KU1

Engineering Tripos Part IIA, 3C8: Machine Design, 2025-26

Module Leader

Prof MPF Sutcliffe

Lecturers

Prof M Sutcliffe, Dr R Roebuck, Dr X Na

Lab Leader

Dr X Na

Timing and Structure

Michaelmas term.16 lectures.

Aims

The aims of the course are to:

Analyse the contact stresses and kinematical behaviour of solid contacts and to understand the design of rolling element bearings and other machine elements.
Understand the design of involute gears and appreciate the stress limits and practical problems of gears.
To analyse the behaviour of multiple gear drives and planetary gears.
Understand how components are combined to make up a mechanical power transmission system, including power matching to achieve a desired operating point.
Apply the principles of power matching to hybrid drives.
Introduce methods for specifying the type and arrangement of rolling element bearings to meet a specified duty.

Objectives

As specific objectives, by the end of the course students should be able to:

Calculate the strength limitations of solid contacts.
Analyse the kinematical behaviour of contacts, especially in rotating machinery.
Understand and analyse the performance of friction drives.
Be familiar with the geometry and kinematics of involute gear wheels and racks.
Understand the criterion for tooth bending failure and be able to derive the Hertz pressure at tooth contacts.
Use power and torque calculations to analyse epicyclic gears and multiple gear drives.
Understand how power transmission components are used as part of a system, including hybrid drives.
Determine the operating point and calculate the optimum speed ratio for specified conditions.
Select a rolling element bearing for a specific duty.

Content

Mechanics of contacts (5L) Dr Richard Roebuck

Hertzian point contacts
Stresses and stiffness
Hertzian line contacts
Applications in bearings and CVTs
Traction drives and CVTs

Gears (6L) Prof. Michael Sutcliffe

Geometry and kinematics
Failure, root bending and contact fatigue
Design and applications
Multiple drives and planetary gears
Design calculations for planetary gears

Power matching (3L) Dr Xiaoxiang Na

Introduction and applications: automotive transmission, bicycle transmission
Sources and loads; devices and their characteristics
Power matching using a simple gear ratio
Hybrid drives

Rolling element bearings (2L) Dr Xiaoxiang Na

Bearing types; life equation
Shaft and bearing arrangements

Examples papers

Examples Paper 1 - Mechanics of contacts (issued at lecture 1)

Examples Paper 2 - Gears (issued at lecture 6)

Examples Paper 3 - Power matching, rolling element bearings (issued at lecture 12)

Coursework

Power output characteristic of a cyclist

In this experiment the power output charateristic of a cyclist will be determined by holding the heart rate (a proxy for power input) constant and determining the dependence of crank torque and crank power on crank speed.

Learning objectives:

to calibrate and operate instrumentation to measure human power output
to propose and test an hypothesis using measured data with large inherent uncertainty
to understand the power output characteristic of a cyclist

Practical information:

Sessions will take place in the Baker Building, South Wing Mechanics Laboratory, during weeks 2 to 8 (Fridays and Wednesdays, 11am-1pm)
This activity does involve preliminary work, approximately 40 minutes: read the lab sheet carefully and watch the demonstration video before the session.
Book a timeslot online via the moodle site.
The practical needs to be done in pairs, with at least one member of the pair being comfortable riding the stationary bicycle. It is not possible to perform the experiment individually.
The lab report must be written individually. All data processing, analysis and interpretation performed after the lab session must be done independently and not in collaboration with each other or anyone else.

Full Technical Report:

Students will have the option to submit a Full Technical Report. The FTR should be a complete, detailed, formal report of the experiment, suitable for publication in an engineering journal. It should include all of the information necessary for the reader to understand the aim, objectives, apparatus, method, results, analysis, discussion and conclusions. In addition the FTR should describe in precise engineering terms the operating principles of three different commercially-available devices for measuring cyclist power output, and comment upon likely sources and magnitudes of error.

Booklists

Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

Last modified: 04/06/2025 13:18

Engineering Tripos Part IIA, 3C8: Machine Design, 2021-22

Timing and Structure

Michaelmas term.16 lectures. All lectures to be delivered in-person.

Aims

The aims of the course are to:

Analyse the contact stresses and kinematical behaviour of solid contacts and to understand the design of rolling element bearings and other machine elements.
Understand the design of involute gears and appreciate the stress limits and practical problems of gears.
To analyse the behaviour of multiple gear drives and planetary gears.
Understand how components are combined to make up a mechanical power transmission system, including power matching to achieve a desired operating point.
Apply the principles of power matching to hybrid drives.
Introduce methods for specifying the type and arrangement of rolling element bearings to meet a specified duty.

