# Sizing Motor For High Inertia Starting Load

5 replies to this topic

### #1 Cbas

Cbas

Junior Member

• Full Member
• 5 posts

Posted 14 September 2010 - 10:06 AM

Hi All
I need a quick bit of advice (I've searched the thread, and cant really find my answer)
I am trying to size a DC motor. The speed is not important, it will be be seriously low speed like 1RPD (revolution per day ) to achieve this I am seriously gearing the motor down with a sprocket drive. The load it balanced and the center of rotation is co-indecent with the center of gravity.
Correct me if I'm wrong, but once the motor is running at a constant speed, it will only have to over come the friction of the system - as it is balanced - therefore the main concern of sizing the motor is the starting torque, as the mass moment of inertia is very large (large sprocket).
T=J X angular acceleration
My question is this: Knowing the mass moment of inertia of my system how do i size a DC motor with the least power requirements.

Oh, and one more thing,I predict the motor is likely to stop start many many time.

### #2 jOmega

jOmega

Senior Member

• Full Member
• 254 posts
• Gender:Male
• Location:Midwest, USA

Posted 14 September 2010 - 02:04 PM

QUOTE (Cbas @ Sep 14 2010, 04:06 AM) <{POST_SNAPBACK}>
Hi All
I need a quick bit of advice (I've searched the thread, and cant really find my answer)
I am trying to size a DC motor. The speed is not important, it will be be seriously low speed like 1RPD (revolution per day ) to achieve this I am seriously gearing the motor down with a sprocket drive. The load it balanced and the center of rotation is co-indecent with the center of gravity.
Correct me if I'm wrong, but once the motor is running at a constant speed, it will only have to over come the friction of the system - as it is balanced - therefore the main concern of sizing the motor is the starting torque, as the mass moment of inertia is very large (large sprocket).
T=J X angular acceleration
My question is this: Knowing the mass moment of inertia of my system how do i size a DC motor with the least power requirements.

Oh, and one more thing,I predict the motor is likely to stop start many many time.

Speed is important.

Consider: HP = (Torque x Speed) / constant
..............................where torque is in foot-lbs, speed is in RPM, constant = 5250 (some use 5252)
or
..............................where torque is in N-m, speed is in RPM, constant = 9550

Here are some additional factors you'll need to consider.

1. From a dead stop, how quickly does it need to attain what speed. This, along with knowing how much inertia is reflected to the motor shaft, allows you is a key ingredient in determining the HP requirement of motor. The inertia of the driven load is reflected back to the motor shaft by 1/gr^2.

When calculating accel & decel time, you need to use the Total Inertia at the motor shaft, including the inertia of the motor armature.

2. You will also need to specify how quickly the motor must come to a stop from running speed and calculate the braking torque ..... HP requirements.

3. You then need to define the duty cycle for starting - running - stopping ..... This too factors into the determination of the motor HP. Don't forget to factor in the overload requirements into this.

Theoretically, your assumption is correct; i.e., once the motor is at running speed, it need only supply the mechanical losses .... Friction being one of the losses; windage (if any) being another.

### #3 Cbas

Cbas

Junior Member

• Full Member
• 5 posts

Posted 14 September 2010 - 02:48 PM

So, let me make sure I understand you.
I've been trying to size my motor with a torque large enough to overcome the inertia of the system. - I neglected the start up acc and brake decc as this can take the entire day for intensive purposes - but, not what you saying, is that its the HP not the torque which should be my main focus.

I know inertia J
I can guess an angular acceleration a
I can guess a speed RPM

With J and a i can find torque
and with torque and RPM i can find HP
Then size a motor with motor curves?

Which leads to second question if T=J X a , then theoretically, any motor will turn any load although the acceleration will be small.

