displacement of hydraulic gear motor?

[brents]

Hopefully I can explain this...

I have a hydraulic gear motor, which has two spur type gears that mesh with each other inside the housing. The dimensions are:

O.D of each gear=.858" dia.
thickness of gear=.625"
# of teeth= 11 teeth per gear
distance between centers is .750"
flow= 7 gallons per minute..

The formula for finding RPM is= N=231(GPM)/displacement

How do I figure out the displacement? I am totally stumped here...this is a motor that I have made, so I can't go to a manufacture for this..

thanks,
Brent

 

[DesignerMike]

You didn't state the rpm associated with 7 gpm.

I think it will be difficult to determine the displacement without knowing the speed (or the speed without knowing the displacemnt)

That will give you gal/rev, and a simple conversion to in^3 per revolution (or any other volume unit)

Doing the math would require much more exact gear information. There are quite a few different gear profiles.

 

[MikeHalloran]

ROUGHLY,

there are two flow paths of dimension .625" x .108", and the length of a circle at the pitch line is 2.3562", so the displacement per revolution would be:

.625 x .108 x 2.3562 x 2 = 0.318087 in^3,

if the teeth were of zero thickness. Assuming as a w.a.g. that the teeth occupy half the swept volume, the displacement per rev is then

0.318087 / 2 = 0.1590435 in^3.

There are 231 in^3 in a gallon, so this motor would displace

231 in^3/gal / 0.1590435 in^3/rev = 1452 -ish rev/gal

revolutions to displace a gallon. Pushed with a flow of 7 gallons/ minute, the motor would then spin

7 gal/min * 1452 rev/gal = 10167 rev/min

... again, ROUGHLY, and that's assuming I haven't left something out completely, which does happen.

Since that's about five to ten times the speed at which gear pumps are normally happy, I'd expect durability problems.

For a more accurate answer about the displacement per revolution, slowly pump a known volume of grease through it and count the rotations.




Mike Halloran
Pembroke Pines, FL, USA

 

[jet1749]

For easy rough calculation of displacement per revolution you need the gear tip diameter and the gear root diameter. Work out the volume of the gear assuming it to be a cylinder (using tip dia) subtract the volume of the gear (using root diameter) Divide it by half (each gear space has a corresponding tooth) Multiply it by 2 (for the number of gears) Have used this and found it to be reasonably accurate on gear or lobe pumps, but usually a little bit bigger!

 

[krb]

I have a fluid power data book and it gives a formula for calculating cubic inches displacement per shaft revolution as CIR displacement=6 x W x (2D-L) x (L-D)/2
where W=Width of gear, D=diameter of diameter of gear housing and L=Length of gear housing (for the two gears, roughly 2xgear diameter minus tooth height)

Hope this helps
KRB

 

[brents]

Thanks everyone for the replies...

As soon as I get a free second, I'll calculate and see if the #'s are reasonably accurate..

I very much appreciate the advice..

thanks,
Brent