Mechanism Feasibility Design Task Dr. James Gopsill Design & - - PowerPoint PPT Presentation

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Mechanism Feasibility Design Task Dr. James Gopsill Design & - - PowerPoint PPT Presentation

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2017 Mechanism Feasibility Design Task Dr. James Gopsill Design & Manufacture 2 Mechanism Feasibility Design 1 Lecture 5 2017 Contents 1. Last Week 2. Types of Gear 3. Gear Definitions 4. Gear Forces 5. Multi-Stage Gearbox

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SLIDE 1

Mechanism Feasibility Design Task

  • Dr. James Gopsill

2017 1 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 2

Contents

1. Last Week 2. Types of Gear 3. Gear Definitions 4. Gear Forces 5. Multi-Stage Gearbox Example 6. Gearbox Design Report Section 7. This Weeks Task

2 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 3

Last Week

Systems Modelling in Simulink

  • Demo: Stopping the simulation at a

specific point

  • Demo: Adding damping to a system
  • Demo: Four-bar mechanism

Where you should be at:

  • Mechanism modelled in Simulink
  • Evaluated a range of motors, gear

ratios and level of damping

3 2017

Product Design Specification Concept Design Concept Selection Deployment Modelling Motor, Gear Ratio & Damping Selection Gearbox Design Stage-Gate

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 4

Types of Gear

4 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 5

Spur

5 2017

  • Applications
  • Low/Moderate speed environments (Pitch Line Velocity < 25ms-1)
  • Engines, Power Plants, Fuel Pumps, Washing Machines, Rack & Pinion

mechanisms

  • Pros
  • Can transmit large amounts of power (50,000kW)
  • High Reliability
  • Constant Velocity Ratio
  • Simple to Manufacture
  • Cons
  • Initial contact is across entire tooth width leading to higher stresses
  • Noise at high speeds
  • Can’t transfer power between non-parallel shafts

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 6

Helical

6 2017

  • Applications
  • High speed environments (> 25ms-1)
  • Automotive industry
  • Elevators, conveyors
  • Pros
  • Smoother running compared to spur
  • Higher load transfer per width of gear compared to spur
  • Typically longer maintenance cycles
  • Cons
  • Thrust bearings required to counter axial forces
  • Greater heat generation compared to spur due to gear mating
  • Typically less efficient than spur gears

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 7

Herringbone

7 2017

  • Applications
  • 3D Printers
  • Heavy Machinery
  • Pros
  • Smoother power transmission
  • Resistant to operation disruption from missing/damaged

teeth

  • Cons
  • Difficult to manufacture and hence more expensive

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 8

Epicyclic

8 2017

  • Applications
  • Lathes, hoists, pulley blocks, watches
  • Automatic Transmissions
  • Hybrid Vehicles (engine and motor)
  • Pros
  • Higher efficiency
  • Higher power density
  • Accurate gearing
  • Packaging (Achieve higher ratios in the same area)
  • In-line input-output shafts
  • Cons
  • Loud operation
  • High accuracy manufacturing required to ensure equal load sharing

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 9

Worm

9 2017

  • Applications
  • Elevators, hoists
  • Packaging equipment
  • Rock Crushers
  • Tuning Instruments
  • Pros
  • Near silent and smooth operation
  • Self-locking
  • Occupy less space of equivalent spur gear ratio
  • High velocity ratio can be attained within a single step (approx. 100:1)
  • Absorb shock loading
  • Cons
  • Expensive to manufacture
  • Higher power losses compared
  • Greater heat generation due to increased teeth contact

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 10

Bevel

10 2017

  • Applications
  • Differential drives (e.g. vehicles)
  • Hand drills
  • Assembly machinery
  • Pros
  • Change direction of power transmission
  • Cons
  • Difficult to manufacture
  • Precision mountings

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 11

Car Convertible Roof

  • Worm Gear to Multi-Stage

Gearbox

  • We will solely design a

multi-stage spur/helical gear set

11 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 12

Gear Definitions

12 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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Gear Definitions

