Department of Mechanical & Aerospace Engineering

Coursework Assignment Cover Sheet

Class No: 16429

Coursework Title: Stress Concentrators Associated with ‘Split’ Kayak Paddles

Computer Aided Engineering Design ANSYS FEA Report

Submission to: Dr. H Chen and B Keating

Date Stamp (recorded on Myplace)

Surname : Simpson

First Name : Campbell

Degree Course : MEng Mechanical Engineering (e.g. Mech Eng, Chem Eng, Naval, etc)

Year 4th

(e.g. 1st, 2nd)

I confirm that this work is my own and is the final version

Signed C.Simpson

Submission Details / Deadline

DEADLINE:- This assignment must be submitted electronically to Myplace no later than 11 p.m. 15th February 2016. Exercises/ Reports that are submitted late will not be

accepted. A printed submission is not required.

Return Details An announcement will be made when feedback is available on Myplace.

Stress Concentrators Associated with ‘Split’

Kayak Paddles

Campbell Simpson

MEng Mechanical Engineering

Word Count: 2963

Abstract This report makes use of the FEA software ANSYS Workbench to approach

the possibility of achieving an equally performing kayak paddle using

aluminium as a material option over commonly used composite. The analyses

is taken a step further by approaching the design problem of also creating

detachable ‘split’ kayak paddles out of this material as opposed to composite.

The joining areas of the paddle sections act as stress concentrators and are

analysed using frictional, non-linear contact analysis. Optimisation studies are

carried out to find the necessary geometries to minimise mass while

maintaining the performance of the original, composite, one-piece paddle.

Data for loading and boundary conditions is taken from experimental values

and optimised masses are compared with actual paddle weights.

It is found that similar performance can be achieved by around a 12% mass

increase in aluminium compared with composite ‘split’ paddles.

Contents

STRESS CONCENTRATORS ASSOCIATED WITH ‘SPLIT’ KAYAK PADDLES ..................................... 2

Abstract .............................................................................................................................................. 2

Nomenclature ..................................................................................................................................... 3

Introduction ........................................................................................................................................ 3

One-piece Shaft - Model Setup .......................................................................................................... 6

One-piece Shaft - Bending .................................................................................................................. 7

One-piece Shaft – Other Loading Conditions ..................................................................................... 8

Split Shaft - Model setup .................................................................................................................... 9

Split Shaft - Analyses ........................................................................................................................ 10

Split Shaft – Thickness Optimisation ................................................................................................ 12

Conclusion ........................................................................................................................................ 13

References ........................................................................................................................................ 15

Appendix ........................................................................................................................................... 15

Nomenclature 3D – Three Dimensional

A – Cross-Sectional Area

BKIN – Bilinear Kinematic Hardening

CAD – Computer Aided Design

cm – centimetres

FEA – Finite Element Analysis

g – Grams

Kg – Kilograms

Kgm^-3 – Kilomgrams per Metre Cubed

KN – Kilonewtons

L – Linear

l – Length m – Mass

mm – Milimetres

MPa – Megapascals

N – Newtons

NL – Non-Linear

Nm – Newton-metres

Pa – Pascals

– Inner Radius

– Density

– Outer Radius

UTS – Ultimate Tensile Strength

Introduction The structure which will be analysed is a kayak paddle. This is an interesting

structure to analyse as it undergoes a large variety of loading conditions

during its working life due to the extremely unpredictable environment it is

used in. The ‘split’ paddle, described later, is also a perfect example of an

engineering challenge where the kayaker’s ability to enjoy the sport and be

safe on the river is dictated by the quality of their equipment.

Due to this unpredictable working environment, working loads are extremely

difficult to estimate or calculate. Hence all analyses carried out on this

structure must encompass the isolated extremes of each loading case,

bending, torsion and tension / compression.

Figure 1 – A paddle in its working environment

Figure 1 shows how a kayaker makes use of their paddle to stay upright. It is

clear that this structure undergoes a multitude of loading conditions during

use.

Experimental results were available for a full, one piece composite paddle

shaft under isolated loading conditions however it was deemed of interest to

investigate the option of making a paddle of equivalent performance out of

aluminium. Aluminium used to be a common material for shafts before the

lighter composites became favourable. Because of this, mass difference

would be compared with performance under the same loading conditions to

assess how much of an advantage composites really are.

The analyses would be taken one step further, looking into how this material

would fare being used in ‘split’ paddles.

For safety, when undertaking a descent of a long and challenging river,

kayakers take spare paddles with them in the event of one of their primary

paddles being lost or damaged. In order to transport such a long piece of

equipment, systems have been designed to allow paddles to be broken up

and stored in separate, easily assembled parts.