Objectives

As specific objectives, by the end of the course students should be able to:

Calculate the strength limitations of solid contacts.
Analyse the kinematical behaviour of contacts, especially in rotating machinery.
Understand and analyse the performance of friction drives.
Be familiar with the geometry and kinematics of involute gear wheels and racks.
Understand the criterion for tooth bending failure and be able to derive the Hertz pressure at tooth contacts.
Use power and torque calculations to analyse epicyclic gears and multiple gear drives.
Understand how power transmission components are used as part of a system, including hybrid drives.
Determine the operating point and calculate the optimum speed ratio for specified conditions.
Select a rolling element bearing for a specific duty.

Content

Mechanics of contacts (5L) Dr Richard Roebuck

Hertzian point contacts
Stresses and stiffness
Hertzian line contacts
Applications in bearings and CVTs
Traction drives and CVTs

Gears (6L) Prof Michael Sutcliffe

Geometry and kinematics
Failure, root bending and contact fatigue
Design and applications
Multiple drives and planetary gears
Design calculations for planetary gears

Power matching (3L) Dr David Cole

Introduction and applications: automotive transmission, bicycle transmission
Sources and loads; devices and their characteristics
Power matching using a simple gear ratio
Hybrid drives

Rolling element bearings (2L) Dr David Cole

Bearing types; life equation
Shaft and bearing arrangements

Further notes

3C8 Teaching Arrangements for Michaelmas Term 2021

It is planned to teach this module entirely in person, while following all guidelines and regulations concerning covid. Since the module is likely to have fewer than 100 students, all lectures will be delivered in person. Lectures will be recorded but not live-streamed. Supervision arrangements are still to be finalised. It is hoped that normal supervision arrangements will be possible (groups of 2-4 students, 3 supervsions in Mich term plus one revision supervision), but social distancing constraints might require a blend of in person and online provision. Supervisions will be augmented by video cribs of the examples papers. It is planned that the courework experiment will be performed as normal, with students working in the lab in pairs with appropriate mask wearing and social distancing.

Examples papers

Examples Paper 1 - Mechanics of contacts (issued at lecture 1)

Examples Paper 2 - Gears (issued at lecture 6)

Examples Paper 3 - Power matching, rolling element bearings (issued at lecture 12)

Coursework

Power output characteristic of a cyclist

Learning objectives:

to calibrate and operate instrumentation to measure human power output
to propose and test an hypothesis using measured data with large inherent uncertainty
to understand the power output characteristic of a cyclist

Practical information:

Sessions will take place in the Baker Building, South Wing Mechanics Laboratory, during weeks 2 to 8.
This activity does involve preliminary work, approximately 40 minutes: read the lab sheet carefully and watch the demonstration video before the session.
Book a timeslot online via the moodle site.
The practical needs to be done in pairs, with at least one member of the pair being comfortable riding the stationary bicycle

Full Technical Report:

Booklists

Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

Last modified: 24/09/2021 15:27

Engineering Tripos Part IIA, 3C8: Machine Design, 2024-25

Module Leader

Prof MPF Sutcliffe

Lecturers

Prof M Sutcliffe, Dr R Roebuck, Dr X Na

Lab Leader

Dr X Na

Timing and Structure

Michaelmas term.16 lectures.

Aims

The aims of the course are to:

Analyse the contact stresses and kinematical behaviour of solid contacts and to understand the design of rolling element bearings and other machine elements.
Understand the design of involute gears and appreciate the stress limits and practical problems of gears.
To analyse the behaviour of multiple gear drives and planetary gears.
Understand how components are combined to make up a mechanical power transmission system, including power matching to achieve a desired operating point.
Apply the principles of power matching to hybrid drives.
Introduce methods for specifying the type and arrangement of rolling element bearings to meet a specified duty.

Objectives

As specific objectives, by the end of the course students should be able to:

Calculate the strength limitations of solid contacts.
Analyse the kinematical behaviour of contacts, especially in rotating machinery.
Understand and analyse the performance of friction drives.
Be familiar with the geometry and kinematics of involute gear wheels and racks.
Understand the criterion for tooth bending failure and be able to derive the Hertz pressure at tooth contacts.
Use power and torque calculations to analyse epicyclic gears and multiple gear drives.
Understand how power transmission components are used as part of a system, including hybrid drives.
Determine the operating point and calculate the optimum speed ratio for specified conditions.
Select a rolling element bearing for a specific duty.

