To your question, this object can not be made.
I have tried to make a simple spring with a straight line has gone perfect, when trying with a closed circle Shapr3D can not perform this type of actions at the moment.
the only option of how to do it would be to create a spring as shown in the image, once it was done it would be duplicated and rotated using a circle.
I hope I helped you or clarified your question
I appreciate your best idea to my question!
I finally figured it out how to close the circle perfectly!
See attached images, the key step is to set a rotate angle of the transform which can be divided by 360 degrees, such as 10 degrees with 36 revolved bodies.
Thanks again for your excellent answer!
When I get home I will try your method