The necessity for absolute tt speed control
- Thread starter spiritofmusic
- Start date
There appear to be some bad misconceptions about basic physics here. Morricab is correct that a higher inertia platter will resist changes in speed better than a low inertia platter which should improve speed stability. His formula (P=mv) is for linear momentum however, not rotational inertia. Although rotational momentum and inertia can be related, momentum does not affect resistance to speed change; resistance to speed change is controlled by inertia. For a UNIFORM solid disk, inertia I=mr²/2. Note there is no speed component in this formula only mass and distance from the axis. Adding mass at the periphery increases inertia at the square of the distance from the axis of rotation so it will have an outsized effect on inertia. As the disc is no longer uniform density, you will need to integrate the inertia of each uniform section to obtain a total inertia. The angular velocity of mass does not affect inertia.
Overshoot or undershoot does not have to occur regardless of the mass or inertia of the platter. This is function of the control algorithm and the available power from the motor. If the motor cannot provide enough correction in the time window required for the change in speed experienced, the speed will "hunt". In control systems, there is a trade off between response time and settling time so a proper target needs to be specified and the control algorithm needs to match these requirements for optimum performance. Increased inertia will improve native speed stability but it will also increase the demands on the motor and control system. As long as the components are matched to the performance requirements, there should be no reason why a high mass platter overshoots or undershoots.
Overshoot or undershoot does not have to occur regardless of the mass or inertia of the platter. This is function of the control algorithm and the available power from the motor. If the motor cannot provide enough correction in the time window required for the change in speed experienced, the speed will "hunt". In control systems, there is a trade off between response time and settling time so a proper target needs to be specified and the control algorithm needs to match these requirements for optimum performance. Increased inertia will improve native speed stability but it will also increase the demands on the motor and control system. As long as the components are matched to the performance requirements, there should be no reason why a high mass platter overshoots or undershoots.
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A somewhat belated response but hopefully relevant:
Win's design was influenced by many things and amongst them was a conviction that a certain arrangement of masses and inertias gave the best result in terms of speed stability.
If I may be so bold as to attempt to articulate this in terms of physics, it is that the time constant of the platter inertia and drive system elasticity be kept as short as possible and that the system inertia should be concentrated before the more elastic components.
A long time ago on a forum far far away I postulated that we could express the inertia of any part of the drive system in terms of equivalent mass, the analogy being with the way that the polar moment of inertia of a tonearm is conveniently expressed as being equivalent to a mass suspended at the cartridge end.
For drive system components I proposed that the equivalent mass is the point mass that would have the same inertial effect if it were rotating at platter speed at a radius of 150mm. Thus a platter with a normal diameter will have an equivalent mass somewhat less than its actual mass: as an example an isotropic cylindrical platter would have an equivalent mass 0.3 x its actual mass while an edge weighted platter might be 0.6 or more, conversely a centre weighted one might be 0.15 or less.
For parts of the drives system that rotate at different speeds (eg motors, pulleys, idlers and flywheels) the equivalent mass will scale with the speed ratio, so a motor like the Papst outrunner which has a large soft iron outer ring to create the magnetisation essential for it to lock into synchrony with the supply frequency and which runs at say 1800 RPM will have an equivalent mass which is a large multiple of its actual mass: I did calculate this once, I forget the exact number but it's somewhere around 50kg.
All drive systems display some elasticity: in the case of a belt it's pretty easy to conceptualise and quantify, it's the stretchiness of the belt, so the length of the belt divided by the product of the modulus of the belt material and its X sectional area. In the case of an idler it's less easy to quantify but easy to conceptualise: just as tyres on a car squish slightly when transmitting torque so too does the tyre on the idler. In the case of direct drive it is harder to conceptualise: the magnetic field of the drive system must always lead the magnetic field of the platter rotor, at zero torque the angle between them will be minimised and just before drop out torque it will be at a maximum. Since energy is stored in the magnetic field this creates a torque spring.
The time constant of the platter / drive system is then the square root of the product of the equivalent mass and drive system elasticity. Obviously a heavy, edge weighted platter driven by a soft rubber belt will have a long time constant while a centre weighted platter driven by an idler with a thin tyre of high durometer rubber will be much shorter. A direct drive system will be somewhere between the two.
My understanding of what Win found is that the shorter this time constant the better he liked it.
Win probably wouldn't express it that way: he's a very talented designer with a clear idea of what he wants but he isn't a theoretical physicist by training. Fortunately he has a willingness to call on others for help with things that are beyond his expertise; I was privileged to be one of those people at the beginning of this project. I am no longer involved in any way (beyond dreaming that I may one day be able to afford one of these).
Win's design was influenced by many things and amongst them was a conviction that a certain arrangement of masses and inertias gave the best result in terms of speed stability.
If I may be so bold as to attempt to articulate this in terms of physics, it is that the time constant of the platter inertia and drive system elasticity be kept as short as possible and that the system inertia should be concentrated before the more elastic components.
A long time ago on a forum far far away I postulated that we could express the inertia of any part of the drive system in terms of equivalent mass, the analogy being with the way that the polar moment of inertia of a tonearm is conveniently expressed as being equivalent to a mass suspended at the cartridge end.
For drive system components I proposed that the equivalent mass is the point mass that would have the same inertial effect if it were rotating at platter speed at a radius of 150mm. Thus a platter with a normal diameter will have an equivalent mass somewhat less than its actual mass: as an example an isotropic cylindrical platter would have an equivalent mass 0.3 x its actual mass while an edge weighted platter might be 0.6 or more, conversely a centre weighted one might be 0.15 or less.
For parts of the drives system that rotate at different speeds (eg motors, pulleys, idlers and flywheels) the equivalent mass will scale with the speed ratio, so a motor like the Papst outrunner which has a large soft iron outer ring to create the magnetisation essential for it to lock into synchrony with the supply frequency and which runs at say 1800 RPM will have an equivalent mass which is a large multiple of its actual mass: I did calculate this once, I forget the exact number but it's somewhere around 50kg.
All drive systems display some elasticity: in the case of a belt it's pretty easy to conceptualise and quantify, it's the stretchiness of the belt, so the length of the belt divided by the product of the modulus of the belt material and its X sectional area. In the case of an idler it's less easy to quantify but easy to conceptualise: just as tyres on a car squish slightly when transmitting torque so too does the tyre on the idler. In the case of direct drive it is harder to conceptualise: the magnetic field of the drive system must always lead the magnetic field of the platter rotor, at zero torque the angle between them will be minimised and just before drop out torque it will be at a maximum. Since energy is stored in the magnetic field this creates a torque spring.
The time constant of the platter / drive system is then the square root of the product of the equivalent mass and drive system elasticity. Obviously a heavy, edge weighted platter driven by a soft rubber belt will have a long time constant while a centre weighted platter driven by an idler with a thin tyre of high durometer rubber will be much shorter. A direct drive system will be somewhere between the two.
My understanding of what Win found is that the shorter this time constant the better he liked it.
Win probably wouldn't express it that way: he's a very talented designer with a clear idea of what he wants but he isn't a theoretical physicist by training. Fortunately he has a willingness to call on others for help with things that are beyond his expertise; I was privileged to be one of those people at the beginning of this project. I am no longer involved in any way (beyond dreaming that I may one day be able to afford one of these).
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@lyrebirdcycles I appreciate how clear and understandable your explanations on a complex ( to me as a non physicist ) topic were written!
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