Content

Mechanics of contacts (5L) Dr Richard Roebuck

Hertzian point contacts
Stresses and stiffness
Hertzian line contacts
Applications in bearings and CVTs
Traction drives and CVTs

Gears (6L) Prof. Michael Sutcliffe

Geometry and kinematics
Failure, root bending and contact fatigue
Design and applications
Multiple drives and planetary gears
Design calculations for planetary gears

Power matching (3L) Dr Xiaoxiang Na

Introduction and applications: automotive transmission, bicycle transmission
Sources and loads; devices and their characteristics
Power matching using a simple gear ratio
Hybrid drives

Rolling element bearings (2L) Dr Xiaoxiang Na

Bearing types; life equation
Shaft and bearing arrangements

Examples papers

Examples Paper 1 - Mechanics of contacts (issued at lecture 1)

Examples Paper 2 - Gears (issued at lecture 6)

Examples Paper 3 - Power matching, rolling element bearings (issued at lecture 12)

Coursework

Power output characteristic of a cyclist

Learning objectives:

to calibrate and operate instrumentation to measure human power output
to propose and test an hypothesis using measured data with large inherent uncertainty
to understand the power output characteristic of a cyclist

Practical information:

Sessions will take place in the Baker Building, South Wing Mechanics Laboratory, during weeks 2 to 8 (Fridays and Wednesdays, 11am-1pm)
This activity does involve preliminary work, approximately 40 minutes: read the lab sheet carefully and watch the demonstration video before the session.
Book a timeslot online via the moodle site.
The practical needs to be done in pairs, with at least one member of the pair being comfortable riding the stationary bicycle. It is not possible to perform the experiment individually.
The lab report must be written individually. All data processing, analysis and interpretation performed after the lab session must be done independently and not in collaboration with each other or anyone else.

Full Technical Report:

Booklists

Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

Last modified: 31/05/2024 07:28

Engineering Tripos Part IIA, 3C8: Machine Design, 2022-23

Module Leader

Prof. DJ Cole

Lecturers

Prof. DJ Cole, Prof. MPF Sutcliffe and Dr RL Roebuck

Lab Leader

Prof. DJ Cole

Timing and Structure

Michaelmas term.16 lectures.

Aims

The aims of the course are to:

Analyse the contact stresses and kinematical behaviour of solid contacts and to understand the design of rolling element bearings and other machine elements.
Understand the design of involute gears and appreciate the stress limits and practical problems of gears.
To analyse the behaviour of multiple gear drives and planetary gears.
Understand how components are combined to make up a mechanical power transmission system, including power matching to achieve a desired operating point.
Apply the principles of power matching to hybrid drives.
Introduce methods for specifying the type and arrangement of rolling element bearings to meet a specified duty.

Objectives

As specific objectives, by the end of the course students should be able to:

Calculate the strength limitations of solid contacts.
Analyse the kinematical behaviour of contacts, especially in rotating machinery.
Understand and analyse the performance of friction drives.
Be familiar with the geometry and kinematics of involute gear wheels and racks.
Understand the criterion for tooth bending failure and be able to derive the Hertz pressure at tooth contacts.
Use power and torque calculations to analyse epicyclic gears and multiple gear drives.
Understand how power transmission components are used as part of a system, including hybrid drives.
Determine the operating point and calculate the optimum speed ratio for specified conditions.
Select a rolling element bearing for a specific duty.

Content

Mechanics of contacts (5L) Dr Richard Roebuck

Hertzian point contacts
Stresses and stiffness
Hertzian line contacts
Applications in bearings and CVTs
Traction drives and CVTs

Gears (6L) Prof. Michael Sutcliffe

Geometry and kinematics
Failure, root bending and contact fatigue
Design and applications
Multiple drives and planetary gears
Design calculations for planetary gears

Power matching (3L) Prof. David Cole

Introduction and applications: automotive transmission, bicycle transmission
Sources and loads; devices and their characteristics
Power matching using a simple gear ratio
Hybrid drives

Rolling element bearings (2L) Prof. David Cole

Bearing types; life equation
Shaft and bearing arrangements

Examples papers

Examples Paper 1 - Mechanics of contacts (issued at lecture 1)

Examples Paper 2 - Gears (issued at lecture 6)

Examples Paper 3 - Power matching, rolling element bearings (issued at lecture 12)

Coursework

Power output characteristic of a cyclist

Learning objectives:

to calibrate and operate instrumentation to measure human power output
to propose and test an hypothesis using measured data with large inherent uncertainty
to understand the power output characteristic of a cyclist

Practical information:

Sessions will take place in the Baker Building, South Wing Mechanics Laboratory, during weeks 2 to 8 (Fridays and Wednesdays, 11am-1pm)
This activity does involve preliminary work, approximately 40 minutes: read the lab sheet carefully and watch the demonstration video before the session.
Book a timeslot online via the moodle site.
The practical needs to be done in pairs, with at least one member of the pair being comfortable riding the stationary bicycle. It is not possible to perform the experiment individually.
The lab report must be written individually. All data processing, analysis and interpretation performed after the lab session must be done independently and not in collaboration with each other or anyone else.

