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A Finite Element Analysis of a Brake Lever

Report By: Nicole Andrews

Student Number: 14816648

Module Title: Finite Element Analysis in Design

Module Number: DP238

Module Leader: Derek Covill

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Contents

1 Introduction 2

2 Background Information to the Problem

2.1 Component Function 3

2.2 Relevant BS, ISO, EN, ASTM Standards 3

2.3 Hand Grip Strength 4

3 Design Details

3.1 Schematic Drawing 1

3.2 Free Body Diagrams 5

3.2.1 Components 5

3.2.2 Load Cases 5

3.2.3 Restraints 6

4 Analysis Method

4.1 Analysis Type and Assumptions 6

4.2 Theory and Equations 6

4.3 Failure 7

4.4 Materials, Properties and Costs 7

4.5 Mesh 8

4.6 Convergence Graph 9

4.7 Assumptions 10

5 Results of Analysis

5.1 Stress Results 10

5.2 Displacement Results 10

5.3 Improvements 11

6 Discussion of results

6.1 Limitations 11

6.2 Evaluation 11

7 Conclusion 12

8 Reflections 13

9 References 14

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1 Introduction

The component that will be used for the Finite Element Analysis is a bicycle brake lever.

Brake levers are an important and legal part to many products that are used on the roads. This

specific bicycle part was purchased through amazon.co.uk and cost the price of £1.99 for a

pair of Bicycle Brake Levers. These did not come with the wire used to pull on the brake

pads around the wheel.

2 Background information to the problem

2.1 Component Function

The brake levers work when applying a force

to the handle. This pulls the handle down and

pulls on the connecting wire. At the other end

of this wire when pulled up it pulls together

two brake pads which together make contact

with the wheel. The contact creates a force on

the wheel slowing it down or causing it to

stop depending on how much force is applied

to the handle. The more force the quicker the

braking. There are different methods used,

this is the simplest explanation of how a brake

lever works.

2.2 Relevant BS, ISO, EN, ASTM

standards for your study

Since 2010 the Legislation for The Pedal Bicycles has stated that each bicycle should be

‘fitted with brakes which are intended to be hand operated’ (Paul Clark, 2010).

There is not a great deal about the standardisation for bicycle brakes. Just two simple

standards which companies that supply whole bicycles must abide by. ‘(a) The brake lever

intended to be operated by the right hand must operate the front brake; and (b) The brake

lever intended to be operated by the left hand must operate the rear brake’ (Paul Clark, 2010).

ISO 4210-4:2014 tests have multiple parts involved. The parts regarding the brake levers

alone have to sections out and shown in the images above. The ISO states that ‘Apply a

handgrip force not exceeding 180 N at the point as specified in Figure 5. Check before and

after’. This would be for the product to pas British Standard willing to be sold in the UK.

This FEA will be focused on if the part can withstand the maximum force that can be applied

by a hand grip. Where the tests are a more realistic day to day Newton measure. This FEA

will be set with a more extreme circumstance for example an emergency stop.

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2.3 Hand Grip Strength

The Hand grip strength used was the highest value recorded. In this case it was males 25-29

and the right hand. This was done to see if the brake lever will yield under maximum force.

This value was discovered as 140.3lb (the value has been highlighted below).

(Richard W. Bohannon, et al. 2006)

3 Design details: Details of your design including

3.1 Schematic drawings

This Schematic drawing was created by measuring with a ruler in mm’s. This was created for

the purposes of making an accurate Solidworks part to represent the real part.

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3.2 Free body diagrams and description

3.2.1 Components

This model wasn’t enough on its own. The force used to pull against the lever being pulled

needs to be represented properly with the correct component. Therefore an extra part was

made. This is not exact to what may come with a bicycle break lever, however it is suitable

representation for applying a more accurate force onto. This was researched and the

assumption that it was made from galvanised steel, a very common material for brake wires.

3.2.2 Load cases

There are two main load cases in this simulation. The first load case is the maximum grip

strength that can be applied onto the lever. This was found to be 140.03lb. The second being

the opposite force pulling back on the part via the wire. This however is unknown. To work

Actual Part Solidworks Part

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out this force it needs to be understood this part is in equilibrium. Therefore the calculations

below show the resulting force of the wire to be 1,717N.

Force 1: Grip Strength

The 624.4N was applied to the length of the brake lever. This is to mimic the width of a hand

and forcing the full force across the length. This is believed to be the most suitable to

represent a palm applying the force.

Force 2: Wire

This is to represent the wire, a full force of 1717N. The wire is being pulled from both sides

of the part so the force was halved to 858.5N and applied onto each side to make the force

equal 1717N.

3.2.3 Restraints

The restraint of this model is a fixture on the part where it pivots from. If the part was not

restrained in this way there would be no controlling the degrees of freedom that the part can

deform in. This is the most accurate to represent the part in the simulation.

