Actuated Linear Motion Axis

I ordered a cheap leadscrew assembly intended for low-cost 3D printers from Amazon. The leadscrew came with a brass flanged lead nut, a pair of ball bearings mounted in zinc blocks, and a flexible coupling that fits the NEMA 17 motor output shaft. The leadscrew has a diameter of 8 mm, a pitch of 2 mm, and 4 starts. This means it has an overall lead of 8 mm/rev.

A quick note about running leadscrews directly in bearing bores: conventional engineering wisdom states that it is a bad idea to run threaded rods in bearings because of small load-bearing area results in high stresses. This is still true for leadscrews, but the trapezoidal threadform retains the major diameter across the width of its lands, making it less problematic to run them in bearing bores compared to “standard” fastener threadforms which are triangular and taper to an acute angle.

Repeatability Testing

Actuated Linear Motion Axis Test from Shien Yang Lee on Vimeo.

I tested the repeatability of the actuated linear motion axis in two ways.

Repeatability along motion axis

First, I repeated the “straightness” test I carried out last week for the linear axis without the actuator.After running the carriage back and forth between its extreme positions 8 times, I got a group of laser projection points with the maximum spread of 15 mm at a distance of 2.9 m. This translates to a side-to-side angular error of 0.3°, which is a ~75% improvement from the 1.29° measured on the non-actuated axis. I think there are two factors contributing to this improvement.

First, the motor and leadscrew is able to repeat axial position better than I could by hand. This places the carriage closer to the same locations when each measurement is taken. This theory is supported by the observation that points measured at each position (X0 vs. X100) all lay within 5 mm of each other (angular uncertainty of <0.1°). This suggests that most of the error measured comes from global straightness and parallelism errors in the box way instead of local “wiggling” of the slider.

Second, the leadscrew provides a degree of preload to take up part of the radial clearance. I drilled the slider for the lead nut using a portable drill and did not make the hole perfectly square to the faces of the slider. This slight misalignment places the simply-supported leadscrew (I left it floating in the bearing on the non-driven side) under bending, causing it to act as a preload spring. However, as we learned in class, this is not a good preload configuration since the system’s stiffness varies according to the square of carriage’s distance from one end.

Repeatability orthogonal to motion axis

My second repeatability test was aimed at measuring the precision with which the actuator can move the carriage to a specified position. I attached my laser pointer to the carriage orthogonally, such that it projected a beam perpendicular to the direction of motion. For the adjustable standing desk, this is the sensitive direction.

I recorded the position of the projected beam across the 100 mm-long travel of the carriage on 10-mm intervals. The repeatability at each position was within 1 mm. Note that we are now measuring axial displacement instead of angular error, so using a laser pointer conferred no resolution advantage.

More interestingly, I observed the effects of backlash in this test. I moved the carriage to each position in the following sequence:

0 > 100 > 10 > 90 > 20 > 80 > 30 > 70 > 60 > 40 > 50

Each reversal in direction caused the distance traveled to be short by approximately 1 mm. This is consistent with the perceptible backlash in the low-quality lead nut.

Leave a Reply

Your email address will not be published. Required fields are marked *