Full Technical Report:

Booklists

Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

Last modified: 29/09/2022 11:11

Engineering Tripos Part IIA, 3C8: Machine Design, 2017-18

Module Leader

Dr D Cole

Lecturers

Dr D Cole and Dr R Roebuck

Lab Leader

Dr D Cole

Timing and Structure

Michaelmas term. 16 lectures.

Aims

The aims of the course are to:

Analyse the contact stresses and kinematical behaviour of solid contacts and to understand the design of rolling element bearings and other machine elements.
Understand the design of involute gears and appreciate the stress limits and practical problems of gears.
To analyse the behaviour of multiple gear drives and planetary gears.
Understand how components are combined to make up a mechanical power transmission system, including power matching to achieve a desired operating point.
Apply the principles of power matching to hybrid drives.
Introduce methods for specifying the type and arrangement of rolling element bearings to meet a specified duty.

Objectives

As specific objectives, by the end of the course students should be able to:

Calculate the strength limitations of solid contacts.
Analyse the kinematical behaviour of contacts, especially in rotating machinery.
Understand and analyse the performance of friction drives.
Be familiar with the geometry and kinematics of involute gear wheels and racks.
Understand the criterion for tooth bending failure and be able to derive the Hertz pressure at tooth contacts.
Use power and torque calculations to analyse epicyclic gears and multiple gear drives.
Understand how power transmission components are used as part of a system, including hybrid drives.
Determine the operating point and calculate the optimum speed ratio for specified conditions.
Select a rolling element bearing for a specific duty.

Content

Mechanics of contacts (5L) Dr Richard Roebuck

Hertzian point contacts
Stresses and stiffness
Hertzian line contacts
Applications in bearings and CVTs
Traction drives and CVTs

Gears (6L) Dr David Cole

Geometry and kinematics

Failure, root bending and contact fatigue
Design and applications
Multiple drives and planetary gears
Design calculations for planetary gears

Power matching (3L) Dr David Cole

Introduction and applications: automotive transmission, bicycle transmission
Sources and loads; devices and their characteristics
Power matching using a simple gear ratio
Hybrid drives

Rolling element bearings (2L) Dr David Cole

Bearing types; life equation
Shaft and bearing arrangements

Examples papers

Examples paper 1 - Mechanics of contacts (issued at lecture 1)

Examples paper 2 - Gears (issued at lecture 6)

Examples paper 3 - Power matching, rolling element bearings (issued at lecture 12)

Coursework

Power output characteristic of a cyclist

In this experiment the power output charateristic of a cyclist will be determined by holding the heart rate (that is, power input) constant and determining the dependence of crank torque and crank power on crank speed.

Learning objectives:

to calibrate and operate instrumentation to measure human power output
to propose and test an hypothesis using measured data with large inherent uncertainty
to understand the power output characteristic of a cyclist

Practical information:

Sessions will take place in the Baker Building, South Wing Mechanics Laboratory, during weeks 2 to 8.
This activity does involve preliminary work, approximately 30 minutes: read the lab sheet carefully before the session.
Book a timeslot online.

Full Technical Report:

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

Last modified: 22/09/2017 16:12

Engineering Tripos Part IIA, 3C8: Machine Design, 2023-24

Module Leader

Prof MPF Sutcliffe

Lecturers

Prof M Sutcliffe, Dr R Roebuck, Dr X Na

Lab Leader

Dr X Na

Timing and Structure

Michaelmas term.16 lectures.

Aims

The aims of the course are to:

Analyse the contact stresses and kinematical behaviour of solid contacts and to understand the design of rolling element bearings and other machine elements.
Understand the design of involute gears and appreciate the stress limits and practical problems of gears.
To analyse the behaviour of multiple gear drives and planetary gears.
Understand how components are combined to make up a mechanical power transmission system, including power matching to achieve a desired operating point.
Apply the principles of power matching to hybrid drives.
Introduce methods for specifying the type and arrangement of rolling element bearings to meet a specified duty.

