[damunk]

how much kg can a 1000Fanm(N) tension member loading lift at speeds of up to 0.5M per second using a lead screw. (2500rpm)

Is there any formulas out there work out the correct belt to use on a pulley system.

the belt manufacuters can only give the N rating on a belt.

[peteeng]

Hi Dam - If I interpret you correctly you are using a belt to lift a weight? or are you using the leadscrew and driving the screw with a belt? (so you have linear bearings in there as well) The issue is the acceleration you require. If the weight is accelerating slowly then its inertial force can be neglected. If its accelerating which at some point it has to then the lifting system is lifting the weight and the inertial force. This then translates back to your drive via the belt.. a diagram would help... At 2500rpm you maybe close to vibration speeds. Depends on the length of the screw... There's a few things to figure out before you can answer your question. The belt manufacturers have manuals that describe how to size and select belts. There's a little more to it then just the single load strength of the belt. Depends on if you want the drive to go 5 cycles or 1 million cycles. Plus is it just moving or do you need to move it accurately from place to place? A transport belt can be much smaller than a control belt. Peter

optibelt provide a very good design manual. Its too big to load here so find optibelt.com and you will be able to download the manual...

[damunk]

pete, thank you for your reply. ;

1) you are using a belt to lift a weight? yes 40kg (EDIT: but via pulleys and leadscrew)
2) are you using the leadscrew and driving the screw with a belt? YES
3) (so you have linear bearings in there as well) YES
4)The issue is the acceleration you require. If the weight is accelerating slowly then its inertial force can be neglected. If its accelerating which at some point it has to then the lifting system is lifting the weight and the inertial force. This then translates back to your drive via the belt.. YES sudden fast accelerations in either direction
5) a diagram would help.(BIG PULLEY 1500RPM; Small pulley driving the lead screw at around 2500RPM..
6) At 2500rpm you maybe close to vibration speeds.I never felt viberation with a weaker belt. I switched to a 1200N belt because I thought I would find the strongest belt that suited the width of the pulley.
7) Depends on the length of the screw... 400mm length ; that is the travel distance
8) There's a few things to figure out before you can answer your question. The belt manufacturers have manuals that describe how to size and select belts. None given apart from belt tensile strength rating
9)There's a little more to it then just the single load strength of the belt. Depends on if you want the drive to go 5 cycles or 1 million cycles.... 1 million cycles per year.
10) Plus is it just moving or do you need to move it accurately from place to place? it is being moved accuratley place to place; i have a controller board that does all the positioning.

I thought a belt tensile strength along with weight being moved at a certain speed would be enough to use a formula to work out a force then use that against the belt rating.

[peteeng]

Hi Dam - To calculate the max tension in the belt we need to know the acceleration of the weight. Does this occur over 50mm? 20mm? This acceleration will determine the forces not the speed. Then the least accel would be over 200mm so it speeds up to halfway then slows down to the end. It reverses and repeats. The average speed would be half the max speed. Will this run 24hrs a day?

2 secs cycle = 1,000,000x2=2M sec 2M/60/60= 556hrs = 23days so a 20sec cycle would be 230days ? what sort of cycle time are you aiming at???? What does it do? Does it make milk shakes? Peter

If I were making such a rig I'd use a crank not a belt and pulley.... much easier. Whats the pitch of the screw? Vibration is in the lead screw not in the belt. Long screws vibrate but a short screw like this probably would not vibrate. Whats the diameter of the screw? Also need to know the inertia of the motor, do you have the motor spec? The motr needs to accelrate itself, the screw and the mass. Often the motor and screw are the highest inertial loads in such a system....

[damunk]

Hi Dam - To calculate the max tension in the belt we need to know the acceleration of the weight. Does this occur over 50mm? 20mm? This acceleration will determine the forces not the speed. Then the least accel would be over 200mm so it speeds up to halfway then slows down to the end. It reverses and repeats. The average speed would be half the max speed. Will this run 24hrs a day?

2 secs cycle = 1,000,000x2=2M sec 2M/60/60= 556hrs = 23days so a 20sec cycle would be 230days ? what sort of cycle time are you aiming at???? What does it do? Does it make milk shakes? Peter

If I were making such a rig I'd use a crank not a belt and pulley.... much easier. Whats the pitch of the screw? Vibration is in the lead screw not in the belt. Long screws vibrate but a short screw like this probably would not vibrate. Whats the diameter of the screw? Also need to know the inertia of the motor, do you have the motor spec? The motr needs to accelrate itself, the screw and the mass. Often the motor and screw are the highest inertial loads in such a system....

The max speed is 0.4Mper second and there is hardley any viberation in the leadscrew that is 25mm thick. short lead screw so that is a bonus.
the acceleration is instant. 400mm/s instant acceleration but not all the time. only when required.

probably only run a few hours a day. I just read on cam belts for cars and they are around 1200-1400N tensile strength and similar thickness to my belt 2-3mm toothed belts.
you woudl think the forces in a car engine on a belt are alot more than 40kg going in either direction .

