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Worm Wheel moment of Inertia
- Thread starter roozle
- Start date
PeterCharles
Mechanical
Most reputable gearbox makers will be able to tell you the inertia of their gearboxes (referred to either the high or low speed shafts). To try and do it yourself without the manufacturing drawings would be quite a challenge.
Perhaps you could set up an experiment.
1) wrap a cord around the input shaft
2) add weights to just overcome friction
3) add more weight and measure the time/distance travelled intervals
4) from (3)calculate the acceleration
5) from (4)calculate the inertia
Well, it's an idea working from first principles.
Any others??
Perhaps you could set up an experiment.
1) wrap a cord around the input shaft
2) add weights to just overcome friction
3) add more weight and measure the time/distance travelled intervals
4) from (3)calculate the acceleration
5) from (4)calculate the inertia
Well, it's an idea working from first principles.
Any others??
roozle,
Do not ignore the inertia of the worm, or of the motor armature. Calculate it, then multiply it by the square of the gear ratio.
Can you take the gearmotor apart and do measurements?
Can the gearmotor manufacturer tell you the total inertia of the unit?
JHG
Do not ignore the inertia of the worm, or of the motor armature. Calculate it, then multiply it by the square of the gear ratio.
Can you take the gearmotor apart and do measurements?
Can the gearmotor manufacturer tell you the total inertia of the unit?
I am all for experimental methods.
Here is one that works:
- Find a disk of any kind preferably not something that has too much mass.
- Get 3 wires or strings of equal length to support the disk at points 120 degrees apart. (you now have a simple disk suspended with flat faces facing up and down)
- place the worm in the direct center of the disc with the axis that you want to measure the inertia of coinciding with the center axis of the disk. (make sure it is firm, you could use wax or whatever you have that won't effect the experiment)
- measure the period of oscillation T. (about the vertical)
- It can then be shown that: I=g*T^2*ro^2*(mo+m)/(4*pi^2*l)-Io
where, I is the mass moment of inertia of your worm, m is the mass of the worm, mo is the mass of the disk, ro is the radius of the disk, l is the length of the wires, Io is the moment of inertia of the disk, and g is the gravitational accel. constant.
Have fun, I know I would.
![[peace]](/data/assets/smilies/peace.gif "[peace] [peace]")
Fe
Here is one that works:
- Find a disk of any kind preferably not something that has too much mass.
- Get 3 wires or strings of equal length to support the disk at points 120 degrees apart. (you now have a simple disk suspended with flat faces facing up and down)
- place the worm in the direct center of the disc with the axis that you want to measure the inertia of coinciding with the center axis of the disk. (make sure it is firm, you could use wax or whatever you have that won't effect the experiment)
- measure the period of oscillation T. (about the vertical)
- It can then be shown that: I=g*T^2*ro^2*(mo+m)/(4*pi^2*l)-Io
where, I is the mass moment of inertia of your worm, m is the mass of the worm, mo is the mass of the disk, ro is the radius of the disk, l is the length of the wires, Io is the moment of inertia of the disk, and g is the gravitational accel. constant.
Have fun, I know I would.
Fe
PeterCharles
Mechanical
That's an interesting experiment.
Are the three suspension wires/strings brought to a common centre point above the centre of the disc?
Only downside I can see is taking the gearbox apart to remove the worm wheel. And is it just the inertia of the worm wheel that is wanted or the entire gearbox?
Are the three suspension wires/strings brought to a common centre point above the centre of the disc?
Only downside I can see is taking the gearbox apart to remove the worm wheel. And is it just the inertia of the worm wheel that is wanted or the entire gearbox?
PeterCharles,
The wires are not brought to a common center, they are left vertical.
Yes, I wasn't sure if the OP was asking about the worm or the entire box. Irregular shapes such as the worm could be done like this, the rest like shafts are known values. You are right, if taking apart the box is a pain then this will also be a pain.![[pipe]](/data/assets/smilies/pipe.gif "[pipe] [pipe]")
If the OP was talking about the entire box, I don't see a reason why what you mentioned above with the weights would not work. It's a good idea because it shows an understanding of the fundamentals.
To add, maybe in order to get an accurate measurement of the displacement and time of the shaft you could use reflective tape (placed of the shaft) and an optical sensor to measure the number of times the tape passes by over a certain time.
Then utilize, T=Jo*alpha and determine an experimental Jo.
just a thought,
Fe
The wires are not brought to a common center, they are left vertical.
Yes, I wasn't sure if the OP was asking about the worm or the entire box. Irregular shapes such as the worm could be done like this, the rest like shafts are known values. You are right, if taking apart the box is a pain then this will also be a pain.
If the OP was talking about the entire box, I don't see a reason why what you mentioned above with the weights would not work. It's a good idea because it shows an understanding of the fundamentals.
To add, maybe in order to get an accurate measurement of the displacement and time of the shaft you could use reflective tape (placed of the shaft) and an optical sensor to measure the number of times the tape passes by over a certain time.
Then utilize, T=Jo*alpha and determine an experimental Jo.
just a thought,
Fe
PeterCharles
Mechanical
My thinking regarding bringing the suspension wires/strings to a common centre point was that the resulting torsional pendulum could operate without the disc being lifted vertically. (Though I'm not sure it matters).
I like the idea of the reflective tape on the shaft. The last time I tried to measure the acceleration of a body was in school physics in the early 1960's. We had a pencil on a springy arm that traced out a natural frequency wave form on paper attached to a trolley accelerated by a falling weight. Knowing the natural frequency we were able to measure the distance moved against time, do a graphical differentiation and plot speed against time to get acceleration. I'm sure it must be more high tech these days! (Is practical experimental work still done or is it just a computer simulation?)
I like the idea of the reflective tape on the shaft. The last time I tried to measure the acceleration of a body was in school physics in the early 1960's. We had a pencil on a springy arm that traced out a natural frequency wave form on paper attached to a trolley accelerated by a falling weight. Knowing the natural frequency we were able to measure the distance moved against time, do a graphical differentiation and plot speed against time to get acceleration. I'm sure it must be more high tech these days! (Is practical experimental work still done or is it just a computer simulation?)
Most of my experimental work involves collecting data through a data acquisition board. Then performing off-line analysis.
Although, the odd time I have done a bit of practical experimental work as you say. I can remember a simple one where I measured the deflection of a beam with a ruler after placing a known mass onto it. With this, I was able to estimate the modulus of elasticity.
Otherwise, I mostly use a D-Space setup (software and DAQ boards) to collect data and mainly Matlab to process and manipulate the data.
I never did anything like you describe in school. I guess I am a bit of a newbee![[smile]](/data/assets/smilies/smile.gif "[smile] [smile]")
Although, I see the benefit that we are missing nowadays.
Fe
Although, the odd time I have done a bit of practical experimental work as you say. I can remember a simple one where I measured the deflection of a beam with a ruler after placing a known mass onto it. With this, I was able to estimate the modulus of elasticity.
Otherwise, I mostly use a D-Space setup (software and DAQ boards) to collect data and mainly Matlab to process and manipulate the data.
I never did anything like you describe in school. I guess I am a bit of a newbee
Although, I see the benefit that we are missing nowadays.Fe
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