Objectives

As specific objectives, by the end of the course students should be able to:

Calculate the strength limitations of solid contacts.
Analyse the kinematical behaviour of contacts, especially in rotating machinery.
Understand and analyse the performance of friction drives.
Be familiar with the geometry and kinematics of involute gear wheels and racks.
Understand the criterion for tooth bending failure and be able to derive the Hertz pressure at tooth contacts.
Use power and torque calculations to analyse epicyclic gears and multiple gear drives.
Understand how power transmission components are used as part of a system, including hybrid drives.
Determine the operating point and calculate the optimum speed ratio for specified conditions.
Select a rolling element bearing for a specific duty.

Content

Mechanics of contacts (5L) Dr Richard Roebuck

Hertzian point contacts
Stresses and stiffness
Hertzian line contacts
Applications in bearings and CVTs
Traction drives and CVTs

Gears (6L) Prof. Michael Sutcliffe

Geometry and kinematics
Failure, root bending and contact fatigue
Design and applications
Multiple drives and planetary gears
Design calculations for planetary gears

Power matching (3L) Dr Xiaoxiang Na

Introduction and applications: automotive transmission, bicycle transmission
Sources and loads; devices and their characteristics
Power matching using a simple gear ratio
Hybrid drives

Rolling element bearings (2L) Dr Xiaoxiang Na

Bearing types; life equation
Shaft and bearing arrangements

Examples papers

Examples Paper 1 - Mechanics of contacts (issued at lecture 1)

Examples Paper 2 - Gears (issued at lecture 6)

Examples Paper 3 - Power matching, rolling element bearings (issued at lecture 12)

Coursework

Power output characteristic of a cyclist

Learning objectives:

to calibrate and operate instrumentation to measure human power output
to propose and test an hypothesis using measured data with large inherent uncertainty
to understand the power output characteristic of a cyclist

Practical information:

Sessions will take place in the Baker Building, South Wing Mechanics Laboratory, during weeks 2 to 8 (Fridays and Wednesdays, 11am-1pm)
This activity does involve preliminary work, approximately 40 minutes: read the lab sheet carefully and watch the demonstration video before the session.
Book a timeslot online via the moodle site.
The practical needs to be done in pairs, with at least one member of the pair being comfortable riding the stationary bicycle. It is not possible to perform the experiment individually.
The lab report must be written individually. All data processing, analysis and interpretation performed after the lab session must be done independently and not in collaboration with each other or anyone else.

Full Technical Report:

Booklists

Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

Last modified: 04/07/2023 15:50

Engineering Tripos Part IIA, 3C8: Machine Design, 2020-21

Module Leader

Prof M P F Sutcliffe

Lecturers

Prof. M P F Sutcliffe and Dr R L Roebuck

Lab Leaders

Prof. M P F Sutcliffe and Dr R L Roebuck

Timing and Structure

Michaelmas term. 16 lectures.

Aims

The aims of the course are to:

Analyse the contact stresses and kinematical behaviour of solid contacts and to understand the design of rolling element bearings and other machine elements.
Understand the design of involute gears and appreciate the stress limits and practical problems of gears.
To analyse the behaviour of multiple gear drives and planetary gears.
Understand how components are combined to make up a mechanical power transmission system, including power matching to achieve a desired operating point.
Apply the principles of power matching to hybrid drives.
Introduce methods for specifying the type and arrangement of rolling element bearings to meet a specified duty.

Objectives

As specific objectives, by the end of the course students should be able to:

Calculate the strength limitations of solid contacts.
Analyse the kinematical behaviour of contacts, especially in rotating machinery.
Understand and analyse the performance of friction drives.
Be familiar with the geometry and kinematics of involute gear wheels and racks.
Understand the criterion for tooth bending failure and be able to derive the Hertz pressure at tooth contacts.
Use power and torque calculations to analyse epicyclic gears and multiple gear drives.
Understand how power transmission components are used as part of a system, including hybrid drives.
Determine the operating point and calculate the optimum speed ratio for specified conditions.
Select a rolling element bearing for a specific duty.