[peteeng]

Hi Dam - Car engine timing belts run at relatively low speeds and accelerations and in one direction. Your machine stops, starts and reverses meaning it has potentially very high accelerations and jerk. Totally different conditions. So if it's working why ask these questions? Timing belts fatigue and their lifetime is rarely coupled to their static strength. Manufactures do lots of testing and produce data that relates their static strength to their fatigue life (empirical data) and publish service factors to estimate life vs strength. The teeth wear and the plastic ages thats the main contributor to death, not the fibre strength.

The accel cannot be instant otherwise the force is infinite and it will break any belt or machine. If the max speed is 0.4m/s then the min average accel is 0.4m/s/s as you have suggested. V^2=U^2 + 2xaxs where V=0.4 U=0 s=200mm this implies a minimum cycle time of 2 secs V=u = at V=0.4 u=0 a=0.4 ie t= 1sec to mid motion. So when the weight is accelerating upwards it has its weight, its inertia & friction to deal with so it has (40x9.81) + (0.4*40) = 408.4N or 41.6kgf (ignore friction for now, leadscrews have high frictions)

But we need to know the screw pitch and the motor inertia to calculate the rotational inertial loads to complete the calculation.. But if it works it works so why continue? These are the travel conditions, the end conditions (stop and start ) are controlled by your controller settings the stop/start accels can be 2 or 3x the travel conditions...

The screw pitch determines the torque required to push the 41.6kgf then the resulting torque can be converted into a belt tension (including the inertia of the screw and the motor).... Happy milk shake making Peter

edit - the screw thread is a force multiple (lever) so the belt is unlikely to see 41.6kgf... but need to complete the calcs to find out...

[damunk]

we are nearly there. i am able to reduce the accleration in what is called "smoothing" which is the smoothing of the profile to provide less "jerk"

anyhow; the pitch of the screw is 20mm which is one rotation = 20mm of travel.

happy calculation. i am glad there is someone who is gifted enough to do it.

when you ask if it is working why discuss. well. the belt that i was using was a t5. i gone to a stronger belt because i was redesigning the tensioner pully and i thought i might aswell use a 1300N belt and it's always good to learn along the way.

I just had a feeling I needed a belt as strong as a cam belt atleast.

[peteeng]

Hi Dam - What size motor are you using? I can't complete the calculation unless we know the inertia of the motor. This is published in its data sheet. What is your average cycle time? and the length of the screw as this tells me its inertia. We are a little way off yet from the answer. Peter

[damunk]

the motor inertia is :

Torque coefficient(N.m/A)				1.58
Rotor inertia (kg.m2)				1.94*10-3

but i can reduce that from the servo which i intend to as motor is a big 2KW . and I probably only need a 1KW
the length of the lead screw is 400mm. average time cycle per day is 4 hours

[peteeng]

Hi Dam - The cycle time is from start to finish of the cycle not how long it is used during a day. 2sec? 4secs? 10secs? so how many cycles does it do in 4 hrs? Regards Peter

[damunk]

so like 10 cycles in a minute which is like 6 seconds

[peteeng]

So its 3secs up and 3secs down? So too slow to make milk shakes Peter

[damunk]

So its 3secs up and 3secs down? So too slow to make milk shakes Peter

Keep getting stuff wrong. It’s around 400m/s so it’s like between half a second to a second up and then down so like you said 2 seconds . So fast enough for the milk shake lol. If you can work it out , you can choose the flavour you want and I’ll make you some lol

[peteeng]

Hi Damunk - I have assumed the pulley diameter on the screw is 120mm. I have assumed the cycle time is 6secs of which a half cycle is 1sec accel 1sec constant V and 1sec decel... Gravity sucks so the major load is when the weight is accelerating upward.

I have done a quick calc not detailed eg I have not accounted for the difference in pulley diameter which will affect the inertial calc a bit. But the loadings are small. This calc is typically what would be done to the "size" a motor and components. Its a dimensioning calc not a detailed calc as we do not know the exact accels in the stop start area. We do know what the transfer accels are so if we say the actual forces are 2x this one then you have a belt tension of around 50N maybe 75N. See numbers attached.

Hope that's what you asked for. Peter

[peteeng]

OK so I'll redo the numbers based on 1 sec up or 0.5sec up? will make a difference... ... and what is the screw pulley diameter? You say lead screw but at 20mm pitch its a ballscrew??? Peter

[damunk]

OK so I'll redo the numbers based on 1 sec up or 0.5sec up? will make a difference... ... and what is the screw pulley diameter? You say lead screw but at 20mm pitch its a ballscrew??? Peter

Yes ball screw and the pulley on that is 50mm in diameter.
Yes about second up and then a second down
That equates to 400mm per second

Edit/ and yes I have limited the speed to that otherwise the milkshake will be all over the place

[peteeng]

Morning - Here's the new numbers - around 55N tension plus belt preload. So in reality maybe 100N. Check the numbers. I have not balanced the inertia via the belt ratio. But it would change the numbers only slightly. Check the math I have been wrong in the past. Lime is a fav. Peter

[damunk]

you have any links to vids or web where i can learn more about this. ive seen alot of pulley rope physics classes but not pulley/belt drive stuff

[peteeng]

Hi Damunk - I studied this some 45 years ago in uni doing mech eng. I'll dig around for you. Peter

[peteeng]

Hi Damunk- Firstly you have to study motion. Here's something on Kinematics. I haven't looked at it closely, first glance seems good. Peter

https://study.com/academy/topic/over...inematics.html