As Bill said the best way is to copy someone else. Find the specification of a commercial machine, and buy a similar motor.
To design from first principles its necessary to clear up confusion about Work, Power and Torque. Be warned, the scientific and engineering definitions of 'Force', 'Energy', 'Work' and 'Power' are far more specific than the same words used loosely in day to day chat. It matters.
Work is the amount on energy needed to achieve a task. It's measured in Joules and time taken is not considered.
Power is the rate at which work is done. It is measured in Watts, where a Watt is 1 Joule per Second. If a 1000W motor takes 10 seconds to complete a job then 100W motor will take 100 seconds to deliver the same result. Both motors do 10000 joules of work. Time is considered!
Torque is the measure of turning force in Newton Metres and time is not relevant.
Although power and torque are intertwined they're not the same thing, and the motor type chosen impacts on both. For example, an electric stepper motor has excellent torque even when stopped between steps, whereas a single phase motor has poor torque at low speeds and improves as it speeds up. The relationship between torque, power and speed isn't linear, and each motor will have graphs showing the relationship over a range of speeds and loads. Very often these graphs aren't provided and have to be asked for. Although maximum Torque is not achieved at maximum power and neither are achieved at maximum speed, reasonable performance can be expected somewhere in the middle.
It takes a certain amount of work to cut metal. Table XIX of my 1947 Newnes Engineer's Reference Book gives examples, all in Cubic Inches per Horse Power per Minute:
- Mild Steel – 0.75
- High Tensile Steels – 0.87
- Cast Iron – 1
- Soft Brass – 2.3
- Hard Brass – 0.9
- Aluminium – 3.0
- Duralumin – 2.7
- Magnesium alloy – 3.5
One Horse Power is about 735W
So, given the rate at which it is wanted to remove a particular metal it's possible to calculate the minimum output power needed from the motor.
However, there are many booby traps. One is optimum cutting speeds vary by metal, as does the ability of cutters to cope with the heat generated. Carbon steel (like a file) loses hardness at low temperatures, say 120C; HSS is much better, staying hard up to a low red-heat, though this is not recommended for long life; carbide out-performs HSS by a factor or at least two, major advantage. As cutting at high temperature softens metals, considerably less work is needed to remove metal when carbide is used brutally, saving the big boys lots of money. But getting the best out of carbide needs fast powerful machines, not often found in a home workshop. Other limits apply, for example the brazing on a brazed carbide tool melts before the carbide tip. Diamond is an interesting one. Carbon has a very high melting point but the advantage disappears in air because Carbon burns. Likewise the relatively poor temperature characteristics of the diamond disk and bonding agent prevent diamond performing to maximum potential. Further, the need to achieve a particular speed and the torque required to maintain a particular feed-rate are as interesting to the designer as a motor's power output. Another booby trap is the machines ability to deliver power to the cutting point – the drive-train and air resistance consume power. Not only does motor efficiency varies by speed and motor type, but many motors are rated to work in bursts and need time to cool-down before the next effort. Putting a continuously rated motor on intermittent work wastes money, overloading an intermittently rated motor risks burning it out. And it would be unwise to fit a motor sized to meet a minimum calculated load only by working flat out – prudent to add a safety margin!
In practice, machine tool designed take all these factors into consideration and the usual result is a somewhat over-powered motor for the machine, and a bunch of limitations, often related to cost! An industrial machine will be expensively built to do a lot of work quickly, while a hobby lathe won't. The Sherline is a small hobby lathe with a tiny motor, emphatically not designed to remove metal at high-speed on a production line! May not matter – within limits, hobbyists manage well within a range of motor powers even on the same machine, for example early Myford lathes used 1/3HP single-phase motors and upgraded later to 1/2HP. Some owners have upgraded to as much as 1HP 3-phase. From this you can conclude that 1/3HP is a little too small, and 1HP is plenty. 1/2 or 3/4HP single-phase is 'sensible', 3HP would be too much.
If the diamond disk is for sharpening cutters, the amount of metal removed is low, and a small fast motor plus patience would be appropriate. Cutting removes a lot more metal and generally the operator wants it done quickly. This requires a much bigger motor: my bench grinder and angle grinder are both 750W at 3000rpm. For fine work, my Dremel is about 150W max, speed variable between 5000 and 30000rpm. I don't use the Dremel to cut paving slabs!
As this is complicated, and there's more to worry about, Bob's advice is rock-solid. Copy someone else!
Dave