Mechanism Feasibility Design Task

2017Mechanism Feasibility Design TaskDr. James GopsillDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 51

2017Contents1.2.3.4.5.6.7.Last WeekTypes of GearGear DefinitionsGear ForcesMulti-Stage Gearbox ExampleGearbox Design Report SectionThis Weeks TaskDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 52

2017Product Design SpecificationLast WeekConcept DesignConcept SelectionSystems Modelling in Simulink Demo: Stopping the simulation at aspecific pointDemo: Adding damping to a systemDemo: Four-bar mechanismWhere you should be at:Deployment ModellingMotor, Gear Ratio & Damping SelectionGearbox Design Mechanism modelled in Simulink Evaluated a range of motors, gearratios and level of dampingDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 5Stage-Gate3

2017Types of GearDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 54

2017Spur Applications Low/Moderate speed environments (Pitch Line Velocity 25ms-1) Engines, Power Plants, Fuel Pumps, Washing Machines, Rack & Pinionmechanisms Pros Can transmit large amounts of power (50,000kW)High ReliabilityConstant Velocity RatioSimple 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 shaftsDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 55

2017Helical 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 gearsDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 56

2017Herringbone Applications 3D Printers Heavy Machinery Pros Smoother power transmission Resistant to operation disruption from missing/damagedteeth Cons Difficult to manufacture and hence more expensiveDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 57

2017Epicyclic Applications Lathes, hoists, pulley blocks, watches Automatic Transmissions Hybrid Vehicles (engine and motor) Pros Higher efficiencyHigher power densityAccurate gearingPackaging (Achieve higher ratios in the same area)In-line input-output shafts Cons Loud operation High accuracy manufacturing required to ensure equal load sharingDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 58

2017Worm Applications Pros Elevators, hoistsPackaging equipmentRock CrushersTuning InstrumentsNear silent and smooth operationSelf-lockingOccupy less space of equivalent spur gear ratioHigh velocity ratio can be attained within a single step (approx. 100:1)Absorb shock loadingCons Expensive to manufactureHigher power losses comparedGreater heat generation due to increased teeth contactDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 59

2017Bevel Applications Differential drives (e.g. vehicles) Hand drills Assembly machinery Pros Change direction of power transmission Cons Difficult to manufacture Precision mountingsDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 510

2017Car Convertible Roof Worm Gear to Multi-StageGearbox We will solely design amulti-stage spur/helicalgear setDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 511

2017Gear DefinitionsDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 512

2017Gear Definitions Pinion Smaller Gear (𝑛, 𝑑) number of teeth, PCD Wheel Larger Gear (𝑁, 𝐷) number of teeth, PCDDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 513

2017Gear Definitions Velocity Ratio𝑁 𝐷𝑉𝑅 𝑛 𝑑 Examples Pinion has 20 teeth and Wheel has 4040𝑉𝑅 220 If connected to a wheel of 60 and pinion of 2040 60𝑉𝑅 620 20Design & Manufacture 2 – Mechanism Feasibility DesignLecture 514

2017Gear Definitions Limiting Velocity RatiosType of gear pair VR lower limit VR upper limitWorm and wheel 560All others51 Pinion and wheel efficiency (𝜂)95-96% per stageDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 515

2017Gear Definitions Module (𝑀)𝑑 𝐷𝑀 𝑛 𝑁 Addendum (𝐴)𝐴 𝑀 Dedendum (𝐵)𝐵 1.25𝑀 Tooth depth𝐴 𝐵 2.25𝑀Design & Manufacture 2 – Mechanism Feasibility DesignLecture 516

2017Module Selection ChartsExample: Pinion Speed 200rev/min Power 200WDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 517

2017Module Selection ChartsExample: Pinion Speed 200rev/min Power 200WAnswer: Modules 2.5Design & Manufacture 2 – Mechanism Feasibility DesignLecture 518

2017Gear Definitions Face Widths Relatively light loads (W 8𝑀) Moderate loads (W 10𝑀) Heavy loads (W 12𝑀)Design & Manufacture 2 – Mechanism Feasibility DesignLecture 519

