A Finite Element Analysis of a Brake Lever

Transcription

1 A Finite Element Analysis of a Brake Lever Report By: Nicole Andrews Student Number: Module Title: Finite Element Analysis in Design Module Number: DP238 Module Leader: Derek Covill 1

2 Contents 1 Introduction 2 2 Background Information to the Problem 2.1 Component Function Relevant BS, ISO, EN, ASTM Standards Hand Grip Strength 4 3 Design Details 3.1 Schematic Drawing Free Body Diagrams Components Load Cases Restraints 6 4 Analysis Method 4.1 Analysis Type and Assumptions Theory and Equations Failure Materials, Properties and Costs Mesh Convergence Graph Assumptions 10 5 Results of Analysis 5.1 Stress Results Displacement Results Improvements 11 6 Discussion of results 6.1 Limitations Evaluation 11 7 Conclusion 12 8 Reflections 13 9 References 14 2

3 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 :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. 3

4 2.3 Hand Grip Strength The Hand grip strength used was the highest value recorded. In this case it was males 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. 4

5 Actual Part Solidworks Part 3.2 Free body diagrams and description 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 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 lb. The second being the opposite force pulling back on the part via the wire. This however is unknown. To work 5

6 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. 2 1 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 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. 6

7 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 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 7

8 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 SW Unit Conversation Final Value Unit Elastic Modulus 70.5 GPa N/mm^2 GPa-Pa-N/mm^ Poisson s Ratio N/A Shear Modulus 26 GPa N/mm^2 GPa-Pa-N/mm^ Mass Density Kg/m^3 Kg/m^3 None Tensile Strength 80 Mpa N/mm^2 MPa-Pa-N/mm^2 80 Compression Strength Mpa N/mm^2 MPa-Pa-N/mm^ 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. 8

9 4.6 Convergence Graph Von Mises (N/m^2) 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. 9

10 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. 10

11 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. Tension Tension Compression 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. 11

12 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 e+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: 12

13 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. 13

14 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 : /07/2014. Cycles -- Safety requirements for bicycles -- Part 4: Braking test methods. 14