Belt Compliance Measurement
The purpose of this page is to propose a standardized, easily replicable test stand and procedure to obtain belt compliance data, otherwise known as belt stretch. This is important because the belt must first be stretched by the motor to pull the load of the head or carriage before it will start to move. This displacement is an error in the print. Currently, real performance data for the tiny belts used in 3d printers is difficult to find and this makes designing the system difficult. A standard test method could help the community generate data to fill this information gap and to compare belt suppliers, brands, and models quantitatively. The bill of materials, construction details, theory, and use are covered in this page.
The engineering of industrial mechatronic systems requires some key pieces of data. The amount of compliance (spring-back) of the belts is one such critical piece of data. During acceleration force is applied against the belts creating position error. Position error is the difference between where the motor should have moved the load and the actual position of the load. Finding belts with the minimum compliance (stretchiness) and maximum stiffness will create a system with the best positioning accuracy and most faithful reproduction of the model being printed.
Links to other information on belts
The proposed method of measuring belt compliance is to suspend a long arm from a belt and apply force by hanging weight from the arm. The movement of the arm is measured with a dial indicator. The reason for using the long arm is to keep the measuring surface located below the indicator without affecting the measurement. The tension in the belt also helps keep things centered.
- 1ea Dial Indicator (Currently Harbor Freight Tools No. 623)
- 1ea 96 inch (8ft) long 1x4 pine boards.
- 1ea Piece of plywood 3" x 3" to make knobs from
- 4ea 2 inch Drywall Screws for the clamp knobs (coarse thread flat head screws)
- 18ea 1-5/8" Drywall Screws (coarse thread flat head screws)
- 2ea 1.25" drywall screws
- 2ea pieces of 3/4" x 3/4" x 2.5" wood to make the clamp blocks
Print out the templates at 1:1 scale (life size) and use them to make the pieces for the test stand. Most print dialog boxes give the option to adjust the scale of the print to get the template exactly at 1:1. This makes building the test stand easier to build. If you can't get them to print out at 1:1, just used the drawings the old fashioned way :)
The dial indicator fits snugly into the drilled 3/8" hole in the indicator mount. A second hole (5/16) is drilled through the edge and tapped for a 3/8-16 bolt. This tapped hole has a 3/8 x 2 inch bolt threaded into it and tightens against the dial indicator stem. Snug up the bolt, but do not over-tighten as you could strip the threads out of the wood or bend the indicator stem.
The pivoting tongue board should have the indicator bolt hole drilled with a drill press so that it is as perpendicular as possible so that side-to-side movement does not change the reading much. Gravity pulling down will mostly compensate for problems here, but straighter is better.
Most bolts have some marks to indicate the grade of the bolt and the manufacturer. The bolt head of the 1/4 inch bolt should be filed flat so the indicator has a flat surface to measure from without these marks. The upper tongue pivot should be drilled while mocked up to the frame because it can be aligned to match the rest of stand after it is already constructed.
For the clamp blocks and knobs, the idea is to make the knob thread onto the screws so that any simple object a screw can be driven into can be used for a knob. A piece of broom handle or a plug cut out of a board with a hole-saw would work fine. If the stand gets a lot of use the knobs will wear out. They can be replaced with knobs that can accept a machine screw or wing nuts and machine screws if that happens someday. I used a rectangular hunk of wood for mine and that worked fine. Maybe there is a stick in the yard?
Two bags of sand or something else heavy will be needed to create a pre-load mass, and a test mass. The test mass should be created first. Ideally, this would be 1.02kg (2.25lbs). This the amount of mass that will make 10N of force in normal earth gravity. Two sandwich or quart storage bags work well for this.
Filling of the preload bag of sand is trickier. The weight of the preload bag and the weight of the tongue together should be 1kg. This isn't really critical, but only has to be done once, and if people use different amounts of preload, it could add noise to the community's measurements and that is undesirable. The end of the pivoting tongue should be placed on a scale with the weight hopper suspended below the tongue. The preload bag of sand is filled until everything on the scale reads 1.02kg.
- Take a piece of belt and mark it at 1 inch (25.4mm) and 19 inches (482.6mm) . These marks will be used to align the belt to the edge of the clamp blocks so we know exactly how much belt is being pulled on. The longer the belt under a given weight, the more it stretches, so getting this correct is important.
- Loosen the knobs on the upper clamp block so the belt being tested can be threaded through the gap between the screws. Pull through about 21" of belt so there is slack to reach the pivoting tongue board.
