Are the two different masses of the XCarriage and whole Y+X gantries for the other mass a real issue?

Hi guys, i've heard that with corexy the two different masses that have to be moved, XCarriage in X direction and whole Y+X gantries for Y direction could be an issue. Is that true? I can't seem to be able to wrap my head around it. Each motor in corexy, when moving, will move both masses so there is no differentiation in torque needed or anything else. I could be wrong though so I want some feedback from community here. Thanks.

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Worst case is when you're making 45/135 degree lines - only one motor is turning and must move both X and Y axes. As long as each motor has adequate torque to move both masses with the speed, acceleration, jerk, and precision you want, it will work fine. The X and Y axis performance will necessarily be different because you're using one set of motors to move the axes. The Y axis is higher mass than the X axis, so the Y axis performance will always be worse than the X axis performance. The 45/135 degree performance will define the limits of the machine- moving mass is highest and torque to move it (supplied entirely by one motor) is lowest.

The typical i-type printer uses identical motors in the X and Y axes even though the Y axis is much more massive than the X axis. In such machines the Y axis defines the performance limits of the machine. Unlike coreXY, it is possible to select different motor/driver/power supply to bring the Y axis performance in line with the X axis performance.

With any printer, the print quality suffers if you try to push the machine beyond its limits. Limits are not just defined by the motor/electronic performance but also by the structural performance. It doesn't matter if your motors can run at 300 mm/sec and start and stop motion within 1 um if bearings have play, the machine's frame shakes all over, and/or the guide rails flex and wobble.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Thanks D_D, this is one aspect of corexy design that I haven't considered until now and it is quite a surprise to me that it wasn't obvious from the start.

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One thought, with corexy would it be possible somehow to balance the two axes by assigning different accellerations, etc so that the performance of the Y gets closer to the one of X? Just a thought...

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I could be wrong, but if X and Y don't accelerate the same, trying to move in a straight line (or to follow any other line) could be a problem.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Quote
the_digital_dentist
Worst case is when you're making 45/135 degree lines - only one motor is turning and must move both X and Y axes. As long as each motor has adequate torque to move both masses with the speed, acceleration, jerk, and precision you want, it will work fine. The X and Y axis performance will necessarily be different because you're using one set of motors to move the axes. The Y axis is higher mass than the X axis, so the Y axis performance will always be worse than the X axis performance. The 45/135 degree performance will define the limits of the machine- moving mass is highest and torque to move it (supplied entirely by one motor) is lowest.

I'm confused (not hard), on my D-Bot variant, the diagonal moves require the same power for each motor.
With X motor still, the hot end moves from front right to rear left.
With the Y motor still the hot end moves from front left to rear right.

Also moving left to right or front to back also requires both motors to move, either the same direction or contra directions.

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Quote
realthor
One thought, with corexy would it be possible somehow to balance the two axes by assigning different accellerations, etc so that the performance of the Y gets closer to the one of X? Just a thought...

Do you mean because the y axis is heavier than the x axis? This is probably only true for a square corexy, mine is rectangular longer in x, so whilst I haven't weighed them I suspect my x axis has similar mass to my two y axes.

I think so long as your motors are not massively dissimilar, preferably the same motors (I don't know of a firmware that allows for different accel/jerk for x and y motors configured as corexy they are intrinsically linked in the firmware like on a delta) or one axis binds a lot, its more a theoretical problem than a real world one.

Edited 1 time(s). Last edit at 01/04/2017 02:45PM by DjDemonD.

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Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

In a CoreXY machine, there is one X axis and one Y axis, and there is no X motor or Y motor - neither of the motors moves just X or just Y. There are A and B motors (which you plug into the X and Y motor ports on your controller board).

The X axis is a part of the Y axis. When you move the extruder in the Y direction, you're moving the entire X axis with it. That's why the Y axis is always more massive than the X axis. When you move the extruder in the X direction, all you're moving is the extruder carriage. It doesn't matter whether the mechanism is square or rectangular.

