Centripital Force Turntable (record player)

[jamuses]

Homework Statement

This is not a homework question, just a problem I want help solving. Don't be afraid of giving too much of the answer, I am not even in a physics course right now.

When setting up a turntable/record player, you need to dial in an "antiskate force". This is an outward applied force on the arm to make sure the needle sits in the middle of the record groove. It counteracts centripetal force.

What we are trying to figure out, is how much anti skating force is required to counteract the centripetal force on the record needle. Perhaps derive an equation for the force required with a given position on the record.

The arm is on a pivot 21cm away from the center of the platter, and the distance from the pivot to the needle on the arm 23cm.

The needle is moving towards the center of the record and therefore the radius of the rotation is changing. This means that the velocity of the stylus relative to the record is changing, even though the platter spins at a constant 33rpm.

The record grooves have modulations, they wave back and forth under magnification, they have bumps on their walls.

A constant downward force of about 2grams is applied by the tonearm.

Homework Equations

Fc=m(v^2)/r

Is friction somehow involved?

The Attempt at a Solution

No idea where to start. I guess some sort of force diagram.

 

[Simon Bridge]

No idea where to start. I guess some sort of force diagram.

Yep - you need to draw the forces on the needle-point as if in a smooth groove wider than the point.

Without a balancing force, the needle will rest on the outside edge of the groove - so this is providing a radially inwards force. But the needle does not do circular motion with the record! Instead the needle has a radial motion because the groove is a spiral.

But the point of the needle is on an arm - so the overall sweep of the needle-point across the turntable is an arc with the radius of the arm: circular motion.

That help?

 

[jamuses]

Are you sure that it rides on the outer edge of the groove? If you were to play a vinyl sheet with no grooves, with no antiskating force, the arm would glide inwards. Hence my question, how does friction come into play?

Would an increase in friction, say from choppy modulations in the grooves, cause an increased centripetal force?

 

[Simon Bridge]

Just thinking about this... on a circular groove, with nothing to hold the needle to the outer edge, it would lift away (from the edge) off the contact friction. If it started out not touching any of the sides, then, all other things equal, it would stay there. However, a record groove is a spiral - so the outer edge is always approaching.

You can think of friction as having an effect like cellotape - sticky-side up. Things will catch on the tape and pull away with a bit of a jolt.

For a vinyl sheet without grooves ...
An object sitting on the sheet will want to fall over, or slide, towards the outer rim.
You can see this by putting small objects on a turntable.

The arm is constraining that motion to an arc. I'd have to do the math.

 

[PeterO]

Are you sure that it rides on the outer edge of the groove? If you were to play a vinyl sheet with no grooves, with no antiskating force, the arm would glide inwards. Hence my question, how does friction come into play?

Would an increase in friction, say from choppy modulations in the grooves, cause an increased centripetal force?

Are you sure about the above?

If there were no grooves, and no anti-skate force, I can't see why the needle would go anywhere. What force may convince the needle to move in any direction?

I could understand the needle moving in on a smooth vinyl due to the anti-skate force. The trick then is to set the anti-skate force so that the needle tends to move in at exactly the same rate as the grooves spiral in, so that the needle does not have to be "pushed in" by the outer edge of the groove, thus failing to remain central in the groove.

 

[jamuses]

Here is a link to a video showing this phenomena. Watch at 4:45.


From my own table, I can tell that the anti skate is most definitely an outwards applied force on the arm. When antiskate is set, without lowering the needle onto the record, the arm will glide back to the armrest on its own.

Turntable aficionados claim that the left channel is louder without antiskate. The left channel corresponds with the inner side of the groove.

Also: note that the method presented in the video for setting the antiskate is largely rejected. The interaction of the stylus with the groove is more complex. Most people set antiskate by ear.

At a quick glance it may seem like a simple "car on a banked curve" problem, but there are obviously some weird things going on here. I remember reading once that because of the small area of the needle, the pressure of the stylus is very great, and briefly deforms the vinyl as it passes over it.

 

[rcgldr]

From what I recall, at least part (if not most) of the skate reaction on a tonearm is due to the direction of the drag force at the needle not lining up with the pivot point of the tone arm, resulting in a net torque on the tonearm. I'm not sure how much of the skate reaction is due to centripetal force from the outside wall of the groove on the needle.

One alternative to this is / was to use a linear tracking tonearm. The tonearm was mounted so that it could move perpendicularly with respect to the record grooves. One method was to mount the tonearm via a bearing onto a thin and long (a bit over 1/2 the size of a record) rotating cylinder (the tonearm would be perpendicular to the rotating cylinder).

 

[Simon Bridge]

Well - looking at the dynamics of just having a mass on a groovless turntable, and at how the armature is connected to the head, there is an unbalanced force on the head pointing towards the center of the turntable. See:

... it looks to me that the design of the armature means that the moment arm (pivot to needle) is only tangent to the motion of the record when the needle meets the label.

