Mechanical DesignControl System Design

Rafael Quintanilla Escalante

March 22, 2005

Lecture Contents

• Design Process *

• Miscellaneous Components **•Gears and Belts •Flexible Couplings

•Bearings •Fixing Components to Shafts

• Stress and Strain Analysis

• Design Studies• TIM (Infrared Mexican Telescope)

* Based on the notes of Douglas Wright on Mechanical Analysis of Machine Elements, Department of Mechanical and Materials Engineering, University of Western Australia.** Based on last year’s lecture on Mechanical Design given by Ben Potsaid to the CSD class, ECSE, RPI.

What is Design ?

Goal Plan

InventionThinking process

Interpretation of Design:

Design is the application of creativity to plan the optimum solution of a given problem and the communication of that plan to others.

The Rudimentary Design ProcessSTATE THE PROBLEM

broad, complete

GENERATE IDEASmethods

AVAILABLEKNOWLEDGE

BANK OF SOLUTION CANDIDATESuncritical – quantity not quality

RENDERPRACTICABLE

SPECIFY CONTRAINTS& CRITERIA

EVALUATECANDIDATES

OPTIMUM SOLUTION

communicate

Problem Statement• Understand the problem – communicate

Designer’s responsibility to initiate communication and clear up any misunderstanding.

• Avoid artificial constraintsReal boundary

Solution Space

Fictitious restrictions

Your limitation knowledge

Example: Team 4 - … track a target in various lighting conditions.

• Broaden the problemExample:

moreHow to reduce car’s fuel consumption? How to reduce car’s running costs?

broadlyFinancialProblems !!

Improvedriving habits

Tuneengine

Switch offengine atred lights

Ignoremaintenance

Fuelconsumption

Problem Statement (Cont.)

moremoreHow to travel between home and work at minimum cost? How to get money?broadlybroadly

walk bike bus Go to work Lotterycar Get anotherjob

• Complete the problemIdentify everyone and everything likely to be affected by any solution.

Examples: • Inaccurate launching system causes iterative refinement not been able to compensate errors.

• Team 1 spills water on the car of Team3

You must ask the right questions

BEFORE NEXT STAGE OF DESIGN, PROBLEM STATEMENTMUST BE AS BROAD AND COMPLETE AS POSSIBLE

Generation of IdeasAvoid ALL criticism while creating

Inventiveness depends upon:

• Inherited qualities: Leonardo DaVinci• Attitude: Be positive. • Knowledge: Understanding of similar problems and area of study.• Effort: Edison, inventor of the light bulb, said:

“Invention is 1% inspiration and 99% perspiration”

Ideation is carried out before considering constraints and criteria (crazy candidates trigger or are transformed into practical solutions)

QU

IT T

IME?

Rate of idea generation

Cumulative numberof ideas generated

Generate as many ideas as possible; quality doesn’t matter at this stage. However, recognize when stop inventing.

time

Specify Constraints and CriteriaIdentify ALL the constraints and criteria

• Constraints: Bounds that every candidate solution must satisfy to be valid.Examples:

• Pour water from a bottle into a cup without spilling.• The motor current should be lower than 300mA.

• Criteria: Measurements used to judge different candidate solutions.

The degree by which candidate i satisfies the criterion j may be expressed by the utility,uij, often a real number between 0 and 100%.

Examples: • Pour water from a bottle into a cup minimizing spilling.• The motor circuit should be cooled down.

Solution space can be increased by converting constraints into equivalent criteria

A common criterion which is often neglected is the need for simplicity

Render Practical

Solve secondaryproblems, modify

Candidate CANsatisfies ALL constraints ?

Candidate CANNOTsatisfies ALL constraints ?

candidate solution from bank

NO

NO

YES YES

practical solution to evaluation activity

impractical solutionto trash

A problem is trivial if it has been previously solved satisfactorily.

PROBLEM

TRIVIALSOLUTION

NEW SOLUTION

SECONDARYPROBLEM

…TERTIARYPROBLEM

TRIVIALSOLUTION

NEW SOLUTION

NEW SOLUTION

TRIVIALSOLUTION

DONE ! DONE ! DONE !

Render Practical (Cont.)

Need to consider the manufacture and operation of the candidate solution in detail.

