Please can someone explain pulleys to me

[fozz]

Hi there Folks,

During my last lathe restoration I came up against a brick wall trying to work out shaft speeds and pulley sizes. came to the rescue working out the speeds for me which helped me immensely but now finding myself restoring another lathe the need arises again to work out speeds and pulley sizes and I'm finding myself fast going bawled trying to do the calculations.

I know I should be able to work this out but for the life of me I'm getting more and more confused.

I'll supply the numbers I already have and what I'd really like is for someone not to calculate the results but to explain to me in simple english how the calculation is done :)

Ok, as follows,

motor rpm = 1440
motor pulley block from end of shaft = 109/109 to be resized from final calculation

the old motor's pulley block from end of shaft was 45/69/93/119 giving final speeds of 280/600/1090/2240
jack shaft pulley block = 119/93/69/45
jack shaft pulley = 47
headstock shaft pulley = 115

The motor is going to be run via a VFD from 10 hertz to 100 hertz.

I am hoping to get a final speed range from about 50rpm to as near as 3000rpm.

For those of you who understand these numbers I'm sure its easy but its making my head hurt, any help will be most appreciated.

Ross.

[artful bodger]

Hi Foz. That is a pretty unusual question. Do you restore pulley/less lathes? Are you a mathematics buff?
One of my lathes (a woodfast) has 4 speeds. Slow, a bit faster, a little bit faster and flat out.The choice of speeds has never let me down. My other one has 8 speeds that incrementally work in a similar fashion. Ditto
Would not have a clue what any of the actual RPM's are. Just use the one that suits the job at the time.
Not sure but perhaps your over analysing things a tad?
Anyway, good luck with the restorations.

[fozz]

The reason I need to know how to do the calculations is so that I can know what diameters the motor's pulleys need to be turned down to so that I can get the results I'm after in the final setup.

[artful bodger]

Ok. So your restoring a lathe with no pulleys then?

[fozz]

Check out this thread, should explain everything :)

http://www.woodworkforums.com/f8/identifying-lathe-177954/

[pjt]

I'm not sure I understand your explanation (109/109??) and I assume that is diameters of pulley you have listed, I don't get those speeds???, anyway here is what I have taken from what you have described, the dots represent the belts, the 47 to 115 doesn't change but the other does.
302694

Basically at 10hz use the 45/119 ratio will give you 50rpm, (a tad less in reality) and at 100hz use 119/45 which will give you 3000rpm
If you want more explanation feel free, or if I haven't understood your explanation.



Pete

[BobL]

motor rpm = 1440
motor pulley block from end of shaft = 109/109 to be resized from final calculation
the old motor's pulley block from end of shaft was 45/69/93/119 giving final speeds of 280/600/1090/2240
jack shaft pulley block = 119/93/69/45
jack shaft pulley = 47
headstock shaft pulley = 115


OK let me get this straight

motor pulley block of 45/69/93/119 mm is paired via a movable belt to the jack pulley pulley of 119/93/69/45 mm?

At the end of the jack pulley block there is a 45 mm pulley with a fixed belt connecting to a 115 pulley on the headstock?

if this is the case at the motor is at 1440 RPM the the jack pulley shaft RPMs at the 4 different belt positions are

45/119 * 1440 = 544 RPM
69/93 *1440 = 1068 RPM
93/69 *1440 = 1940 RPM
119/45 *1440 = 3080 RPM

Then the 47 mm jack pulley connected via a fixed belt to the 115 mm Head stock pulley will reduce those RPMs by 47/115

Final RPMs should then be 222, 436, 793 and 1156 RPM - and apart from the first one, these do not agree with your final values.
Can you please check the measurements of the pulleys


The motor is going to be run via a VFD from 10 hertz to 100 hertz.
Unless the motor is specifically designed for it I would not run a standard 50Hz mootor on a lathe at 10Hz as the motor may not get enough internal cooling. It's OK for something like a drill press where the motor operates for only short periods but not for a lathe where it could sit at that speed for many minutes. I would recommend 20 Hz as a lower end operational point for a standard 50Hz motor.


