I am looking for a motor which can run from 200 RPM to about 2000 RPM with a torque more than 0.8 to 1 N.m. The problem I am finding is that it is hard to find a high torque motor with this RPM range. What would be the best solution for this?
Should a BLDC motor do the trick. But also I don’t want to design a speed controller.

 

You need a gear motor. Gearing lowers the RPM and increases the torque by the same factor.

 

What voltage are you working with?
A DC motor should fill the bill, what power is required .
How do you plan on using variable speed without a controller?

 

INDEED! an adequately sized brush type motor will deliver that range, and only need an adequate DC voltage supply to set the speed. The speed will vary with the torque required, but with an adequately sized motor the change will not be a lot.

One caution is that at the slow speed and high torque the internal cooling fan will not provide enough cooling air.

 

No need to design anything. There are many DC motor speed controllers available on all of the usual (Amazon, Ebay, Alibaba, etc) online stores.

 

No need to design anything. There are many DC motor speed controllers available on all of the usual (Amazon, Ebay, Alibaba, etc) online stores.

There are also much better products available from honest sellers who are able to provide customers with useful customer support staff. Including not a single one of those listed above.

 

I am looking for a motor which can run from 200 RPM to about 2000 RPM with a torque more than 0.8 to 1 N.m. The problem I am finding is that it is hard to find a high torque motor with this RPM range. What would be the best solution for this?
Should a BLDC motor do the trick. But also I don’t want to design a speed controller.

see Maxon for DC motors, gearheads, and speed controls.
You'll have to search the site with your specifications:
https://www.maxongroup.com/maxon/view/product/gear/planetary/gp26/406762

 

see Maxon for DC motors, gearheads, and speed controls.

Planetary G.B's are nice, especially for zero back-lash, but expensive $$.