2017Gear Definition - Teeth Hunting Transmission forces are often cyclical Some teeth may experience higherforces than others Having the teeth hunt distributes thecyclic loading across all the teeth ingear Uniform wear Also, maximise the number of cyclesbefore two damaged gears will meshwith one anotherDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 520

2017Gear Definition - Teeth HuntingDetermining Hunting ToothFrequencies1.2.3.Calculate the common factors(𝐶𝐹) between the teethLooking for the highest commonfactor (12)Hunting Tooth Frequency (𝐻𝑇𝐹)𝐺𝑀𝐹 𝐶𝐹𝐻𝑇𝐹 𝑛 𝑁𝐺𝑀𝐹 gear mesh frequencyDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 521

2017Gear Definition - Teeth HuntingDetermining Hunting ToothFrequenciesDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 5Example:2000rpm, 24 pinion teeth, 84 wheel teeth22

2017Gear Definition - Teeth HuntingDetermining Hunting ToothFrequencies1.Example:2000rpm, 24 pinion teeth, 84 wheel teethCalculate the common factors(𝐶𝐹) between the teethDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 523Pinion (24 Teeth)Wheel (84 Teeth)1 x 242 x 123x84x61 x 842 x 423 x 284 x 216 x 147 x 12

2017Gear Definition - Teeth HuntingDetermining Hunting ToothFrequencies1.2.Example:2000rpm, 24 pinion teeth, 84 wheel teethCalculate the common factors(𝐶𝐹) between the teethLooking for the highestcommon factor ( 12 in this case)Design & Manufacture 2 – Mechanism Feasibility DesignLecture 524Pinion (24 Teeth)Wheel (84 Teeth)1 x 242 x 123x84x61 x 842 x 423 x 284 x 216 x 147 x 12

2017Gear Definition - Teeth HuntingDetermining Hunting ToothFrequencies1.2.3.Example:2000rpm, 24 pinion teeth, 84 wheel teethCalculate the common factors(𝐶𝐹) between the teethLooking for the highestcommon factor ( 12 in this case)Hunting Tooth Frequency(𝐻𝑇𝐹)𝐺𝑀𝐹 𝐶𝐹𝐻𝑇𝐹 𝑛 𝑁Where 𝐺𝑀𝐹 is the gear meshfrequency (𝐺𝑀𝐹)𝐺𝑀𝐹 𝑟𝑝𝑚 𝑛Design & Manufacture 2 – Mechanism Feasibility DesignLecture 5Pinion (24 Teeth)Wheel (84 Teeth)1 x 242 x 123x84x61 x 842 x 423 x 284 x 216 x 147 x 12(2000 24) 12 48000 12 24 8424 84 285.7 clashes per min25

2017Gear ForcesDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 526

2017Spur Gear Forces Pressure Angle (𝜃) Typically 20 degrees unless otherwise stated Tangential Force (𝐹𝑡 ) 𝐹𝑡 2𝑇𝑑 𝑇 Torque (Nm) Separating Force (𝐹𝑠 ) 𝐹𝑠 𝐹𝑡 tan 𝜃 Resultant Force (𝐹) 𝐹 𝐹𝑡2 𝐹𝑠2Design & Manufacture 2 – Mechanism Feasibility DesignLecture 527

2017Helical Gear Forces Tangential Force (𝐹𝑡 ) Same as for Spur 𝐹𝑡 2𝑇𝑑 𝑇 Torque (Nm) Separating Force (𝐹𝑠 ) 𝐹𝑠 𝐹𝑡 tan 𝜃,cos 𝛼𝛼 helix angle (assume 20 degrees unless otherwise stated) Axial Force (𝐹𝑎 ) 𝐹𝑎 𝐹𝑡 tan 𝛼 Resultant Force (𝐹) 𝐹 𝐹𝑡2 𝐹𝑠2Design & Manufacture 2 – Mechanism Feasibility DesignLecture 528

2017Example GearboxDesign & Manufacture 2 – Mechanism Feasibility DesignLecture 529