These paddle sections tend to be connected by an overlap and aligned holes

with a spring loaded pin in order to fix them in place.

Flow of Water

Weight of Paddler

Re-righting the Craft

Figure 2 – Standard ‘split’ paddle connection

Figure 2 shows the standard set up for the connection of ‘split’ paddle

sections.

The same, experimental loading conditions would be applied to a model of

this kind of split configuration and the stress concentrator of the connection

would be analysed. The necessary thickness of reinforcement around this

stress concentrator would also be discussed as well as the associated further

addition of mass to see if aluminium shaft splits are a realistic alternative to

the commonly used, brittle composites.

Making use of experimental data from (Millar, 2013), we know that failure of a

composite shaft occurs in bending at 1.44 KN applied at a distance of 11.5 cm

from two supports.

Figure 3 – Composite paddle bending test

Figure 3 shows one of the experiments in which the bending limit load was

found. Due to the necessity for a straight and aligned paddle, any plastic

deformation along the length of the shaft would result in a bend and serious

issues to the user. Hence if the aluminium shaft approaches yield under this

23cm

Load

same bending limit load, it can be considered of equal performance to the

composite shaft.

Figure 4 – Composite shaft extension and failure under tensile loading

Figure 4 graphs applied load to extension of a similar shaft under tension. As

failure occurred at around 8KN, if the aluminium model has an equal tensile

limit, it can be deemed of equal performance.

One-piece Shaft - Model Setup Dimensions for outer radius and blades were measured independently with a

digital Vernier calliper. The wall thickness would then be altered based upon

the stress results from the model.

The full structure was initially meshed though the interest area was around the

centre of the shaft. Figure 5 visibly shows an increase in mesh density at the

centre, where face sizes and refinements were added and the element quality

was hence improved for more accurate analyses where relevant.

Figure 5 – Improved mesh

The computational material values used were those of standard aluminium in

Workbench with a density of 2770 kg m^-3, Young’s modulus of 7.1e10 Pa,

yield stress of 2.8e8 Pa and UTS of 3.1e8 Pa. With research, (ASM, 2011)

these values were deemed suitable to represent the vast majority of

aluminium alloys.

One-piece Shaft - Bending With this initial geometry, material choice and refined mesh, the bending test

was then simulated by accurately representing the loading conditions from the

previous page. Fixed supports were inserted equidistant from the centre of the

shaft and the limit load of 1.44 KN was applied at the centre.

Analysis was carried out using linear material properties for aluminium.

Iteration 1 2 3 4 5 6

Max V-M Stress

(Pa)

2.07e8 2.36e8 2.69e8 2.73e8 2.76e8 2.78e8

Wall Thickness

(mm)

2 1.5 1 0.98 0.96 0.95

Non-linear analyses was also undertaken, using non-linear aluminium

material properties and allowing large deflections in order to take account of

the extreme cases of deflection which may occur. Bilinear Kinematic

Hardening (BKIN) was chosen as this analyses is of a metallic structure and is

unlikely to undergo high strains in comparison to its stresses.

Iteration 1 2 3 4 5 6 7 8

Max V-M

Stress (Pa)

2.13e8 2.45e8 - - 2.54e8 2.648e8 - -

Wall

Thickness

(mm)

2 1.5 1 1.3 1.4 1.35 1.33 1.34

The values represented by ‘–‘ either failed to converge or expressed values

far beyond yield. Comparing to real life geometry, the wall thickness found

with non-linear analysis seemed more realistic though is still thin. This

demonstrates the role material defects play during failure in real life testing.

Non-Linear analyses was used wherever possible from here on.

Figure 6 shows and exaggerated representation of the stresses and

deformations on the paddle shaft just before yield due to bending.

Figure 6 – Maximum bending stress on optimised shaft

Having used this limit load method to find a geometry which yields under the

same conditions as its composite counterpart, we can say that it performs

equally under bending.

One-piece Shaft – Other Loading Conditions Making use of the same geometry, mesh, material data and analyses type as

in bending but by removing the supports and applying tensile loads equal to

half the failure tensile load from (Mitchell, 2016) on either half of the shaft with

the application divide at the midpoint, it can be seen that this geometry

appears to also hold up to tension though it does also approach the

aluminium yield point of 280 MPa.

Figure 7 – Maximum tensile stress on optimised shaft

This shows clearly that a model with this wall thickness of aluminium is a

reasonably accurate equivalent for the real life performance of a composite

shaft.

