Mitigating stick-slip effects in rotary steerable tools

A method, comprising:

• introducing a steering assembly into a wellbore on a drill string, the steering assembly including a housing having an actuator and a planetary gearbox positioned within the housing, the planetary gearbox including a ring gear operatively coupled to the housing, and one of a sun gear and a planet carrier coupled to a drive shaft of the actuator;
• rotating the drill string in a first direction and thereby rotating the housing and the ring gear in the first direction;
• operating the actuator to rotate the drive shaft and an offset mandrel coupled to one of the sun gear and the planet carrier in a second direction opposite the first direction;
• and
• mitigating stick-slip disturbance transmitted between the housing and the ring gear and to the offset mandrel with a mechanical coupling that operatively couples the ring gear to the housing, wherein the mechanical coupling is selected based on an ability of one or more mechanical parameters of the mechanical coupling to mitigate the stick-slip disturbance.

A well system, comprising:

• a drill string extendable into a wellbore and having a drill bit coupled to an end of the drill string;
• a steering assembly arranged in the drill string and including a housing rotatable with the drill string, the housing having an actuator and a planetary gearbox positioned within the housing, and the planetary gearbox including a ring gear operatively coupled to the housing, and one of a sun gear and a planet carrier coupled to a drive shaft of the actuator;
• a mechanical coupling operatively coupling the ring gear to the housing such that rotation of the housing rotates the ring gear, wherein the mechanical coupling is selected based on one or more mechanical parameters of the mechanical coupling and the ability of the one or more mechanical parameters to mitigate stick-slip disturbance transmitted between the housing and the ring gear;
• and
• an offset mandrel coupled to one of the sun gear and the planet carrier such that rotation of the one of the sun gear and planet carrier causes the offset mandrel to correspondingly rotate, wherein the offset mandrel is independently rotatable with respect to the housing.