Hi all,
It will take someone with better math skills than I have to answer and explain this question.
Does increasing or decreasing the size of an idler affect the platter speed?
John
Idler diameter has NO effect on platter speed! Think of the motor and platter combo as a reduction gear, because essentially, that is EXACTLY what it is.
It is related to the RATIO of the CIRCUMFERENCE of the motor drive pulley to the CIRCUMFERENCE of the inner surface of the platter - the inside circular surface where the idler makes contact.
EXAMPLE: Common A/C motors - including the kind used in most idler-wheel turntables - typically run at 1800 RPM.
...<brief side rant below>
I learned to my utter shock that to most people like my nephew (born in 1989) an LP record may as well be a stone tablet or a papyrus scroll for all they know about what they are - or were, let alone what their rotational speed was supposed to be, or even what they looked like up close. Showing him an LP record was like a trip to the Smithsonian, as far as he was concerned. Heck, people like my nephew barely remember what a COMPACT DISC is, because they don't own any. CD's are like Depends - they're both for OLD people; It's all low-fi, low bit-rate compressed files crammed onto key drives and iPods for him and the people he hangs with.
Everyone else - besides people like my nephew above - remembers that the desired rotational speed of an LP record is 33⅓ RPM - or in more calculator-friendly decimal form - 33.333333333333... until the universe falls in on itself or whatever is out there that passes for God pulls the plug in disgust over His botched creation.
In order to transfer that torque and RPM from the 1800 RPM motor to the platter, all that is needed is a method of transferring that motion and torque from one spinning thing that is under power - the motor - to the other round thing that is normally static but which we want to move too - like the platter. If speed and torque transfer is all you want, theoretically, all you need to do is mount the motor to the side, attach a platter the same size as the record platter to the motor shaft, then grind gear teeth into both the motor platter and the record platter. Finally, slide the two things together until the teeth mesh, turn it on, and "Voilà!" Your platter is spinning.
The trouble is, the motor is spinning at 1800 RPM. And so is the record platter! Since both are the same circumference, and they are mechanically linked, there is a 1:1 correspondence between the angular velocities - or, if you will, rotational speed - of each...NOT ACCEPTABLE! So, what do you do? To reduce the spin of the record platter, you must reduce the diameter of the motor-driven gear, so that its circumference covers less linear distance per rotation than the record platter.
If you want the record platter disc to spin SLOWER, you must reduce the diameter of the motor -driven disc. If the record platter is 12" in diameter, its circumference is therefore 37.7" (actually, it's 37.699111843077518861551720599354", but I rounded up to nearest hundredth - so SHOOT me) - based on the formula for calculating circumference from the diameter:
CIRCUMFERENCE = Π(or "Pi" or 3.1415926535897932384626433832795) X DIAMETER
Let's reduce the motor shaft-driven disc to HALF that figure, or 18.85" - again rounded to nearest hundredth. In order to achieve that circumference, we must use an algebraic variant of that same formula to calculate the right diameter:
DIAMETER = 18.85 ÷ Π or...
Six inches... So, we put the motor disc on our lathe and cut her down. Then, we cut some more teeth into the diameter - ones that match the platter's teeth, we put it all back together and we turn it on...
RATS!!.... The platter is still spinning too fast! Using a strobe we measure that it is turning at one-half the speed of the motor - 900 RPM. Well, we are least going in the right direction. For every rotation of the motor the turntable platter goes one-half of a rotation - a ratio of 2:1. This happens because with every rotation the motor shaft gear rim travels 18.85". Since the two rotating bodies are locked mechanically together at their rims, the turntable platter gear travels the exact same distance. But since that is precisely HALF the distance around the platter, that means it travels only HALF of one rotation.
Clearly, while we are going in the right direction, we must go much further to achieve our desired rotational speed of 33⅓ RPM. To make a long story short (or at least a little bit short-ER), in order to transfer motor rotation to the platter while simultaneously reducing the rotational speed from the motor's 1800 RPM to the platter's desired 33⅓ RPM, we must cut the circumference of the motor shaft side to 1/54th the size of the platter side. This is because the reduction ratio between 1800 RPM and 33⅓ RPM is 54:1. So, in order for us to make that ratio happen, we must lathe that motor shaft down so that its circumference is 0.698" - or 0.222222222" in diameter. That way, for every 54 rotations of the motor, the platter will spin exactly ONE. At the motor's 1800 RPM, that gets us - at the platter - what we want - 33⅓ RPM.