Using the measured thickness of an E-glass composite shaft and comparing it

with this aluminium equivalent, the mass increase in small, only 52g

(Appendix 1).

An additional analysis was carried out to show how the structure copes under

torsion. Moments were applied to the outer faces of either half of the shaft in

opposite directions and the limit torsion before yield was found to be 500 Nm.

Split Shaft - Model setup It was deemed appropriate to simplify the geometry for analysis of the stress

concentrator associated with the ‘split’ version of the paddle to reduce

computational load while maintaining accuracy. The length of this section was

dictated by the necessary distance at which loads and supports would be

applied to replicate the analyses of the one-piece shaft. Diameters and wall

thicknesses were taken from the earlier analyses to keep the model

consistent while the specific connection sizes such as the pin, hole and

overlapping areas were measured from a composite split paddle.

Figure 8 – ‘Split’ paddle connection assembly (including the spring & pin)

Figure 8 shows the three-part assembly of the central connection of the splits.

It quickly became apparent that the analyses of a spring loaded pin system

would be extremely complex and not relevant to the aims of this report so for

analyses purposes the spring and pin component was left out. Instead the two

halves of the shaft were constrained at their connection to the pin, basing this

assumption on the pin being of an extremely hard and durable material,

allowing more simple analysis of the shaft stresses and deformations. Loading

conditions would be kept consistent to the previous investigation to allow

comparison with the one-piece shaft.

Figure 9 – Element quality improvement

Figure 9 shows improvement in element quality from the automatically

generated mesh to the refined mesh with smaller element sizes around the

hole and overlap. Figure 10 shows how the remaining low quality elements

are concentrated around the ends of the section, where analysis is less

relevant. Figure 10 also shows the full mesh with increased density visibly

obvious around the stress concentrator.

Figure 10 – Number of elements, meshed model & low quality element positions

Non-linear analyses was again used for the same reasons as stated in the

previous section with the same material properties for non-linear aluminium

alloy.

Split Shaft - Analyses Under the designated bending conditions, the model was found to yield, with

the maximum stresses around the pin and at the connection between the

surfaces.

Figure 11 – Maximum stresses under bending

Large strains are also obvious at the contact between the overlapping faces,

this shows how the applied forces will cause deformation at the overlap and

ultimately lead to failure. Maximum stress and deformation occurred on the

male component.

Again in tension, the male component displays the highest stress

concentration at its connection areas and the female component is also found

to yield. Deformation plots demonstrate how the sections will come apart on

the opposite side to the pin. Under the same torque as the one-piece shaft,

the splits drastically fail.

These 3 analyses were carried out with both frictionless and frictional contacts

between the components of the shaft in in order to observe the difference in

results.

Loading

Mechanism

Applied Load Analyses

Type

Max (V-M)

Stress (Pa)

Max (V-M)

Strain

Max

Deformation

(m)

Bending 720 N at 115

mm

= 82.8 Nm

Frictionless,

NL

3.31e8 0.0047 0.0012

Frictional, NL 3.342e8 0.00472 0.0011

Torsion 500 Nm Frictionless, L 1.946e9 0.0279 0.00138

Frictional, L 1.946e9 0.0279 0.00138

Tension 10, 000 N Frictionless,

NL

3.022e8 0.00433 0.001426

Frictional, NL 3.022e8 0.00433 0.001426

Under bending, maximum stress increased and changed position, though still

on the male part, it was now at the bottom of the connection with the pin. This

seems likely and may also be where the maximum shear would occur on the

pin. Despite this slight increase in stress with the addition of friction, total

deformation was actually slightly reduced. Under torsion, frictionless and

frictional results are identical, this could be to do with the fact that both

analyses were carried out linearly, resulting in elastic behaviour. All attempts

at convergence with non-linear materials under torsion failed to converse on a

solution.

From these analyses the only notable difference in result was bending stress

where, though both models failed, the frictional contact recorded a higher

maximum stress. It was concluded that a more realistic and safer model

would include friction.

Split Shaft – Thickness Optimisation Below shows improvements on the wall thickness, starting at 1.35 mm with a

max stress of 3.342e8 Pa.

Iteration 1 2 3 4 5 6 7 8 9 10 11 12 11

Max V-M

Stress

(e8 Pa)

3.08 2.97 2.99 2.86 2.89 3.21 3.21 1.12 2.63 2.64 2.59 2.56 2.48

Wall

Thickness

(mm)

2 2.35 2.45 2.5 2.55 2.6 2.6 2.7 2.7 2.8 2.9 3 3.1

The above table clearly shows the thinnest possible wall dimension before

yield is reached under bending. This is a thickness of 2.8 mm, producing 264

MPa. Thicker walled shafts produce lower stresses and any thinner and the

values stop acting in the linear region, having deformed.

