Parting is a very brutal process - if you use a standard size parting tool (rather than a thin "hacksaw blade" tool) you are probably cutting a groove about 1/8th inch wide (sorry to revert to aliquot parts but I'm of an age where the inch is my natural unit). Something to remember is the available power on a hobby size lathe
I was taught the rule of thumb that on a small machine you can reasonably remove about 1.5 cubic inches of steel per HP per minute. (This is power at the tool cutting edge, not at the motor)
So if you have a 750W / 1HP motor and ignore inefficiencies, effect of blunt tool, poor cutting fluid supply, etc, etc, and you part a 1/8 inch width with a depth of cut of 10 thou (1/100 inch), then in one minute you can expect to cut off a strip of swarf which is 1/100 thick, 1/8 wide and 1200 inches long.
Given a work piece diameter of one inch and a value of pi = 3 you have a circumference of 3 inches, so 1200 inches of swarf is cut in 400 revolutions i.e. a cutting speed of 400 RPM max. Now factor in the inefficiencies and it is reasonable to halve this speed estimate. On my 100 year old lathe I have a choice of three direct speeds via the layshaft pulleys and three backgear speeds so I can get full motor power at chuck speeds as low as 40 RPM, but "cheap" VFDs will not be able to deliver full shaft power at low speeds (whatever the makers may claim.....)
Bearing in mind the above, and the fact that early chattering is corrected by increasing the depth of cut, it is easy to push a small machine outside of its comfort zone when parting. If you do this, then you can expect to have a few interesting issues from time to time.
All the best,