I am hoping to get a final speed range from about 50rpm to as near as 3000rpm.
You won't get that on a single pair of pulleys as you are asking for a 60:1 (3000/50) ratio of RPMs whereas using a VFD on a standard motor will only do ~5:1 (i.e. 100 - 20 Hz)

If my final RPMs are correct and you did nothing to the pulleys and used a VFD with a 5:1 Hz range you would have the following ranges

on lowest range pulley 89 - 445
Next one would be 175 - 873
Next 317 - 1586
Top pulley 622 - 3112

That's pretty reasonable in my book for a lathe.

[fozz]

Pete, Bob,

The speeds I have were written on the front of the lathe when I bought, as to how accurate they are I have no idea. Now as to the figures you have both worked out, the new motors pulley block is 109 on each pulley. My friend who is setting this up for me has suggested that because the motors shaft is 28mm and pulleys for that size are like hens teeth the idea was to reduce the 109 down to two seperate values to give two different ranges of speed.

Hell my head hurts :)

Hope thats clearer,

Ross.

[Mobyturns]

Single Belt Transmission - one driving and one driven pulley
from Pulley Diameters and Speeds (http://www.engineeringtoolbox.com/pulley-diameters-speeds-d_1620.html)

For a system with two shafts and two pulleys - as indicated with pulley 1 and 2 in the figure above:

d1 n1= d2 n2 (1)

where

d1 = driving pulley diameter (inch, mm)

n1 = revolutions of driving pulley (rpm - rounds per minute)

d2 = driven pulley diameter (inch, mm)

n2 = revolutions of driven pulley (rpm - rounds per minute)

Equation (1) can be transformed to express the

Revolution of Driven Pulley n2 = d1 * n1 / d2 (2)

Revolution of Driver Pulley n1 = d2 * n2 / d1 (3)

Diameter of Driven Pulley d2 = d1 * n1 / n2 (4)

Diameter of Driver Pulley d1 = d2 * n2 / n1 (5)

Multiple Belt Transmission Systems


For a system a with three shafts and four pulleys - as indicated in the figure above:

n2 = n3 (6)

n4 = n1 (d1 d3) / (d2 d4) (7)



In your case using the pulley diameters given the speeds calculate as


<tbody>
input rpm

Motor out

jackshaft in

jackshaft rpm in

jackshaft rpm out

jackshaft out

headstock in

headstock rpm

multiplier



n1

d1

d2

n2=n1 x d1 / d2

n2=n3

d3

d4

n4=n3 x d3/d4





1440

45

119

545

545

47

115

223

0.154549



1440

69

93

1068

1068

47

115

437

0.303226



1440

93

69

1941

1941

47

115

793

0.550851



1440

119

45

3808

3808

47

115

1556

1.080773


</tbody>


I have a feeling that you have given outer diameter of the pulley & not the driven diameter which would account to the difference in speeds you quote to calculated.

To calculate the VFD final output speeds
From VFDs How Do I Calculate RPM For Three Phase Induction Motors? | Precision Electric, Inc. (http://www.precision-elec.com/faq-vfd-how-do-i-calculate-rpm-for-three-phase-induction-motors/)

AC Three Phase Induction Motor <st1:stockticker>RPM</st1:stockticker> is determined by the formula:
<st1:stockticker>RPM</st1:stockticker> = (120 * Frequency) / # of poles in the motor
Since the number of poles of a three phase induction motor is established when it is manufactured, the only way to change the speed of the motor is to change the Frequency.


If you keep the original pulley set the final drive to output motor pulley multiplier will be the same, however the motor output speed now varies

The VFD is 10 to 100hz with standard at 50hz so the speeds above will need to be recalculated for the variable frequency assuming similar 4 pole motor speed of 1500rpm. The quoted motor speed of 1440 rpm accounts for slip & losses etc its theoretical speed is 1500rpm, which accounts for the speed differences at orig & 50hz in the table below.



<tbody>
VFD FREQUENCY

vfd motor output

pulley 1

pulley 2

pulley 3

pulley 4



ORIG


223

437

793

1556



multiplier


0.154

0.303

0.550

1.081



10

300

46

91

165

324



20

600

92

182

330

649



30

900

139

273

495

973



40

1200

185

364

660

1297



50

1500

231

455

825

1622



60

1800

277

545

990

1946



70

2100

323

636

1155

2270



80

2400

370

727

1320

2594



90

2700

416

818

1485

2919



100

3000

462

909

1650

3243


</tbody>

Simplified but gives figures near enough for your purposes.

