Distortion Energy Theory Problem?

[PLEngineer]

Trying to calculate the forces holding a cylinder in a hole.

A solid cylinder of 15mm is pressed into a hole, ductile steel, of 15.1mm

Max D.E.T. : Sys=0.577*Sy

Yield Strength = Sy, given variable constant

I am not sure if the hole material is plastically deformed by the increase in diameter or if the hole change in diameter is within the elastic limit.

Any thought on how to calculate this would be appreciated.
1. calculating the force that hold the solid cylinder in the hole
2. Frictional forces between the hole and the solid cylinder.

 

[KENAT]

Maybe check out the FAQ section, I think this or similar is covered, maybe faq404-1230.

Posting guidelines faq731-376

http://eng-tips.com/market.cfm?

(probably not aimed specifically at you)
What is Engineering anyway: faq1088-1484​

 

[rb1957]

assuming the pin isn't compressed as it fits the hole, what's the strain at the edge of the hole ... 0.1/15 ... less than yield strain (sy/E) ? (probably not)

 

[Cockroach]

This is standard interference fit theory, Lames Equations, which can be handled sufficiently using Thick Wall Pressure Vessel Theory. The Von Mises-Hencky Theory is a natural consequence of this analysis, common on the web or in this forum, having been copied not so long ago.

Typical interference fits are something along the order of 0.0005/0.0008 inch, roughly 0.02 mm. Your situation is of higher interference which would essentially imply a larger axial pressing force, necessarily part of the computation. I have seen deformation in members being pressed into tight holes as a consequence of such a large interference, so be careful.

For example, using your situation, I have a 0.5945 inch (15.1 mm) solid pin being pressed into a 0.5906 inch (15.0 mm) bore, both of mild steel (43 ksi yield, 29.6E6 psi Young's Modulus). The contact pressure at the mating surface is 89,535 psi, compressive of course.

I further assume that I wish to press the Dowel Pin approximately 0.500 inch into the bore. Arbitrarily selecting a friction factor of 0.15, I will require 12,542 lbf of axial force to accomplish this. The resulting stress induced by the hydraulic ram doing the pressing is 45,183 psi normal on the Dowel Pin. This exceeds the yield strength of material, thus I expect deformation of the member being pressed into the bore.

Applying Mohrs Circle, I find 1.339 clockwise rotation of a wall element to the Principle Stress, so we are experiencing very little shear in the press fit event. You would further find the Dowel Pin would be capable of withstanding 3748 in lbf of torque, rotating the member during press fit would be a challenge.

As such, I would recommend lowering the Dowel Pin OD to something along the order of 15.02 mm. You now have 18,048 psi contact pressure requiring only 2515 lbf axial load for the press fit. This results in the male member stress of 9,159 psi for the Dowel Pin, clearly a much healthier factor of safety. This fit is roughly FM3, standard in the literature.

Watch the venting of air from below the Dowel Pin during the press event. Putting a viscous oil fluid to address friction and heating often contributes to over loading of the member as air is unable to escape from below. Often I simply put a small V groove in the longitudinal wall of the Pin to address this situation. Works fairly slick.

Good luck with it. Compared to pressing forces I monitor with stand gauges and hydraulic pressing, the numbers are almost bang on, less than 2% error. I am fairly confident your situation would be similar in nature.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[desertfox]

hi PLEngineer

Do you mean the hole is 15mm and the cylinder pressed into it, is 15.1mm diameter?
Try this calculator it might help:-

http://www.tribology-abc.com/calculators/e3_8.htm

desertfox