Gates, the creator of the GT2 belt, recommends a tension of 6 to 8 pounds of tension when using a 6mm GT2 belt for registration like in a printer. A NEMA 17 stepper motor can handle 6.7 pounds (30N) of radial force centered at 17mm from the motor's face (something to bear in mind if you're using dampers).
Because the belt wraps around the motor's shaft, the radial force on the stepper is double the belt tension, at the minimum of 6 pounds tension recommended by Gates, there's 12 pounds of radial force on the shaft. However, the allowed radial force increases linearly inversely proportional to the pulley center to motor's face distance. For example, if the pulley is centered at 8.5mm from the motor's face (half of 17mm), then the maximum allowed tension doubles to 13.4 pounds.
NOTE: Moon's bearing life charts indicate the radial limit can go as high as 8 pounds, though with reduced bearing life.
To actually measure the tension the easiest and most precise way is via its vibration frequency. To calculate our target frequency we use Mersenne's equation 22:
Where f is the frequency, L is the length of the belt between contact points in meters, μ is the belt density in kilograms per meter, and F is the tension in Newtons (1 pound equals 4.44822 N). The density of a 6mm GT2 belt is 0.0083 kg/m (both stock and genuine Gates).
Given this, we want a belt tension of 6 pounds with the pulley centered 9.5mm or less from the motor's face. If the pulley center is further out, then the belt must either be tensioned lower or reduced bearing life must be accepted.
NOTE: The Ender 3 pulleys are centered 10mm from the motor's face. In practice I've found tensioning the belts at 6 pounds doesn't appreciably decrease the stepper bearing life
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| From the Moons' catalog (see link below). |
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| From the Gates catalog (see link below). |
To actually measure the tension the easiest and most precise way is via its vibration frequency. To calculate our target frequency we use Mersenne's equation 22:
Simplified, for 6 pounds force with a GT2 belt, the formula is:
Hertz = 28531 / mm
On the Ender 3 specifically, with the hotend carriage against the limit switch, the belt between the carriage and idler is 0.302 meters (302mm) long, so the target frequency is 94 Hz.
On the Ender 3 specifically, with the hotend carriage against the limit switch, the belt between the carriage and idler is 0.302 meters (302mm) long, so the target frequency is 94 Hz.
NOTE: Previously this number was mistakenly changed to 86 Hz. The correct figure is 94 Hz.
Again on the Ender 3, with the bed pushed all the way back, the exposed belt is 0.253 meters (253mm) long, so the target frequency is 113 Hz.
I found the best way to measure the frequency is the Spectroid app for Android. It produces a waterfall display of the frequency, so it's easy to see what the belt frequency actually is. Pluck the belt like a guitar string and look for the biggest spike. Just tap the waterfall display and it'll give you the frequency selected. The belt will naturally have multiple harmonics, but those will be significantly smaller on the waterfall display and can be ignored. From there just adjust the belt tension until you hit the target frequency.
Again on the Ender 3, with the bed pushed all the way back, the exposed belt is 0.253 meters (253mm) long, so the target frequency is 113 Hz.
I found the best way to measure the frequency is the Spectroid app for Android. It produces a waterfall display of the frequency, so it's easy to see what the belt frequency actually is. Pluck the belt like a guitar string and look for the biggest spike. Just tap the waterfall display and it'll give you the frequency selected. The belt will naturally have multiple harmonics, but those will be significantly smaller on the waterfall display and can be ignored. From there just adjust the belt tension until you hit the target frequency.
you could also use a stroboscope app on your phone to measure frequency
ReplyDeletebrilliant
ReplyDeleteIt's a shame that you don't read anything else about it.
It is really easy.
And everyone just tries to adjust it by feeling.
https://www.wolframalpha.com/input/?i=f0+%3D+1%2F%28L*2%29+*+sqrt%28%284.44822*6%29%2F0.0083%29
ReplyDeletefast way to do the math, replace L with mentioned contact distance
"On the Ender 3 specifically, with the hotend carriage against the limit switch, the belt between the carriage and idler is 0.302 meters (302mm) long, so the target frequency is 94 Hz."
ReplyDeleteAm I missing something? Based on this example, if the Hertz is 25.8856/measurement, and the measurement is 0.302m, why is the Hertz 94? When I run that equation, I arrive at 85.713, so 86 Hz. Where did 94 come from?
I must have copied/pasted the wrong cell from my spreadsheet. Thank you for catching that. I've updated the article with the correct number.
Deletejust to confirm the correct hz for the hotend carriege is 86hz ? as it's still showing 94hz also is 112hz correct for the bed
DeleteI thought I fixed it. It's definitely fixed now though.
DeleteWhen I run the formula I arrive at 94Hz - where is that 86Hz coming from? I think it's actually the Hz/mm that's wrong.
DeleteThis is now the THIRD time I've changed 86Hz to 94Hz. I don't understand why my edits keep reverting, but it's getting really dang annoying. Hopefully this is the last time.
