Optimizing Gear Ratio for Maximum Angular Acceleration

[prshptl]

Hi Russ,

Could you help me with this question

An electric motor drives a machine through a reduction gear ratio of 9 to 1. The masses rotating with the motor shaft have a moment of inertia of 0.5kg m2 and the masses rotating with the machine shaft have a moment of inertia of 38kg m2. A constant torque of 100Nm resistst the rotation of the machine shaft and the efficiency of the reduction hear is 95%. The motor can develop a maximum torque of 27Nm.

Determine the power the motor develops when the machine shaft is driven at the uniform speed of 150 revmin-1
Determine the least time requred for the speed of the machine shaft to increase from zero to 150 rev min-1
If the gear ratio were altered so as to give the machine shaft the greatest possible angular acceleration, what would then the gear ratio be?

Gear ratio-angular speed of high-speed shaft/ angular speed of low speed shaft.

 

[prshptl]

Motor/Torque Question

Homework Statement

Hi Russ,

Could you help me with this question

An electric motor drives a machine through a reduction gear ratio of 9 to 1. The masses rotating with the motor shaft have a moment of inertia of 0.5kg m2 and the masses rotating with the machine shaft have a moment of inertia of 38kg m2. A constant torque of 100Nm resistst the rotation of the machine shaft and the efficiency of the reduction hear is 95%. The motor can develop a maximum torque of 27Nm.

Determine the power the motor develops when the machine shaft is driven at the uniform speed of 150 revmin-1
Determine the least time requred for the speed of the machine shaft to increase from zero to 150 rev min-1
If the gear ratio were altered so as to give the machine shaft the greatest possible angular acceleration, what would then the gear ratio be?

Homework Equations

Gear ratio=angular speed of high-speed shaft/ angular speed of low speed shaft.

The Attempt at a Solution

I tried to find the first part by using Torque-wR.

By the link with I is confusing

 

[firavia]

I would recommend you to check this page out : http://industrial.panasonic.com/ww/i_e/25000/fa_pro_sgeard_shing1_e/fa_pro_sgeard_shing1_e/ctlg_geared_e_9.pdf

it explains all the procedures you should take to solve what you are asking for.

 

[prshptl]

Hi, i was looking for an explanation of what is actually goin.
So i can apply for the formulas

 

[prshptl]

I had a good look,but its still not making any sense.
Do you know anyone with expertise in this field

 

[tvavanasd]

Be sure to convert units to those required by the equations.

Part 1
Calculate the load shaft speed in radians/sec.
Calculate the shaft power taking into account gear efficiency losses.

Part 2
Find the final motor shaft speed in radias/sec.
Calculate the maximum possible acceleration for the system (usually done relative to the motor shaft).
Determine the torque equation for the system as seen by the motor:
motor torque required = (motor inertia)x(motor angular accel) + ... + ...

Note that the load inertia as seen by the motor is equal to:
(load inertia)/(gear ratio)^2

Calculate time to accelerate to required speed.

Part 3
Review the following:
http://www.diequa.com/download/articles/inertia.pdf
"Maximum Power Transfer For Maximum Acceleration"
Maximum acceleration occurs when the load inertia reflected through the reducer (as seen by the motor) is equal to the motor inertia. That is when the "inertia mismatch" is equal to one.

 

[prshptl]

Hi tvavanasd
I have done parts of the questions ,can you check answers
1654watts
Pa

8.52seconds

Cheers

 

[tvavanasd]

1654 watts is correct (though you should watch your significant digits).

What is "Pa"?

Not sure about the accel time; I'll have to calculate it to compare.

Please show your work.

 

[prshptl]

Hi TVAVANSD

My answers for part b are:

Torque avaliable =16.5Nm

Total inertia-0.994(0.5+494)

Max angular acceleration=16.6 rad/secs squared

Time=8.52 seconds

part c

8.72

using equation in the article you provided.

 

[prshptl]

I am concerned about part c,we have ignored the efficiency of 95%
The answer should be around,Gear ratio=13

 

[tvavanasd]

Time=8.52 seconds

part c

8.72

using equation in the article you provided.

Your answer for part b is too high. I calculate the accel time to be just over 1 second if load accel gearbox losses are considered, and just under 1 sec if they are not.

Yes, based on inertia mismatch theory alone, a gear ratio of 8.72:1 is correct.

I just checked using a spreadsheet and found either 13.5 or 13.7:1 to be best (depending on load accel losses)...

What makes you think that it should be 13:1?