2017Three Stage GearboxDesign ExampleGear StageA three-stage spur gearbox is to provide a1:125 total gear ratio for a motor providing500W @ 1000 rev/min.Pinion TeethVRCombined VRModulePinion PCD (mm)Wheel TeethWheel PCD (mm)Hunting Tooth FrequencyEfficiencyPinion Speed (rev/min)Wheel Speed (rev/min)Pinion Torque (Nm)Wheel Torque (Nm)Pinion ForcesTangential Force (kN)Separating Force (kN)Resultant Force (kN)Design & Manufacture 2 – Mechanism Feasibility DesignLecture 530123

2017Three Stage GearboxDesign ExampleGear StageA three-stage spur gearbox is to provide a1:125 total gear ratio for a motor providing500W @ 1000 rev/min.Pinion Teeth1. Put in the initial conditionsWheel PCD (mm)1230.95 (1)0.95 (1)0.95 (1)VRCombined VRModulePinion PCD (mm)Wheel TeethHunting Tooth FrequencyEfficiencyPinion Speed (rev/min)1000.00 (1)Wheel Speed (rev/min)Pinion Torque (Nm)Wheel Torque (Nm)Pinion ForcesTangential Force (kN)Separating Force (kN)Resultant Force (kN)Design & Manufacture 2 – Mechanism Feasibility DesignLecture 531104.70 (1)

2017Three Stage GearboxDesign ExampleGear Stage123VR5.00 (2)5.00 (2)5.00 (2)Combined VR5.00 (2)25.00 (2)125.00 (2)A three-stage spur gearbox is to provide a1:125 total gear ratio for a motor providing500W @ 1000 rev/min.Pinion Teeth1. Put in the initial conditions2. Make an initial guess at the VR foreach stage to generate the correctcombined VRWheel PCD (mm)0.95 (1)0.95 (1)0.95 (1)ModulePinion PCD (mm)Wheel TeethHunting Tooth FrequencyEfficiencyPinion Speed (rev/min)1000.00 (1)Wheel Speed (rev/min)Pinion Torque (Nm)Wheel Torque (Nm)Pinion ForcesTangential Force (kN)Separating Force (kN)Resultant Force (kN)Design & Manufacture 2 – Mechanism Feasibility DesignLecture 532104.70 (1)

2017Three Stage GearboxDesign ExampleGear Stage123VR5.00 (2)5.00 (2)5.00 (2)Combined VR5.00 (2)25.00 (2)125.00 (2)Module2.00 (3)A three-stage spur gearbox is to provide a1:125 total gear ratio for a motor providing500W @ 1000 rev/min.Pinion Teeth1. Put in the initial conditions2. Make an initial guess at the VR foreach stage to generate the correctcombined VR3. Determine ModuleWheel PCD (mm)0.95 (1)0.95 (1)Pinion PCD (mm)Wheel TeethHunting Tooth FrequencyEfficiencyPinion Speed (rev/min)1000.00 (1)Wheel Speed (rev/min)Pinion Torque (Nm)Wheel Torque (Nm)Pinion ForcesTangential Force (kN)Separating Force (kN)Resultant Force (kN)Design & Manufacture 2 – Mechanism Feasibility DesignLecture 50.95 (1)33104.70 (1)

2017Three Stage GearboxDesign ExampleGear Stage123VR5.00 (2)5.00 (2)5.00 (2)Combined VR5.00 (2)25.00 (2)125.00 (2)Module2.00 (3)A three-stage spur gearbox is to provide a1:125 total gear ratio for a motor providing500W @ 1000 rev/min.Pinion Teeth19.00 (4)Pinion PCD (mm)38.00 (4)Wheel Teeth95.00 (4)1. Put in the initial conditions2. Make an initial guess at the VR foreach stage to generate the correctcombined VR3. Determine Module4. Calculate Pinion/Wheel PCDs &Hunting Tooth FrequencyWheel PCD (mm)190.00 (4)Hunting Tooth Frequency200.00 (4)0.95 (1)0.95 (1)EfficiencyPinion Speed (rev/min)1000.00 (1)Wheel Speed (rev/min)Pinion Torque (Nm)Wheel Torque (Nm)Pinion ForcesTangential Force (kN)Separating Force (kN)Resultant Force (kN)Design & Manufacture 2 – Mechanism Feasibility DesignLecture 50.95 (1)34104.70 (1)