### #4 jOmega

jOmega

Senior Member

• Full Member
• 254 posts
• Gender:Male
• Location:Midwest, USA

Posted 14 September 2010 - 08:40 PM

QUOTE (Cbas @ Sep 14 2010, 08:48 AM) <{POST_SNAPBACK}>
So, let me make sure I understand you.
I've been trying to size my motor with a torque large enough to overcome the inertia of the system. - I neglected the start up acc and brake decc as this can take the entire day for intensive purposes - but, not what you saying, is that its the HP not the torque which should be my main focus.

I know inertia J
I can guess an angular acceleration a
I can guess a speed RPM

With J and a i can find torque
and with torque and RPM i can find HP
Then size a motor with motor curves?

Which leads to second question if T=J X a , then theoretically, any motor will turn any load although the acceleration will be small.

you said:
"I've been trying to size my motor with a torque large enough to overcome the inertia of the system. - I neglected the start up acc and brake decc as this can take the entire day for intensive purposes - but, not what you saying, is that its the HP not the torque which should be my main focus."

Let me answer your last statement first: "... is that its the HP not the torque which should be my main focus."

Consider the relationship: HP = (T x N) / constant (as defined previously)

By manipulation of terms, we can solve for Torque as follows:

T = (HP x constant) / N

The terms, HP, T, N, are interrelated. You must define two of the terms in order to find the third term.

Torque and Angular Acceleration

It would seem that your focus is on the "break-away" torque; i.e., the torque necessary to overcome the resistance of the inertia (Newton's first law of motion).

Ok ... that torque gets it into motion .... and now you have to apply additional torque (force) in order to get it into motion at some defined speed, in some defined time.

At time zero, the torque requirement is the Break-away torque...and at time zero plus... the required torque becomes the acceleration torque ....(torque required for angular acceleration so as to achieve the desired angular velocity). Again, time is an integral consideration.

from this you can solve for torque .... by interchanging Tx with t

Another consideration, depending upon how long the accel and decel times are ... you may choose a motor with a lesser rated torque value, allowing the motor to accelerate the load while operating in the overload region of the motor and its power source. Here again, determination of duty cyle is important, not only for the motor, but also for the power source for the motor. Also, be sure that the overload current supplying the accelerating/decelerating torque is within the commutation limits of the motor.

"...I neglected the start up acc and brake decc as this can take the entire day for intensive purposes..."

"Oh, and one more thing,I predict the motor is likely to stop start many many time."
..... which would seem to be somewhat contradictory ....

Without additional and more specific detail of your application, the above is the limit of my ability to be of further assistance.

Hope this helps ....

### #5 Cbas

Cbas

Junior Member

• Full Member
• 5 posts

Posted 15 September 2010 - 07:47 AM

Jomega
That was exactly what I needed, thank you once again.
Sorry, I should have been more specific in the beginning. I'm designing a solar tracker, so the panel only needs to do 180 degree turn in 12 hours (at solstice) Thats why I said it can take a full day. But I don't think I will be able to gear a motor down so drastically, and thats why I predicted multiple start stops.

I think what I'm struggling with is in fact ("The terms, HP, T, N, are interrelated. You must define two of the terms in order to find the third term.") the circular iteration I need to perform. Kinda of like: I need to size a motor, but to do that I need the breakaway torque which is a function of acceleration which is a characteristic of the motor.

I am going to change my approach to: Thumb suck a motor, find out if it will operate under the set conditions, if it can, choose a smaller motor, etc...

Sebastian

### #6 jOmega

jOmega

Senior Member

• Full Member
• 254 posts
• Gender:Male
• Location:Midwest, USA

Posted 15 September 2010 - 02:28 PM

QUOTE (Cbas @ Sep 15 2010, 01:47 AM) <{POST_SNAPBACK}>
Jomega
That was exactly what I needed, thank you once again.
Sorry, I should have been more specific in the beginning. I'm designing a solar tracker, so the panel only needs to do 180 degree turn in 12 hours (at solstice) Thats why I said it can take a full day.

Sebastian,

Here are linked references to some web pages you may find of beneficial. The 2nd & 3rd links are videos ..

Solar Tracker