Starting Torque - Positive Displacement Pump 1

[BCpowertrain]

Hello,

I am looking for some help in determining the torque required to start a positive displacement reciprocating pump which has its' discharge connected to a manifold under pressure.

The pump in question would either be a triplex or quintuplex piston pump, with known plunger size and plunger stroke, and known manifold pressure that it must start against.

Consider for discussions sake a triplex pump, with a stroke of 5", plunger diameter 3", and a manifold pressure of 10,000 psi which the pump must be started against.

My understanding is that if this were a single cylinder pump, and the pump was to be started at the worst case position where the crank throw was at a right angle to the stroke, then the torque required would be the connecting rod load multiplied by the crank throw [pressure x cylinder area = 10,000 psi x pi()*(1.5^2)] * [1/2 stroke = crank throw].

Can someone please confirm my analogy above for a single piston pump is correct?

Now with a multiple piston pump there must be some formula around that allow for consideration of the effects of the other cylinders, as some would have a rod load from generating pressure at some crank angle other than 90 degrees to the crank throw, and other cylinders would have some rod load requirement the suction work.

If anyone could shed some light on this subject for me it would be much appreciated.

Thanks for your assistance.

 

[micalbrch]

Torque req. = A x p x s/2 x 1/i x 1.15 where
A = plunger area (face)
p = pressure
s = stroke length
i = total reduction (motor speed/stroke nos.)
1.15 = correction factor for triplex pumps

The correction factors considers the 120° crank offset of a triplex plunger pump.

And yes your formula is not wrong but only valid for direct driven single cylinder pumps which operate at motor speed as it contains no gear or v-belt reduction.

 

[BCpowertrain]

Micalbrch - thanks for your quick response.

Do you know what the correction factor is for a quintuplex pump as well?

 

[micalbrch]

No, sorry.

 

[curtis26]

Here is an alternative method.
First, let’s determine the flowrate.

Q = pi x r^2 x l x n x s /231
Where,
Q = flowrate [GPM]
r = plunger diameter [inches]
l = stroke length
n = number of plungers
S = pump speed [RPM]
231 = conversion factor from in^3 to Gallons
Assuming a maximum pump speed of 400 RPM yields 184 GPM

Now let’s calculate the Break Horse Power
BHP = (Q x Pd)/ (1714 * Em)
Where,
Q = Flowrate [GPM]
Pd = Discharge Pressure [PSI]
1714 = conversion factor from GPM x PSI to HP
Em = Mechanical Efficiency

Assuming a mechanical Efficiency of 85% results in 1260 HP
Now we can apply the Torque Equation
T = 5252 x HP / RPM
Where,
T = Torque [lb-ft]
HP = Break Horse Power of the Pump [HP]
RPM = Shaft speed at the point you are evaluating the torque.
I see two problems here.
1) We are assuming that the pump will be started at full load (i.e. maximum pressure for 10,000 PSI and maximum pump speed of 400 RPM (thus Maximum flowrate). I don’t know of anyone who starts a Triplex pump at full load. The pump usually has a recycle valve that can be opened during start up so it can start without a load as well as a soft starter of VFD so that it slowly ramps up to full speed. Starting it under full load is very hard on the pump and a bad practice.

2) Where are you evaluating the torque? The pump? The driver? Multiplex pumps operate at slow speeds and therefore require gear reduction from a belt drive or gear box. If you have a gear ration of 4.38:1, then the pump torque (400 RPM in the Torque equation) will be 16,546 lb-ft and the torque on the driver operating 1750 RPM will be 3,782 lb-ft.

 

[micalbrch]

Curtis. Your formulas do not consider the triplex characteristic. The 120° crank offset of a triplex pump leads to the situation that two plungers perform a discharge stroke ot the same time. They don't do it 1:1 in parallel but one is nearly finished while another one has already started.

Just to make your torque calculation more clear: 3782 lb-ft. x 4.38 (reduction) = 16564 lb-ft. I think that's what you said but it took me some time to understand it.

 

[BCpowertrain]

Curtis,

Thanks for the comments.

This application will be starting from zero pump speed, with the pump directly connected to a high pressure manifold.

I understand the comments regarding releif valves, re-circ valves, soft start, etc etc - but that is not the application here.

Micalbrch - I think your formula is the one I need - in determining the starting torque to get the pump moving while under load.

Thanks.