13 2017

  • Pinion
  • Smaller Gear
  • (𝑜, 𝑒) = number of teeth, PCD
  • Wheel
  • Larger Gear
  • (𝑂, 𝐸) = number of teeth, PCD

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 14

Gear Definitions

14 2017

  • Velocity Ratio

𝑊𝑆 = 𝑂 𝑜 = 𝐸 𝑒

  • Examples
  • Pinion has 20 teeth and Wheel has 40

𝑊𝑆 = 40 20 = 2

  • If connected to a wheel of 60 and pinion of 20

𝑊𝑆 = 40 20 × 60 20 = 6

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 15

Gear Definitions

15 2017

  • Limiting Velocity Ratios
  • Pinion and wheel efficiency (𝜃)

95-96% per stage

Type of gear pair VR lower limit VR upper limit Worm and wheel 5 60 All others 1 5

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 16

Gear Definitions

  • Module (𝑁)

𝑁 = 𝑒 𝑜 = 𝐸 𝑂

  • Addendum (𝐵)

𝐵 = 𝑁

  • Dedendum (𝐶)

𝐶 = 1.25𝑁

  • Tooth depth

𝐵 + 𝐶 = 2.25𝑁

16 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 17

Module Selection Charts

Example:

  • Pinion Speed = 200rev/min
  • Power = 200W

17 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 18

Module Selection Charts

Example:

  • Pinion Speed = 200rev/min
  • Power = 200W

Answer:

  • Modules > 2.5

18 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 19

Gear Definitions

  • Face Widths
  • Relatively light loads (W = 8𝑁)
  • Moderate loads (W = 10𝑁)
  • Heavy loads (W = 12𝑁)

19 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 20

Gear Definition - Teeth Hunting

  • Transmission forces are often cyclical
  • Some teeth may experience higher

forces than others

  • Having the teeth hunt distributes the

cyclic loading across all the teeth in gear

  • Uniform wear
  • Also, maximise the number of cycles

before two damaged gears will mesh with one another

20 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 21

Gear Definition - Teeth Hunting

Determining Hunting Tooth Frequencies

1. Calculate the common factors (𝐷𝐺) between the teeth 2. Looking for the highest common factor (12) 3. Hunting Tooth Frequency (𝐼𝑈𝐺)

𝐼𝑈𝐺 = 𝐻𝑁𝐺 × 𝐷𝐺 𝑜 × 𝑂

𝐻𝑁𝐺 = gear mesh frequency

21 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 22

Gear Definition - Teeth Hunting

Determining Hunting Tooth Frequencies

22 2017

Example: 2000rpm, 24 pinion teeth, 84 wheel teeth

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 23

Gear Definition - Teeth Hunting

23 2017

Example: 2000rpm, 24 pinion teeth, 84 wheel teeth Pinion (24 Teeth) Wheel (84 Teeth) 1 x 24 2 x 12 3 x 8 4 x 6 1 x 84 2 x 42 3 x 28 4 x 21 6 x 14 7 x 12

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

Determining Hunting Tooth Frequencies

1. Calculate the common factors (𝐷𝐺) between the teeth

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SLIDE 24

Gear Definition - Teeth Hunting

24 2017

Example: 2000rpm, 24 pinion teeth, 84 wheel teeth

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

Determining Hunting Tooth Frequencies

1. Calculate the common factors (𝐷𝐺) between the teeth 2. Looking for the highest common factor (=12 in this case)

Pinion (24 Teeth) Wheel (84 Teeth) 1 x 24 2 x 12 3 x 8 4 x 6 1 x 84 2 x 42 3 x 28 4 x 21 6 x 14 7 x 12

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SLIDE 25

Gear Definition - Teeth Hunting

Determining Hunting Tooth Frequencies

1. Calculate the common factors (𝐷𝐺) between the teeth 2. Looking for the highest common factor (=12 in this case) 3. Hunting Tooth Frequency (𝐼𝑈𝐺)

