SketchUp only works with flat surfaces. You can increase the number of segments that make up the curves which results in smaller faces which tends to create a smoother appearance but you’ll never eliminate the facets altogether. Keep in mind that SketchUp doesn’t like very short edges (less than about .01 in. so if your model is small you will need to do something to be able to create very tiny faces. Working at a larger scale is one way, The Dave Method is another. Box did a nice tutorial on that method which you can find in the search.
Here’s an example from a recent model I did. This is certainly overkill for most applications.
Nice apparently smooth surfaces.
Hidden geometry displayed. There’s nearly 100k edges in this model.
The collar and screw make a file that is over 11.5 Mb. Not so bad on it’s own but way too much detail to use in a larger model. FWIW, this was done because someone elsewhere made a statement SketchUp can’t be used for detailed models. This is a locking collar to go on 1/4 in. diameter Acme-threaded lead screw.