[pjt]

Ahh so you have a twin groove pulley of 109 diameter which is going on the motor and then onto the jack shaft pulley block as per normal, and your thinking is to turn down the "spare" groove to a smaller dia and you want to know what diameter that is, doing this you lose two grooves which you had on the original motor pulley thus loosing a range of speeds.
Is it possible to get the original bored out to 28 + keyway to suit the new motor, at a guess there might not be enough meat left in the pulley for the 45 end of the pulley block



Pete

[fozz]

Yeah, Pete, if we bored the original pulley out there'd be nothing left of it. I do lose two ranges but my hope is that with whats left I can overlap, hopefully :) My friend has suggested we turn one of the 109's down as far as possible we should be able to get the needed range.

[BobL]

Pete, Bob,
The speeds I have were written on the front of the lathe when I bought, as to how accurate they are I have no idea. Now as to the figures you have both worked out, the new motors pulley block is 109 on each pulley. My friend who is setting this up for me has suggested that because the motors shaft is 28mm and pulleys for that size are like hens teeth the idea was to reduce the 109 down to two seperate values to give two different ranges of speed.


OK so you can't go bigger than 109 on the motor so that fixes one parameter.

Then you can't use anything other than 2 side by side pulleys on the jack shaft pulley block lets start with the smallest pulley in that set and see what gives you in terms of max RPM when connected to the 45 jack pulley

at 100Hz I get 109/45 *1440 * 47/115 * 100/50 = 2850 RPM - you can't get anymore that that but it might be enough for you
Lowest speed at 20 Hz is 570 RPM, half that (285) at 10Hz


If the second motor 109 mm pulley alongside the other one is now connected to the 69 mm pulley (alongside 45 mm pulley on jack shaft pulley block used in the previous calculation) it won't produce a low enough speed so as you say the second motor 109 pull needs to be turned down.

The smallest you could probably turn the second 109 motor pulley down to will be something like 45 mm (actually that is really pushing it on a 28 mm bore but lets see how it goes) but the lowest speed that will generate at 20Hz is:

45/119 *1440 *47/115 *20/50 = 153 RPM, and half that again if you go to 10Hz which might work for you.
Highest speed at 100 Hz is 445 RPM so the two pulleys will not overlap if you restrict to 20Hz for the faster pulley.

To get 50 RPM at 20Hz the motor pulley needs to be 15 mm i.e. smaller than your shaft so it aint going to happen.
You can of course use move to larger pairs of pulleys on the jack shaft pulley block but that will then reduce your top speed.

A two pulley system will be a PITA because even at 10Hz you only have an overlap of 285 - 445 which is not enough.
You really will need something that will generate a useful range like 250 to 1250 RPM and not be constantly changing belts to move between these two RPMs.

I have a 6 pulley system on my small lathe and my overlaps (20 to 100Hz) are
144 - 792
269 - 1340 - this is the one I most commonly use - in fact I rarely move my belt to any other range.
408 - 2040
604 - 3020
892 - 4460
1300 - 6500
Of course I do not use the high frequency ends of the top two ranges.

[fozz]

This is why I do like this forum, you guys are brilliant!!!! Now I understand how the figures work enough to make valued decisions so thanks all of you.

[pjt]

Moby has done a nice chart which is instructive, it shows that apart from the slowest speeds you will have a good range of speeds, if the 109 goes on all those speeds will be a little slower, so you could go from 109 to 45 and have a high range of speeds or from 109 to 69 which will be a slower set of speeds and the same for the other jack shaft diameters, assuming you can position the 109 to line up with any of the jack shaft grooves.

I take it that the jack shaft is fixed, i.e no adjustment but the motor is on an adjustable bracket that allows for belt changes, I'm thinking two possibilities, leave the 109 as is but just swap from the 45 to the 69 for two higher ranges of speeds but there has to be enough motor mount bracket travel to accomadate this, to get a bigger change in speed range turn down the 109 as your thinking, at this point I would be determining the center distances between jack shaft and motor, measure at the maximum travel and the minimum travel, from this we can determine belt length and a possible size to turn the spare 109 groove down to.



Pete

[BobL]

This is why I do like this forum, you guys are brilliant!!!! Now I understand how the figures work enough to make valued decisions so thanks all of you.

It's great when the penny drops. Just keep playing around and eventually "CA-CHING!"