The horizontal forces, without the grooves, are friction (in the tangential direction of rotation), and tension (pointing back to the pivot of the armature). These forces form an obtuse angle - the component of the friction perpendicular to the moment arm is providing (in the picture) a clockwise torque.

I didn't account for that - it means that, unbalanced, the needle will tend to ride the inner edge.
Notice how much balancing gets done?
There is a counterweight on the armature to put the center of mass on the pivot (so it takes almost no effort to move the head) and a counter-torque (provided by a spring at the pivot?) - which is presumably adjustable with a screw. You want to set it so the signal response/strength in each channel is about the same, with equal amps, on a test disk. The relative signal strength will vary as the record plays anyway - and you can fine-adjust electronically.

If you just balance the torque, then the grooves will be pushing the head around and the needle will ride the outer edge ... so you want to, very slightly, under-balance it.
All this sound familiar?

 

[jamuses]

... it looks to me that the design of the armature means that the moment arm (pivot to needle) is only tangent to the motion of the record when the needle meets the label.

The horizontal forces, without the grooves, are friction (in the tangential direction of rotation), and tension (pointing back to the pivot of the armature). These forces form an obtuse angle - the component of the friction perpendicular to the moment arm is providing (in the picture) a clockwise torque.

I didn't account for that - it means that, unbalanced, the needle will tend to ride the inner edge.
Notice how much balancing gets done?
There is a counterweight on the armature to put the center of mass on the pivot (so it takes almost no effort to move the head) and a counter-torque (provided by a spring at the pivot?) - which is presumably adjustable with a screw. You want to set it so the signal response/strength in each channel is about the same, with equal amps, on a test disk. The relative signal strength will vary as the record plays anyway - and you can fine-adjust electronically.

If you just balance the torque, then the grooves will be pushing the head around and the needle will ride the outer edge ... so you want to, very slightly, under-balance it.
All this sound familiar?

This makes a lot of sense. I get it now.

The moment arm is never actually tangent to the motion of the record. In fact I think it may even get worse as it gets closer to the center. This is due to the offset angle of the headshell. It is set up so that the oblong shape of elliptical stylus remains tangent to the the grooves with a minimal angle of error (2 degrees on my table).

The direction the stylus is being pulled in is not the same direction as the tension in the arm, resulting in a net force.

Further, if the friction were to increase, at a highly modulated passage, this could possibly increase the tangential force and cause a need for a greater antiskating force. This is the reason why styluses mistrack on high amplitude passages.

In theory, a servo mechanism could be constructed that variably adjusts antiskate in real time based on the audio output.

Or far easier, a tangential tracking table as mentioned above. They can be a bit tricky to adjust though.

 

[rcgldr]

In theory, a servo mechanism could be constructed that variably adjusts antiskate in real time based on the audio output. Or far easier, a tangential tracking table as mentioned above. They can be a bit tricky to adjust though.

Image of an example of a linear tracking tonearm (there are several methods of implementing these: servo, rotating cylinder bearing, air bearing, ... . Tangential tonearm is an alternate name for these).

 

[jamuses]

nvm.

 

[Simon Bridge]

Out of curiosity I drew the lines on that picture (showing the arm in two places):

... I think this is quite clever actually.
At first I thought that the tangent and the moment arm would line up close to the hub - but from above, they seem to form about the same angle right through the motion. That's cool.

Note: in case it is not obvious...
Red are radial lines, the grey line is the arc.
Yellow and off-yellow are tangent to the rotation.
green and magenta are the moment arms at each end of the motion.
You can see how the unbalanced force comes in.

 

[jamus]

Crunching the numbers, I get 157.23 degrees for the outer, 164.37 for the inner angle. Highly doubt the picture is taken from directly above
though.

There is something called IGD, meaning inner groove distortion, the grooves at the center of the record have a greater tendency to mistrack. A decrease or an increase in angle could correspond to this as both would effect the amount of antiskate required. I have a record that skips backwards on one of the last grooves, plays a part of a song on a loop. All of this is conjecture .

I suspect that IGD has more to do with the elliptical stylus not being aligned tangentially to the curve however,a tracking angle error point.

 

[Simon Bridge]

You could work it out from the standard dimensions of the record.
If you used my lines - those were lined up by sight and I only noticed the similarity in the angles after I'd killed the xcf.

There are quite a lot of intreguing relationships there - like the initial radius (long red) is perpendicular to the final moment arm (magenta).

Up by the pivot you can see the two adjustment screws (counter-weight, and -guessing - anti-skate : it's labelled "anti-somethingsomething" though.) I grew up with these things - amazing what I've forgotten.