4 Analysis methods 4.1 Analysis Type and Assumptions

In these simulations the aim was to find the yield strength. But also test if the maximum grip

load was within the yield or not. As well as this the aim was to find the type of deformation.

4.2 Theory and Equations

By using the calculation Stress (Pa) = Force (N)/Area (m^2) it can be hand calculated at the

point of bending what the stress will be. Then this value of hand calculation can be compared

to the simulation results and work out a percentage difference.

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The final value for stress across the cross section was 7.26e+006. The next step was to create

the cross section in the simulation in the same area and plot the stress to see if the values

match.

4.3 Failure

The definition of failure for this part would be to yield below the maximum grip strength. If

the part moved from elastic deformation to plastic deformation.

4.4 Materials, Properties and Costs

A material property that is known is that the part was cheap. The cost for both left and right

break levers as a whole was £1.99. Making it clear whatever material used had a cheap

material and manufacturing process.

The material at this stage was unknown. The method of deduction started with identifying

what process was used. This then helped deduce the material by removing multiple alloys

that didn’t use this process. The manufacturing process was Gravity Die Casting. The break

lever was believed to have been made using this method because it had distinctive flash lines.

This is know because these solid moulds may be expensive to start off with however, the

price per unit is minimal in the running time of the process. Products that are produced

through Gravity Die-casting have to have a ‘relatively low melting point’ (Dr Steve Plumber,

2015) such as aluminium or magnesium. Dr Steve Plumber (2015) also mentions that any

other alloy such as steel alloys can be used in this process but die cast life is short and the

process is uneconomical. This method seemed the most logical for a product with such a

cheap purchase cost.

The material of the break lever is Aluminium Alloy S150.1:LMO-M. Which costs between

1.25 and 1.38 GBP/kg. This was deduced by method of elimination via the use of CES

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Edupack. It was known that the product was very cheap to purchase making the search focus

on the least expensive aluminium alloys. From these Aluminium Alloy S150.1:LMO-M was

chosen because it was the most popular alloy and widely used alloy. When checking the

property it was also the only alloy out of the five cheapest alloys that was not processed with

sand casting. Therefore it matched in multiple property area and was decided as a suitable

material for the part.

Aluminium Alloy needed to be made in Solidworks as a new material in the library. The CES

Edu pack supply a range of values for each property. The average of property values were

used. To create a new material on Solidworks CES Edupack’s units into the units that

Solidworks uses. The table below shows the conversions and process used.

Relevant Properties Value CES

Unit

SW Unit Conversation Final Value

Elastic Modulus 70.5 GPa N/mm^2 GPa-Pa-N/mm^2 70500

Poisson’s Ratio 0.36 - N/A - 0.36

Shear Modulus 26 GPa N/mm^2 GPa-Pa-N/mm^2 26000

Mass Density 27000 Kg/m^3 Kg/m^3 None 27000

Tensile Strength 80 Mpa N/mm^2 MPa-Pa-N/mm^2 80

Compression Strength 30.05 Mpa N/mm^2 MPa-Pa-N/mm^2 30.05

Yield Strength 30 Mpa N/mm^2 MPa-Pa-N/mm^2 30

(GPa to Pa = x1,000,000,000)(Pa to N/mm^2 = /1,000,000) (Cancel Out: Simply x1,000)

(Mpa to Pa = x1,000,000)

4.5 Mesh

The mesh started off with the most course level as possible. The simulation was then run to

show the points of interest where the mesh would need to be more defined. Any part of the

resulting simulation that had no stress or deformation was left with the courses mesh to save

time when creating future simulations.

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4.6 Convergence Graph

This convergence graph goes from the most course element size of 4.8mm and then tested at

different intervals towards the finer end of the scale to 3.4mm. The convergence graph is very

flat and steady excluding the small peak at 3.7mm. This shows that the Solidworks part

created was a precise representation.

0.00

1000000000.00

2000000000.00

3000000000.00

4000000000.00

5000000000.00

6000000000.00

7000000000.00

8000000000.00

9000000000.00

3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5

Von Mises (N/m^2)

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4.7 Assumptions

How max was wrong, tried a smaller Newton. Yielded.

During the first round of simulation to create the convergence graph, it was noticed that there

was no yield strength. It was decided that by halving the load sizes the results for Van Mises

would be lower and possibly have a yield emerge. It’s known that the part yields at

3.00e+007 because of the smaller load case simulation. This is the same yield for the larger

loads case because it is a linear model.

5 Results of Analysis

5.1 Stress Results

The Von Mises results showed that the part came under large displacement. This shows the

part did not withstand the maximum stress of 8.25e+009 N/m^2. Therefore the Part failed.

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5.2 Displacement Results

The part has the deformation of bending.

The simulation above didn’t have a yield value. Therefore by halving the force on each part

and re running the simulation the yield was discovered to be 3.00e+007. Therefore the part,

when placed under the maximum force found in the Richard W. Bohannon hand strength

study, would stop deforming elastically and begin deforming plastically.

