diseno_cilindro_hidraulico

Chapter 3

DESIGN OF A HYDRAULIC CYLINDER

3.1 Introduction

This chapter describes a design procedure of a hydraulic cylinder as an example for

the design of a pressure vessel. Engineers can use classical design and stress

analysis methods to design pressure vessels; still it is advisable to refer to standard

codes and their materials selection to check their results. An important reference in

this area is the ASME Pressure Vessel Code VIII [12], available in KFUPM library.

In this chapter, both classical stress analysis and the ASME methods are used to

illustrate the design procedure for a hydraulic cylinder.

3.2 Objectives of the design project

This design project will teach the student how to:

1.Design a hydraulic or a pneumatic cylinder (pressure vessel).

2.Make stress analysis for pressure vessels using both classical stress analysis

(available in your textbook) and ASME Pressure Vessel Code VIII [12] and

compare the results. Also, derived stress formulas in books such as formulas

for stress and strain by Roark [13] can be used to compare results.

3.Select the proper materials for such an application.

4.Select the standard parts including bolts, nuts, ...

5.Apply the theories of fatigue failure to the design of structures.

6.Design fillet welds

3.3 Description of the design project

The student is expected to design a general-purpose hydraulic cylinder with certain

specifications:

1.Pushing load = compression load F (in metric tons or kip)

2.Stroke (in mm or in).

3.Mounting type (End conditions and type of support). A more practical design

involves all possible types of mountings, such as, male and female clevis

mountings and base mounting.

4.Safety factor (A high value should be selected for such an application).

5.Pressure:- Working pressure Pmax

- Design pressure Pdesign: it is equal to a design factor multiplied by

the working pressure. The design factor value is usually between

1.5 and 2 and it is considered as an extra safety factor.

6.Any size limitations.

3.4 Design procedure

3.4.1 Making a design sketch

Depending on the specified type of mounting, the designer can make a sketch for

the suggested design. A possible design sketch is shown in the figure 3.1. Three

types of mounting are shown in the sketch. This will make the product of more

general use. The sketch shows the main parts of the suggested cylinder design. As

usual in design many other design sketches can be made and that depends on the

experience and the creativity of the designer.

Male

clevis

Female

clevis

Connecting

rodPiston

Flange

Base

mount

BarrelCover

Hex

slotted

nutConnecting

bolts

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Figure 3.1 A design sketch for a suggested design for a hydraulic cylinder with all types

of possible mounting available [14]

3.4.2 Selection of materials

It is preferred for students and beginning engineers to start the design by selecting

proper materials for the different parts of the suggested model, especially if there

are no size limitations.

A- Material of the connecting rod

A cold-drawn medium to high carbon steel should be used for such an application.

The reasons behind this selection are:

1. The connecting rod is supposed to be subjected to wear due to friction with the

cover of the cylinder and cold-drawn materials are more resistant to wear.

2. The connecting rod is assumed to have very accurate surface finish and it is

cheaper and easier to achieve that with cold-drawn materials.

3. The connecting rod is subjected to large compressive stresses. To avoid ending

up with an excessive size for the cylinder, a medium to high carbon steel should

be used. AISI 1045 CD (Table E 20 [4]) is an example for such a selection.

Also, cold-drawn materials are stronger than hot-rolled materials having the

same carbon percentage.

B- Material of the barrel

A low to medium carbon cold-drawn steel with a quenching and tempering heat

treatment can be used for this part of the cylinder. The reasons behind this selection

are:

1.The different other parts of the cylinder (such as flanges and mounts) are usually

welded to the barrel. It is difficult and time consuming to weld high carbon

steel. Low to medium carbon steels are more preferred for this application.

2.The barrel will be subjected to wear due to contact with the piston and accurate

tolerances are needed for the finish of the inside of the barrel. A cold-drawn

material is more suitable for the barrel.

3.Cold drawn materials are usually followed by heat treatment to relieve the

residual stresses in the material. Quenching and tempering heat treatment is

preferred over annealing to achieve the highest possible strength of the material.

It is true that annealing produces softer materials, but their ultimate strength is

much lower, which could result in a much larger cylinder.

Also, It is strongly recommended that the designer select a material for the barrel

according to ASME code section VIII [12] recommendation, for example SA-53.

C- Material of the cover

Gray cast iron can be used for such an application, since it is a good wear resistant

material. Also, low carbon cold-drawn steel can be selected. The cost of the two

materials has to be compared.

