Hertz contact problems of three cylinders

[Amaelle]

Homework Statement

look at the image

Relevant Equations

hertz contact

Greetings
i´m trying to find the Force applied by the upper roller to calculate the contact surface.

Here is indeed my solution

2*FR1* cos31,38=F=1500N
FR1=878,57N (which is wrong the correct solution says 818,1N)
FR1 is the force normal to the surface of contact.

any help would highly appreciated

thank you!

 

[berkeman]

Sorry, I'm not seeing where "L" is defined...

 

[Amaelle]

Sorry L and S are equal to 0 , it was for the students so that each one do a different assignment sorry for the confusion :)

 

[berkeman]

Homework Statement:: look at the image
Relevant Equations:: hertz contact

cos31,38

In that case, I get a different value for that angle. Can you show your calculation for how you solved for it?

 

[Amaelle]

Thank you here it is

we have an isoscele triangle
as you can see the first side is the some of the R1+R2=48
I got the other side by Pythagore
48^2-25^2=1679 means the side value is 40,97
and then the angle =invers.tangente(25/40,97) =31,38°
thank you!

 

[berkeman]

Oh, I see now that I misread this as c = 25 + 5. But if that is "S" and not "5", then I get the same angle as you. I'm not sure where the discrepancy is in your solution then...

 

[Amaelle]

thank you for taking time to answer me!

 

[berkeman]

I'm not sure where the discrepancy is in your solution then...

Could it have something to do with slight deformation or friction at the contact points? If they are infinitely hard and frictionless surfaces I think your answer is correct. But since they give so much other information... What chapter is this out of in the book? Do they discuss any other factors that would affect this calculation in that part of the text?

 

[berkeman]

paging... @jrmichler

 

[Amaelle]

Could it have something to do with slight deformation or friction at the contact points? If they are infinitely hard and frictionless surfaces I think your answer is correct. But since they give so much other information... What chapter is this out of in the book? Do they discuss any other factors that would affect this calculation in that part of the text?

Indeed one of the asymptions is the absence of frictions, indeed I'm surprised as you because this is an undergrad course so there shouldn't be any hidden tricks

 

[jrmichler]

Realistic assumptions, given the material properties and that this is an undergrad problem:

Zero deflection of rollers due to Hertz contact stress
Zero deflection in bearings
Zero friction
No hidden tricks

I get exactly the same contact force as the OP - 878.57 N.

I agree with the calculations by both @Amaelle and @berkeman, and have no idea where the given answer came from. I can only guess that somebody entered a number wrong.

 

[Amaelle]

@berkeman @jrmichler thanks a million for your time and help!

 

[Amaelle]

just an update! the solution was correct it was the Professor mistake to give wrong numbers
Thanks a million guys!