5.3 Improvements

This part cold have been improved in a number of ways. However, all these improvements

would increase the parts price per unit.

Change in manufacture:

Changing the manufacturing process from gravity die casting to sand casting. Sand

casting is a more expensive method and requires making a new mould each time.

However, the products produced are of a much higher standard.

Sand casting can use a wider range of materials. A material with more desirable

properties than the original material could be chosen.

This sand effect left on the part would also create a surface that can be gripped onto

better then a smooth shiny surface.

Change in material:

The material could be changed from Aluminium alloy S150.1:LMO-M The cheapest

of the casted alloys. To an Aluminium-Zinc alloy. These alloys have the highest

strengths of all the aluminium alloys, and can be made with sand casting, so would be

an appropriate substitute.

Change in Design:

Making the handle thicker at the base where the bending occurs. As well as

thickening around the pivot point.

6 Discussion of results

6.1 Limitations

There are a number of limitations to any Solidworks simulations:

The dimensions are not exact. The Solidworks part may differ slightly to the actual

part via problems in measuring, fillets not being the right measurement or it doesn’t

include any chips or marks on the actual piece. Making the Solidworks model ‘too

perfect’.

Tension

Compression

Tension

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In actual life the brake lever isn’t connected to the pivot, the pivot allows some

leeway. This hasn’t been simulated in the FEA.

The force applied is the maximum force found through research of full hand grips.

This is not a realistic representation of how a brake lever would be used on a daily

basis. Daily, the lever would have multiple cycles of many minimum forces. Only on

a rare occasion such as an emergency stop could the lever be possibly put under this

pressure.

The force applied to the handle is applied to only the top and side fillets of the handle.

This may not accurately the whole hands grip on the part. The force may be

distributed in a different way than the simulation.

The material in this case was chosen via process of elimination through the properties

that were known about the part. This decision of material may possibly be the wrong

one.

6.2 Evaluation

From the simulation cross section cut, at the same place as the hand calculation. This showed

the cross section Stress to be -6.543e+006 N/m^2. The hand calculations worked out the

stress for this cross section to be 7.260e+006 N/m^2. This is a percentage difference of 9.9%.

The difference in results can be attributed to multiple things, the most likely one being that

the hand calculations were done assuming the area was a perfect rectangle, and didn’t remove

area for the fileted edges of the part.

7 Conclusions

Main Results:

Yield: 3.00e+007 N/m^2.

The part Deformed via Bending. With compression and tension.

Hand calculations related to simulation: 9.9% Difference.

8 Reflection

From this I have learnt a number of things. Firstly how to do a basic FEA. Including loads,

fixtures and receiving stress plots from the data. I also learnt basic supporting calculations

and units.

Believed to go well:

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Accuracy of hand calculations. Even though the results were off by 9.9% it shows an

understanding of how the calculations worked.

The accuracy of the Solidworks model to the actual brake lever. The two were very

similar is measurement and believe it helps for an accurate FEA.

The convergence graph was very flat and steady suggesting a precise Solidworks

model.

Didn’t work:

A lack of engineering mathematics was present throughout the report as only simple

hand calculations were performed.

More complicated and accurate calculations could have been done to lower the

percentage difference between the Solidworks model and the hand calculation.

A Deeper understanding of how to analyse results and the best way of analysing

would be helpful to have a better review of the simulations.

If the report could be redone, there would be:

A simulation showing the multiple cycles of the ISO testing method. To see if the

product complies with British standards in a simulation. Following the ISO method.

Create the improved part. Change the material and design then re-run the simulation

with the same forces and see if the yield increased due to the re design and see by

what percentage the yield increase did.

Use a part where the specific alloy is known and not educed by process of elimination

on CES Edupack (which still may not be the right material).

More time would be spent learning the specific loads and restraints this specific part

goes through to create an even more specific simulation.

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9 Reference list

Dr JCS Plumber. 01/10/2015. Level four note on manufacture (module ME113). Issue 7. Page

8 of 25. Brighton University

Richard W. Bohannon, Jane Bear-Lehman, Johanne Desrosiers, Nicola Massy-Westropp,

Anneli Peolsson. 03/2006. Reference values for adult grip strength measured with a Jamar

dynamometer: A descriptive analysis. Research Centre on Aging and Faculty of Medicine,

Department of Family Medicine, Université de Sherbrooke, Sherbrooke, Québec, Canada.

Paul Clark, Secretary of state. 30/01/2010 No. 198, the Pedal Bicycles (Safety) Regulations.

Printed and published in the UK by The Stationery Office Limited under the authority and

superintendence of Carol Tullo, Controller of Her Majesty’s Stationery Office and Queen’s

Printer of Acts of Parliament.

ISO 4210-4:2014. 01/07/2014. Cycles -- Safety requirements for bicycles -- Part 4: Braking

test methods.