 

[BCpowertrain]

Correction factor for quintuplex pump anyone?
Last bit of info I need to finish my analysis.

Thanks for your help Eng-Tips!

 

[ccfowler]

BCpowertrain,

I would by-pass this problem to some extent by installing a relief/recirculation valve for starting. This would eliminate the nasty, hard starts for the motor and allow for a more gentle start for everything. The best way to get maximum service life and reliability from components is to avoid excessive or shock loadings. Orderly closing of the relief/recirculation valve minimizes acceleration loadings for the entire system.

I'm reminded of an experience many years ago with a system to transfer #2 fuel oil between two tanks that were a significant distance apart with a simple induction motor driven gear pump as the only means of control. The piping configuration prevented flow in either direction when the pump was not running. (There were manual isolation valves, but they were only intended for maintenance purposes.) Since there was no remarkable head and no restrictions involved (open end of pipe in receiving tank), no pressure limiting devices were employed. The first time the system was started all went well because the bulk of the line to the receiving tank was empty. The second time the pump was started, much excitement followed in the form of ruined pressure gauges, leaking fittings, "straightened" elbows, etc. The inertia of the oil in the pipeline has not been considered, and the abrupt acceleration of the oil resulted in a pressure spike many times the anticipated working pressure. Fortunately, no tragedies resulted from the incident, but a relief/recirculation valve (with necessary piping) produced a thoroughly trouble-free system--after all of the leaking joints and distorted elbows were "fixed."

Valuable advice from a professor many years ago: First, design for graceful failure. Everything we build will eventually fail, so we must strive to avoid injuries or secondary damage when that failure occurs. Only then can practicality and economics be properly considered.

 

[micalbrch]

Definitely a valuable post. Calculating the torque is one issue but you cannot start the pump with full speed against full pressure. VFD or soft starter are possible options or the proposed bypass valve. Triplex/quintuplex pump manufactures usually have such valves in their program.

 

[BCpowertrain]

Ok, I am in complete agreement with everyone on the bypass valve / recirc loop / soft start comments - but they are not applicable to this application. I have a real (i.e. existing and in widespread use) situation here where a PD pump must be started under high load and I need to determine the starting torque in order to design an appropriate gear ratio and clutching mechanism to get the pump on-line.

Please consider that the recirc / bypass valving is not possible here - what is important is the true value of input torque required to get one of these triplex or quintuplex pumps moving.

Can anyone make a suggestion or comment as to whether or not the quint. pump will be more difficult to start than the triplex?

Micalbrch - do you know how the 1.15 fiddle factor was derived for the triplex pump? Is it a purely geometric factor considering the crank position of each of the con rod throws on the pump shaft? Or is it more involved than this?

Does anyone have any idea what the torque vs. time trend would look like when starting a tri. or quint. PD pump. I am interested to see how much it oscillates around the theoretical value as determined by the formula in the second post.

I dont mean to shoot down everyones concerns and comments about the inherit risk and short sightedness of the configuration of this pumping system (i.e. no soft start, etc) - but this is a real application.

Thanks to all for there comments.

Regards

 

[micalbrch]

The 1.15 factor is a geometric factor caused by the crank offset. Because of that the factor for a quintuplex pump should be slightly higher as there are more than 2 plungers moving into the same direction at the same time.

 

[ccfowler]

BCpowertrain,

From your comments, I am inferring that your pump will probably be driven by a friction clutch powered by a running engine or motor that may be driving some other equipment or devices in addition to the subject pump.

Since you have an existing system on which to base the design your drive system, you should be able to make or compute reasonable estimates for most of the elements involved. I would pay some attention to the inertia of the pump and clutch mechanism and to the inertia of the fluid in the system that must be accelerated. As with my example above, accelerating the fluid will produce a pressure spike. I doubt that the spike will be relatively as great as the one in that example, but it may be enough to produce a significant additional burden on the clutch system. The pumped fluid must be acting against something, so I would also look at the inertia of whatever the fluid is acting upon. The frequency of starts will also be a matter of concern. If you can control the rate of engagement of the clutch, that can provide the needed cushion to minimize the acceleration burdens thereby providing a substitute for the relief valve and recirculation piping.

Valuable advice from a professor many years ago: First, design for graceful failure. Everything we build will eventually fail, so we must strive to avoid injuries or secondary damage when that failure occurs. Only then can practicality and economics be properly considered.