How do I determine I for a truncated cone in the bending of a Stylus Shaft?

[draculamedula]

TL;DR

Calculation of Bending of the stylus shaft.

So I have a Stylus as shown in above fig. Fixed at Point A, Force (F) is applied perpendicular to the stylus axis. How do we find deflection at the end of the Stylus (Made of Two Different Materials as shown in the figure)? Hand Calculations are much appreciated. Thank you.

 

[davenn]

Summary:: Calculation of Bending of the stylus shaft.

So I have a Stylus as shown in above fig.

what sort of stylus ??
what is it being used for ?
what are the forces "F" on the end of it ?

 

[Chestermiller]

Do you know how to solve beam bending problems? I mean do you have some experience solving beam bending problems?

 

[draculamedula]

what sort of stylus ??
what is it being used for ?
what are the forces "F" on the end of it ?

It is a Probing Stylus,
It is used in inspection.
Force F is the force exerted by Workpiece on the stylus.

 

[draculamedula]

Do you know how to solve beam bending problems? I mean do you have some experience solving beam bending problems?

Yes I do, I have problem with the Truncated Cone Part (Tapered Cylinder).

 

[Lnewqban]

How are the two materials connected?
Is the conical section hollow?

 

[Chestermiller]

Yes I do, I have problem with the Truncated Cone Part (Tapered Cylinder).

So you are able to do the shear load and moment diagrams? If so, how is y'' related to M? What do you think the matching conditions at the junction should be?

 

[draculamedula]

How are the two materials connected?
Is the conical section hollow?

using screw joints

 

[Lnewqban]

using screw joints

What material is the female thread?
How big the thread? M4?

 

[draculamedula]

What material is the female thread?
How big the thread? M4?

Stainless Steel and yes M4

 

[draculamedula]

So you are able to do the shear load and moment diagrams? If so, how is y'' related to M? What do you think the matching conditions at the junction should be?

No, I am not able to.

 

[Lnewqban]

Stainless Steel

Could we assume that the weakest link is the female thread into the ceramic rod?
Thread could be M2 x 0.40, M2,5 x 0.50, M3 x 0.5 or M3 x 0.25.

 

[draculamedula]

Could we assume that the weakest link is the female thread into the ceramic rod?

For now, consider the beam with no joints. Just assume it as a composite beam.
One end fixed, applying 1N force at the end as shown in figure. To Find: Deflection of the beam

 

[Chestermiller]

No, I am not able to.

If you have experience doing beam bending problems, what is your difficulty with developing the shear and moment diagrams for this beam?

 

[draculamedula]

If you have experience doing beam bending problems, what is your difficulty with developing the shear and moment diagrams for this beam?

I only have a problem with the truncated cone (varying cross-section) part as I have said earlier.

 

[Chestermiller]

I only have a problem with the truncated cone (varying cross-section) part as I have said earlier.

The shear and moment diagrams involve pure force and moment balances, independent of the shape of the cone.

 

[draculamedula]

The shear and moment diagrams involve pure force and moment balances, independent of the shape of the cone.

what about the area moment of inertia?

 

[Chestermiller]

what about the area moment of inertia?

That's in the equation relating y'' to M.

 

[draculamedula]

That's in the equation relating y'' to M.

Exactly. How can I find that for a truncated cone?

 

[Chestermiller]

Exactly. How can I find that for a truncated cone?

The equation is EIy'' = M. Do you not know how to determine I at each cross section x for a circular cross section?