D- Material of the piston

For the reason of wear again, a cold-drawn material has to be selected for the

piston.

E- Material of the base and clevis mounts and the flanges

Low carbon hot rolled steels can be selected for these parts, since they are usually

welded to the barrel.

3.4.3 Sizing the different parts of the cylinder

The sizes of the different components of the cylinder can be determined as follows:

A- Determining the diameter of the connecting rod

The connecting rod is subjected to a buckling load. According to the suggested

design, the 4 types of possible different end conditions can be assumed:

1.One end-fixed, one end free

2.Rounded-Rounded ends

3.One end fixed- one end rounded

4.Both ends fixed

Then, based on the above analysis, the highest resulting diameter can be selected

(The next preferred size should be selected from Table E-17 of the textbook [4]).

Similar analysis has been made in the project of screw-jack design (chapter 2). It

can be used as a reference. It is important to note here that the buckling analysis

should be made using the maximum stroke of the piston.

B- Determining the required inside diameter of the barrel

The inside barrel diameter D can be calculated from the balance of forces (see

figure 3.2)

×=

4

πD P F

2

(3-1)

where P is the design pressure and F is the compression load on the connecting rod.

It is important here to remember that if there is a push-pull cylinder, then the

pulling load should be equivalent to P × π (D2-d

2)/4.

P

d

D

F

Figure 3.2. A force balance on the piston-rod assembly.

C- Determining the required thickness of the barrel

The ASME code [12] stress and shell thickness formula, based on inside radius of

the cylinder, approximates the more accurate thick-wall formula of Lame’as

follows:

P 0.6 -SE

PR t = (3-2)

where

R= inner radius of barrel = (D/2)

S = the allowable ASME code stress and it can be considered as the yield stress of

the barrel material.

E = the code weld-joint efficiency (joints with flanges and mounts welded to the

barrel).

See also reference 5 for more detail on this formula.

To determine the weld joint efficiency, the following information should be

provided:

1.Type of weld: usually flanges and nozzles are welded to pressure vessels, using

double welding butt type with an extra fillet weld for rigidity purposes (see

chapter 4 of manual and 9 of textbook [4]).

2.Degree of weld examination: it is recommended that spot-welding be used for

such an application.

For a double welded butt type joint with spot examination, the efficiency of the

joint specified by ASME is 0.85 [12]. It is also important to notice that the

condition of Pdesign < 0.385 SE is also satisfied when applying the above equation

for finding the thickness of the barrel [12].

The specification of the selected standard barrel requires the following information:

- Outer diameter of the barrel (OD).

- Thickness of the barrel (t).

- Identification code No.

D- Flange design

The design of the flanges requires the following information:

1.Type, size and location of bolts:

Tentatively, standard metric bolts can be selected (Tables 8.4 and 8.5,

textbook, [3, 4]) with medium to high carbon content steel. The selection of the

standard size here is important, since according to ASME code section VIII

[12], there is a minimum number of bolts that should be used for such an

application.

2.Thickness of the circular cover:

The bolts connecting the cover are placed at a diametral circumference equal to

d1 and the cover is pressurized from inside as shown in figure 3.3. For stress

analysis it can be assumed that the cover acts as a beam, which is fixed at a

certain location and subjected at its surface to a distributed load. Figure 3.4

shows the applied loads at the section, where the beam is fixed (the location of

bolts). The resulting loads are:

The shear load:

(3-3) FV =

The bending moment:

)4.3(2

d FM 1×=

The resulting stresses are calculated and based on this the thickness of the plate

is specified.

t1

AA

A-A

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d1

P

D

Figure 3.3. A schematic representation for the cover of the pressure vessel.

t1

π d1

V

M

Figure 3.4. Resultant loads on the cover due to the applied pressure.

ASME code section VIII provides the following formula to determine the thickness

of the cover of a pressure vessel:

S

CPdt 11 = (3-5)

where

d1 = Diametral circumference at which the connected bolts are placed (in.)

P = Design pressure (psi)

S = Maximum allowable stress value (psi) depending on the choice of material of

the cover (yield strength of the cover material).

C = Factor depending on the method of attachment. For bolted connections, this

value is equal to 0.25.

Based on proper assumptions, it is also possible to determine the thickness of the

cover using the book Formulas for stress and strain by Roark [11] and compare

the results with the value obtained from the above classical stress analysis.

