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mechanicalengineer
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Join Date: Apr 2012
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Pull/Push Force For A Cart (With Load) on 4 V Groove Caster Wheels and Rails.

04/30/2012 12:04 PM

I am designing a push/pull system for a cart (weighs approx 300 lbs) on 4 wheels. The wheels are V-groove caster wheels on two inverted V rails. I want to calculate the horizontal force required to push and pull the cart (with a maximum load of 3200 lbs) so that I can design the system. I am calculating the force as follows but the friction coefficient that i am using does not seem to be right.

Other important things to consider is that the cart is placed in an oven for a considerable period of time with temperatures reaching upto 600 degrees Celcius. According to my research, at such temperatures steel wheels on steel rails develop microwelds. And it becomes difficult to move the cart. The wheels and the rails are rusty so the friction coefficient needs to be modified. My calculations are as follows. Can anyone please check and see where I am doing a mistake.

Total load on the cart = 300 + 3200 = 3500 lbs

Coefficient of friction (Wheels on rails) = 0.5 (http://sci-lib.org/books_1/I/iwnicki_01_05.pdf)

Total horizontal force required = 3500 * 0.5 = 1750 lbs?

If I divide the force required by 4 (because 4 wheels are used) = 1750/4 = 437.5

I actually measured the force required. The scale stayed in the range of 300 - 400 lbs with just one time reaching 580 lbs.
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PWSlack
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#1

Re: Pull/Push force for a cart (with load) on 4 V groove caster wheels and rails.

04/30/2012 12:15 PM

The wheel/rail interface in the scheme currently exerts more friction than were a proper wheel/rail interface to be used.

This arrangement of wheel, rail and flange presents the lowest friction of all the options. And it works - even at 600degC. Which is sort-of-why it is used worldwide. "There is no need to reinvent the wheel."

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mechanicalengineer
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#2
In reply to #1

Re: Pull/Push force for a cart (with load) on 4 V groove caster wheels and rails.

04/30/2012 12:21 PM

Thanks PWSlack for the quick response. My problem is that I cannot change the rail wheel interface even if it is inefficient. The wheels and rails are already in place. My problem is to calculate the maximum pulling/pushing force required to move the cart on the current setup.
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Tornado
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#3

Re: Pull/Push Force For A Cart (With Load) on 4 V Groove Caster Wheels and Rails.

04/30/2012 1:18 PM

Why not just use your empirical results and call it 600 lb max, or maybe 700?

[There are some oddities in your calculation.]

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mechanicalengineer
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#4
In reply to #3

Re: Pull/Push Force For A Cart (With Load) on 4 V Groove Caster Wheels and Rails.

04/30/2012 1:25 PM

I want to justify the emperical results with some kind of calculations.

And if all else fails then I might have to go with the empirical values.
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Tornado
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#5

Re: Pull/Push Force For A Cart (With Load) on 4 V Groove Caster Wheels and Rails.

04/30/2012 1:33 PM

A CoF of 0.5 might befit wheels sliding on a rail, but for rolling it should be much less (depending on the type of wheel bearings). It doesn't depend significantly on how many wheels. There will be some acceleration/deceleration to account for.

I don't know about the suggested micro-welding, but there might be a way to avoid that by dithering the cart while it is in the oven.

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mechanicalengineer
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#6
In reply to #5

Re: Pull/Push Force For A Cart (With Load) on 4 V Groove Caster Wheels and Rails.

04/30/2012 1:43 PM

I guess your are talking about using the equations of motion to calculate the required force? The CoF that I am currently using is for sliding. I know that for rolling it should be 0.001 - 0.002. I have to calculate the maximum force required. So that maximum force should be the one that is required to start the wheels rollings from a complete stop position (not considering the microwelding problem).
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nick name
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#7

Re: Pull/Push Force For A Cart (With Load) on 4 V Groove Caster Wheels and Rails.

05/01/2012 2:43 AM

You have 2 frictions :

- rolling between wheel and rail for which you should consider the angle of 45° since friction is proportional to NORMAL force component and

- sliding friction in the bearing

The equation will be : Ftr = G*( f/cos(α)+d/2*µ)/(D/2) where

G - total weight 3500 lbs

f- rolling friction coefficient which is for steel on steel around 0.03

α- flank angle of rail/wheel groove or side 45°

d- axle diameter

µ- friction coefficient -sliding- axle on bearing for dry steel on steel around 0.3 to 0.5.

In your case presence of rust can reduce the friction (a kind of "roller" effect in the bearing).

D- mean wheel contact diameter to .

The ratio Ftr/G can be around 0.144 which corresponds to your measurements as order of magnitude ( 0.086 to 0.114 and up to 0.165).

Of course values are estimated and those available in the literature are only valid for the analyzed case which is not always well specified.
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