DeleteDear Zoltan, thank you for doing all of this work- but I think I can see the problem here. The Hz/mm listed in Anarasha's initial comment is 25.8856/m which differs from your figure of 28531/mm in the article. It seems Anarasha used the troy pound for force (3.66 N) mistakenly rather than the standard pound of force (4.45 N), which gives this incorrect figure. It seems you took Anarasha at their word and tried to change the value on June 8th, or perhaps you rechecked your math and found your value was correct and did not change it. Then come January 2022, Geeuk00 asks you if the value is correct, and you now change it and make for sure it is changed without considering checking the math- understandably frustrating, it makes sense why you'd focus on making sure it changes. Now come March 6th, you see bberger checking the math and pointing out it should be 94Hz, and your frustration of changing this value leads to you changing it back. A good lesson in trust, but verify!
DeleteThe good news is you were right in the first place! Anarasha made an easy mistake for someone not familiar with using pounds, and it led to a lot of confusion. An interesting phenomena has occurred, where this incorrect value of 86hz has spread to other communities and here we are discovering the source of this error! How fun.
Your comment didn't immediately post because I've had to moderate the comments due to the amount of spam this blog receives.
DeleteThank you for catching that! It makes me feel a lot better. However, I've actually been struggling with the blog because for some unknown reason after several days it keeps reverting back the change to 94 Hz.
Wouldn't the tension increase during operation whenever acceleration is applied? In this case, the tension of the belt at rest could be a bit lower than recommended (like 5 pounds instead of 6) to avoid overstress during operation.
ReplyDeleteObviously, this depends on the settings: with defaults of 500-1500 mm/s² for most printers there's no problem, but once you start setting 5000-15000 mm/s², tension during operation plays a role too
No.
DeleteFirst, Gates says to use 6 pounds of force, and they've already calculated those factors in. Second, it won't "overstress" during operation because while one side of the belt will see slightly increased tension, the other side of the belt will see slightly decreased tension, and the two will average out. Finally, if your printer is doing 15,000mm/s^2 you'll want to use something stronger than just a 6mm gt2 belt.
Does gates not recommend 4lbs tension, not 6-8, or am I reading that table wrong?
ReplyDeleteNote the added instruction which says multiple the value in the table by 1.5 to 2 for for registration drives (which is what a printer uses). 4 pounds time 1.5 to 2 gives the usable range of 6-8 pounds.
DeleteCould you pull the belt tensioner manually with a luggage scale to 6lb and then fix it at that position? I can't get a reliable frequency measurement since the belt hits the frame.
ReplyDeleteYes, and I've done exactly that. However, you'd want 12 pounds of tension since you're tensioning two sections of belt (top and bottom).
Deletehow does tuning with a luggage scale work?
Deletecouldn't you just pull as hard as you want and get any random value? or do you have to deflect it by X mm at 12lb to get correct tension?
You pull on the tensioner, parallel with the belt. You're not pulled perpendicularly on the belt itself.
DeleteVery interesting article. Thanks for sharing.
ReplyDeleteJust a quick question: not that it makes a huge difference in the end result, but when I plug the numbers in the formula, I don't get the same result as you.
I find Herz = 28353 per mm, not Hertz = 28531 / mm
Here are my calculations:
F = 6 pounds = 26.6893 N
mu = 0.0083 kg/m
L = 1 mm = 0.001 m
f0 = (1/2L) * sqrt(F/mu) = (1/(2*0.001)) * sqrt(26.68932/0.0083)
f0 = 28353 Hz per mm
Also, I would like to know what is your long term experience with tightening the GT2 at this tension? Any bearing or motor failure since 2019?
Thanks for your article.
A variation that small looks like a rounding difference to me.
DeleteI've had zero stepper failures and all the stepper bearings still turn smoothly by hand.
Great article! Where did you find the belt density? I have tried to doublecheck it for a 9mm belt and can't find it anywhere. Would reasonably be 6mm density *1,5 but wanted a sanity check...
ReplyDeleteI calculated it by weighing a known length of belt.
DeleteGreat article!
ReplyDeleteWould the calculation differ significatlly for a 9mm belt?
Yes, because the kilogram/meter value of the belt would change.
DeleteWhere did you find the kilogram/meter value? I'm searching for these values for 9mm and 12mm belts
ReplyDeleteI calculated it by weighing a known length of belt.
DeleteI have measured my new belts. Gates GT2 9mm and 12mm, each ~10m. See https://docs.google.com/spreadsheets/d/163FNNyaZhuiAcWyV9s1QX9_T_f7A-h2OZ4063P-52Ss/edit?usp=sharing
ReplyDeleteValues for both 9mm and 12mm agree quite good but are significantly higher than your corresponding 6mm value.
Using a "Width Factor" of 0.0146, the 6mm belt would have 0,0876 kg/m. Around 5.5% deviation
I'd guess the 9mm and 12mm belts have additional reinforcement which makes up the difference in mass. I only had 6mm belts to weigh, and all of them were very consistent.
Delete