Content

Mechanics of contacts (5L) Dr Richard Roebuck

Hertzian point contacts
Stresses and stiffness
Hertzian line contacts
Applications in bearings and CVTs
Traction drives and CVTs

Gears (6L) Prof Michael Sutcliffe

Geometry and kinematics
Failure, root bending and contact fatigue
Design and applications
Multiple drives and planetary gears
Design calculations for planetary gears

Power matching (3L) Prof Michael Sutcliffe

Introduction and applications: automotive transmission, bicycle transmission
Sources and loads; devices and their characteristics
Power matching using a simple gear ratio
Hybrid drives

Rolling element bearings (2L) Prof Michael Sutcliffe

Bearing types; life equation
Shaft and bearing arrangements

Examples papers

Examples Paper 1 - Mechanics of contacts (issued at lecture 1)

Examples Paper 2 - Gears (issued at lecture 6)

Examples Paper 3 - Power matching, rolling element bearings (issued at lecture 12)

Coursework

Power output characteristic of a cyclist

Learning objectives:

to calibrate and operate instrumentation to measure human power output
to propose and test an hypothesis using measured data with large inherent uncertainty
to understand the power output characteristic of a cyclist

Practical information:

Sessions will take place in the Baker Building, South Wing Mechanics Laboratory, during weeks 2 to 8.
This activity does involve preliminary work, approximately 40 minutes: read the lab sheet carefully and watch the demonstration video before the session.
Book a timeslot online via the moodle site.
The practical needs to be done in pairs, with one of the pair comfortable riding the fixed bike

Full Technical Report:

Booklists

Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

Last modified: 25/09/2020 10:10

Engineering Tripos Part IIA, 3C6: Vibration, 2021-22

Module Leader

Prof D. Cebon

Lecturers

Prof D Cebon, Prof R.S. Langley

Lab Leader

Prof D. Cebon

Timing and Structure

Lent term. Vibration of Continuous Systems: 1 lecture/week, weeks 1-8 Lent term (Dr T Butlin), Vibration of Lumped Systems: Rayleigh's method, 1 lecture/week, weeks 1-8 Lent term (Prof D Cebon). 16 lectures.

Prerequisites

3C5 useful (there is one particular result from the Lagrange section of 3C5 which will be quoted without proof)

Aims

The aims of the course are to:

Introduce the central ideas and tools for the analysis of small (linear) vibration in mechanical systems.
Introduce simple continuous systems which may be combined as components of larger systems.
Introduce the general approach to lumped systems via mass and stiffness matrices, and the resulting properties of vibration modes and their frequencies.

Objectives

As specific objectives, by the end of the course students should be able to:

Derive the partial differential equations governing the forced or free motion of uniform one-dimensional systems.
Use these equations and appropriate boundary conditions to obtain vibration modes and natural frequencies.
Analyse continuous systems using modal methods.
Compute impulse and harmonic response by modal and direct methods.
Be able to derive the dispersion relation for wave propagation in 1D structures.
Understand that vibration can be expressed in terms of wave propagation or superposition of modes.
Calculate the response of a coupled system from a knowledge of the responses of the separate subsystems.
Apply Rayleigh's method to continuous systems.
Take advantage of the link between Lagrange's equations and small vibration.
Explain the concept of a vibration mode, and be able to find the modes and their natural frequencies by an eigenvector/eigenvaluecalculation.
Understand orthogonality of modes, modal damping, modal density and modal overlap factor.
Express the frequency response functions or the impulse response functions of a system in terms of the normal modes, and be familiar with the concepts of resonances and antiresonances.
Recognise and apply the reciprocal theorem for responses.
Use the stationary property of normal mode frequencies to estimate frequencies given assumed mode shapes, using minimisation with respect to any free parameters.

Content

This course aims to present a systematic approach to the study of small vibration of engineering components and structures. The course picks up where Part IA Linear Systems and Vibration left off. Concepts which were barely discussed (e.g. reciprocity and the orthogonality of vibration modes) are important for building up qualitative insights into vibration behaviour. Alongside the mathematical tools for quantitative analysis the course offers vital ingredients for an engineer's education.

Vibration of Continuous Systems (8L)

Vibration of strings; axial and transverse vibration of beams, torsional vibration of circular shafts; 1D acoustic vibration in a duct;
Modal analysis of simple systems;
Electrical transmission line analogy of 1D mechanical wave propagation;
D'Alembert's solution;
Dispersion relation for travelling waves;
Response to impulse and harmonic excitation;
Transfer functions and the meaning of poles and zeros;
Coupling of systems;
Rayleigh's method for continuous systems.

Vibration of Lumped Systems (8L)

Application of Lagrange's equations to small vibrations; undamped vibration of systems with N degrees of freedom;
Matrix methods and modal analysis;
Response functions in frequency and time domains; properties of frequency-response functions; reciprocal theorems;
Modal damping and modal overlap;
Rayleigh's method for discrete systems.