If you can move the extruder in Y without moving the X axis, you don't have a corexy mechanism.

I'm assuming you define X and Y in the conventional sense, with X moving left - right and Y moving toward - away from you when facing the mechanism. If you define the axes the opposite way, just swap X and Y in the above statements.

45 or 135 degree movement will set the machine's speed limit because only one motor must supply all the torque to move both X and Y axes. When that motor runs out of torque, you've hit the maximum speed that you can use to print. For any other motion, both motors are contributing to the movement, so more torque is available. You can print extra fast if all the motion runs parallel to the X and Y axes because you have 2x as much torque available compared to printing at 45 or 135 degrees.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

That's a fair point about the difference between square and rectangular.

In an attempt to address Realthor's quite reasonable question (if you haven't built or used a corexy) about whether you need to balance the two motors perhaps a better answer is no, as they are inherently linked like on a delta, except there are two motors not three. As long as they both move the required distance with the required torque then the mechanism works. It's easiest to use identical motors to eliminate a possible source of problems, but no firmware allows for corexy operation with different movement settings for A and B motors.

Edited 1 time(s). Last edit at 01/07/2017 06:38AM by DjDemonD.

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Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

Quote
DjDemonD
... but no firmware allows for corexy operation with different movement settings for A and B motors.

Actually, RepRapFirmware does. But you shouldn't need to use that facility with a conventional CoreXY build

Edited 1 time(s). Last edit at 01/07/2017 12:30PM by dc42.

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I don't agree in a CoreXY at 45/135 only one motor is working.
Yes, only 1 is rotating. However there is equilibrium. One motor spins while the other brakes, or in other words, one accelerates while the other decelerates. The torques are still added, and neither is zero.

Do agree is that the X-carriage mass is less than the Y-gantry with a X-carriage, so therefore will their accelerations.

CoreXY equations for movement:

dX = ( dA+dB )/2, dY = ( dA-dB )/2

dA = dX+dY, dB = dX-dY

However, the above is for the kinematics, not dynamics.
Given the following (using Hlidskjalf as reference build):

X-Carriage = .30 kg
Y-Gantry = 2.20 kg
Torque per stepper = .54 N-m (.54 kg-m²/s² )
Vi = 0, initial velocity
Vf = .10 m/s, final velocity (100 mm/sec)

12.73mm = pitch diameter of 20T GT2 pulley (40mm/rev)
@ 8.78 kg-m/s² ea. Stepper

25.46mm = pitch diameter of 40T GT2 pulley (80mm/rev)
2:1 @ 17.56 kg-m/s²

Equations for motion dynamics:

F=ma
Vf = at + Vi

Conditions for CoreXY:

1, accelerating X carriage only.

F=ma
17.56 kg-m/s² = .30kg(a)
a = 58.53 m/s²

Vf = at + Vi
.10 m/s = 58.53 m/s² (t) + 0
= .002 seconds

2, accelerating Y with X carriage stationary.

F=ma
17.56 kg-m/s² = 2.50 kg(a)
a = 7.02 m/s²

Vf = at + Vi
.10 m/s = 7.02 m/s² (t) + 0
= .014 seconds

3, accelerating in X and in Y.

F=ma
17.56 kg-m/s² = 2.80 kg(a)
a = 6.27 m/s²

Vf = at + Vi
.10 m/s = 7.02 m/s² (t) + 0
= .016 seconds

Obviously, even without the math, it takes longer to accelerate more mass. Eight times longer in this case, with the heavy gantry. Most CoreXY builds won't be so bad.

Now for something completely different...
Hlidskjalf uses 4 motors to drive two X-carriages.

Conditions for CoreXYU:

1, accelerating one X-carriage only, Y stationary.
F=ma
17.56 kg-m/s² = .30kg(a)
a = 58.53 m/s²

Vf = at + Vi
.10 m/s = 58.53 m/s² (t) + 0
= .002 seconds

2, accelerating Y-gantry with both X-carriages stationary.

F=ma
35.12 kg-m/s² = 2.80 kg(a)
a = 12.54 m/s²

Vf = at + Vi
.10 m/s = 12.54 m/s² (t) + 0
= .008 seconds

2, accelerating Y-gantry and one X-carriage in X.

F=ma
35.12 kg-m/s² = 3.10 kg(a)
a = 11.33 m/s²

Vf = at + Vi
.10 m/s = 11.33 m/s² (t) + 0
= .009 seconds

By adding a second X-carriage, acceleration dropped from .016 to .009 seconds when accelerating in both axis to 100 mm/sec each.

4, accelerating Y-gantry and both X-carriages in synch.

F=ma
35.12 kg-m/s² = 3.40 kg(a)
a = 10.33 m/s²

Vf = at + Vi
.10 m/s = 10.33 m/s² (t) + 0
= .010 seconds

Moving both X carriages, rather than only one only differs by .001 seconds for acceleration.

Edited 1 time(s). Last edit at 01/14/2017 07:52PM by prot0typ1cal.

When I manually move one motor in my coreXY mechanism, the detent torque of the other motor (and friction) is sufficient to prevent it from turning. The second motor is not contributing to the motion whether it is powered or not.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Quote
the_digital_dentist
When I manually move one motor in my coreXY mechanism, the detent torque of the other motor (and friction) is sufficient to prevent it from turning. The second motor is not contributing to the motion whether it is powered or not.

The locking torque must counter act the inertial loading of the combined masses of the gantry and X-carriage moving, thereby significantly affecting both axis resulting in the 45/135 degree vector.
If that motor was allowed to turn, there would be a completely different motion, thereby absolutely contributing to the system.

Whether or not that torque aids in acceleration? Is tension through the X-carriage just wasted potential energy? Still on the fence about negative energy. It certainly can have an impact.
One test, would be to put an accelerometer on the X-carriage. If the changing magnitude measurements were greater than what a single motor could supply, that would clinch it.

On the other hand, if a 45/135 move's acceleration dropped by 50%, as suggested. That would counter the notion CoreXY was isotropic, and merely a state of fluctuating equilibrium.
In which case I'll need to make another crack at my acceleration equations (i'm sure they're flawed anyways). How much does each motor contributes to acceleration for a given vector?

Edited 1 time(s). Last edit at 01/14/2017 11:11PM by prot0typ1cal.

The non turning motor during a diagonal move has to remain stationary and powered. Whilst the detent torque might hold it, on my corexy it doesn't, if I turn one motor by hand the other will turn slightly at certain x, y positions.

I'm not a physicist so do the mathematics above suggest you need different settings for A and B motors, because practically I've never seen a corexy with anything but two identical motors, identically configured.

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Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

No, they don't need different settings. They need to be matched. The mechanism is symmetrical as far as the motors are concerned. 45 degree movement is driven by one motor, 135 degree motion is driven by the other. They are both driving the same mass. At any other angle of motion, both motors contribute more or less torque to that motion. At zero degrees they are contributing equally, and at 90 degrees they are contributing equally (that's why you have to turn both motors to make those motions).

When you move one motor by hand and the other motor turns a little it isn't because it's supposed to. It's just friction or some slight misalignment of the pulleys that are causing some drag sufficient to overcome that motor's detent torque. In operation that motor will have some current that will keep it locked in place.

There's no need to put an accelerometer on the carriage. All you have to do is look at how the mechanism works. Here's a simpler test: Remove one belt and turn the motor that remains connected. The mechanism will move at either 45 or 135 degrees. That will tell you that the second motor is not contributing anything to the motion along that line. A motor that isn't turning isn't contributing to motion, so all the torque required to move the extruder for a 45 or 135 degree motion comes entirely from one motor.

"negative energy", "fluctuating equilibrium"? Gimme a break... I think you've been studying too many youtube videos of perpetual motion/free energy scams.

Edited 3 time(s). Last edit at 01/15/2017 07:24AM by the_digital_dentist.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Quote
the_digital_dentist
"negative energy", "fluctuating equilibrium"? Gimme a break... I think you've been studying too many youtube videos of perpetual motion/free energy scams.

LOL

Based on your observations then, would the graph for "contributed motion" be a sine wave?
That is to say, there's two horizontal parallel lines, one is Motor A at 100% with B at zero, the lower line B @ 100% and A @ 0. Where the intercepts are at 45 and 135 degrees.
Load will follow the same curve, only the top and bottom lines represent a mass of the Y-gantry and X-carriage combined, while the center line is X-carriage only.

True?

I haven't the faintest idea. Maybe it's a hyperbolic tangent, or a catenary, or how about a Witch of Agnesi? I really haven't given it much thought. If I were writing the controller code to drive the motors I suppose I might, but I'm not, so I don't.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

One way to balance loads in a coreXY would be to mate it with the cross beam design of the Ultimaker.
Their kid's coyote ugly, here's the required late night sketch with twice the hardware and the ultimately unnecessary long belt runs:


Edited 2 time(s). Last edit at 01/17/2017 02:30AM by prot0typ1cal.

So which unbalanced loads in a standard corexy does the design above compensate for then? As balanced mechanisms go, my corexy (standard belt configuration on two planes rather than crossed over) is one of the most balanced I've come across.

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Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

Quote
DjDemonD
So which unbalanced loads in a standard corexy does the design above compensate for then?

Inertia...
The Ultimaker style XY carriage provides for the same mass being moved in both axis, something that most other configurations don't.
Don't be misled by the kinematic equations for CoreXY, it does not incorporate mass (variables).

Forces are balanced in a CoreXY at the out board idlers on the Y-gantry, so there's no racking. Plus, forces are balanced on the X-carriage.. The force on the Y-gantry is the same as on the X-carriage while not moving (equilibrium).
Even though the forces are equal, the acceleration once things get moving will differ by this equation:

Force = Mass x Acceleration.

When you examine the dynamics, moving the X in a CoreXY, only the mass of the X-carriage is accelerated. Low mass, high acceleration.
When accelerating only in Y in a CoreXY, both the Y-gantry and X-carriage have a higher combined mass. High mass, low acceleration.
The bad, when accelerating at a 45 or 135 degree vector, only one motor drives acceleration in a CoreXY. Since the masses are constrained in two axis, the total mass in the equation is X + Y, where X is X-carriage, and Y is Y-Gantry + X-carriage.
The really bad, momentum. While you can accelerate over time, stopping requires more force or an equal amount of time. Higher the mass, the more it will impart it's momentum on the frame during acceleration/deceleration.
Therefore, Y moves will be more violent in a coreXY, as two motors contribute to the acceleration, and 45/135 degree XY moves will be under powered.

Thing is, there's no reason to drive the Ultimaker cross with CoreXY, the motors on each axis are already remote, and don't add to the moving mass.
The CoreXY is more efficient at true X or Y only 2 motor moves (better at X with higher acceleration). the Ultimaker is more efficient at 45/135 degree moves with two motors contributing, same with H-bots or Cartesian printers.
Need to keep that in mind for infill patterns.

/rant

That makes sense, I follow your reasoning. So given that practically at normal (80mm/s or less) printing speeds this seems to have no manifestation do you only see this as a problem when at the extreme end of the mechanisms capabilities?

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Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

You can make a brick fly with enough thrust.

Every build is going to be a combination of mass, force, friction, strength and rigidity, regardless of configuration (CoreXY, Ultimaker, H-bot, Cartesian, etc)
Where those limits are will depend on those variables. It's only a problem if the design uses a bad combination.
Calculating accel/decel curves so there's no missed steps or stutter, is where you'll find the mathematical extreme ends.

You're right but you're telling mainly people who already know this.

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Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

Amen brother