Good morning
I've run into a problem that may or may not need a s curve.
I'm driving the x and y gantry with a brushless/ encoder + lead screw setup and am able to get speeds up to 1mtr/s.
The whole hotend assembly is rather hefty at 0.5 kg. At quick direction changes (corners of Infill at 45 degrees in a cube) it shakes uncomfortably much and I have to reduce to 500mm/s^2. At this acceleration it would take 1.5 seconds and approximately 500mm to get to its maximum speed.
I did some tests and when printing a corner in a radius of 75mm an acceleration of 10.000mm/S^2 even seems reasonable
My thought would be that the slower ramping up is what is causing this improvement. (as the direction turns from x to y the y gantry has to move exponentially faster)
At 10.000mm/s^2 it only takes 0.07 second and 25mm to get to its maximum.
If we interpolate between the two that gives 0.75 seconds and 262mm to obtain maximum speed. (in reality this would only be 25% quicker) this could decrease the overall print time on long complicated prints by quite a lot.
I think printers with either a high capability of speed or a heavy hotend assembly will greatly benefit from a ramping acceleration/deceleration.
I don't know if this is easier to setup than a s curve but perhaps it would be an idea to multiply the acceleration by time and by a factor in time to reach the max acceleration.
In this case we could ramp up to 10.000mm/s^2 in 1 second and it would look like this:
Acceleration = (acceleration*((t/factor) ^2))
After 0.1 seconds:
Acceleration= (10.000*((0.1/1) ^2)=100mm/s^2
After 0.5 seconds:
Acceleration=(10.000*((0.5/1) ^2)=2500mm/s^2
After 0.75 seconds:
Acceleration=(10.000*((0.75/1) ^2)=5625mm/s^2
After 1.0 seconds:
Acceleration=(10.000*((1.0/1) ^2)=10.000mm/s^2
Ramping up to 5000mm/s2 in 3 seconds:
After 1 seconds:
Acceleration= (5000*((1/3) ^2)=555mm/s^2
After 2 seconds:
Acceleration=(5000*((2/3) ^2)=2222mm/s^2
After 2.5 seconds:
Acceleration =(5000*((2.5/3)^2)=3472mm/s^2
After 3 seconds:
Acceleration=(5000*((3/3) ^2)=5000mm/s^2
Applying the same formula to the extruder would also ramp the extruder to not create under or over extrution during the ramping up.
I've never heard of issues caused by the jerk between acceleration and max speed so this may or may not be a problem.
Keeping acceleration and deceleration seperate would lead to even more tuneability as acceleration tends to be able to be a little bit higher.
Jeff