Design study of a small pressure vessel endplate

Assignment Brief: 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

2.
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

2.
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