This is why free play (a nasty word amongst modern educators) is so effing valuable and a useful way to learn.

[fozz]

Pete, Moby's explaination was indeed instructive but reading it made my head start to hurt again. Both the numbers and working that you and Bob did I found easier to understand and then work on. As you guys are typing I'm also nutting this out with my friend on skype and we've worked out that because the 109 pulley block is so wide, i.e, nearly as wide as the old 4 pulley block we should be able to have the belt use all 4 of the jack shafts pulleys, thats the theory anyways. Means the belt probably wont track exactly straight, probably shorten its life somewhat and yes there is still the matter of belt length and motor swing to work out, hhhhhhmmmm, anyone wanna buy a used lathe......just joking :)

I'll get out into the shed tomorrow and take some more measurements re longest and shortest distances.

[Sam-Q]

Unless the motor is specifically designed for it I would not run a standard 50Hz mootor on a lathe at 10Hz as the motor may not get enough internal cooling. It's OK for something like a drill press where the motor operates for only short periods but not for a lathe where it could sit at that speed for many minutes. I would recommend 20 Hz as a lower end operational point for a standard 50Hz motor.



I am the friend whose helping to set all of this up. I purposefully chose an oversize motor to help offset the heat issue. I happen to find a cheap 4kw (5.4Hp) model with an aluminium housing. This will still be run only off a 2.2kw drive so it will be powered to only about half of it's rating. What I am hoping is that due it being de-rated in it's use and the housing being an excellent heat conductor that the motor may be able to keep it's heat to a manageable level even without any decent airflow through it at all. We will do some load testing to determine the minimum speeds while keeping a close eye on how it's reacting.

[fozz]

Pete, Bob, Moby, meet my friend Sam, you 4 should get along nicely. I might just sit back now, have a drink and smoke and watch you guys get my lathe working :)

[pjt]

Pete, Moby's explaination was indeed instructive but reading it made my head start to hurt again. Both the numbers and working that you and Bob did I found easier to understand and then work on. As you guys are typing I'm also nutting this out with my friend on skype and we've worked out that because the 109 pulley block is so wide, i.e, nearly as wide as the old 4 pulley block we should be able to have the belt use all 4 of the jack shafts pulleys, thats the theory anyways. Means the belt probably wont track exactly straight, probably shorten its life somewhat and yes there is still the matter of belt length and motor swing to work out, hhhhhhmmmm, anyone wanna buy a used lathe......just joking :)

I'll get out into the shed tomorrow and take some more measurements re longest and shortest distances.

You can get away with some misalignment but a belt width over a short distance is not good, Are you sure the 109 is the same section as the existing? Sounds a bit odd for it to be nearly as wide as the old pulley block.
Another idea, a bit of engineering reqd and that is the motor mount bracket could be made to locate in two discrete positions, (sideways) position A picks up 45 and 69, position B picks up 93 and 119.


Pete


PS a small computer fan might be a good idea to provide some cooling if the motor is looking like getting too hot.

[Mobyturns]

Pete, Bob, Moby, meet my friend Sam, you 4 should get along nicely. I might just sit back now, have a drink and smoke and watch you guys get my lathe working :)

You can lead a horse to water but at some point in time it must drink! :D

[fozz]

Moby, I can comfortably drink now but up until I started this thread I felt like I was going down for the third time never to be seen again.

[BobL]

Another idea, a bit of engineering reqd and that is the motor mount bracket could be made to locate in two discrete positions, (sideways) position A picks up 45 and 69, position B picks up 93 and 119.

:2tsup:



a small computer fan might be a good idea to provide some cooling if the motor is looking like getting too hot.
Good idea but instead of a 12V I wound go with a 240V jobbie.
Something like this Altronics - F1028 120mm 240VAC Sleeve Bearing Slimline Fan (http://www.altronics.com.au/index.asp?area=item&id=F1028) or the ball bearing version like this Altronics - F1130 120mm 240VAC Ball Bearing Fan (http://www.altronics.com.au/index.asp?area=item&id=F1130)
They are pretty rugged and plug straight into the mains so there is no mucking around with getting 12V.

[fozz]

As to a fan, great idea and I think it will be an Altronic 240v one as they wont break the bank and they are just down the road from me.