- Loosen the knobs on the lower clamp block to make space to slip the belt under the block. The belt should enter from the back side of the block and 1/4" should be sticking out from the front of the block (if it is a 3/4" block). Alight the 1" mark on the belt to the very inside-most edge of the clamp block and make sure the belt is centered in the clamp block. Tighten the knobs.
- Pull the top belt up until the 19" mark is aligned to the very bottom edge of the clamp block. Make sure the belt is centered between the two screws. Tighten the knobs.
- Drape the excess belt (assuming this is a roll of belt) over one side so it does not touch the pivoting tongue board.
- Put the pre-load weight into the weight hopper suspended by the strings. This tightens everything up and gets slack out of the system.
- Zero the dial indicator by loosening the lock knob on the side of the dial indicator and rotating the scale until it reads zero.
- Put an additional 1.02kg bag of sand into the weight hopper. I like to use 1.02kg of sand in a zip-lock plastic bag.
- Measure the deflection of the dial indicator. If you take the sand bag out, the needles should go back to zero displacement. If it doesn't, something slipped or the belt has broken in a little. Re-zero and try the measurement again.
- The % deflection per Newton of applied force can be calculated as
( Displacement (in)/Initial Length (in)) * ( Dbelt to pivot (in) / Ddial indicator to pivot (in)) / Applied Load(N) * 100% = %/N
Shortcut Method Calculation
See the example calculation below to understand why this works. The % elongation per Newton of applied force can be calculated by taking the elongation measured by the dial indicator (example 0.011 inches) and multiplying 0.6%/(in*N). THIS ONLY WORKS IF THE STAND IS BUILT EXACTLY PER THE DRAWINGS AND THE TEST MASS IS EXACTLY 1.02kg.
0.011 inches of displacement * 0.6%/(N*in) = 0.0067%/N applied.
I measured a 6mm wide belt on the stand.
- Initial Length = 18 inches.
- Displacement with test mass 0.011 inches.
- Test Mass 1.02kg.
- Gravity: 9.81m/s^2.
- Distance between belt and pivot: 17.8 inches
- Distance between indicator and pivot: 16.5 inches
First, convert the displacement at the indicator to the amount of displacement at the belt. We know the belt moved a little bit more than the indicator because it is further out on the lever.
D(belt to pivot)/D(indicator to pivot)*(Displacement at Indicator)
17.8/16.5 * 0.011 inches = 0.012 inches
Now, find what percentage the belt changed in length
(Displacement at the belt)/(Initial Lenght) = 0.012 inches / 18 inches * 100% = 0.067%
Now, find the number of newtons of force that were applied:
f = m * a
f = 1.02kg * 9.81mm/s^2 = 10.0N
Now, divide the % change by the amount of force applied (N)
0.067%/10N = 0.0067%/N.
FEEL FREE TO ADD YOUR BELT DATA TO THIS TABLE OR PM ME AND I WILL ADD IT.
ACTUALLY, IF YOU SEND ME 20 INCHES OF BELT, I WILL MEASURE IT AND ADD IT.
Use of the Data to Calculate Position Error
Calculate the force exerted on the belt by the mass of the axis being moved (think Y carriage in an XY gantry Prusa style machine).
This is done by the use of force = mass * acceleration.
For this example we will have a 1kg carriage being accelerated at 3000mm/s^2.
force (N) = 1kg * 3m/s^2 = 3N.
Calculate the percentage change in belt length at 3N.
Assume we have a 6mm belt that has been measured and has a modulus of 0.006%/N.
percent length change = modulus (%/N) * force (N)
0.0067 %/N * 3 N = 0.02%
Now assume that you have 1000mm of belt in a loop that drives the Y carriage.
The change in belt length (or delta between true position and the desired position) = length(mm)* % Change / 100
0.02 % * 1000mm / 100% = 0.2mm
In this example, if we assume that a typical bead of plastic is 0.5mm, we have missed the desired position by almost half of the total width of a pass of the extruder.
|1||ebay:shoptopstar||2M GATES 6mm 2GT GT2 RF Fiber Glass Reinforced Rubber Timing Belt for 3D Printer||6||0.0067%/N||Generic GT2 Belt|
|2||zyltech||Steel-Reinforced GT2 T2 Timing Belt - 6mm||6||0.0024%/N||Urethane??? GT2 Profile Steel Reinforced|