The design of the flange shown in figure 3.5 is a common type, where the flange is

joined to the barrel by a fully penetrated double butt-welding, reinforced with a

single fillet weld.

t2

t

Full penetration

double-butt

welding

Fillet welding

Figure 3.5 A schematic representation for a flange with full penetration butt-

welding reinforced with a single fillet weld.

The flange can be considered here as a beam, which is supported at the end as

shown in figure 3.6.

t2

F

X

V

M

Figure 3.6 Loads acting on the flange.

It is clear that this is a triaxial stress state (figure 3.7) and the safety analysis should

be made based on that. The diameter at the base of the beam (flange), db, is

equivalent to the outside diameter of the selected barrel.

t2σ

τ

πdb

Figure 3.7 Stresses acting at the base of the flange.

Appendix II (Rules for bolted flange connections), ASME code, section VIII [12]

provides very detailed procedures and laws for designing and selecting standard and

non standard flanges. This includes the size of flange, gasket type and location, size

of bolts and welding size. Designers can follow such instructions.

This type of flange is considered as an optional type of flange according to ASME

code section VIII [12] and its thickness is given by the formula:

1f

p

2dS

M1.78t = (3-6)

where Mp is the resulting moment due to hydrostatic forces and gasket load due to

seating pressure on the flange (Ib-in). Sf is the allowable design stress for material

of the flange (psi) and d1 is the bolt-circle diameter (inches) (Fig. 3.3.).

The strength analysis for welding is not required for the flange; since the full

strength of the weld is achieved by full penetration all around double butt welds.

The fillet weld will be used here for rigidity purposes. A rigidity design is 33%

stronger than a strength design. This means that the fillet weld will add strength to

the joint that is equivalent to 33 % of the full strength, which is achieved by the butt

welds [12]

According to the rule of thumb by AWS [11], the required fillet weld leg size for

rigidity design is equivalent to 1/4 t to 3/8 t, where t is the thickness of the thinner

of the two parts, assuming that both sides are welded for full length. Since in this

case, the weld is only from one side, this means that the size of fillet weld has to be

doubled, which is equivalent to 1/2 t to 3/4 t. The AWS provides complete details

(angles and sizes) for butt and fillet welds (See Appendix).

E- Determining the required number of connecting bolts

Reference [4] provides a suitable fatigue analysis procedure to determine the

required number of bolts for such a case. It is assumed in this case that the failure

will occur only due to the fatigue load and the minimum stress can be assumed to

be zero, since there is no load on the cylinder when it is not in operation.

The alternating stress is given as:

N2A

FCσ

t

1a = (3-7)

where

N = number of bolts

F = total load transmitted to bolts

cb

b

1kk

kC

+= (3-8)

where

kb = stiffness constant of bolt and

km = combined stiffness of both the cover and the flange

To find the required number of bolts, the alternating stress should be compared with

the allowable alternating stress Sa / n, where n is the design safety factor and Sa is

given by the formula (Eq. 8-35, [3,4]):

e

ut

t

iut

a

S

S1

A

FS

S

+

−= (3-9)

where

Sut = the ultimate strength of the bolt material (Tables 8-4 – 8-6)

At = the tensile strength of the bolt material (Tables 8-1 and 8-2)

Fi = the preload applied to bolt = 75 % of the proof load of the bolt for

reused connections, (Eq. 8-25).

Se = the endurance limit of the selected bolt.

Another simple approach to find the number of bolts is to calculate the tensile

stresses on each the bolts and compare that with the ultimate stress, but since this

approach does not take the conditions of fatigue, a much larger safety factor should

be used.

Whatever the used approach, it is preferred to check the calculated number of bolts

with the minimum number specified by ASME code, section VIII [12].

F- Design of the piston

To design the piston (figure 3.8), it is required to determine both the piston

thickness (t3) and the piston-rod engagement length (t4).

t3

t4

D

Figure 3.8 A schematic representation for the piston.

The piston in this case can be considered as a flat circular plate subjected to uniform

pressure from one side only, with the outer edge free and the inner edge fixed as

shown in figure 3.9.

d

DP

Figure 3.9: Pressure acting on the piston plate.

Many books including formulas for stress and strain by Roark [13] provide the

unit-shear force (pounds per inch of circumference) and the unit radial bending

moment (Inch-pounds per inch of circumference). Bending stress and shear force

can be evaluated based on that and the proper failure theory can be used to estimate

the thickness of the piston. Also, classical stress analysis can be made to determine

the thickness of the piston by treating it as a beam and finding the stresses at the

fixed position of the piston, then applying failure theories..

