Sizing a shaft for a V-Roller 1

[RGNCJN]

Hello all!,

First time posting.

I am confronted in sizing a shaft for a polyurethane v-roller. The roller will carry pipes of various sizes. The shaft will be supported with a pillow block bearing on each end. There will be no torque applied to the shafts b/c the pipe is being pulled along the rollers (simple bending). Instead of assuming a point load in the center of the shaft I drew the avg. pipe size and the roller to scale and measured the point of contact from the center of the roller. The speed of the rollers will be fairly slow est. below 5 mph. My questions are:

Is it okay to assume two points of load on the shaft due to the v-roller? The length between bearings is 43" and the distance between contact points is 8.5".

Do I consider the support reactions of a bearing to be a fixed support (having a moment) or a simple support (not having a moment)?

Should I use the stress-life method in anyalyzing the shaft. Using an modified endurance limit based on a endurance limit of .504 Ult. strength? or is this two conservative. Can I just use (2/3) of the yield? and a simple beam equation?

How should the shear stress be evaluated due to fatique?

Thank you in advance.

 

[dvd]

How do the v-rollers attach to the shaft? If they are keyed then your assumptions are affected. I find that the formulas given in Machiery's Handbook have given me good results over the years; they are simple and quick calculations.

What kind of bearings are you using? Self-aligning pillow blocks would be a simple-support.

 

[RGNCJN]

dvd thanks for the response,

The polyurethane is poured into a mold (in which the shafts are centered) as a liquid around the shafts and cured. The shafts are lightly blasted and a adhesive is also applied to them before the polyurethane is poured.

Our customer already has a specific bearing in mind and I will ask them if it is self-aligning however if it isn't then can I assume it is a fixed support.

Also I don't have a copy of the Machinery's Handbook in my office but I do have a copy of Mark's Standard Handbook of Mechancial Engineers. Would you suggest that I purchase the Machinery's Handbook? Does it cover more mechanical design elements in greater detail than the Mark's book?

 

[Bribyk]

If your bearing isn't self-aligning (and even if it is to an extent) you have to watch the angular deflection of the shaft as it bends. Bearings have a certain angular tolerance and if you exceed it you will destroy the bearings in a hurry.

I haven't looked at Mark's but Machinery's Handbook is a must-have for mechanical design. It covers everything from welding to machining to rigging to bearings to chains/sprockets, etc...

 

[Yagonyonok]

If you get Machinery's Handbook, look for one that comes with a cd. I prefer the pdf version personally. Easier to search, right at my fingertips, and I can print pages off for when I'm out in the shop and don't want to destroy my book. Just my $0.02

 

[RGNCJN]

Anyone have any other thoughts about sizing this shaft??

 

[dvd]

It would be better to move the bearings in closer to the v-guide.

 

[RGNCJN]

I have incuded a Free Body Diagram of what I was talking about and some of the calculations to show what I was doing. Does any of this throw up any red flags?? Also if there is no stated saftey factor or design factor is there a widely use value for certain applications??

 

[RGNCJN]

Sorry I tried to attach both pages in one post but it only attached the 2nd page, so here is the 1st page.

 

[wahoo88]

The forces acting on the roller surfaces will be normal to the pipe, not vertical. Therefore, there will be a horizontal component to these forces which will produce an additional tensile stress in the shaft.

Does the shaft really have an abrupt change in diameter at the outer edges of the rollers? If so, does it have to?

Calculate the von Mises stress to account for the direct shear stress on the shaft (although this will probably be fairly insignificant).

 

[RGNCJN]

Thank you for the response wahoo88. I know that there will be horizontal forces that act on the surface of the polyurethane but I assumed that this force will be negligible at the shaft. The shaft does step down because the customer wanted to use a 3" pillow block bearing and I calculated that a 3" shaft was too small. I figured the modifying factors for point b (where the step down is) on a .25" R fillet.

 

[dvd]

rgncjn:

You can't serve two masters. If your customer wants to design this part, then don't get in their way. If you design part of it and they design part of it, you are asking for problems. Somebody has to lead, you should step back and follow instructions.

Your F/2 force directions look a little dubious to me, I would make them normal to the surface of the v-roller. (The horizontal components will cancel out.) But to simplify and take worst case, I would just put the load of the pipe at mid-span on the roller shaft. For a piece of industrial equipment you can't factor in enough safety factors. The amount of time you spend analyzing can buy quite a bit of steel. How many of these are you making? Are you trying to protect the pipe o.d. with the urethane? Otherwise, making the whole piece from steel may actually be cheaper.

 

[RGNCJN]

It isn't the case were the customer started to design and we took over they just asked to stay with a 3" roller bearing. It was basically their only input. We are going to produce 36 of these polyurethane rollers. The application for them is to assist in the laying of a concrete coated pipeline. We are a polyurethane shop and the polyurethane is needed to protect the pipe coating. I know the simplest case is to consider the load in the middle of the shaft but to be more competitive when doing shaft sizing and bidding we were looking at this analysis as an option. I just wanted to get some opinions on it. Also I thought there might be a rule of thumb for safety factors for different applications and industries.

 

[Bribyk]

If these rollers are used in a hoisting/lifting application you should get copies of ASME B30.20 & BTH-1. These standards should give you some direction with respect to designing below-the-hook devices.

Also, think about what happens if the shaft breaks when determining your fatigue and yield safety factors as well as shock loading. Concrete pipe installation sounds like a rough environment to me. Could the pipe fall on someone or part of them? What happens to the shaft when it gets a gouge or nick (stress concentration) in it?

You need to determine a service life for the part. Is the company going to bother replacing bearings when they wear out (has this been calculated/estimated?) or are they going to just buy a new complete assembly? If they are going to buy a new assembly then you only have to make the shaft last longer than the bearings, with some safety fatigue safety factor because the shaft failure is more likely to cause injury or further damage.

This is a straight-forward mechanical calculation once you have the requirements.

 

[desertfox]

Hi RGNCJN

I agree with dvd the horizontal forces due to the angled roller face will cancel each other out which means that you are just left with the vertical component to deal with in terms of bending the shaft.
The critical part of the shaft as I see it is where the shaft is stepped down, a rough calculation of bending stress at that juncture without a stress concentration factor is about 30,000lbs/in^2 assuming a point load of 38000lbf at beam centre, so depending on your fillet radius between the large and smaller sections of the shaft it is this that will determine the stress concentration factor and hence the level of stress at that point, if you can tell us what the fillet radius is I can give you the stress concentration factor from the charts I have.
AS it stands at present you could be looking at a stress concentration factor between 2 and 4 which means a stress level between 60 and 120,000lbf/in^2.

regards

desertfox

 

[RGNCJN]

Hello Deserfox,

Thanks for the responses guys. The fillet will be at least a .25" R. That is what I used in the calculations that I have attached above.

Regards

 

[desertfox]

Hi RGNCJN

Not at home at the moment will give you the stress riser factor on Friday.

Regards

desertfox

 

[desertfox]

Hi RGNCJN

From my charts it looks as though the stress concentration factor is about 1.8 so I would probably use 2 just to give a bit more margin, so your stress level at the change of section is about 60000lbf/in^2, however its the cyclic change in stress during operation that will cause fatigue.

regards

desertfox