Discussion:
[Arm-netbook] physics analysis needed of belt-driven pulley system
Luke Kenneth Casson Leighton
2017-08-19 09:51:01 UTC
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some background:
http://forums.reprap.org/read.php?177,767087,784083#msg-784083

and the same question here:
https://physics.stackexchange.com/questions/352661/

can anyone help? basically - and i really should have done this
before going ahead... *sigh*... - when you have a pulley system is the
amount of force on the belt less, equal, or greater, under the same
*print-head* acceleration conditions, compared to a *non* pulley
system?

l.

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Hrvoje Lasic
2017-08-19 10:38:55 UTC
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Ok, so correct me if I am wrong but you are asking some mechanical
questions.

so, I speak in general now and if you have question ask deeper.

Force needed to drive whatever you want to drive will be exactly the same
at the end part of system. But efficiency of belt system could be slightly
different then efficiency of `non` pulley system (whatever it is). But
again, efficiency could be neglected for sake of easy of calculation or you
can put around some value that (guess) could be 80-90%.

What you will be looking is gear ratio on pulley that could alter
force/speed ratio and same thing on other system.

also, you will be looking on backlash.
Post by Luke Kenneth Casson Leighton
http://forums.reprap.org/read.php?177,767087,784083#msg-784083
https://physics.stackexchange.com/questions/352661/
can anyone help? basically - and i really should have done this
before going ahead... *sigh*... - when you have a pulley system is the
amount of force on the belt less, equal, or greater, under the same
*print-head* acceleration conditions, compared to a *non* pulley
system?
l.
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Luke Kenneth Casson Leighton
2017-08-19 10:52:42 UTC
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---
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Post by Hrvoje Lasic
Ok, so correct me if I am wrong but you are asking some mechanical
questions.
mechanical / physics, yes.
Post by Hrvoje Lasic
so, I speak in general now and if you have question ask deeper.
Force needed to drive whatever you want to drive will be exactly the same
at the end part of system.
on the print-head yes. but because of the doubled speed, the DRIVE
end *NO*, the force is NOT the same.
Post by Hrvoje Lasic
But efficiency of belt system could be slightly
different then efficiency of `non` pulley system (whatever it is). But
again, efficiency could be neglected for sake of easy of calculation or you
can put around some value that (guess) could be 80-90%.
i'm assuming that there are no significant losses around pulley bearings.
Post by Hrvoje Lasic
What you will be looking is gear ratio on pulley that could alter
force/speed ratio and same thing on other system.
the gear ratio on a single pulley system is 2:1.
Post by Hrvoje Lasic
also, you will be looking on backlash.
*thinks*... backlash should be reduced (halved) due to the better
effectiveness of the pulleys - assuming that there is no "play" in the
bearings (we can assume decent bearings / idlers).

l.

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Hrvoje Lasic
2017-08-19 14:00:30 UTC
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below are answers
Post by Luke Kenneth Casson Leighton
---
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Post by Hrvoje Lasic
Ok, so correct me if I am wrong but you are asking some mechanical
questions.
mechanical / physics, yes.
Post by Hrvoje Lasic
so, I speak in general now and if you have question ask deeper.
Force needed to drive whatever you want to drive will be exactly the same
at the end part of system.
on the print-head yes. but because of the doubled speed, the DRIVE
end *NO*, the force is NOT the same.
so, if on the print head-side force is the same then it is on the drive
side same as well (work can not be missing somewhere). However, if you are
doubling the speeds, then overall work required will be some higher value
so, correct would be to say that because of double speed you are having
more force on print head needed and as result drive will also have to work
more, losses will be bigger etc.

anyway, that is all theoretical. Real value would be to find out force you
need to have on print head then do some sort of calculation back to the
drive. I guess you don't know that but maybe you can see what has been done
on system that have other drive and then try to extrapolate what you will
need. We can also assume here that someone has already put some reserve on
what is now there, so possibly you can leave same motor or if you have
problem increase force at disposal assuming you can do that on same motor
size (nema 17 or so)

I think backlash here will be your biggest problem here. Backlash is in
fact inertia of the system. So, for example when you run you want to stop
you cant do it right away, you need some time/distance. Or comparing to
electrical engineering you can compare it to inductance. Inductance is
resistance plus reactance.

You said that you expect lesser backlash on pulley system. If that is the
case (I am not sure why or why not this statement would be truth) you will
be able to increase speed up to certain point but you will have to test
where is that point. Basically you will have to do a lot of testing.
Post by Luke Kenneth Casson Leighton
Post by Hrvoje Lasic
But efficiency of belt system could be slightly
different then efficiency of `non` pulley system (whatever it is). But
again, efficiency could be neglected for sake of easy of calculation or
you
Post by Hrvoje Lasic
can put around some value that (guess) could be 80-90%.
i'm assuming that there are no significant losses around pulley bearings.
Post by Hrvoje Lasic
What you will be looking is gear ratio on pulley that could alter
force/speed ratio and same thing on other system.
the gear ratio on a single pulley system is 2:1.
Post by Hrvoje Lasic
also, you will be looking on backlash.
*thinks*... backlash should be reduced (halved) due to the better
effectiveness of the pulleys - assuming that there is no "play" in the
bearings (we can assume decent bearings / idlers).
l.
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Hrvoje Lasić
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Gračanska 120a
10000 Zagreb
Croatia
tel +385 1 6152 706 <+385%201%206152%20706>
tel +38598 450 603 <+385%2098%20450%20603>


