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

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 Example 6. Gearbox Design Report Section 7. This Weeks Task Design & Manufacture 2 – Mechanism Feasibility Design 2 Lecture 5

2017 Product Design Specification Last Week Concept Design Concept Selection Systems Modelling in Simulink • Demo: Stopping the simulation at a Stage-Gate specific point Deployment Modelling • Demo: Adding damping to a system Motor, Gear Ratio & Damping Selection • Demo: Four-bar mechanism Where you should be at: Gearbox Design • Mechanism modelled in Simulink • Evaluated a range of motors, gear ratios and level of damping Design & Manufacture 2 – Mechanism Feasibility Design 3 Lecture 5

2017 Types of Gear Design & Manufacture 2 – Mechanism Feasibility Design 4 Lecture 5

2017 Spur • 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 5 Lecture 5

2017 Helical • 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 6 Lecture 5

2017 Herringbone • 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 7 Lecture 5

2017 Epicyclic • 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 8 Lecture 5

2017 Worm • 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 9 Lecture 5

2017 Bevel • 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 10 Lecture 5

2017 Car Convertible Roof • Worm Gear to Multi-Stage Gearbox • We will solely design a multi-stage spur/helical gear set Design & Manufacture 2 – Mechanism Feasibility Design 11 Lecture 5

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

2017 Gear Definitions • Pinion • Smaller Gear • ( 𝑜, 𝑒 ) = number of teeth, PCD • Wheel • Larger Gear • ( 𝑂, 𝐸 ) = number of teeth, PCD Design & Manufacture 2 – Mechanism Feasibility Design 13 Lecture 5

2017 Gear Definitions • 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 14 Lecture 5

2017 Gear Definitions • Limiting Velocity Ratios Type of gear pair VR lower limit VR upper limit Worm and wheel 5 60 All others 1 5 • Pinion and wheel efficiency ( 𝜃 ) 95-96% per stage Design & Manufacture 2 – Mechanism Feasibility Design 15 Lecture 5

2017 Gear Definitions • Module ( 𝑁 ) 𝑁 = 𝑒 𝑜 = 𝐸 𝑂 • Addendum ( 𝐵 ) 𝐵 = 𝑁 • Dedendum ( 𝐶 ) 𝐶 = 1.25𝑁 • Tooth depth 𝐵 + 𝐶 = 2.25𝑁 Design & Manufacture 2 – Mechanism Feasibility Design 16 Lecture 5

2017 Module Selection Charts Example: • Pinion Speed = 200rev/min • Power = 200W Design & Manufacture 2 – Mechanism Feasibility Design 17 Lecture 5

2017 Module Selection Charts Example: • Pinion Speed = 200rev/min • Power = 200W Answer: • Modules > 2.5 Design & Manufacture 2 – Mechanism Feasibility Design 18 Lecture 5

2017 Gear Definitions • Face Widths • Relatively light loads ( W = 8𝑁 ) • Moderate loads ( W = 10𝑁 ) • Heavy loads ( W = 12𝑁 ) Design & Manufacture 2 – Mechanism Feasibility Design 19 Lecture 5

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

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

2017 Gear Definition - Teeth Hunting Determining Hunting Tooth Example: 2000rpm, 24 pinion teeth, 84 wheel teeth Frequencies Design & Manufacture 2 – Mechanism Feasibility Design 22 Lecture 5

2017 Gear Definition - Teeth Hunting Determining Hunting Tooth Example: 2000rpm, 24 pinion teeth, 84 wheel teeth Frequencies Pinion (24 Teeth) Wheel (84 Teeth) 1. Calculate the common factors ( 𝐷𝐺 ) between the teeth 1 x 24 1 x 84 2 x 12 2 x 42 3 x 8 3 x 28 4 x 6 4 x 21 6 x 14 7 x 12 Design & Manufacture 2 – Mechanism Feasibility Design 23 Lecture 5

2017 Gear Definition - Teeth Hunting Determining Hunting Tooth Example: 2000rpm, 24 pinion teeth, 84 wheel teeth Frequencies Pinion (24 Teeth) Wheel (84 Teeth) 1. Calculate the common factors ( 𝐷𝐺 ) between the teeth 1 x 24 1 x 84 2 x 12 2 x 42 2. Looking for the highest 3 x 8 3 x 28 common factor (=12 in this case) 4 x 6 4 x 21 6 x 14 7 x 12 Design & Manufacture 2 – Mechanism Feasibility Design 24 Lecture 5

2017 Gear Definition - Teeth Hunting Determining Hunting Tooth Example: 2000rpm, 24 pinion teeth, 84 wheel teeth Frequencies Pinion (24 Teeth) Wheel (84 Teeth) 1. Calculate the common factors ( 𝐷𝐺 ) between the teeth 1 x 24 1 x 84 2 x 12 2 x 42 2. Looking for the highest 3 x 8 3 x 28 common factor (=12 in this case) 4 x 6 4 x 21 3. Hunting Tooth Frequency 6 x 14 ( 𝐼𝑈𝐺 ) 7 x 12 𝐼𝑈𝐺 = 𝐻𝑁𝐺 × 𝐷𝐺 𝑜 × 𝑂 (2000 × 24) × 12 = 48000 × 12 Where 𝐻𝑁𝐺 is the gear mesh 24 × 84 24 × 84 frequency ( 𝐻𝑁𝐺 ) = 285.7 clashes per min 𝐻𝑁𝐺 = 𝑠𝑞𝑛 × 𝑜 Design & Manufacture 2 – Mechanism Feasibility Design 25 Lecture 5

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

2017 Spur Gear Forces • Pressure Angle ( 𝜄 ) • Typically 20 degrees unless otherwise stated • Tangential Force ( 𝐺 𝑢 ) 2𝑈 • 𝐺 𝑢 = 𝑒 • 𝑈 = Torque (Nm) • Separating Force ( 𝐺 𝑡 ) • 𝐺 𝑡 = 𝐺 𝑢 tan 𝜄 • Resultant Force ( 𝐺 ) 2 + 𝐺 2 • 𝐺 = 𝐺 𝑢 𝑡 Design & Manufacture 2 – Mechanism Feasibility Design 27 Lecture 5

2017 Helical Gear Forces • Tangential Force ( 𝐺 𝑢 ) • Same as for Spur 𝐺 𝑢 = 2𝑈 • 𝑒 • 𝑈 = Torque (Nm) • Separating Force ( 𝐺 𝑡 ) 𝑡 = 𝐺 𝑢 tan 𝜄 • cos 𝛽 , 𝛽 = helix angle (assume 20 degrees unless otherwise stated) 𝐺 • Axial Force ( 𝐺 𝑏 ) • 𝐺 𝑏 = 𝐺 𝑢 tan 𝛽 • Resultant Force ( 𝐺 ) 2 + 𝐺 2 • 𝐺 = 𝐺 𝑢 𝑡 Design & Manufacture 2 – Mechanism Feasibility Design 28 Lecture 5

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