Gantry design advice please

[irving2008]

I was thinking about powering the gantry and the rest of the machine via rack and pinion. The rack will be mounted on the top of the gantry. So from the verticle Ali plate will be a piece of Ali coming off at 90 degrees, to accommodate the motor and possible rack and pinion drive. I will attach a picture of the gantry as it is now.... Please note that the machine is still in raw state simply until I get her performing how I would like her to. Also the 25mm X axis is also temp so I can cut parts as I need them to upgrade

The main issues with rack and pinion, tho it can be done, are backlash and acceleration. Getting an accurate mating across the length is tricky. Also high accelerations and high resolutions are difficult because there is limited mechanical advantage. The following calculations show its possible however...

Thinking about traverse speed and acceleration, lets say you want 1.5m/s2 acceleration and your gantry weighs in at 25kg. F = ma = 25 * 1.5 = 37.5N. with a motor each side you need 18.75N from each. Lets assume you want to use a 50mm pd (25mm radius) gear then torque required = 18.75 * .025 = 0.46Nm. A 50mm pd gear gives 50 * pi = 157mm traverse per rev, a resolution of 157/200 = 0.785mm, So you'll probably want to 1/8 step it for 0.1mm resolution (guessing wood only). Now check the inertia of that 50mm gearwheel, its about 1.875e-5Nm2 together with the motor inertia of 8.4e-5 is 1.02e-4Nm2. Angular acceleration at 1.5m/s2 = 1.5/.157 * 2pi = 60rad/s2, so at the motor you'll need another 1.02e-4 * 60 = 0.01Nm of torque adding 20% or so for losses, etc. Microstepping 1/8 step means the motor only gives 20% of stall torque approx which means a motor torque of (.46+.01)/.2 = 2.35Nm at the required traverse speed

OK, so we are geared at 1:1 from stepper to drive gear. 1 rev of drive gear = 157mm = 1 rev of stepper, so for a traverse speed of 6m/min... stepper revs = 6000/157 = 38rpm. At 38rpm a 3Nm stepper should get close to that 2.35Nm but it could be marginal, so I'd advise a smaller drive gear, say 40mm and 1/8 stepping requires 2Nm @ 48rpm which is safer and gives a resolution of 0.078mm/step. You could even go down to a 30mm gear, but the smaller you go the less teeth in contact so backlash and other issues arise...

Other considerations: with a 50mm or smller gear, the physicality of mounting the driver stepper gets harder, there's not a lot of room to play and the stepper needs to be outboard of the rack, making it very bulky width wise. As an alternative consider direct belt drive. Stepper remains static at one end of the bed and drives a belt thats fixed to the gantry. With a larger double ended stepper you can drive belts on both sides with an additional coupler and axle off the back of the stepper, or drive a common intermediate axle which drives the belt on both sides.