Hello,
Thanks for your replies. Before I prepare a clean file (will take time, now have deadlines for several things), let me describe my case in more detail, and what has led to choosing the particular solution I am using now (which is not a solid body sweep yet).
We design a mandrel for a high-temperature superconductor magnet. The conductor is a tape which has very strict requirements on how it can be bent. The tape is wound into grooves which are machined into a cylinder. The winding path is described by a 3D curve r(t), where t is some parameter along the curve. The Frenet-Serret frame is the curve is defined as follows. T is the tangential unit vector defined as T=r'(t)/|r'(t)|. The normal unit vector is defined as N=T'/|T'|, and the binormal vector as B = T x N. There are several tapes wound into the groove on top of each other, and the groove must be oriented along the N vector, to simplify the case (to be more precise: we have a groove direction vector S which lies in the plane spanned by B and N, i.e. perpendicular to T, but this does not matter for the description of the problem). All of these vectors T,N,B,S are changing along the path, i.e. dependent on t, but T,N,B form an orthonormal set.
My first approach was to export discrete points along two paths from my C++ code, and import it into Inventor: the top center path of the groove, and the bottom center path. The top center path is the reference path, the bottom center path is calculated as r(t)+D*N(t) where D is the groove's depth. So by construction, the distance between the two paths is always D, *along the N direction* (which is perpendicular to the tangential of the reference path). I swept a rectangular cross section along the reference path, using the bottom center path as guide rail. I was surprised to see that neighbouring turns of this winding were intercepting. It turned out that the "scale" option of the Sweep feature was turned on, which scales the swept cross section according to the distance between the sweep path and the guide rail. Since the distance between the two paths is by construction constant *in the plane perpendicular to the tangential*, this implicitly implied that Inventor is not "progressing" along the sweep path and the guide rail in this way, i.e. the swept cross section is not perpendicular to the sweep path. Switching off the scaling option helped somewhat, but did not fully solve the problem, making me believe that my last assumption is valid.
Finally I choose the Loft feature, because that can define cross sections at regular intervals along the sweep. From the exported points I create guide rails for the Loft by an iLogic macro, and also rectangular cross sections at regular intervals, which regularly enforce some kind of "synchronization" between the progress along the different rails. This produces nice results, but is rather complicated. And it is not perfectly exact (this is probably not a problem, differences are tiny). See the attached illustration: the red pair of lines indicates the top edges of the groove, the blue pair of lines indicates the bottom edges of the groove. The black circle represents the mill. At this instant, the mill's axis is perpendicular to the plane of the figure, but is then rotated if we progress back or forward. What is interesting is that at the top and bottom of the groove, different azimuthal positions of the mill are actually cutting (red and blue dashed lines). This would not be reproduced by a swept planar cross section, unless I miss something. The true machined shape could be modelled exactly with a solid body sweep with the following feature: (1) I can give the sweep path (center line between the two red lines) which defines the position of the top center of the mill, (2) I can give a guide rail (center line between the two blue lines), towards which the axis of the mill is oriented, and (3) the axis of the mill is also perpendicular to the tangential of the sweep path of point (1).
A few specific questions:
- What is the mathematical apparatus behind these sweep features? How is the orientation of the swept cross section determined?
- Is the "Spline control points" feature a Bezier curve?
The helps of these features give the impression of having quickly and easily understood what is going on, but are lacking the exact (mathematical) description.
Thank you
Daniel