But that doesn't finish the project. We have a reduction gear setup that is getting us the right speed, but a direct gear drive around the perimeter of the platter is hardly practical for a record player - gear noise transmission through the record, stylus, up the tonearm to the electronics is the worst for sure. So, instead of a direct, motor-to-platter drive, we need to isolate the two - transferring the motion and torque from the motor to the platter in such a way as to dampen the vibration and noise of the motor before it gets to the platter.
There are two ways to do it. One is by means of a rubber belt. This works very well - many insist this is the best way to do it. The other way to isolate the motor from the platter is to use a rubber wheel called an "idler" inserted between the spinning motor and the platter. This rubber "idler" transfers the motion and the torque, but it doesn't contribute to the reduction ratio at all. THAT IS WHY IT IS CALLED AN "IDLER!" If the reduction between the motor and platter is 54:1, inserting a 2-inch-wide idler wheel yields a final ratio of precisely 54:1. If you take it out and substitute it in the mechanism with an idler that is 3-inches wide (assuming you can get it to fit in there properly), the resulting final drive ratio is STILL 54:1!
Why is this? VISUALIZE!!!.... All three of these pieces - motor, shaft, platter - are in direct mechanical connection. So, LINEAR velocity of any hypothetical point on the motor shaft pulley IS EXACTLY THE SAME as the linear velocity of any given point on the outside of the idler, which in turn IS EXACTLY THE SAME as any arbitrary point on the platter. SO... In terms of ANGULAR velocity, the reduction ratio of the outer two rotating elements remains unchanged whether the "idler" is present or not.
You can - theoretically - add more idlers between - two more, three more, any number more. And the final ratio remains 54:1.
Instead of the cave-man set-up I illustrated, real-world idler turntables have motors that drive the platter from INSIDE, not the outside. So the motor transfers power and torque though the idler and finally to the inside of a ring cast/pressed/glued/duct-taped to the bottom of the platter.
Visualizing all this in terms of circumferences transferring motion and power through direct contact results in calculations which are more complicated than necessary, but I think it aids in visualizing the actual motions involved. The first thing you really need to know is the rotation speed of the motor being used to drive the turntable; it is usually 1800 RPM, but there are exceptions. Then, simply divide the motor RPM by 33.33333333. That will give you the final drive reduction ratio. The second thing you need to establish is the inner diameter of that ring on the bottom of the platter. Depending on the size of the platter itself, it will be 8"-10". WHATEVER it is, the outer diameter of the motor drive pulley MUST be of a size so that the ratio of this inner platter drive ring to the motor shaft pulley is EQUAL TO the ratio of the motor speed to 33⅓ RPM.
If the ratio of motor speed to 33⅓ is calculated to be 54:1, the ratio of the diameters of the driven ring under the platter AND the outer diameter of the motor pulley MUST ALSO be 54:1 - or the speed will NOT be accurate.
The idler affects speed potentially only in TWO ways. It could get old and start slipping, so that some of the motion and torque of the motor is lost in its transfer to the platter. OR, if the idler is the wrong size and doesn't fit properly within the space between the motor shaft and the platter drive ring, it could be excessively compressed. Depending on the type of motor and its power supply, this could result in either slowing the platter down from friction, OR actually speeding the platter up because the motor's circuitry is overcompensating for the extra friction by making the motor spin faster.
I think this step-by-step, "the hip-bone's-connected-to-the-thigh-bone's-connected-to-the-knee-bone's-connected-to-the-ankle-bone" method of breaking it down is what many people need to do. At some point, hopefully there will be an "AHA!" moment and there will be true understanding.
This whole question demonstrates that even mechanical principles that seem fairly simple and fundamental actually involve many logic steps - sometimes many, MANY of them - for all the dots to thoroughly connect. So, actually, they are not really simple at all!
:thmbsp::thmbsp::thmbsp::thmbsp: