Engineering - working out a problem with thick and thin hydraulic cylinders

In summary, the conversation revolved around calculating the principal stresses on the surface of a hydraulic cylinder with specified inner and outer diameters and internal pressure. Different equations and methods were discussed, but ultimately the correct answer was obtained using the equations for thick cylinders with internal pressure only. The maximum stresses were found to be 200.8 N/m2 for the circumferential stress and 22.0 N/m2 for the longitudinal stress.
  • #1
ironlight
2
0
"A hydraulic cylinder has an inner diameter 25mm, an outer diameter 34mm and an internal pressure of 60bar. Calculate the principal stresses on the cylinder surface."

2) Listed in the revision notes are several different equations for this question. I've tried each one from thick cylinders to cylinders with internal pressure only, and each one gives me a completely different answer. Listed in the exam papers are Lamé's Equations

1. σ(r) = A - B/r^2
2. σ(Ѳ) = A+ B/r^2

but I'm not sure if this will give the right answer either.

I've also tried Thick Cylinders with Internal Pressure Only:

maximum σc= (r1^2+ r2^2)/(r2^2- r1^2 ) " x" P
maximum σl= (Pr1^2)/(r2^2- r1^2 )


3. I've tried this way first:

r1 = 25/2 = 12.5mm = 0.0125m

r2 = 34/2 = 17mm = 0.017m


maximum σc= (r1^2+ r2^2)/(r2^2- r1^2 ) " x" P


maximum σc= (12.5〖 "x10^-3" 〗^2+17〖 "x10^-3" 〗^2)/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 ) " x" P


maximum σc= (12.5〖 "x10^-3" 〗^2+17〖 "x10^-3" 〗^2)/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 ) " x" 60


maximum σc= (0.156"x10^-3" +0.289"x10^-3" )/(0.289"x10^-3" - 0.156"x10^-3" ) " x" 60


maximum σc= (0.445"x" 10^-3)/(0.133"x" 10^-3) " x" 60


maximum σc= 3.346 "x" 60


maximum σc= 200.76 N/m2



The same figures are used to find the stress of l, σl.


maximum σl= (Pr1^2)/(r2^2- r1^2 ) " "

maximum σl= (60 "x" 12.5〖 "x10^-3" 〗^2)/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 ) " "


maximum σl= (60 "x" 0.156"x10^-3" )/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 )


maximum σl= (9.36"x" 〖10〗^(-3))/(17〖 "x10^-3" 〗^2- 12.5〖 "x10^-3" 〗^2 )


maximum σl= (9.36"x" 〖10〗^(-3))/(0.289"x10^-3" - 0.156"x10^-3" )


maximum σl= (9.36"x" 〖10〗^(-3))/(0.133"x" 〖10〗^(-3) )


maximum σl=22.02"x" 〖10〗^(-6) N/m2


This seems a little odd, so I tried Lamés equations to compare:

Inside radius 12.5mm
Outside radius 17mm

6x10^6 = a - b/r^2

0 = a +b/r^2



6x10^6 = a - b/0.0125^2

a = 6x10^6 + b/0.0125^2



0 = a + b/r^2

0 = 6x10^6 + b/0.0125^2 + b/0.017^2

-6x10^6 = b (1/0.0125^2 + 1/0.017^2)

-6x10^6 = b(9860.2)

b = -608.5



6x10^6 = a - (-)608.5/0.0125^2

6x10^6 - 608.5/0.0125^2 = a

a = 2105600

I also have no idea what a and b should be on here; I just guessed!

Any help appreciated!
 
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  • #2
The correct answer is obtained by using the equations for thick cylinders with internal pressure only:Maximum σc = (r1^2 + r2^2)/(r2^2 - r1^2) x PMaximum σl = (Pr1^2)/(r2^2 - r1^2)where r1 = 25/2 = 12.5 mm and r2 = 34/2 = 17 mm Maximum σc = (12.5^2 + 17^2)/(17^2 - 12.5^2) x 60 = 200.8 N/m2Maximum σl = (60 x 12.5^2)/(17^2 - 12.5^2) = 22.0 N/m2
 

1. How do thick and thin hydraulic cylinders work together?

Thick and thin hydraulic cylinders work together through a process called hydraulic amplification. This means that the thicker cylinder, which has a larger surface area, is able to generate more force than the thinner cylinder. The thinner cylinder is used to control the movement and speed of the thicker cylinder.

2. What are the common issues that can arise when using thick and thin hydraulic cylinders?

Some common issues that can arise when working with thick and thin hydraulic cylinders include leaks, overheating, and uneven wear on the cylinders. These issues can be caused by improper maintenance, incorrect sizing of the cylinders, or using the cylinders in conditions they are not designed for.

3. How do you determine the right size and type of hydraulic cylinders for a specific problem?

Determining the right size and type of hydraulic cylinders for a specific problem involves considering factors such as the required force, speed, and working conditions. Calculations and simulations may also be used to determine the optimal size and type of cylinders for the problem at hand.

4. What are some tips for maintaining and troubleshooting thick and thin hydraulic cylinders?

To maintain and troubleshoot thick and thin hydraulic cylinders, it is important to regularly check for leaks, ensure proper lubrication, and replace worn or damaged parts. Troubleshooting may involve checking for air in the system, inspecting the seals and connections, and adjusting the flow rate or pressure.

5. How do advancements in technology impact the use of thick and thin hydraulic cylinders?

Advancements in technology have led to the development of more efficient and precise hydraulic cylinders, as well as new materials and designs that can withstand higher pressures and temperatures. These advancements have also made it easier to monitor and control the performance of hydraulic systems, resulting in improved reliability and safety.

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