how can I create 3d model of a tube clip which is mathematically correct? I'm willing to 3d print a tube clip. In the photo is a simplified figure . The only thing that I know is the diameter of the tube that will enter in the tube-clip.


*

*is there relation between diameter and x ?

*is there relation between diameter and z ?

*how will the length y affect the strength of holding the tube ?

*what is the appropriate value of y so the tube clip doesn't break ?



 A: To answer questions 1 and 2, there is a relationship between $x$, $z$, and the diameter. The relationship is
$$x=2\sqrt{r^2-(z-r)^2}$$
where $r$ is the radius, half the diameter. You can solve for $z$, if you would prefer to go the other way, but your choice of $z$ (which must be greater than $r$) will determine the gap space you call $x$.
To answer questions 3 and 4, The strength of the clip will be determined partly by the length of $y$. The longer $y$ is, the stronger the clip. How large $y$ needs to be is something you'll have to determine based on what you'll be using the clip for and the material using to build it.
A: Questions 1,2
Geometry
$$ R= D/2 $$
$$ z = R ( 1+ \cos \alpha ) $$
$$ x = 2 R \sin \alpha $$
Questions 3,4
Mechanics of Materials
Do you want to load test after 3d printing? You should give tube material, diameter, thickness, dimension y,how the force is to be applied, strength/ modulus of material to be used for clamp, the remainder of horizontal dimension $h$ in block etc.
Tensile, compressive stresses can be evaluated first  using direct statics. We find bending and direct stresses, next superimpose them. The design is not mentioned in math site. Recommended to go to mechanical engg SE.
