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Rotation distance

Stepper motor drivers on Klipper require a rotation_distance parameter in each stepper config section. The rotation_distance is the amount of distance that the axis moves with one full revolution of the stepper motor. This document describes how one can configure this value.

Obtaining rotation_distance from steps_per_mm (or step_distance)

The designers of your 3d printer originally calculated steps_per_mm from a rotation distance. If you know the steps_per_mm then it is possible to use this general formula to obtain that original rotation distance:

rotation_distance = <full_steps_per_rotation> * <microsteps> / <steps_per_mm>

Or, if you have an older Klipper configuration and know the step_distance parameter you can use this formula:

rotation_distance = <full_steps_per_rotation> * <microsteps> * <step_distance>

The <full_steps_per_rotation> setting is determined from the type of stepper motor. Most stepper motors are "1.8 degree steppers" and therefore have 200 full steps per rotation (360 divided by 1.8 is 200). Some stepper motors are "0.9 degree steppers" and thus have 400 full steps per rotation. Other stepper motors are rare. If unsure, do not set full_steps_per_rotation in the config file and use 200 in the formula above.

The <microsteps> setting is determined by the stepper motor driver. Most drivers use 16 microsteps. If unsure, set microsteps: 16 in the config and use 16 in the formula above.

Almost all printers should have a whole number for rotation_distance on x, y, and z type axes. If the above formula results in a rotation_distance that is within .01 of a whole number then round the final value to that whole_number.

Calibrating rotation_distance on extruders

On an extruder, the rotation_distance is the amount of distance the filament travels for one full rotation of the stepper motor. The best way to get an accurate value for this setting is to use a "measure and trim" procedure.

First start with an initial guess for the rotation distance. This may be obtained from steps_per_mm or by inspecting the hardware.

Then use the following procedure to "measure and trim":

Make sure the extruder has filament in it, the hotend is heated to an appropriate temperature, and the printer is ready to extrude.
Use a marker to place a mark on the filament around 70mm from the intake of the extruder body. Then use a digital calipers to measure the actual distance of that mark as precisely as one can. Note this as <initial_mark_distance>.
Extrude 50mm of filament with the following command sequence: G91 followed by G1 E50 F60. Note 50mm as <requested_extrude_distance>. Wait for the extruder to finish the move (it will take about 50 seconds). It is important to use the slow extrusion rate for this test as a faster rate can cause high pressure in the extruder which will skew the results. (Do not use the "extrude button" on graphical front-ends for this test as they extrude at a fast rate.)
Use the digital calipers to measure the new distance between the extruder body and the mark on the filament. Note this as <subsequent_mark_distance>. Then calculate: actual_extrude_distance = <initial_mark_distance> - <subsequent_mark_distance>
Calculate rotation_distance as: rotation_distance = <previous_rotation_distance> * <actual_extrude_distance> / <requested_extrude_distance> Round the new rotation_distance to three decimal places.

If the actual_extrude_distance differs from requested_extrude_distance by more than about 2mm then it is a good idea to perform the steps above a second time.

Note: Do not use a "measure and trim" type of method to calibrate x, y, or z type axes. The "measure and trim" method is not accurate enough for those axes and will likely lead to a worse configuration. Instead, if needed, those axes can be determined by measuring the belts, pulleys, and lead screw hardware.

Obtaining rotation_distance by inspecting the hardware

It's possible to calculate rotation_distance with knowledge of the stepper motors and printer kinematics. This may be useful if the steps_per_mm is not known or if designing a new printer.

Belt driven axes

It is easy to calculate rotation_distance for a linear axis that uses a belt and pulley.

First determine the type of belt. Most printers use a 2mm belt pitch (that is, each tooth on the belt is 2mm apart). Then count the number of teeth on the stepper motor pulley. The rotation_distance is then calculated as:

rotation_distance = <belt_pitch> * <number_of_teeth_on_pulley>

For example, if a printer has a 2mm belt and uses a pulley with 20 teeth, then the rotation distance is 40.

Axes with a lead screw

It is easy to calculate the rotation_distance for common lead screws using the following formula:

rotation_distance = <screw_pitch> * <number_of_separate_threads>

For example, the common "T8 leadscrew" has a rotation distance of 8 (it has a pitch of 2mm and has 4 separate threads).

Older printers with "threaded rods" have only one "thread" on the lead screw and thus the rotation distance is the pitch of the screw. (The screw pitch is the distance between each groove on the screw.) So, for example, an M6 metric rod has a rotation distance of 1 and an M8 rod has a rotation distance of 1.25.

Extruder

It's possible to obtain an initial rotation distance for extruders by measuring the diameter of the "hobbed bolt" that pushes the filament and using the following formula: rotation_distance = <diameter> * 3.14

If the extruder uses gears then it will also be necessary to determine and set the gear_ratio for the extruder.

The actual rotation distance on an extruder will vary from printer to printer, because the grip of the "hobbed bolt" that engages the filament can vary. It can even vary between filament spools. After obtaining an initial rotation_distance, use the measure and trim procedure to obtain a more accurate setting.

Using a gear_ratio

Setting a gear_ratio can make it easier to configure the rotation_distance on steppers that have a gear box (or similar) attached to it. Most steppers do not have a gear box - if unsure then do not set gear_ratio in the config.

When gear_ratio is set, the rotation_distance represents the distance the axis moves with one full rotation of the final gear on the gear box. If, for example, one is using a gearbox with a "5:1" ratio, then one could calculate the rotation_distance with knowledge of the hardware and then add gear_ratio: 5:1 to the config.

For gearing implemented with belts and pulleys, it is possible to determine the gear_ratio by counting the teeth on the pulleys. For example, if a stepper with a 16 toothed pulley drives the next pulley with 80 teeth then one would use gear_ratio: 80:16. Indeed, one could open a common off the shelf "gear box" and count the teeth in it to confirm its gear ratio.

Note that sometimes a gearbox will have a slightly different gear ratio than what it is advertised as. The common BMG extruder motor gears are an example of this - they are advertised as "3:1" but actually use "50:17" gearing. (Using teeth numbers without a common denominator may improve overall gear wear as the teeth don't always mesh the same way with each revolution.) The common "5.18:1 planetary gearbox", is more accurately configured with gear_ratio: 57:11.

If several gears are used on an axis then it is possible to provide a comma separated list to gear_ratio. For example, a "5:1" gear box driving a 16 toothed to 80 toothed pulley could use gear_ratio: 5:1, 80:16.

In most cases, gear_ratio should be defined with whole numbers as common gears and pulleys have a whole number of teeth on them. However, in cases where a belt drives a pulley using friction instead of teeth, it may make sense to use a floating point number in the gear ratio (eg, gear_ratio: 107.237:16).

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