Please Create a New Section in your Document labeled Brake Pedal Design. Also create an excel spreadsheet to enter your calculations into, named in the same convention as your design document.
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First, using a moment balance equation about the pivot (where the reaction forces are) we can solve to get that the force on the pedal from the master cylinder. Once we have that we can sum the forces in the X Direction to get that the reaction for in the X direction. Since the mass of the pedal is negligible in comparison, we will consider the Ry force value to be 0 for now.
Deliverable 3.1: Calculate the Reaction forces from the brake, Fb, and the pivot point, Rx.
Stress Analysis
Now we need to figure out the internal stress of the part. To do that we first need to discuss different types of forces and stresses.
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The three main categories of direct stress are tensile, compressive and shear.
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Tensile force is the pulling force. Simple tensile stress can be calculated as the tensile force being applied divided by the area that the force is being applied over.
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To calculate our bending stress, we first need to understand the internal forces at play. The below tutorial will show you how to draw a bending moment and shear force diagram for a beam:
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Deliverable 3.2: Watch the above video and draw a bending/shear diagram for the brake pedal with forces calculated above. Put the value of the moment into your excel sheet labeled with the appropriate units.
Once you have completed the above diagrams, we can calculate the stress inside the part.
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Here, we are going to make another set of assumptions. Lets set the value of b to 0.5 in and d to 1 in.
Deliverable 3.3: Use the link above with provided geometry to find the equation for I (area moment of inertia about the neutral axis). Then, enter the part geometry into excel, and label each cell with the appropriate units. Using excel formulas, calculate the value of I and label it in a new cell with the appropriate units (in^4). Assume b = 0.5 and d = 1 in. You must do this with a formula to complete later steps. Then, using y = 0.5*d, furthest distance away from the neutral axis, calculate the stress of the part in psi and label accordingly. Did I mention label everything? In your word document, record the stress value.
As you can see from the equation of I in this calculator, the value of I depends much more heavily on d, the measured width along the shear stress direction, than it does on b, or the width perpendicular to the stress direction. Thus, since stress goes down as I goes up, this indicates that material further away from the neutral axis is significantly more effective in resisting stress than material close to the neutral axis. This is a great example of how learning the governing equations and principles is key to making more materially efficient parts.
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Taking your stress value previously calculated, we will calculate the factory of safety relative to each materials yield strength. Factor of safety is a measure used by engineers to build in margins to account for and variance in the design and assembly process. This may include part tolerance, impure materials, uncertainty in load estimates and many other factors. To calculate your factor of safety, divide the materials yield strength by the stress value you calculated previously.
Deliverable 3.4: Calculate your factor of safety for each material and record in your excel sheet.
Now, since this load case is a rules requirement, and through previous testing we have found to not be a realistic operating load case, any factor above 1.1 is acceptable. Given the certainty of our load though, there is little reason to exceed this value significantly.
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Since we also care about weight, use the density of each material to calculate the weight in lbs of the brake pedal (dimensions of 8*0.5*1).
Deliverable 3.5: Use all of this information, as well as the functional requirements above to make an argument for what material you would choose for this application.
Deliverable 3.6: Now make changes to the part geometry (values of b and d) to optimize for the lowest weight with a minimum factor of safety of 1.1 and argue for what material would serve the best for this application. Is your material of choice the same as in Deliverable 3.5? If not, why is your answer different?
Deliverable 3.7: Now you are going to add your word doc and excel sheet to SharePoint. Navigate to this link: https://northeastern.sharepoint.com/sites/northeasternelectricracing . Then navigate to Documents->Mechanical->Onboarding. Create a new folder inside the onboarding folder named Lastname_Firstname, obviously replace with your last and first name though. Then drag your word and excel docs into the folder you just created. Send the link to this folder to your system head.
Congratulations, you have finished Module 3!