𝐼𝑈𝐺 = 𝐻𝑁𝐺 × 𝐷𝐺 𝑜 × 𝑂

Where 𝐻𝑁𝐺 is the gear mesh frequency (𝐻𝑁𝐺) 𝐻𝑁𝐺 = 𝑠𝑞𝑛 × 𝑜

25 2017

Example: 2000rpm, 24 pinion teeth, 84 wheel teeth

(2000 × 24) × 12 24 × 84 = 48000 × 12 24 × 84 = 285.7 clashes per min

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

Pinion (24 Teeth) Wheel (84 Teeth) 1 x 24 2 x 12 3 x 8 4 x 6 1 x 84 2 x 42 3 x 28 4 x 21 6 x 14 7 x 12

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SLIDE 26

Gear Forces

26 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 27

Spur Gear Forces

27 2017

  • Pressure Angle (𝜄)
  • Typically 20 degrees unless otherwise stated
  • Tangential Force (𝐺𝑢)
  • 𝐺𝑢 =

2𝑈 𝑒

  • 𝑈 = Torque (Nm)
  • Separating Force (𝐺

𝑡)

  • 𝐺

𝑡 = 𝐺𝑢 tan 𝜄

  • Resultant Force (𝐺)
  • 𝐺 =

𝐺𝑢

2 + 𝐺 𝑡 2

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 28

Helical Gear Forces

28 2017

  • Tangential Force (𝐺

𝑢)

  • Same as for Spur
  • 𝐺𝑢 = 2𝑈

𝑒

  • 𝑈 = Torque (Nm)
  • Separating Force (𝐺

𝑡)

  • 𝐺

𝑡 = 𝐺

𝑢 tan 𝜄

cos 𝛽 , 𝛽 = helix angle (assume 20 degrees unless otherwise stated)

  • Axial Force (𝐺

𝑏)

  • 𝐺

𝑏 = 𝐺𝑢 tan 𝛽

  • Resultant Force (𝐺)
  • 𝐺 =

𝐺𝑢

2 + 𝐺 𝑡 2

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 29

Example Gearbox

29 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 30

Three Stage Gearbox Design Example

30 2017

A three-stage spur gearbox is to provide a 1:125 total gear ratio for a motor providing 500W @ 1000 rev/min.

Gear Stage 1 2 3 VR Combined VR Module Pinion Teeth Pinion PCD (mm) Wheel Teeth Wheel PCD (mm) Hunting Tooth Frequency Efficiency Pinion Speed (rev/min) Wheel Speed (rev/min) Pinion Torque (Nm) Wheel Torque (Nm) Pinion Forces Tangential Force (kN) Separating Force (kN) Resultant Force (kN) Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 31

Three Stage Gearbox Design Example

31 2017

A three-stage spur gearbox is to provide a 1:125 total gear ratio for a motor providing 500W @ 1000 rev/min.

Gear Stage 1 2 3 VR Combined VR Module Pinion Teeth Pinion PCD (mm) Wheel Teeth Wheel PCD (mm) Hunting Tooth Frequency Efficiency 0.95 (1) 0.95 (1) 0.95 (1) Pinion Speed (rev/min) 1000.00 (1) Wheel Speed (rev/min) Pinion Torque (Nm) 104.70 (1) Wheel Torque (Nm) Pinion Forces Tangential Force (kN) Separating Force (kN) Resultant Force (kN) Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

  • 1. Put in the initial conditions
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SLIDE 32

Three Stage Gearbox Design Example

32 2017

A three-stage spur gearbox is to provide a 1:125 total gear ratio for a motor providing 500W @ 1000 rev/min.