Using this new thickness under the other established loads, it records a

slightly higher stress under tension, 2.71e8 Pa but doesn’t fail yet drastically

fails under the established torsional loads.

Using equations from appendix 1, this resulted in a mass increase of 0.478kg,

almost double.

Taking this new thickness as acceptably strong but considering the stress

concentration around the join, it was clear that at some distance from the

overlap, the shaft could return to the thickness of the single piece shaft in

order to reduce mass.

Iteration 1 2 3 4 5 6

Max V-M Stress (e8

Pa)

2.64 2.64 2.66 2.65 2.63 3.02

Distance from centre

before returning to

original Diameter

(mm)

Full Shaft 85 45 30 25 20

It can be seen that with a mere 20mm of thickened shaft, the paddle will hold

up to the required bending loads but this geometry will fail under the other

loading conditions with over 3e8 Pa in tension and over 4e8 in torsion.

Iteration 1 2 3 4 5

Max V-M Stress

(e8 Pa)

3.08 3.05 2.98 2.77 2.73

Distance from

centre before

returning to

original Diameter

(mm)

25 35 40 45 50

Now, optimising again to ensure the paddle will hold up to the required

tension, we can see the optimum area for reinforcement is 45mm either side

of the central connection.

This will result in a final mass of 5.4 kg for the 1.3m shaft, a far more usable weight and only 0.13kg heavier than its composite counterpart.

Conclusion Through this project, the finite element analyses software ANSYS Workbench

was successfully used to analyse the stress concentrator of a join between

two halves of a ‘split’ kayak paddle.

3D models were created on CAD and all non-critical, external dimensions

were measured independently with use of accurate lab equipment. Model

meshing was investigated and altered for improved accuracy and minimising

of computational load. Workbench material properties were used after

checking with external sources for legitimacy.

Initially, experimental data from composite shafts was taken as a bench mark

of performance and the alternative material of aluminium was investigated. By

simulating the same loading and boundary conditions as these experiments, a

limit load investigation could be used to find the geometry for an aluminium

shaft of adequate equivalent performance. The aluminium shaft required

increased thickness and subsequently increased mass by 52g, a marginal

value in real terms.

Further, non-linear contact analyses was carried out on the situation of a ‘split’

kayak paddle if it were to be constructed of aluminium. This was an especially

interesting investigation as it is very rare to find non-composite split paddles.

For simplicity in this analyses, the pin component was assumed as a fixed

support to investigate the shaft failure point and not the required quality of pin.

The same wall thickness as the one-piece shaft was initially used though this

yielded under the required loading conditions. Optimisation was carried out

and the necessary thickness of split shaft was found. This increase in

thickness caused the shaft mass to almost double to almost 1 kg so an

investigation was undertaken to see how far from the central join this

thickness increase was necessary.

After this optimisation, a 130g mass increase was found to be necessary

hence aluminium splits could be considered as a cheaper alternative to the

commonplace composite at an acceptable mass difference. Average paddles

on the market are around 1.1 Kg (Werner, 2015) so this increase is only

around 12%. However products available today often use components such

as spigots and ferules to increase join strength with minimal mass increase.

Extra torsional analyses was carried out throughout, based upon the torsional

limit of the original aluminium, one-piece geometry. These analyses struggled

to converge when non-linear, though did seemed to approach failure with far

smaller loads than the other conditions. Due to the lack of experimental data

under torsional loading, it is unfortunately impossible to validate the legitimacy

of these results.

References 1 – Millar, Scott (2013). Failure Analysis of Composite Materials, University of Edinburgh

2 – Mitchell, Lance (2016). Mitchell Blades, http://www.mitchellblades.co.uk/ 3 – Aerospace Specification Materials Inc. (2011).

http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061t6

4 – Werner Paddles, http://www.wernerpaddles.com/

Figure 1 – Matthew Brook, 2015

Figure 2 – http://www.kayaksession.com/

Figure 3 – (Millar, 2013)

Figure 4 – (Mitchell, 2016)

Figures 5 - 11 – ANSYS Workbench

Appendix Appendices 1 –

Outer diameter = 32.7mm

Composite wall thickness = 1.1mm

Shaft length = 1.3m

Aluminium shaft mass = 0.4667 kg

Composite shaft mass = 0.415 kg.

Aluminium splits mass = 0.4935 kg

Reinforced aluminium splits mass = 0.9717 kg

Optimised, reinforced aluminium splits mass = 0.5413kg