Rpm and power for this electric motor, gearbox and pulley system

[doke]

Homework Statement

an electric motor connected to a gearbox which is connected to the vbelt-pulley system that drives a water pump should run at 200Rpm and 9kw net power should be transmitted to the pump in order to pressurize the water to the desired place
find
the required electric motor power and rpm

Relevant Equations

im confused

i got confused because if the connections btw the parts

 

[berkeman]

That is indeed a confusing problem statement. Is it the whole problem statement? Are there any diagrams associated with this problem? Does this electric motor only drive the water pump through the transmission and V-belt systems, or is it like an electric car where it also drives the wheels to propel the car?

i got confused because if the connections btw the parts

And I was not able to parse what you wrote there. Can you please restate that or elaborate?

 

[doke]

Thanks for reaching out ,The Full Question is :

You are a mechanical system design engineer of factory you have to design a mechanical system with an electric motor connected to a gearbox which is connected to the belt-pulley system that drives a water pump should run at 200Rpm and 9kw net power should be transmitted to the pump in order to pressurize the water to the desired place for24hour a day the small pulley diameter is 100mm and the large pulley diameter is 200, due to the available space constraint the gear box has only one stage made up of spur gears which has the maximum applicable gear ratio to reduce the speed for this mechanical system define/assume/select any other parameters/materials accordingly and find:

a)required electric motor parameters such as power and rpm

b)gear teeth numbers,gear size and gear ratio

c) design a suitable v type belt and estimate the belt life passes and hours
but im confused with only Part A of the Question

 

[doke]

Suddenly the question doesn't provide any figuers

 

[Filip Larsen]

im confused with only Part A of the Question

Do you know how power, rotational speed and torque are related for a rotational system? If the gear train is required to output 9 kW can you then from that requirement alone say how much power should (at least) be in the input?

 

[doke]

P=TW but in the question he is saying to obtain power again while i have net power so i got confused here. also i have no idea which formula can obtain the rpm also question provides Rpm

 

[doke]

does efficiency has a role to obtain the required power?

 

[Filip Larsen]

P=TW but in the question he is saying to obtain power again while i have net power so i got confused here. also i have no idea which formula can obtain the rpm also question provides Rpm

If you by "P=TW" means power equal torque times angular speed, all using compatible units like power in W, torque in Nm and angular speed in s^-1), then you are correct.

Regarding the power, the requirement is 9 kW @200 RPM of mechanical (net) power delivered to the water pump, so how much power must the electrical engine (the sole power source here) at least deliver? (hint: can power be created out of nothing?).

Regarding the rotational speed of the engine, you say you already know the gear ratio of the gear (it is almost stated directly in the problem text), so can you write out how engine RPM relates to pump RPM?

Edit: added missing part in first sentence.

 

[doke]

thanks for reaching out : if i use gear ratio 10:1 that means 200rpm*10 which is the ratio so the motor must run at 2000rpm ? am i correct here ?
regarding to the power :i think i must use concept of efficiency which is P motor=Ppump/efficiency . is that correct

 

[Filip Larsen]

does efficiency has a role to obtain the required power?

The problem text seems to suggest you can define you assumptions. Since there are no mentioning of friction or losses in the text, the simplest is often to assume no friction, but that is up to you.

It is my understanding that it is quite common to specify engine output shaft power, so going with that you only need to consider whether or not you want to estimate gear box losses.

 

[Filip Larsen]

if i use gear ratio 10:1 that means 200rpm*10 which is the ratio so the motor must run at 2000rpm ? am i correct here ?

Given that engine-to-pump gear ratio is 10:1 then yes. But reading the text I come up with a different gear ratio, just so you know.

regarding to the power :i think i must use concept of efficiency which is P motor=Ppump/efficiency . is that correct

Is there a special reason you want to address efficiency? The problem text does not seem to imply you need to address anything regarding efficiency.

 

[doke]

so is finding the Torque will be halpful so i can convert the 2000 rpm to m/s and use t=p/w to find the torque then multiple it by the rpm so i can get the required power.I feel like I'm going in a vicious circle ot that is correct approach

 

[doke]

the motor Rpm also can be 200rpm* 10* 2[ which is the pulley ratio ]= 4000rpm

 

[Lnewqban]

... drives a water pump should run at 200Rpm and 9kw net power...

In order to work properly, the shaft of your pump needs to rotate at 200 rpm while driven by a minimum torque of 430 N-m.

Please, see:
https://www.engineeringtoolbox.com/electrical-motors-hp-torque-rpm-d_1503.html

Moving bacwards toward the motor, you will keep the rpm rates that you choose to have the input rpm that the manufacturer of the motor specifies for certain torque.

Simultaneously, you will be needing increasing transferred power at each step, due to lost torque in friction losses; therefore, your motor will need to deliver more than the 9 KW needed by the pump.

 

[doke]

In order to work properly, the shaft of your pump needs to rotate at 200 rpm while driven by a minimum torque of 430 N-m.

Moving bacwards toward the motor, you will keep the rpm rates that you choose to have the input rpm that the manufacturer of the motor specifies for certain torque.

Simultaneously, you will be needing increasing transferred power at each step, due to lost torque in friction losses; therefore, your motor will need to deliver more than the 9 KW needed by the pump.

thanks for reaching dear, so in which way i can get the required motor power

 

[Lnewqban]

thanks for reaching dear, so in which way i can get the required motor power

Please, check above link.
You are welcome.

 

[doke]

i dont see any link sir

 

[doke]

as a result so T Nm = 9000Watt * 9.549 / 4000 rpm = 21.48Nm .then ω=60*4000rpm×2π≈418.88rad/s so
P=21.48×418.88
P≈8997.8W
Am i correct now ?

 

[Lnewqban]

as a result so T Nm = 9000Watt * 9.549 / 4000 rpm = 21.48Nm .then ω=60*4000rpm×2π≈418.88rad/s so
P=21.48×418.88
P≈8997.8W
Am i correct now ?

See link in post #14 above.

You are back to 9 KW, as you will for any possible combination of torque and rotational velocity that satisfies that number.

Again, your motor will need to supply a little more than 9 KW to satisfy the hungry middle mechanisms (gears, pulleys, belts) and simultaneously keep your pump happy.

 

[doke]

correct sir but i need to reach a specific formula that can calculate the power