Recommended starts per hour

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Other factors come into play. Number of poles and load inertia, for example.
Google will give some general tables.

If we were ever concerned about starting frequency, we always contacted the manufacturer.

And as far as I can recall, the supply voltage did not come into play in the calculation. Rotor temperature was the limiting factor.
 
Up to and including 500HP, motors (in North America) are ostensibly designed around a set of specifications from NEMA (National Electrical Manufacturers Assoc)., specification # MG 1-2016 (meaning last revised in 2016) section 12.54 and in that design spec a motor is required to handle 2 starts per hour with the first one being at ambient temperature, or one start per hour at rated maximum operating temperature, based on the MAXIMUM applied "moment of inertia" (the Wk2) of the mass of the connected load (not the motor mass itself).

But that is the MINIMUM requirement and the MAXIMUM load. NEMA MG 10 then goes on to describe an expected MAXIMUM starts per hour and cool down time, regardless of the connected load, based on the heating effects on the windings and rotor from successive starts. There is another table for that which offers possible scenarios based on calculations you must perform, then you pick the lesser of the values.

Tables are based on HP and synchronous speed (i.e. 1800RPM, 3600RPM etc.) which you didn't provide. The FLA of a 4 pole 4000V motor (HP x .14) should be about 28A worst case, so this is likely a slower motor based on the higher amps. The NEMA MG 10 table is only for 2 pole 4 pole and 6 pole motors, so let's assume this is a 6 pole.

Table 7 of NEMA MG 10 shows a 200HP 6 pole motor is good for a maximum of 4.5 starts per hour with a minimum off time between starts of 265 seconds (just under 5 minutes);

OR you take the number listed in the table as "B" which is the MAXIMUM product of starts per hour times load Wk2, in this case 2262, then divide that value by the actual load Wk2 and if the remainder is less than 4.5, you use that lower value. So for example if your actual load Wk2 is 1130 lb.-ft.2, you take 2262/1130 = 1.5 starts per hour as the maximum number. Again, whichever number is LOWEST is the one you must use.

4.5 S/H and 2262 are the actual numbers in the table for a 6 pole 200HP motor, the 1130 lb.-ft.2 value is just an example, you must find that number yourself. usually the machinery supplier has that value because they needed it in order to select the proper motor HP size in the first place.
 
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