Gear Stage 1 2 3 VR 5.00 (2) 5.00 (2) 5.00 (2) Combined VR 5.00 (2) 25.00 (2) 125.00 (2) Module Pinion Teeth Pinion PCD (mm) Wheel Teeth Wheel PCD (mm) Hunting Tooth Frequency Efficiency 0.95 (1) 0.95 (1) 0.95 (1) Pinion Speed (rev/min) 1000.00 (1) Wheel Speed (rev/min) Pinion Torque (Nm) 104.70 (1) Wheel Torque (Nm) Pinion Forces Tangential Force (kN) Separating Force (kN) Resultant Force (kN) Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

  • 1. Put in the initial conditions
  • 2. Make an initial guess at the VR for

each stage to generate the correct combined VR

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SLIDE 33

Three Stage Gearbox Design Example

33 2017

A three-stage spur gearbox is to provide a 1:125 total gear ratio for a motor providing 500W @ 1000 rev/min.

Gear Stage 1 2 3 VR 5.00 (2) 5.00 (2) 5.00 (2) Combined VR 5.00 (2) 25.00 (2) 125.00 (2) Module 2.00 (3) Pinion Teeth Pinion PCD (mm) Wheel Teeth Wheel PCD (mm) Hunting Tooth Frequency Efficiency 0.95 (1) 0.95 (1) 0.95 (1) Pinion Speed (rev/min) 1000.00 (1) Wheel Speed (rev/min) Pinion Torque (Nm) 104.70 (1) Wheel Torque (Nm) Pinion Forces Tangential Force (kN) Separating Force (kN) Resultant Force (kN) Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

  • 1. Put in the initial conditions
  • 2. Make an initial guess at the VR for

each stage to generate the correct combined VR

  • 3. Determine Module
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SLIDE 34

Three Stage Gearbox Design Example

34 2017

A three-stage spur gearbox is to provide a 1:125 total gear ratio for a motor providing 500W @ 1000 rev/min.

Gear Stage 1 2 3 VR 5.00 (2) 5.00 (2) 5.00 (2) Combined VR 5.00 (2) 25.00 (2) 125.00 (2) Module 2.00 (3) Pinion Teeth 19.00 (4) Pinion PCD (mm) 38.00 (4) Wheel Teeth 95.00 (4) Wheel PCD (mm) 190.00 (4) Hunting Tooth Frequency 200.00 (4) Efficiency 0.95 (1) 0.95 (1) 0.95 (1) Pinion Speed (rev/min) 1000.00 (1) Wheel Speed (rev/min) Pinion Torque (Nm) 104.70 (1) Wheel Torque (Nm) Pinion Forces Tangential Force (kN) Separating Force (kN) Resultant Force (kN) Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

  • 1. Put in the initial conditions
  • 2. Make an initial guess at the VR for

each stage to generate the correct combined VR

  • 3. Determine Module
  • 4. Calculate Pinion/Wheel PCDs &

Hunting Tooth Frequency

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SLIDE 35

Three Stage Gearbox Design Example

35 2017

A three-stage spur gearbox is to provide a 1:125 total gear ratio for a motor providing 500W @ 1000 rev/min.

Gear Stage 1 2 3 VR 5.00 (2) 5.00 (2) 5.00 (2) Combined VR 5.00 (2) 25.00 (2) 125.00 (2) Module 2.00 (3) Pinion Teeth 19.00 (4) Pinion PCD (mm) 38.00 (4) Wheel Teeth 95.00 (4) Wheel PCD (mm) 190.00 (4) Hunting Tooth Frequency 200.00 (4) Efficiency 0.95 (1) 0.95 (1) 0.95 (1) Pinion Speed (rev/min) 1000.00 (1) Wheel Speed (rev/min) 200.00 (5) Pinion Torque (Nm) 104.70 (1) 497.33 (5) Wheel Torque (Nm) 497.33 (5) Pinion Forces Tangential Force (kN) Separating Force (kN) Resultant Force (kN) Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

  • 1. Put in the initial conditions
  • 2. Make an initial guess at the VR for

each stage to generate the correct combined VR

  • 3. Determine Module
  • 4. Calculate Pinion/Wheel PCDs &

Hunting Tooth Frequency

  • 5. Wheel Speed and Torques
  • Note: Efficiency loss
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SLIDE 36

Three Stage Gearbox Design Example

36 2017

A three-stage spur gearbox is to provide a 1:125 total gear ratio for a motor providing 500W @ 1000 rev/min.

Gear Stage 1 2 3 VR 5.00 (2) 5.00 (2) 5.00 (2) Combined VR 5.00 (2) 25.00 (2) 125.00 (2) Module 2.00 (3) Pinion Teeth 19.00 (4) Pinion PCD (mm) 38.00 (4) Wheel Teeth 95.00 (4) Wheel PCD (mm) 190.00 (4) Hunting Tooth Frequency 200.00 (4) Efficiency 0.95 (1) 0.95 (1) 0.95 (1) Pinion Speed (rev/min) 1000.00 (1) Wheel Speed (rev/min) 200.00 (5) Pinion Torque (Nm) 104.70 (1) 497.33 (5) Wheel Torque (Nm) 497.33 (5) Pinion Forces Tangential Force (kN) 5.51 (6) Separating Force (kN) 2.01 (6) Resultant Force (kN) 5.86 (6) Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

  • 1. Put in the initial conditions
  • 2. Make an initial guess at the VR for

each stage to generate the correct combined VR

  • 3. Determine Module
  • 4. Calculate Pinion/Wheel PCDs &

Hunting Tooth Frequency

  • 5. Wheel Speed and Torques
  • Note: Efficiency loss
  • 6. Pinion & Wheel Forces
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SLIDE 37

Three Stage Gearbox Design Example

37 2017

A three-stage spur gearbox is to provide a 1:125 total gear ratio for a motor providing 500W @ 1000 rev/min.

Gear Stage 1 2 3 VR 5.00 (2) 5.00 (2) 5.00 (2) Combined VR 5.00 (2) 25.00 (2) 125.00 (2) Module 2.00 (3) Pinion Teeth 19.00 (4) Pinion PCD (mm) 38.00 (4) Wheel Teeth 95.00 (4) Wheel PCD (mm) 190.00 (4) Hunting Tooth Frequency 200.00 (4) Efficiency 0.95 (1) 0.95 (1) 0.95 (1) Pinion Speed (rev/min) 1000.00 (1) Wheel Speed (rev/min) 200.00 (5) Pinion Torque (Nm) 104.70 (1) 497.33 (5) Wheel Torque (Nm) 497.33 (5) Pinion Forces Tangential Force (kN) 5.51 (6) Separating Force (kN) 2.01 (6) Resultant Force (kN) 5.86 (6)

  • 1. Put in the initial conditions
  • 2. Make an initial guess at the VR for

each stage to generate the correct combined VR

  • 3. Determine Module
  • 4. Calculate Pinion/Wheel PCDs &

Hunting Tooth Frequency

  • 5. Wheel Speed and Torques
  • Note: Efficiency loss
  • 6. Pinion & Wheel Forces
  • 7. Repeat Steps 3-6 for the next stages

Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 38

Gearbox Design

Design Report

  • Gearbox Design
  • Discuss the process you have taken to design the gearbox
  • Compare a spur and helical gearbox that meets your criteria (not just gear ratio but also

your PDS)

  • Rationale behind your chosen design
  • Gear arrangement and space optimisation
  • Could perform checks on minimum shaft sizes & bearings

38 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 39

This Week

  • Generate an initial spur and helical gear set to drive

your mechanism

  • Select type and refine gears
  • Evaluate against forces, packaging and suitability for the

application

  • You may have to compromise on your ideal gear ratio from

your deployment modelling

  • Make sure you record you rationale

39 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5

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SLIDE 40

Happy Easter

40 2017 Design & Manufacture 2 – Mechanism Feasibility Design Lecture 5