[BobL]

Tip, It's a good idea to locate a 240V switch somewhere between the mains and the VFD and I would wire the fan to the switched side of that switch.
This switch can also be the emergency switch but is can also be a separate switch

Since the VFD is used to switch the motor on-off, wiring the fan to the above mentioned switch means the fan is on even when the motor is not running.
So when you have been running for a while and the motor heats up, just stopping the motor will still leave the fan running.

When I installed my first VFD I housed it inside an enclosure made from a plastic power tool box and because I was worried about the VFD heating up inside the enclosure I added a fan to the enclosure in the same manner as mentioned above. My other VFDs are not inside enclosures.

[hughie]

Tip, It's a good idea to locate a 240V switch somewhere between the mains and the VFD and I would wire the fan to the switched side of that switch.
This switch can also be the emergency switch but is can also be a separate switch

Since the VFD is used to switch the motor on-off, wiring the fan to the above mentioned switch means the fan is on even when the motor is not running.
So when you have been running for a while and the motor heats up, just stopping the motor will still leave the fan running.

When I installed my first VFD I housed it inside an enclosure made from a plastic power tool box and because I was worried about the VFD heating up inside the enclosure I added a fan to the enclosure in the same manner as mentioned above. My other VFDs are not inside enclosures.

In my case with VFD's and low rpm on my motors I replaced the fan on the rear of the motor with a 120mm 240 volt fan that runs as long as the power to the VFD is on. Also I use a three pulley system on one lathe that tends to have the motor speed up where the fan can still do its job.

[BobL]

In my case with VFD's and low rpm on my motors I replaced the fan on the rear of the motor with a 120mm 240 volt fan that runs as long as the power to the VFD is on. Also I use a three pulley system on one lathe that tends to have the motor speed up where the fan can still do its job.

What's the lowest frequency you operate continuously at Hughie?

On a related matter I wonder how much better Al bodied motors are at transferring heat than cast iron or steel motors?

[hughie]

What's the lowest frequency you operate continuously at Hughie?

On a related matter I wonder how much better Al bodied motors are at transferring heat than cast iron or steel motors?

Never really checked as I have a remote on a magnet up on the lathe bed. My Lenze had detachable key pad and with out it no reading was available. Now I'm in the process of fitting a Chinese one. But lifes busy so its still sitting in the box waiting for me.
I try and get my mechanical speeds low as possible so as to not have to bring the frequency down low. I like to keep it as high or as close to 50hz as possible as in the past the motor was 1 hp and the loss greatly effected the torque. Currently I'm going to 1.8kw motor on the big lathe. The three pulley lathe is now strictly mechanical as its not meant to be the main lathe.

Ali bodies should transfer heat quicker than cast iron other wise heat-sinks would be made out of cast iron etc. I have fiddled around with over clocking etc in another life and made my own heat-sinks. Some designed from scratch all were either Ali or combination of Ali and Copper etc.

[BobL]

Never really checked as I have a remote on a magnet up on the lathe bed. My Lenze had detachable key pad and with out it no reading was available. Now I'm in the process of fitting a Chinese one. But lifes busy so its still sitting in the box waiting for me.
I try and get my mechanical speeds low as possible so as to not have to bring the frequency down low. I like to keep it as high or as close to 50hz as possible as in the past the motor was 1 hp and the loss greatly effected the torque. Currently I'm going to 1.8kw motor on the big lathe. The three pulley lathe is now strictly mechanical as its not meant to be the main lathe.

Ali bodies should transfer heat quicker than cast iron other wise heat-sinks would be made out of cast iron etc. I have fiddled around with over clocking etc in another life and made my own heat-sinks. Some designed from scratch all were either Ali or combination of Ali and Copper etc.

Thanks for that.

I'm quite comfortable running my 1HP ww lathe from 25 to 100Hz with occasional use at 20Hz. My MW lathe had a 1/2HP cast iron motor and a max frequency of 70 Hz but now that it has a 1HP ally motor I'm thinking of upping that to 100Hz. These are only 1440 RPM motors so double frequency only puts them at 2 pole motor speed so the bearings should cope easily enough. My 1.5HP DP setup gets used between 20 and Hz 100 with occasional short period (10sec) use as low as 10 and up to 120 Hz. So far so good.

