shaft function val = Ytl(x); InitialTopShaft; W1=((R2*(c-b))+wb*(c^2))/c; % Reaction Force 1 W2=(wb*c)-W1+R2; % Reaction Force 2 C3=(wb*(c^4)-W1*(c^3)+R2*((c-b)^3))/c; % Integration Constant C4=0; % Integration Constant val = (1/(E*I))*(-wb*s(x,0,4)+W1*s(x,0,3)-R2*s(x,b,3)+W2*s(x,c,3)+C3*x); %**************************************************************** % Save this file as Yb.m % Deflection Singularity Function for Top Left Shaft function val = Yb(x) InitialBotShaft; W5=((R1*(g-f))-wb*(g^2))/g; % Reaction Force 5 W6=(-wb*g)-W5+R1; % Reaction Force 6 C3=(wb*(g^4)+W5*(g^3)-R1*((g-f)^3))/g; % Integration Constant C4=0; % Integration Constant val = (1/(E*Ib))*(-wb*s(x,0,4)-W5*s(x,0,3)+R1*s(x,f,3)-W6*s(x,g,3)+C3*x); %****************************************************************

88

Appendix D: Shaft Diameter Calculations

Material Constants

E 27.5 106⋅ psi⋅:=

Gsteel 10.7 106⋅ psi⋅:=

σy 40 103⋅ psi⋅:=

σut 110 103⋅ psi⋅:=

Sfprime 50 103⋅ psi⋅:=

Coefficients

Cload .7:= a 2.7:= b .265−:= Sut 110:=

ditr .135:= Csurf a Sut b:= Ctemp 1:=

Csize .869 ditr .097−⋅:= Creliab .814:=

Sf Cload Csize⋅ Csurf⋅ Ctemp⋅ Creliab⋅ Sfprime⋅:=

Diameter Calculations Based on Max Torque

Tmax 4.26lbf in⋅:= Tmin 0lbf in:=

TmTmax Tmin−

2:= Ta

Tmax Tmin−

2:= Nf 2:=

Nfs 1:= Mmax 11.756lbf in⋅:= Mmin 0lbf in:=

MmTmax Tmin−

2:= Ma

Tmax Tmin−

2:=

kf 1:= kfs 1:= kfm 1:= kfsm 1:=

d32 Nf⋅

π

kf Ma⋅( )2 .75 kfs Ta⋅( )2⋅+

Sfkfm Mm⋅( )2 .75 kfsm Tm⋅( )2

+

σut+

⎡⎢⎣

⎤⎥⎦

1

3

:= d 0.135in=

dfs32 Nfs⋅

π

kf Ma⋅( )2 .75 kfs Ta⋅( )2⋅+

Sfkfm Mm⋅( )2 .75 kfsm Tm⋅( )2

+

σut+

⎡⎢⎣

⎤⎥⎦

1

3

:= dfs 0.108in=

FS0.5indfs

:= FS 4.636=