To determine the required length of engagement (t4), a standard unified coarse

thread has to be selected (see tables 8.1 and 8.2, textbook). Then, the required

number of threads needed to fasten the piston and rod can be calculated based on

the shear area of the selected standard thread;

factorsafety

S0.5

threadsofno.areashear

F y=×

(3-10)

where Sy is the yield strength of the weaker of the two materials (rod and piston).

Based on the number of threads calculated, the length of engagement can be

calculated as:

(3-11) PitchThread threadsofno.t 4 ×=

To ensure fastening the piston and rod, both a standard hexagonal slotted nut and a

cotter pin have to be selected for the use in this application.[5, 15].

G- Design of mounts

Design of mounts includes the following points:

1.Selections of appropriate materials for the mount.

2.Use of standard sizes (threaded holes, pins, nuts, etc.) as possible in the design of

the mount.

3.Selecting appropriate method for joining the mount to the structure.

4.Checking safety against all possible stresses on the mount.

For the clevis mounts, the design of either a male or a female clevis system starts by

selecting an appropriate standard pin size and the shearing stresses are checked on

the pin. References [5,15] can be used for such purpose. In this case, as an example,

both types of clevis are used to illustrate the approaches (see figure 3.10).

r1

r2

standard metric

thread

standard pin

hole size

Female clevis Male clevis

Figure 3.10 Male and female clevis mount.

The main stresses to be checked for the clevis are:

1. Tensile stress in the net (narrowest) area of the male clevis.

2. Shear stress in the male clevis due to the tear –out.

3. Tensile stress in the net (narrowest) area of the female clevis.

4. Shear stress in the net (narrowest) area of female clevis due to tear-out.

5. Compressive stress male clevis due to bearing pressure of the pin.

6. Compressive stress in female clevis due to bearing pressure on the pin.

Based on the above stress analysis, the sizes of the male and female clevis mounts

can be found. Usually the outer radius (r2) can be assumed to be 1.5 to 2 times the

radius (r1).

In the second design, the male clevis will be welded to the bottom cover of the

cylinder by using fillet welds. Welding analysis has to be made here to find the

proper welding fillet material and sizes (refer to chapter 9 of your textbook). The

female clevis will be joined to the piston rod by threads. Suitable standard threading

should be used and based on the shear area of the selected thread, the required

number of threads can be found to determine the engagement length. Figure 3.11

illustrates a possible base mount design.

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Standard threaded

holes for standard

selected bolts

Pushing force ( F )

All arroud fillet

joining the base

to the barrel

FshearF

shear

Faxial

Faxial

L

H

Figure 3.11 A possible design for the base mount.

Design of the base includes the following points:

1. Determining the size, material and number of bolts required to hold the

base plate. A suitable standard size of bolts can be selected and based on the

tensile and shear area of the bolts, the number of bolts can be calculated. It

should be reminded here that tensile forces on bolts result from the torque (F×

H). For calculations here, a large safety factor should be considered assuming

fatigue conditions.

2. Determining the sizes of the base plates. An easily-weldable material

should be selected for the plates The safety of the plates should be checked

against the following stresses:

a. Combined bending stresses resulting moments due to the axial and

horizontal forces on the plates.

b. Shearing stresses on the plates due to vertical and horizontal forces.

c. Tensile stresses on the net areas of plates due to the horizontal forces.

d. Shear stresses on plates due to tear out caused by the horizontal forces.

e. Compressive stresses on plates due to bearing pressure caused by the

vertical forces.

f. Shear stresses in the plates due to the vertical forces on the plates.

3. Welding of the plates to the Barrel. The number and length of welding

areas should be specified. Then, based on the total vertical and horizontal shear

forces transmitted to the welds, the size of fillet welds can be calculated.

3-5. Summary

Once you have completed the design, it is recommended that you summarize your

results. Include the standard dimensions of the major parts and their materials.

3-6. Drawings

Make detail and assembly drawings including dimensions, tolerances and surface

finish.

APPENDIX B

Welding Symbols and Loads

B-1 TYPICAL AWS DRAFTING SYMBOLS FOR WELDS [11]

B-2 complete penetration groove welds [11]

B-3 TYPES OF LOADING ON WELDS [Theory & Problems of

Machine Design, Shaume’s Series ]

B-4 PROPERTIES OF LOAD TREATED AS A LINE [Theory &

Problems of Machine Design, Shaume’s Series ]

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