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Luke Kenneth Casson Leighton
2017-08-19 14:12:44 UTC
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Post by Hrvoje Lasic
below are answers
Post by Luke Kenneth Casson Leighton
---
crowd-funded eco-conscious hardware: https://www.crowdsupply.com/eoma68
Post by Hrvoje Lasic
Ok, so correct me if I am wrong but you are asking some mechanical
questions.
mechanical / physics, yes.
Post by Hrvoje Lasic
so, I speak in general now and if you have question ask deeper.
Force needed to drive whatever you want to drive will be exactly the same
at the end part of system.
on the print-head yes. but because of the doubled speed, the DRIVE
end *NO*, the force is NOT the same.
so, if on the print head-side force is the same then it is on the drive
side same as well (work can not be missing somewhere). However, if you are
doubling the speeds, then overall work required will be some higher value
doubling the speed of the *belt* but not the print-head. we're
comparing like-for-like scenario (pulleys / no-pulleys).

btw benson kindly answered on the forum (thank you!) and i think i
have a handle on the situation now.
Post by Hrvoje Lasic
so, correct would be to say that because of double speed you are having
more force on print head needed and as result drive will also have to work
more, losses will be bigger etc.
no, the speed of the print-head should be the same in both scenarios
(pulleys / no-pulleys) therefore the force should be the same.

now, what benson kindly pointed out is that in a pulley system the
force is *SHARED* between the two belt segments, therefore the amount
of "stretch" (which is what i was concerned about) should also be
HALVED compared to a non-pulley system.

where i got confused was, i thought that the belt's actual travel
speed was somehow involved in the equation: it would be.... *if* the
belt's mass was significant.
Post by Hrvoje Lasic
I think backlash here will be your biggest problem here. Backlash is in
fact inertia of the system. So, for example when you run you want to stop
you cant do it right away, you need some time/distance. Or comparing to
electrical engineering you can compare it to inductance. Inductance is
resistance plus reactance.
indeed. so, because the force is halved (for the same speed compared
to a non-pulley system) we *should* also get less backlash as well.
yay.
Post by Hrvoje Lasic
You said that you expect lesser backlash on pulley system. If that is the
case (I am not sure why or why not this statement would be truth) you will
be able to increase speed up to certain point but you will have to test
where is that point. Basically you will have to do a lot of testing.
indeed :) the aim is to use the extra wiggle-room (less backlash,
less load) to increase speed by some factor... probably not double but
a good fraction of that, and see what happens.

certainly someone pointed out that the speed of the NEMA17s, when you
go faster, you actually get less torque. whoops. and the rated
maximum seems to be around 1800 mm / sec. at that point you get
*significantly* less torque.

so it's not going to be a straightforward "go twice as fast" thing.

l.

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Hrvoje Lasic
2017-08-19 14:34:39 UTC
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Post by Luke Kenneth Casson Leighton
certainly someone pointed out that the speed of the NEMA17s, when you
go faster, you actually get less torque. whoops. and the rated
maximum seems to be around 1800 mm / sec. at that point you get
*significantly* less torque.
so, when you say nema 17 you refer to dimensions of the motor, not torque.
it is some American standard,so nema 17 refer to 43.2 mmx 43.2 mm if you
look at face of motor. But you can have different torques at same size of
the motor. They increase the size of the motor in length. so you will be
still able to alter torque to some extent no matter speed. Keep in mind
that you are flexible here up to certain point. After that, if you need
more torque you go to next bigger size of motor nema 23 or so.
Post by Luke Kenneth Casson Leighton
so it's not going to be a straightforward "go twice as fast" thing.
for sure not otherwise you would see some speeds as standard. My guess is
that what you have on market is pretty much optimized per cost/performance
but you may well be more efficient for your particular case.
Post by Luke Kenneth Casson Leighton
l.
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tel +385 1 6152 706
tel +38598 450 603


****@gmail.com <***@gmail.com>***@vebbu.co <***@vebbu.co>m*

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Luke Kenneth Casson Leighton
2017-08-19 14:47:26 UTC
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Post by Hrvoje Lasic
so, when you say nema 17 you refer to dimensions of the motor, not torque.
yes. they're common enough that they're quite low-priced.
Post by Hrvoje Lasic
look at face of motor. But you can have different torques at same size of
the motor.
yes. for the purposes of the analysis (pulley / non-pulley) we
assume exact same motor.
Post by Hrvoje Lasic
They increase the size of the motor in length. so you will be
still able to alter torque to some extent no matter speed. Keep in mind
that you are flexible here up to certain point. After that, if you need
more torque you go to next bigger size of motor nema 23 or so.
yes. that also increases cost, and weight, not just the motor size
but also the holders, and also the ampage needed of the controller.
which again increases cost. so, trying not to do that as it's not
necessary.

l.

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David Niklas
2017-08-22 21:43:08 UTC
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On Sat, 19 Aug 2017 15:47:26 +0100
Post by Luke Kenneth Casson Leighton
Post by Hrvoje Lasic
They increase the size of the motor in length. so you will be
still able to alter torque to some extent no matter speed. Keep in
mind that you are flexible here up to certain point. After that, if
you need more torque you go to next bigger size of motor nema 23 or
so.
yes. that also increases cost, and weight, not just the motor size
but also the holders, and also the ampage needed of the controller.
which again increases cost. so, trying not to do that as it's not
necessary.
l.
Or you could use two nema 17's on one pulley.
Mind, I don't know how you designed the pulley system so this might be
rather difficult or really easy.

Sincerely,
David

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Luke Kenneth Casson Leighton
2017-08-29 17:58:32 UTC
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Post by David Niklas
Or you could use two nema 17's on one pulley.
Mind, I don't know how you designed the pulley system so this might be
rather difficult or really easy.
yyeah... trying that would have me concerned. more tomorrow. 2am now.

l.

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