Coursework

A data-logging and FFT analysis system is used to measure the frequency response of a vibrating system by three different methods, to compare their merits and disadvantages.

[Coursework]

Learning objectives:

To investigate alternative methods of determining calibrated frequency response transfer functions of a mechanical vibrating system, using a digital measuring system;
To predict the response of a system from measured responses of its decoupled subsystems, and to compare with the measured response of the coupled system.

Practical information:

Sessions will take place in the South Wing Mechanics Laboratory, throughout Lent term.
This activity doesn't involve preliminary work.

Full Technical Report:

Students will have the option to submit a Full Technical Report.

Booklists

Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

Last modified: 20/05/2021 07:36

Engineering Tripos Part IIA, 3C6: Vibration, 2018-19

Module Leader

Prof D Cebon

Lecturers

Prof D Cebon, Dr T Butlin

Lab Leader

Dr T Butlin

Timing and Structure

Prerequisites

3C5 useful (there is one particular result from the Lagrange section of 3C5 which will be quoted without proof)

Aims

The aims of the course are to:

Introduce the central ideas and tools for the analysis of small (linear) vibration in mechanical systems.
Introduce simple continuous systems which may be combined as components of larger systems.
Introduce the general approach to lumped systems via mass and stiffness matrices, and the resulting properties of vibration modes and their frequencies.

Objectives

As specific objectives, by the end of the course students should be able to:

Derive the partial differential equations governing the forced or free motion of uniform one-dimensional systems.
Use these equations and appropriate boundary conditions to obtain vibration modes and natural frequencies.
Analyse continuous systems using modal methods.
Compute impulse and harmonic response by modal and direct methods.
Be able to derive the dispersion relation for wave propagation in 1D structures.
Understand that vibration can be expressed in terms of wave propagation or superposition of modes.
Calculate the response of a coupled system from a knowledge of the responses of the separate subsystems.
Apply Rayleigh's method to continuous systems.
Take advantage of the link between Lagrange's equations and small vibration.
Explain the concept of a vibration mode, and be able to find the modes and their natural frequencies by an eigenvector/eigenvaluecalculation.
Understand orthogonality of modes, modal damping, modal density and modal overlap factor.
Express the frequency response functions or the impulse response functions of a system in terms of the normal modes, and be familiar with the concepts of resonances and antiresonances.
Recognise and apply the reciprocal theorem for responses.
Use the stationary property of normal mode frequencies to estimate frequencies given assumed mode shapes, using minimisation with respect to any free parameters.

Content

Vibration of Continuous Systems (8L)

Vibration of strings; axial and transverse vibration of beams, torsional vibration of circular shafts; 1D acoustic vibration in a duct;
Modal analysis of simple systems;
Electrical transmission line analogy of 1D mechanical wave propagation;
D'Alembert's solution;
Dispersion relation for travelling waves;
Response to impulse and harmonic excitation;
Transfer functions and the meaning of poles and zeros;
Coupling of systems;
Rayleigh's method for continuous systems.

Vibration of Lumped Systems (8L)

Application of Lagrange's equations to small vibrations; undamped vibration of systems with N degrees of freedom;
Matrix methods and modal analysis;
Response functions in frequency and time domains; properties of frequency-response functions; reciprocal theorems;
Modal damping and modal overlap;
Rayleigh's method for discrete systems.

Coursework

A data-logging and FFT analysis system is used to measure the frequency response of a vibrating system by three different methods, to compare their merits and disadvantages.

[Coursework]

Learning objectives:

To investigate alternative methods of determining calibrated frequency response transfer functions of a mechanical vibrating system, using a digital measuring system;
To predict the response of a system from measured responses of its decoupled subsystems, and to compare with the measured response of the coupled system.

Practical information:

Sessions will take place in the South Wing Mechanics Laboratory, throughout Lent term.
This activity doesn't involve preliminary work.

Full Technical Report:

Students will have the option to submit a Full Technical Report.

Booklists

Please see the Booklist for Part IIA Courses for references for this module.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

Last modified: 01/06/2018 12:25

Engineering Tripos Part IIA, 3C6: Vibration, 2020-21

Module Leader

Dr T Butlin

Lecturers

Prof D Cebon, Dr T Butlin

Lab Leader

Dr T Butlin

Timing and Structure

Prerequisites

3C5 useful (there is one particular result from the Lagrange section of 3C5 which will be quoted without proof)

Aims

The aims of the course are to:

Introduce the central ideas and tools for the analysis of small (linear) vibration in mechanical systems.
Introduce simple continuous systems which may be combined as components of larger systems.
Introduce the general approach to lumped systems via mass and stiffness matrices, and the resulting properties of vibration modes and their frequencies.

