Design of Main Cylinder

The basic function of the hydraulic cylinder is to convert fluid power into linear machine lift force at that time the cylinder is subjected to internal pressure of the fluid or oil. Since the internal pressure should be high enough to sustain the load then the cylinder must be a heavy-duty cylinder which is expected to be thick to sustain the pressure.

Material selection

Both cast and drawn materials can be selected as cylinder materials for variable height vehicle but the most frequently selected material is called cold drown deep polished low carbon steel with relatively high stress value.

But due to the following reasons we have selected the stainless steel with mechanical properties given below as cylinder material

• Manufacturing feasibility
• Local availability

Material selected	stainless steel
Grade	AISI302
Ultimate tensile stress	σu=655Mpa
Yield tensile stress	σy=260Mpa
Allowable shear stress	τall=150Mpa
Modules of elasticity	E=200Gpa
Modules of rigidity	G=77Gpa

Design snalysis

The wall develops both tangential and radial stress with valves which depend upon the radius.

• Assuming that the longitudinal fibber of the cylinder is equivalently strained
• We can analyze the design as follows

Now the pressure and the thickness can be analyzed using Lame’s equation as follows.

The cylinder is subjected to both radial and tangential stress σ_r and σ_t.

• tangential stress at any radius x

Where, p_i = inner pressure
r_i=inner radius
r_o=outer radius

• radial stress at any radius x is given as:

Since there is no external pressure p_O = 0. Then,

σ_t is maximum at x=r_i and the minimum at x=r_o

 is maximum at x = r_i and 0 at x = r_o

• Now we can use the maximum strain energy theory to evaluate the cylinder failure, Where Bernie equation is derived to calculate the cylinder thickness.
• r_o = r_i + t and the maximum strain theory we get the following equation called Bernie’s equationWhere µ = poison’s ratio
• From geometric analysis the internal diameter of the main cylinder was found to be d₁ = 14cm for diameter of the piston rod (d_p=8cm), but during piston design d_p was corrected to 7cm
  Thus the modified main cylinder is;
  d₁ = 7+2(head thickness of piston) +2(clearance between piston head and the cylinder)
  d₁ = 7+2+2c
  = 7+2(1.5) +2(1)
  = 10cm
• Let us take factor of safety n=2.3
  Then 
• Oil pressure in cylinder tube can be found as:

Balancing force vertically

Assuming the piston is moving upward with uniform velocity the acceleration a=0

Where, d₁– ismain cylinder diameter.

• This pressure is the same over the walls of the tube
• The thickness of the main cylinder isFigure 4.14 Force acting on piston.µ=Poisson’s ratio can be found as follows:Elasticity and rigidity modulus are related by the following equation :Then the thickness t is,The thickness of the main cylinder can be taken as t = 9mm