Design study of a small pressure vessel endplate

A small engineering company is designing an air compressor for a wide range of applications, you are

tasked with the design of the endplate in the pressurised air container with an intended maximum

pressure of 10 bar (1MPa) and a diameter (or square side length a=b) of 0.1m.

There are 4 possible configurations for the vessel and endplate: simply supported circle, simply

supported square, edge clamped circle and edge clamped square (Refer to Configuration Diagrams

on Page 3). The company has also chosen 4 materials from its suppliers to assess: Titanium Alloy,

Aluminium Alloy, Stainless Steel and Mild Steel (Refer to Material Properties Table on Page 3).

I have given you equations for the maximum stress and deflection on Page 5. Do not be alarmed,

that you have not seen them before, it is just a case of applying them. How you set out the report is

your choice but please ensure that the following points are addressed to achieve the best results:

1. Summary of the report: brief description of the design study; the materials and

configurations considered, the final material selected, derived plate thickness for each

material and failure modes. I suggest you write this section of the report last.

2. Parametric design study of the endplate: Using the equations for the maximum stress (smax)

and the supplied dimensions and working pressure, conduct a parametric study with respect

to plate thickness (t), note that smax does not depend on the material. Of the 4

configurations which results in the lowest smax? For this:

? Plot the relationship of smax against t for 0.002<t<0.007 using Excel or Matlab, for

each endplate configuration, on the same graph. Example on Page 4.

? Suggest the best configuration to use for the lowest stress levels.

? The company has not decided on a material but wants some numbers on expected

plate thickness. Suggest a minimum plate thickness, where the maximum stress

does not exceed the yield strength for all materials.

? Finally either draw a diagram, sketch or use CAD software to show the design of

your endplate configuration. Detail any features you have added to reduce stress

concentrations, assess the stresses on the plate (use simple arrows) and suggest

possible manufacturing, machining (if required) processes and how the endplate

would attach to the vessel.

3. Material selection study: The maximum allowable deflection must not exceed 5% of the

plate thickness (customers feel uncomfortable about visible flexing on the vessel surface).

Using this, conduct a material selection study to decide on final plate thickness and chosen

material. For this:

? Use the maximum deflection equation listed for your chosen endplate configuration

to plot ymax against t for 0.002<t<0.007 for each material. Deduce the minimum plate

thickness for each material for a maximum deflection of 5% of the plate thickness.

You may do this visually via a plot or exact solution of equations (I suggest plotting a

line on the same graph of 5% plate thickness and see where this intersects with the

lines for each material).

2

? Using the minimum plate thickness of each material calculate the plate volume and

cost using supplied data.

? Calculate the structural efficiency and cost efficiency of each material using supplied

data. Calculate an application efficiency (Minimum thickness / Cost of Plate) and a

choose a material to use (Hint: Review Worksheet 4 Question 1)

? During the design process a factor of safety (SF) was neglected. Re-plot smax against t

for the chosen configuration and add an SF=2 line. From this decide whether your

chosen material is still suitable, if not suggest a solution.

4. Failure mechanisms and review of study: The performance of an engineered component

must be considered throughout its entire lifetime and to account for usage in the field.

? Given the chosen material give an account of the likely failure modes of vessel; how

can the use and abuse of the vessel lead to premature failure? Consider cyclic stress,

creep, exceeding design pressure, temperature of operation, etc. Give some simple

calculations to back up your explanation.

? From the design study process illustrate any assumptions or simplifications

presented in the brief or made by you. Suggest any improvements to the process

and how you would take the design forward. Would this assessment be sufficient to

progress to production?

5. Conclusion: A brief conclusion to the design study that outlines what you have learned, the

results of the study and how this component could be improved.

General Marks (Total: 100)

? Use of scientific language and correct terminology 5

? Appropriate use and adequate amount of references 5

? Clear labelling and adequate amount of figures, tables, and equations 5

? General presentation of report 10

Report Summary 5

Parametric design study of the endplate mechanism 20

Material Selection Study 20

Failure mechanisms throughout lifecycle and review of study 20

Conclusion 10

Nomenclature

a Rectangular plate length (m)

b Rectangular plate width (m)

E Young’s Modulus of elasticity (N/m2)

p Uniform surface pressure on plate(N/m2)

r Radius of plate (m)

t Thickness of plate (m)

ymax Maximum deflection of plate (m)

smax Maximum stress on plate (N/m2)

*The report should be concise and direct. I recommend that you do not write more than 2000 words

and should take about a working week to complete. For further help please consult the study direct

site for lecture notes and report writing, refer to the following source, or contact me via email:.

http://www.sussex.ac.uk/ei/internal/forstudents/engineeringdesign/studyguides/techreportwriting

3

End Plate Configurations

Source: http://www.roymech.co.uk/Useful_Tables/Mechanics/Plates.html

Case 1 Case 2

Case 3 Case 4

Material Properties (Taken from CES EduPack 2014, Available on Application Jukebox)

Young’s

Modulus

(GPa)

Yield

Strength

(MPa)

Ultimate

Tensile

Strength

(MPa)

Fatigue

Strength

@ 107

cycles

(MPa)

Poisson’s

Ratio

Density

(kg/m3)

Cost

(GBP/kg)

Titanium

Alloy 115 800 1000 600 0.36 4600 15

Aluminium

Alloy 80 120 220 75 0.34 2700 1.4

Stainless

Steel 200 190 480 360 0.27 7800 3.6

Mild Steel 210 300 500 250 0.29 7850 0.35

4

Example Endplate Configuration Graph

Suggested graph of endplate configuration as required by the parametric study. Note that only one

configuration is shown, please plot all four on the same graph.

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

0

100

200

300

400

500

600

700

800

Thickness (mm)

Maximum Stress ?y (MPa)

Maximum Stress against Plate Thickness

Simply Supported Circular

Equations

Disk stress and displacement under constant pressure loads1.Simplifications assuming

the plate to be Steel with a poisson’s ratio of 0.3.

Case 1: Circular Plate, uniform load, edges simply supported.

smax =

1.238pr2

t2 (1)

ymax =

0.696pr4

Et3 (2)

Case 2: Circular Plate, uniform load, edges clamped

smax =

3pr2

4t2 (3)

ymax =

0.171pr4

Et3 (4)

Case 3: Rectangular Flat Plate, uniform load, edges simply supported

smax =

0.75pb2

t2

?

1.61

?

b

a

?3

+ 1

? (5)

ymax =

0.142pb4

Et3

?

2.21

?

b

a

?

+ 1

? (6)

Case 4: Rectangular Flat Plate, uniform load, edges clamped

smax =

pb2

2t2

?

0.623

?

b

a

?6

+ 1

? (7)

ymax =

0.0284pb4

Et3

?

1.056

?

b

a

?5

+ 1

? (8)

1Source of Content: http://www.roymech.co.uk/Useful_Tables/Mechanics/Plates.html

1