Objectives

As specific objectives, by the end of the course students should be able to:

Derive the partial differential equations governing the forced or free motion of uniform one-dimensional systems.
Use these equations and appropriate boundary conditions to obtain vibration modes and natural frequencies.
Analyse continuous systems using modal methods.
Compute impulse and harmonic response by modal and direct methods.
Be able to derive the dispersion relation for wave propagation in 1D structures.
Understand that vibration can be expressed in terms of wave propagation or superposition of modes.
Calculate the response of a coupled system from a knowledge of the responses of the separate subsystems.
Apply Rayleigh's method to continuous systems.
Take advantage of the link between Lagrange's equations and small vibration.
Explain the concept of a vibration mode, and be able to find the modes and their natural frequencies by an eigenvector/eigenvaluecalculation.
Understand orthogonality of modes, modal damping, modal density and modal overlap factor.
Express the frequency response functions or the impulse response functions of a system in terms of the normal modes, and be familiar with the concepts of resonances and antiresonances.
Recognise and apply the reciprocal theorem for responses.
Use the stationary property of normal mode frequencies to estimate frequencies given assumed mode shapes, using minimisation with respect to any free parameters.

Content

Vibration of Continuous Systems (8L)

Vibration of strings; axial and transverse vibration of beams, torsional vibration of circular shafts; 1D acoustic vibration in a duct;
Modal analysis of simple systems;
Electrical transmission line analogy of 1D mechanical wave propagation;
D'Alembert's solution;
Dispersion relation for travelling waves;
Response to impulse and harmonic excitation;
Transfer functions and the meaning of poles and zeros;
Coupling of systems;
Rayleigh's method for continuous systems.

Vibration of Lumped Systems (8L)

Application of Lagrange's equations to small vibrations; undamped vibration of systems with N degrees of freedom;
Matrix methods and modal analysis;
Response functions in frequency and time domains; properties of frequency-response functions; reciprocal theorems;
Modal damping and modal overlap;
Rayleigh's method for discrete systems.

Coursework

A data-logging and FFT analysis system is used to measure the frequency response of a vibrating system by three different methods, to compare their merits and disadvantages.

[Coursework]

Learning objectives:

To investigate alternative methods of determining calibrated frequency response transfer functions of a mechanical vibrating system, using a digital measuring system;
To predict the response of a system from measured responses of its decoupled subsystems, and to compare with the measured response of the coupled system.

Practical information:

Sessions will take place in the South Wing Mechanics Laboratory, throughout Lent term.
This activity doesn't involve preliminary work.

Full Technical Report:

Students will have the option to submit a Full Technical Report.

Booklists

Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

Last modified: 28/08/2020 10:59

Search form

KU1

Module Leader

Lecturers

Lab Leader

Timing and Structure

Aims

Objectives

Content

Mechanics of contacts (5L) Dr Richard Roebuck

Gears (6L) Prof. Michael Sutcliffe

Power matching (3L) Dr Xiaoxiang Na

Rolling element bearings (2L) Dr Xiaoxiang Na

Examples papers

Coursework

Booklists

Examination Guidelines

UK-SPEC

GT1

IA1

KU1

KU2

E1

E2

E3

P1

US1

US2

Module Leader

Lecturers

Lab Leader

Timing and Structure

Aims

Objectives

Content

Mechanics of contacts (5L) Dr Richard Roebuck

Gears (6L) Prof Michael Sutcliffe

Power matching (3L) Dr David Cole

Rolling element bearings (2L) Dr David Cole

Further notes

3C8 Teaching Arrangements for Michaelmas Term 2021

Examples papers

Coursework

Booklists

Examination Guidelines

UK-SPEC

GT1

IA1

KU1

KU2

E1

E2

E3

P1

US1

US2

Module Leader

Lecturers

Lab Leader

Timing and Structure

Aims

Objectives

Content

Mechanics of contacts (5L) Dr Richard Roebuck

Gears (6L) Prof. Michael Sutcliffe

Power matching (3L) Dr Xiaoxiang Na

Rolling element bearings (2L) Dr Xiaoxiang Na

Examples papers

Coursework

Booklists

Examination Guidelines

UK-SPEC

GT1

IA1

KU1

KU2

E1

E2

E3

P1