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

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Discussion Overview

The discussion revolves around determining the deflection of a stylus shaft, specifically one shaped as a truncated cone, under a perpendicular force. Participants are exploring the calculations involved in beam bending, particularly focusing on the effects of varying cross-sections and the connection between different materials used in the stylus.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks to find the deflection at the end of a stylus fixed at one end and subjected to a force, asking for hand calculations.
  • Several participants inquire about the specifics of the stylus, including its application and the nature of the forces acting on it.
  • There is a discussion about the connection between two materials in the stylus and whether the conical section is hollow.
  • Participants express varying levels of experience with beam bending problems, with some indicating difficulties specifically related to the truncated cone geometry.
  • Questions arise regarding the shear and moment diagrams and their relation to the bending of the beam, particularly how to derive the area moment of inertia for the truncated cone.
  • One participant suggests simplifying the problem by considering the beam as a composite structure without joints for initial calculations.

Areas of Agreement / Disagreement

Participants express differing levels of understanding regarding beam bending calculations, particularly in relation to the truncated cone. There is no consensus on how to approach the problem, as some participants are more familiar with the concepts than others.

Contextual Notes

Participants mention various assumptions, such as the nature of the connections between materials and the treatment of the beam as a composite structure. The discussion highlights the complexity of calculating the area moment of inertia for a truncated cone, which remains unresolved.

draculamedula
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TL;DR
Calculation of Bending of the stylus shaft.
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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.
 
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draculamedula said:
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 ?
 
Do you know how to solve beam bending problems? I mean do you have some experience solving beam bending problems?
 
davenn said:
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.
 
Chestermiller said:
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).
 
How are the two materials connected?
Is the conical section hollow?
 
draculamedula said:
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?
 
Lnewqban said:
How are the two materials connected?
Is the conical section hollow?
using screw joints
 
draculamedula said:
using screw joints
What material is the female thread?
How big the thread? M4?
 
  • #10
Lnewqban said:
What material is the female thread?
How big the thread? M4?
Stainless Steel and yes M4
 
  • #11
Chestermiller said:
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.
 
  • #12
draculamedula said:
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.
 
  • #13
Lnewqban said:
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
 
  • #14
draculamedula said:
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?
 
  • #15
Chestermiller said:
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.
 
  • #16
draculamedula said:
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.
 
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  • #17
Chestermiller said:
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?
 
  • #18
draculamedula said:
what about the area moment of inertia?
That's in the equation relating y'' to M.
 
  • #19
Chestermiller said:
That's in the equation relating y'' to M.
Exactly. How can I find that for a truncated cone?
 
  • #20
draculamedula said:
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?
 

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