[fozz]

So Bob, it appears from what you are saying that as you go up in horse power things get better/easier on the motor. If thats the case and I'm understanding correctly, my 4kw motor connected to the 2.2kw VFD should work really well regarding bearings and such ?

Sounds to me that my set up will hardly ever over tax the motor.

Hope to read your thoughts on this.

Ross.

[BobL]

So Bob, it appears from what you are saying that as you go up in horse power things get better/easier on the motor. If thats the case and I'm understanding correctly, my 4kw motor connected to the 2.2kw VFD should work really well regarding bearings and such ?

As you go up in available motor power, for a given task or load, things do indeed get easier on the motor but your statement about running a 4kW motor on a 2.2kW VFD is not correct and may let the smoke out of the VFD

The thing I was referring to was the just the temperature generated in the bearings which relates to the speed of the motor and that relates to the frequency of the VFD.
Motor cooling is also required for the general heating in the coils which relates to the current draw which relates to applied load and speed.

All 3 of my installed VFDs are 1.5kW VFDs connected to less than 1.5kW motors.
Although sparkies will tell you to get the VFD power rating to match the motor I reckon using a VFD being rated higher than the motor is good thing.

Electric power output of motors are not fixed parameters but vary with the load and the speed.
Increasing the speed of the motor by about 50% ~doubles the power draw of the motor and the motor will get correspondingly hotter.
If the motor is already under a load and doing a speed that requires the power already close to the limit of the VFD then just bumping up the frequency can easily drive up the speed so that draws a current above the current damage limit.
This is why monitoring the current output of a VFD is a good idea when heavy loads are applied and speeds are increased - most VFDs have this capability but not many allow you to do that simultaneously.
I have an extension cord with a ammeter and voltmeter built into it. When I first install a VFD I leave that cord in line with the machine so I can monitor current on the meter simultaneously with the frequency on the VFD.
It is most interesting to see what does what.
I can post some numbers if you like?

A quality VFD will cope with a certain amount of current above its rating and if it goes above this will trip out and prevent this happening but that should be for an emergency operation and not a routine modus operand

There may well be a way to program current limit a motor into VFD rated lower than the nominal motor rating but I would not advocate that.

[Sam-Q]

It was my understanding that all VFD's have a built in over current limit to protect themself. I have tripped mine a few times when I managed to stall them.

Now why would the current double when the speed does?

[BobL]

It was my understanding that all VFD's have a built in over current limit to protect themself. I have tripped mine a few times when I managed to stall them.
Few times is fine, but doing that repeated (especially on a cheap one) is not really the way they should routinely be used.


Now why would the current double when the speed does?
Same as when you use the accelerator on a motor vehicle, more energy is needed to make anything go faster.

Kintetic Energy is proportional to the square of the speed (KE = 1/2 m x v2) double the speed requires 4 time more energy

[Sam-Q]

I am a bit confused here, the kinetic energy is the total amount of energy from it being in motion. Isn't this formula only valid for when it spins up and down then? Newtons first law of motion. So therefore the only extra current going through the motor if the speed is constant is from the extra bearing drag and the higher flow of the fan?

[BobL]

I am a bit confused here, the kinetic energy is the total amount of energy from it being in motion. Isn't this formula only valid for when it spins up and down then? Newtons first law of motion. So therefore the only extra current going through the motor if the speed is constant is from the extra bearing drag and the higher flow of the fan?

What you say is correct.
What I said was very much a simplification of what happens.

The frictional forces involved are not constant and generally increase non-linearly with speed. Most motors use a fan, the frictional load for which varies as much as with the cube of the speed, plus there's some funny business going inside the magnetic fields when the motor is driven at speeds outside (usually above) it's design limits. There is some technical detail supplied in the VFD entry on Wikipedia that describes some of this stuff and makes for interesting reading if you are that way inclined.

The frictional forces are usually secondary to final power requirements which depend very much on the types of loads applied to motors.
One example they give on Wikipedia is for a centrifugal pump which on a 30% reduction in speed requires 4 times less power.
Folks with VFDs on their dust extractors will have some idea of the serious increased in currents a motor connected to an impeller will draw on just going from 50 to 60Hz.

[artme]

It's great when the penny drops. Just keep playing around and eventually "CA-CHING!"

This is why free play (a nasty word amongst modern educators) is so effing valuable and a useful way to learn.

Oh so true Bob!!:2tsup::2tsup::2tsup: