Camming and Constant Velocity Countoring Question 2

[funguy123]

I have a question on how to do the following application with 2 servomotors that are being controlled from the same motion controller:

Imagine you have an elliptical shaped part rotating about an axis through it's center. This is being rotated at a constant velocity by servo #1. Then you have a welding tip mounted on a ball screw (controlled by servo #2) that must maintain a constant distance from the edge of the elliptical part. It must also mantain a constant speed in relation to the rotating elliptical part.

Since the part is elliptically shaped, as it's rotating the ballscrew is going to be moving back and forth "tracking" the outside of the ellipse as the ellipse is rotating and the major and minor axes come to the weld point.

I have created a CAM profile to do this with approximately 18 points (X,Y points I drew in CAD). The master points are 0-360 degrees, and the slave points are the min. and max distances of the ellipse edges. It is essentially looks like 2 lobes.

This is my question:

Will it compensate automatically for the velocity change due to the change of position over time of the ellipse rotating or will it not follow it properly or collide? When I say automatically, I mean as it follows the cam profile I created.

Or will I have to create an additional cam to speed up and slow down the rotating axis based on where the minor and major axis of the ellipse are in relation to the welding head for it to follow correctly and at a constant speed?

Any help would be appreciated,

Funguy

 

[MikeHalloran]

Are you actually using physical cams, or are you using theoretical cam functions within the motion controller?

No matter, really. There are at least two related problems.

1. Collision, or near collision, or variation of the arc length, caused by the slope of the elliptical weld line and the torch tip. This is pretty much a geometrical problem that you can evaluate in a CAD system, just like analyzing a cam, except for the complication of dealing with odd gas flows when the (presumed MIG) torch is not at right angles to the workpiece.

2. Welding (arc travel) speed. Keeping the rotation speed of the ellipse' axis constant will cause variations in the speed at the weld line, which will cause variations in the size and character of the weld. Better to modulate the rotational speed so that the weld speed is constant.

I could swear that commercial CNC controllers have been able to do this for decades, while following an arbitrary path, not just an ellipse. I'm sure they can do it for a weld on the end face of the ellipsoid, by leaving the workpiece immobile and translating the torch in two axes, making it follow an elliptical path, or whatever path you like. Making a radial weld on an elliptical shell does require rotation of the piece and radial translation of the torch, but I'm sure it's been done. It might require a third axis to tilt the torch to keep it normal to the surface.

Frankly, it sounds like you are home- brewing a solution to a problem that someone else surely solved long ago. If you are doing it as a learning exercise, have fun. If you are doing it for money, it will be cheaper to buy whatever someone else learned by doing.



Mike Halloran
Pembroke Pines, FL, USA

 

[zekeman]

If you are talking about an elliptical contour, then the solution to your problem is very simple, to wit
If the you call the major axis length 2b and the minor axis 2a, then spinning the plane of the ellipse about the center at an angle of ( this comes out of the wellknown fact that the intersection of a plane and a cylinder is an ellipse as yoy probably know)
theta= arccos(a/b)
would allow you to point the weld tip at the edge of the ellipse. Now the coordinates of a point on the ellpse is (as the servomotor rotates)
y=a*sin(wt)
x=y*tan(theta)=a*sin(wt)*sqrt((b^2-a^2)/a))
where
w=angular velocity of servo
which shows that the lateral motion of the tip, x, is harmonic and can easily be implemented by an edge cylindrical cam of radius a along the same axis.
This is truly a simple problem for an elliptical plane section. Moreover, the relative velocity is constant over the motion.

 

[zekeman]

Now that I think of it,and it should have been obvious from the start, the cam profile, required is the the same elliptical shape along the cam cylinder, so that the the cylindrical piece and the cam profile are identical.

 

[funguy123]

Zekeman,

I agree, the cam driving the linear axis off of the elliptical shape is shaped like 2 lobes up, down, up, down, up.

My question is, will I need to advance or retard the speed of the rotary elliptical axis so that I get a nice consistent, uniform weld on the edge of the ellipse, no jerky motion, consistent matched speed between the two at the weld point?

 

[funguy123]

Zekeman,

And that second cam I believe I need to advance/retard the ellipse would have go from 0-360 degrees and have points of accell and decel (approximately 4)and points of matched speed between the two (when the narrow point of ellipse is at the weld point).

 

[zekeman]

Think about it, you have a cam that is exactly tracking the ellipse. It is like two parallel ellipses spinning at the same rate with a linear follower at one y position (your weld tip) filling the gap between the ellipses. Of course, this assumes that the rotational motion of the workpiece driver and the cam cylinder are locked 1:1 ,with no interference of tip and workpiece possible.
Believe it. It works like magic!
Of course if you don't want a physical cam and you generalize the solution for any elliptical piece , you can use the x coordinate equation I gave in my first post to get the servo driven x coordinates as a function of time.

 

[zekeman]

I just realzed that you are thinking of a cam whose rotational axis is at right angles to the workpiece axis which is also ok. I've been thinking the cammed edge of a cylinder.But isn't the clindrical cam simpler to machine ?
Now, addressing your main concern about relative velocity of tip to the workpiece ellipse is that since the ellipse is generated on the cylinder, the velicity at each point on the ellipse is the same = to a*sin(wt), so you are already getting constant velocity independent of position and the relative x motion has to be zero, so the total relative velocity is constant.

 

[zekeman]

Correction:
Velocity of each point on the ellipse relative to the tip is aw, not a*sinwt.

 

[funguy123]

Zekeman,

Thanks for the info. Yes, the rotational axis is at a right angle to the workpiece axis. I'm not following the math (I'm a PLC guy), can you explain the terms a little better?

Thanks,

Funguy

 

[zekeman]

I'll try to be clearer, but first give us a little more background like tell us if this is a general problem involving one or a class of elliptical shapes, or other closed curves and whether this weld is radial or axial; also, what linear weld speeds and workpiece sizes are we talking?
Also, what variation of angle of weld tip to work and linear speed is allowed?
Thus far the solution I have shown does have some tip angle and some linear speed variations, depending on the eccentricity of the ellipse.
A more precise solution can be achieved at some increased programming cost. For example, if you spin the ellipse with its axis normal to the plane of the ellipse (unlike what I have suggested) and you want a radial constant weld speed, you vary the speed of the rotating servo inversely proportional to the instant radius to the weld point, or you make
r*w a constant
w=RPM
r=radius from rotational axis to the weld point and slave the lateral servo or cam the lateral motion accordingly.

 

[funguy123]

Zekeman,

Thanks for the information again. The weld tip is 90 degrees to the axis of rotation. If you were to view the elliptical part as sitting on a table from above and rotating, the weld tip would be laying on the table, 90 degrees to the axis of rotation of the ellipse and pointing at the axis of roation and moving back and forth towards the axis of rotation.

And using the following equation, i came up with a way to vary the servo speed inversely to the radius to the weld point like you mentioned. And it is a constant.

Weld Speed = 5 ipm surface speed
RPM = ipm/(3.1415 x dia.)
Starting Parameters: 5/(3.1415 x 1") = 1.59 RPM

So now the graph of the position of the servo rotating the elliptical part and time shows that the velocity increases and decreases slightly based on the radius. It's hard to see but it is there.

I want to thank you very much for your help. I am a controls guy trying to help a customer with an application. I do motion control, but the math on this one was beyond me!

Thanks,

Funguy

 

[zekeman]

One more thing, since the motion is so slow, and the ellipse has radial symmetry you could have a leadscrew probe 180 degrees from the weld tip which will move to contact the ellipse, moving in and out as the piece is rotated; with an encoder attached, you would have position signal(count the pulses + and -) to the weld tip leadscrew and a simple position servo or stepping motor would allow the tip to follow the the probe, thus elliminating the need for a physical cam and allowing a whole class of radial symmetric shapes to be controlled this way.