Manufacture:• Knowledge or • Direct experimentation.

Operation:• Direct experimentation if possible (certain components or subsystems), or• Mathematical model

Inter-dependence of kinematics and forces occurs in all devices. Bewarethe dangers of a kinematic analysis without looking also at the forces involve.

Candidates must be rendered practical before evaluation

EvaluationCompare practical solution candidates based on the problem criteria

1) Relative importance of criteria

Weight wj : relative importance of the jth criterion

Example: wmass is 25% for the vacuum cleaner and 75%for the military aircraft

2) Satisfaction of the criteria - utility

Utility uij : degree to which the ith candidate satisfies the jth criterion. ( 0 ≤ uij ≤ 1 or 100%)

3) Overall utility

Ui : degree to which the ith candidate satisfies the whole problem.

∑=

=n

jijji uwU

1n = number of criteria;

Optimum candidate is the one with highest overall utility

Fixing Components to Shafts

Setscrews:

• Low torque transmission• High stress generation• Low cost

UNRELIABLE

Examples:

Fixing Components to Shafts

Pins:

• Low torque transmission• High stress generation• Low cost

Examples:

Circular or roll pinStraight round pin Tapered round pin

Fixing Components to Shafts

Keys:

• Medium torque transmission• High stress generation• Medium cost

Examples:

squarekey

flatkey

roundkey

Fixing Components to Shafts

Spline:

• High torque transmission• Low stress generation• High cost

Examples:

spline

Fixing Components to Shafts

Camp :

• High torque transmission• Low stress generation• Medium cost

Examples:

Fixing Components to Shafts

Mechanical Design

Fixing Components to Shafts

Method Torque Stress Cost

Setscrew Low High Low

Clamp High Low Med

Pin Low High Low

Key Med High Med

Spline High Low High

unreliable

Gears and Belts

Instantaneously, gears and pulleys act like levers

Gears and Belts (Cont.)

At steady state velocity or ignoring inertia

2

1

1

2

2211

ττ

θθ

θτθτ

θτ

==

=

=

N

Powerr F r

Nr F rN

ττ

τ τ

= = =

=

1 1 1 1

2 2 2 2

1 2

Thermodynamic(conservation of energy)

FBD

(F and M balance)

Kinematic

(velocity analysis)

12

1

2

2

1

θθ

θθ

N

rrN

=

==

Conservative System

(Power in = Power out)

Gearheads - Spur

Inexpensive

Efficient

Low torque

Some backlash

Motor and Gearhead often combined

Gearheads - Planetary

Large reduction in a small and lightweight assembly

Large torque capacity

Considerable backlash

Identical stages can be stacked together

Gearheads - Harmonic

Flexspline has 2 fewer teeth than circular spline

One tooth advances every rotation

Huge reduction in small and lightweight assembly

Almost no backlash

Aerospace and robotics applications

Gearheads Comparison

Type Torque Efficiency

Backlash

Cost

Spur Low High Low Low

Planetary

High Low High Med

Harmonic

Med Med Low High

Bearings

Inner race

Outer raceBearings are usually press fit to the shaft or housing.

Correct bearing hole diameter is critical.

Heat expansion can be used to assist assembly.

Bearings allow for slight misalignment

Flexible Couplings

Angular misalignment

Parallel offset misalignment

• Coupling is used to transmit torque between two shafts.

• Coupling is rigid in torsion and flexible in bending.

• Without flexible coupling, there would be excessive loadson the shafts and bearings.

• Without flexible coupling, bearings would fail prematurelyand performance would suffer.

Stress and StrainDynamic forces are exerted on the mechanical components.

θτ JxmF ==

Dynamic forces cause deflections (strain) and internal forces (stresses) in the structural components.

A

oLL∆

=εStrain ( ε ) :

AF

=σStress ( σ ) :

Stress and Strain

Yield Stress

(elongation)

In the linear region, material acts like a spring ( F = kx ).

Stresses in the components should never exceed the Yield Stress to prevent permanent deformation.

Why we do not design to the yield strength?

Design Study - TIM

Conclusions

• Mechanical Design and Control System Design cannot be done separately when high performance is required.

• Apply the Rudimentary Design Process.

• Don’t forget about first principles and the basics.