It is probably easier to make 3D computer images of such methods, using even something simple like geogebra (or using CAD software if you know how to use it), that can be projected during class, than to obtain functional physical models. The latter can be machined or made using a 3D printer, but my impression is that computer visualizations are more adaptable and adjustable, and it's not clear to me that much is gained by using an actual physical model. In most any university physics or engineering department there is someone who knows how to make such physical models, but probably it is a better use of one's time to learn to use software designed for creating visualizations. (It is also cheaper - 3D printers and 3D printing is expensive - there is free software that can be used). Moreover, computer models can be interactive in ways that physical models simply cannot. The student can see a surface of revolution as it is generated, and so forth, and can tune parameters. Physical models will be made for a (usually fairly small) finite set of surfaces of revolution; with a computer model one can visualize the surface generated by any admissible curve.
On the other hand, some students probably benefit from touching an object. The intersection of two cylinders is good example of a surface for which a computer vizualization is probably less communicative than a physical model, simply because the surface is somehow quite hard to see.
One recommendation would be to look into using something like geogebra. The sorts of models you describe (appropriate for a multivariable calculus class) are not hard to realize in such software and there are already many examples available online. Making quality, usable physical models requires skills and access to facilities not all of us have, and in this sense computer visualizations are more easily prepared/generated.