Module 3: Initial Part Design

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.

Before we begin this module, it is time to get added to SharePoint. Add your email to this sheet to get access to the SharePoint: Access Spreadsheet. You will need this later on in the document.

The part design process may look different for a part given its functional requirements. As discussed in the research phase, module 2, many of the requirements for a part come from the series regulations. In the case of the brake pedals the rules define the following requirements.

Rules Requirements:

• The Brake Pedal must be one of:

  • Fabricated from steel or aluminum

  • Machined from steel, aluminum or titanium

• The Brake Pedal and associated components design must withstand a minimum force of 2000 N without any failure of the Brake System, pedal box, chassis mounting, or pedal adjustment

We also would have defined functional requirements in the design phase, such as package size, weight goals, cost goals etc.

For the sake of this project, the functional goals are defined below.

Functional Requirements:

• Pedal Ratio of 6:1 (More commonly this is the ratio of distance from the pivot point. This is not the only way to achieve a pedal ratio, but it is the definition we will use for now)

• Weight: Under 2 lbs

• Pedal Cost: Under $100

• Distance to drivers foot from pivot: 8 inches

With these requirements we can move forward with a rough first iteration of the design. All designs start by making some assumptions to aid in progress, as often there are too many variables to address in totality. The assumption we will make here is that the pedal is vertical and the piston is reacting the force perpendicular to the body of the pedal. This will allow us to perform a simplified hand calculation to come up with initial sizing and material specifications. Often times these “back of the napkin” calculations are required to get a sense of what the project requires.

Force Calculation

We will start with a simple moment balance equation using the parameters given above. The Free Body Diagram is given below.

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.

The three main categories of direct stress are tensile, compressive and shear.

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.

Compressive stress is the same as tensile, just in the opposite direction. The failure modes of tensile and compressive stress however are very different, and depend on different conditions, which you will learn about either in Mechanics of Materials or in your club work as you move forward.

Shear Force can be thought of as a “sliding force.” Think about a tightly packed bookshelf. As you try to pull one of the books out, it will slide, while also pulling the books closest to it slightly out with it. The books here are analogous to the microscopic grain in a material. Typically, materials are weaker in shear than they are in compression or tension, but this may not always be the case.

There are also two types of indirect stress. Torsion is a twisting force, which is another form of shear force, and bending, which is a combination of axial compressive and tensile stress on a part, as well as internal shear forces perpendicular to the axis of a part.

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:

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.

To calculate the bending stress of a part, we first need to know the maximum moment that you calculated from the above step. Assuming a uniform part, the location on the part where this occurs will likely be our failure location. (If you were designing this part with more time and analysis, you could leverage the properties of this moment diagram to make the part even lighter by removing material where it sees less stress!)

The other information we need here is the moment of inertia, calculated from the cross sectional geometry of our beam. The moment of inertia signifies a resistance to movement relative to a rotational axis. The further away material is from this axis, the more efficient it is in resisting a moment about that axis. Think about bending a credit card in your hands. If you try to press on the large face, it is very easy to bend. If you try to press on the thin face, it is very difficult to bend. The cross sectional area hasn’t changed, but the areas distance from its bending axis has changed.

Finally we need the distance away from the neutral axis that we are trying to analyze stress at. Most commonly this is just the farthest distance away from the neutral axis. The neutral axis of a beam in bending can be thought of as the part where no stress occurs axially. In the pink pool noodle above, this is the dotted line.

For common shapes (Rectangle, tube, etc) you can reference engineers edge, they will have calculators more most common shapes.

We will be using a rectangular cross section, so you can go to this link: https://www.engineersedge.com/calculators/section_square_case_6.htm

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.

This video, made by my Mechanics of Materials Professor, Masoud Olia, shows how to do calculate I by hand for a more complex and asymmetric part if you are interested in the derivation of these properties.

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Lets take a quick breather. I know, this is getting intense really quickly and you are probably like oh fuck I don’t think I can do this, this shit sucks. I know, I was there once too. It may take a bit to get used to the terms and equations we are using here, but once you do, you will be designing and building race car parts of your own. Not to mention, you’ll be leaps and bounds ahead of your peers. So keep up the hard work, you are doing great

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Material Selection and Failure Analysis

Now that you have calculated the stress in the part, it is time to select your material for the part.

There are many factors that go into selecting materials for a given part, some of which are listed below.

• Yield Strength (The stress at which a part will permanently deform)

• Ultimate Tensile Strength (The stress at which a part will completely fail and tear apart)

• Hardness

• Corrosion Resistance

• Machinability (How easy is it to subtract material to from your part)

• Cost

• Density (and strength to weight ratio)

• Weldability (How well does a material weld/ what material properties are affected by welding)

Thus, it is imperative to take time and care while selecting the proper material for your use case.

For the brake pedal, we are given the options of titanium, steel and aluminum. I have listed out a few alloys including each category and the relevant material properties of each below. Please add this information somewhere in your excel sheet for reference.

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.

For more frequently seen loading scenarios, you may want to consider a fatigue analysis (failure due to repeated loading) in addition to simple tensile failure however we will not cover that in this module.

Another important note in your material selection process is that we would like to machine this part, as we don’t have cost effective methods to cast more difficult to machine materials. So this part will be programmed and run on a very weak CNC machine, meaning machinability is a very important consideration in this process.

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!