Bending Stresses/Stress Concentrations in Morse Taper w/Slotted Female Component?

[whistleboy]

Hi All,

I really need some help understanding bending stresses and stress concentrations in Morse Tapers. Specifically, I'm trying to understand the influence of a slot (and orientation of the slot) in the female component of a Morse Taper when the male component is subject to bending. I've created an illustration depicting the scenarios I'm trying to wrap my head around in hopes someone may be able to point me in the right direction. Most Morse Taper information I could find deals more with hoop stresses, friction, dissociation, etc., but not bending and modified geometry/stress concentrations in the female component.

I've searched the great forums here, reviewed Peterson's Stress Concentration Factors, looked through many Materials texts and searched the peer-reviewed literature for similar instances. The closest I could find was a finite element model of a hip replacement that utilizes a very similar design (Analysis of the stem-sleeve interface in a modular titanium alloy femoral component for total hip replacement, Kurtz, 2001). They reported that maximum stresses on the male component occurred at the BOTTOM of the taper junction when oriented as shown in the representation second from left (slot centered in view).

Can anyone help me understand how the slot geometry and orientation on the female component might influence the stresses on the male component when the male component is subject to bending?

Thank you so much!

 

[hendersdc]

Morse tapers don't use a drawbar or key and rely on axial load to trasmit the torque to the cutting tool, they are not meant for heavy side loads. What is your aplication that is going to apply so much radial load to a Morse taper that you are worried it may be the point of failure?

 

[whistleboy]

I'm specifically looking at modular hip implants and some existing designs where corrosion by-products have been noted in the morse taper. There have been reports of failures of the male components within the taper junction (not associated with stress concentrations due to corrosion), but never any explanation of why they fail in the junction...usually toward the bottom of the taper. I'm just trying to figure out how to explain this phenomenon from a mathematical standpoint. Perhaps it is too complex for simple back-of-the-envelope calcs? Thanks...

 

[whistleboy]

Perhaps the edited illustration more clearly depicts the loading...

 

[Tmoose]

Any motion brings the risk of fretting. An un-slotted taper is likely to fret, but less than the same un-slotted taper. Heck, the press fitted wrist pins in 1972 Chevy station wagon's engine will show signs of micromotion in use, although I'd guess the load cycles at 2500 rpm are higher and accumulate faster than a hip.

Just building a house of cards, but if titanium is used for strength and basic corrosion resistance, it's reputation for galling still requires special efforts with coatings and what not in sliding applications.

http://www.youtube.com/watch?v=DHGCvJjat1E

 

[hydtools]

What is the element at the very bottom end of the male taper? Does it apply a load that apparently has more leverage than the indicated load arrow? If so, that could put higher stress at the lower part of the engaged taper.

Ted

 

[whistleboy]

Thanks for the responses. The element at the bottom of the male component is there just represent that the end of the male component is often in contact with bone (walls of the medullary canal). In some cases one could probably neglect that support of the bottom of the male component was not in contact.

We know there is micromotion based on fretting that has been documented in implants that have been removed from people for various reasons (infection, loosening, pain, etc.) That's an interesting comparison with the fitted wrist pins...2500 RPM...yikes! The biomechanics world assumes a hip will be "cycled" ~2 million times/year.

Unfortunately, I'm stuck...I can't find any way to estimate the stresses on the male component in the taper or the influence of the slot. Is it possible the slots actually act as stress relievers?

 

[hydtools]

I would imagine that the slot represented in the image second from the left would allow the female 'sleeve' to open at the top requiring greater reaction force at the bottom of the taper engagement than required in the leftmost image. The same effective moment requires greater reaction force through a shorter arm.

Ted

 

[racookpe1978]

A sideways-loaded Morse taper that is wedged into a tapered hole - if it were drawn with no slot at all - would be "pulled" apart at the top by the sideways load, right? It would be under a equal and opposite compression force between the side of the taper sleeve at the bottom of the slot and the fixed base. The distance between the upper (right hand) force pulling the taper apart and the bottom resistance is the lever arm = thickness of the base horizon plate.

So, it a slot were cut in the side of the Morse taper, but the sideways force remains the same, there is now a shorter lever arm (the first point of resistance to stretching is about half-way through the Morse taper sleeve), and so the sideways forces are greater.

If the slot is present, but is rotated so the slot is at the far side of the morse taper, the resistance to stretching the top of the Morse taper is resisted also by the wall of the taper.

The slot reduces (slightly) the area on the base plate able to touch the Morse taper (and so psi of the force on the baseplate wall may increase from that of a solid Morse taper sleeve).

In any case of any slot at any direction, however, the Morse taper resists expansion across the slot by being wedged into the tapered hole in the baseplate. Therefore, the least amount of force (stress) into the baseplate is with no slot all - if that were possible.

 

[whistleboy]

I greatly appreciate the thoughtful response and logical walk-through. Do you know how I could represent this mathematically? Maybe to simplify my question, assuming there is no slot, how does just varying the height of the walls of the Morse taper influence the stress on the male component when side loaded (or in bending) as illustrated above? Would the maximum stress acting on the male component indeed also be located at the base of the taper? Again, thank you so much for your time (and patience) in helping me understand.