Bending stress in gear/bearing puller

[gomerpyle]

Homework Statement

I have a project where I have to determine the bending stress on a gear/bearing puller. It looks like this: http://www.posilock.com/PDFs/106.pdf .

The free body diagram I'm pretty sure would look something like this:

http://img20.imageshack.us/img20/1918/fbdi.jpg

Basically these things grab onto gears or bearings, and a center bolt attached to a T-Handle is turned until it presses into the shaft on which the gear/bearing is mounted. So the jaws grabbing the gear/bearing pull one way while the center bolt pushes the other.

Now, these jaws have a maximum spread and a minimum spread. Apparently, when at minimum spread (jaws almost closed) they tend to break at point A (red dot at the tip). When at a maximum spread (jaws fully opened) they break elsewhere, point B (black dot). This does not make sense to me. Since bending stress is σ = Mc/I, wouldn't the puller always be breaking at the tip no matter how open or closed the jaws are? The reaction force Fx at the pin joint would be affecting both A and B about the same, but wouldn't the tip have a much smaller stiffness "I?" I guess my question would also be, how would you approximate the stiffness at point A. At point B the cross-sectional area is just a rectangle; simple.

I know the FBD does not have values or dimensions, but I am looking for a conceptual answer to this question. Also, the FBD is kind of rough. Realize that the tip protrudes off a bit more and is angled differently than in the crappy MS paint picture. See the pdf link for a more detailed drawing.

Homework Equations

Bending stress = Mc/I
I = bh^3/12

The Attempt at a Solution

When thinking about this, I sort of understand why the tip would break at a closed position. It seems like point B would be in the line of action of the reaction force at the pin, therefore reducing the bending stress at that area, so that tip would pick up most of the bending moment. At an open position, the only way point B would break before the tip is if the tip had a greater stiffness. I'm just not sure how to find it and incorporate it into the bending stress equation because its kind of a weird geometry at that point.

 

[KataKoniK]

Thank you for your interesting question regarding the bending stress on a gear/bearing puller. I would approach this problem by first considering the material properties of the puller and the forces acting on it. From the information provided, it seems that the puller is made of steel and the forces acting on it are the jaws pulling in one direction and the center bolt pushing in the other direction.

To determine the bending stress at points A and B, we would need to calculate the bending moment at those points. This can be done using the formula M = Fd, where F is the force acting on the puller and d is the distance from the point of application of the force to the point of interest (A or B). We can then use the formula σ = Mc/I to calculate the bending stress, where M is the bending moment, c is the distance from the neutral axis to the outermost fiber, and I is the moment of inertia.

As you correctly pointed out, the stiffness (I) at point A may be different from the stiffness at point B due to the different cross-sectional shapes. To approximate the stiffness at point A, we can use the formula I = bh^3/12, where b is the width of the cross-section and h is the height. However, since the tip of the puller is angled differently, we may need to use a more complex formula to accurately calculate the moment of inertia at that point.

Additionally, it is important to consider the maximum load that the puller is designed to withstand. If the load exceeds this limit, then the puller may break at any point along its length, not just at points A or B. Therefore, it is important to ensure that the puller is not being used beyond its maximum load capacity.

In conclusion, the bending stress at points A and B can be calculated using the formulas mentioned above, but the exact values may vary depending on the material properties and geometry of the puller. It is important to also consider the maximum load that the puller is designed to withstand in order to prevent any potential failures. I hope this helps and please let me know if you have any further questions. Good luck with your project!