Gearbox Lubrication Calculations

[pakgears]

I have very little experience/knowledge of fluid flow calculations and I would like some help answering some questions that were posed to me. These questions concern a gearbox with a gerotor oil pump used for gear mesh spray lubrication.

Here is what I know:

The sump from which the pump draws is constantly replenished. Oil enters the pump through a Ø.50" hole. The pump is running at 7000 rev/min. The pump's theoretical displacement is 0.325 in³/rev. Oil exits the pump through a Ø.50" hole. After exiting the pump, the oil enters a sprayer with two exit holes, each Ø.063" in diameter. The oil is SAE Grade 75W-90, viscosity index 106 cst @ 40°C and density 0.859 kg/l. Let's assume an oil temp. of 40°C.

From this information, can I calculate the oil pressure in the line between the sprayer and the pump? If not, what else do I need to know/define? If I can calculate the pressure, how is it done? Let's assume I can neglect piping losses, if that helps.

Thanks in advance for any help.

 

[JJPellin]

This is a positive displacement pump. There should be a relief valve to relieve excess pressure. The relief valve could be internal to the pump, integral to the pump (bolted on the side) or external to the pump (in the piping system). It is probably a full-flow relief valve rather than a "pop" valve (PSV). A full-flow relief valve may be tight shut off, but most of them are designed to leak by. In oil systems they normally have cuts on the seat. The pressure in this system will be determined by the relief valve setting, not by the pump, piping or nozzles. The gearbox manufacture should have designed their oil nozzles for a certain oil supply pressure. And the relief valve should have been field adjusted to provide that pressure. Knowing the pressure and the fluid properties, it is a simple orifice calculation to estimate the oil flow rate from each nozzle. The remaining flow by subtracting the orifice flows from the estimated pump capacity would be the flow passing through the relief valve.

If you are attempting to design a system using a PD pump with no relief valve, I would not recommend it. Even if you could size everything perfectly so that you had the flow and pressure you want, bad things could happen if a nozzle plugged off or if the system was started up with ice cold oil. Any PD pump needs overpressure relief protection.


Johnny Pellin

 

[pakgears]

Thank you Johnny for your insight. This system does not have a pressure relief valve. It does have a breather. Does that change things? Since no pressure relief valve is present, can the pressure still be calculated in the line between the pump and sprayer? If so, may I be shown the necessary equations?

 

[bingopin]

Except for the oil viscosity, this sounds a kinda like a Sundyne gearbox. If by chance it is, it does has a relief valve. It's the plate and spring directly on top of the oil pump.

 

[pakgears]

Thanks for your input bingopin. The system I have described is pretty much hypothetical; it is not a Sundyne gearbox. I am using it as a model that may help me answer the questions posed to me without endangering any confidentiality issues related to this gearbox. I am really after answers to those specific questions:

1. Can I calculate the oil pressure in the line between the sprayer and the pump in the system described?
2. If not, what else do I need to know/define?
3. If I can calculate the pressure, how is it done?
4. Since no pressure relief valve is present, can the pressure still be calculated in the line between the pump and sprayer?
5. If so, may I be shown the necessary equations?

 

[ccfowler]

If you remain serious about not having a truly effective pressure relief valve, just plan on having damaged equipment at the least. Personal injuries are not unlikely, either. Deliberately designing a system with a positive displacement pump without a suitable relief valve is beyond stupid, it is both RECKLESS and IRRESPONSIBLE! It is excellent bait for attracting lawyers, law suits, warranty claims, etc.

The Gerotor pump is an excellent choice due to the combination of the shaft speed and the viscosity. It is the only type of pump that I would seriously consider for the duty that you described. My preference would be to have the relief valve flow return to the sump well below the oil surface.

If the application includes very low ambient temperatures, you should consider a heater to warm the lube oil before a cold startup.

 

[pakgears]

Thanks, ccfowler. We also like the Gerotor. I can assure you that this system is working and you shouldn't worry about litigation. Maybe there is something else (just leakage?) that is relieving pressure, but there is no relief valve. Start-up is under ambient temps > 50°F (if it's cool, a gearbox heateris used prior to start-up). Let's say operating oil temp is 40°C.

Can anybody address my specific questions?

1. Can anyone calculate the oil pressure in the line between the sprayer and the pump in the system described?
2. If not, what else does one need to know/define?
3. If a person can calculate the pressure, how is it done?
4. Since no pressure relief valve is present, can the pressure still be calculated in the line between the pump and sprayer?
5. If so, can you explain/demonstrate the necessary equations?

 

[Artisi]

If the unit is now in operation the answer seems to be very simple - add a pressure gauge.

 

[JJPellin]

If this is a purely hypothetical machine, you can calculate the pressure as follows: If the two oil jets can be approximated as simple orifices, you take the flow, divide it by two and calculate the pressure drop across an orifice of that size and configuration. The size of the suction and discharge lines at the pump is probably not relevant as long as they are not choking the flow. The PD pump will put out (almost) constant flow as long as it is not cavitating.

I am not going to post the orifice formulae here. They can be found in any fluid dynamics text book, Cameron Hydraulics, and probably on-line by searching for orifice flow calculations. And I am at home without access to my books. You need to know the configuration of the orifice (sharp edged, square edged, chamfered, etc.).

Most Sundyne gearboxes actually have a separate internal PSV that is screwed into a port in the center housing of the gearbox. The spring above the oil pump in the old configuration would provide a limit to oil pump pressure as well. But I believe that they are phasing out that design for a more robust pump. This upgrade also involves installing a larger PSV in some models (LMV-313, I believe)


Johnny Pellin

 

[hydromech]

Pakgears...

If this is an open system that cannot generate pressure hydraulically, there is no legal need for a relief valve.

However, if there is a point where you may have cold viscous oil, it would be advisable to limit the pressure in some way.

Delta P = v^2 x f x L x p
---------------
D2

Delta P in Pascals
V = velocity in mtrs/sec
f = friction factor
L = length of tube or pipe
p = fluid density
D = pipe diameter

Velocity(mtrs/sec) = Q x 21.22
-----
D^2
Q = Flow rate in ltrs/sec

As a simpler rule of thumb

Q
------- = X
Orifice area

The square root of X is the pressure drop...

Orifice area is in mm^2

Regards

Adrian

 

[sreid]

Someone should check my math but I calculate the the fluid would be exiting the 1/16 inch holes at 360 miles per hour!

I would guess extremely high pressures determined by nonlinear flow conditions.

 

[Artisi]

I agree you calculatio - I get approx. 350mph

7000rpm x 0.325 inch3/rev = 2275 inch3/ minute.
= 1.32 ft3/min = 9.85 USgpm
2 nozzles = 4.9 USgpm/nozzle
nozzle velocity = 512ft/sec = 350mph
pressure at the nozzle approx 1770psi