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Transmission Machine Components ME14 Introduction to Mechanical Engineering Design Gears • Gears simply change the parameters of mechanical power Pitch-Line Velocity Tinin Toutout V p r11 r22 in NG out NG 1 r2 2 r1 P r1 pinion gear ME14 Introduction to Mechanical Engineering Design r2 Tooth Forces T1 F1r1 T2 T1 F2 T2 F2 r2 F2 F1 r2 T2 T1 r1 r1 r2 F1 ME14 Introduction to Mechanical Engineering Design ME14 Introduction to Mechanical Engineering Design Normal velocity must match. Using similar triangles v2 cosθ2 = v1 cosθ1 where v1 = ω1 . O1C ; v2 = ω2 . O2C Want constant rotation rate ratio ω2 /ω1 = v2 . O1C/v1 . O2C = O1C.cosθ1 /O2C.cosθ2 = O1 C1 /O2 C2 = O1 P / O 2 P Point P must be fixed ME14 Introduction to Mechanical Engineering Design ME14 Introduction to Mechanical Engineering Design Effect of Errors ME14 Shafts at spec. Shafts farther distance apart than spec. Introduction to Mechanical Engineering Design Involute Tooth Profile • The two curved surfaces of mating teeth, contact as a line ME14 Introduction to Mechanical Engineering Design Types of Gears • Spur Gears – Teeth are parallel to rotation axis – Transmit power between shafts with parallel axes • Helical Gears – Teeth inclined to the axis of rotation – Used for the same applications as spur gears, but have less noise due to gradual tooth engagement ME14 Introduction to Mechanical Engineering Design Types of Gears, cont. • Bevel Gears – Teeth on a conical Surface – Used with intersecting shafts • Worm Gears – Similar to a screw – Used with non-parallel and nonintersecting shafts typically with high speed ratios ME14 Introduction to Mechanical Engineering Design Rack and Pinion • A rack is an unwound spur gear • Turns rotary motion in to linear motion ME14 Introduction to Mechanical Engineering Design Anatomy of a Gear • Pitch Circle – Theoretical circle upon with all calculations are based • Diametral Pitch • Module N P= d d m= N • Pressure Angle • For gears to work together they must have the same pitch (or module) and pressure angle ME14 Introduction to Mechanical Engineering Design Multiple Gear Stages • Gear ratios from a multi-stage gear train multiply together T2 T3 T4 T1 2:1 reduction 2:1 reduction 2:1 reduction Overall a 8:1 reduction ME14 Introduction to Mechanical Engineering Design Efficiency • In reality gears are not 100% efficient • Good quality spur gears are typically in the 90+ % efficiency range • This can be a problem with multiple (large) gear reductions Each a 2:1 reduction with 95% efficiency Overall a 32:1 reduction, but only 77% efficient ME14 Introduction to Mechanical Engineering Design Belts and Chains • Belts are essentially the same as spur gears but they have the ability to have large offsets P1 P2 V p1 V p 2 r11 r22 1 r2 NG 2 r1 ME14 Introduction to Mechanical Engineering Design Slip • Belts rely on friction and to prevent slip tension must be maintained • Chains and timing belts that have teeth with positive engagement can help prevent slip ME14 Introduction to Mechanical Engineering Design Shafts Energy used to overcome the forces resulting from misalignment will reduce the overall efficiency of your system Parallel misalignment Angular misalignment This is the key to doing well in the transmission contest ME14 Introduction to Mechanical Engineering Design Pins • Pins hold two parts together based upon the shear strength of the pin • Pins are good when the joint must take both thrust and shear • Pinned joints are easy to analyze and reliable • Pinned joints can be used as a mechanical fuse • Pinned joints are difficult to assemble and disassemble because pins are typically press fit into place ME14 Introduction to Mechanical Engineering Design shaft gear pin 18 Keys • Keys transmit torque in shear across the length of the key • Keys have all the advantages of pins, but they are easy to install in remove • Keys do not take any axial load Woodruff key Used to reduce stress concentrations in the shaft ME14 Introduction to Mechanical Engineering Design 19 Clamp Fit • Clamps depend upon friction and the bolted connection between two parts (or a single part with a flexure) to develop the clamping force • Clamped connections can be easy and reliable for low torque applications ME14 Introduction to Mechanical Engineering Design 20 Press (Interference) Fits • Two parts can be pressed together if the hole is manufactured smaller than the shaft that is installed • The load between these two parts is taken in friction developed by the strain of the press fit • Manufacturing tolerances are very tight for this type of connection – For a 0.25” diameter shaft with a class FN2 fit • Shaft 0.2510” – 0.2514” • Hole 0.2500” – 0.2506” • Difficult to disassemble without damage to the parts ME14 Introduction to Mechanical Engineering Design 21 Splines • Splines are essentially matching internal and external gears used to transmit torque • Splines are extremely reliable and efficient • Splines are difficult to manufacture ME14 Introduction to Mechanical Engineering Design 22 Retaining Rings • Retaining rings are used to constrain things axially in one direction on a shaft • Installed by machining a groove into one of the mating parts • Can be made external or internal External E-Style External ME14 Introduction to Mechanical Engineering Design Internal 23 Shaft Connections Coupler transmits torque and allows for misalignment ME14 Introduction to Mechanical Engineering Design Key or set screw transmits torque Couplers • Bellows • Spider Coupling • Helical • Universal Joint ME14 Introduction to Mechanical Engineering Design Bearing and Bushings ME14 Introduction to Mechanical Engineering Design Bushings • Bushings have sliding contact and rely on low friction at the point or line of contact Ploss F r r F ME14 Introduction to Mechanical Engineering Design Rolling Element Bearings • Replace sliding contact with rolling contact which is much more efficient Outer Race Ball Separator (retainer) Inner Race ME14 Introduction to Mechanical Engineering Design Image courtesy of Barden Precision Bearing Rolling Contact ωb ω1 ri rLi ro rb V rLo V 1rLi b ME14 Introduction to Mechanical Engineering Design V 1rLi rb rb Spherical Bearings • Allows for misalignment in all rotational degrees of freedom • Constrains in all translational degrees of freedom • Good for low speed / high load applications ME14 Introduction to Mechanical Engineering Design A Brief Into to Specifying Electric Motors ME14 Introduction to Mechanical Engineering Design Electric Motors • Torque is proportional to current • Speed is proportional to voltage • An electric motor generates an Electromotive Force (back EMF) as it spins • A portion of the input voltage goes to doing work and a portion goes to overcome the back EMF ME14 Introduction to Mechanical Engineering Design T = Kt I w = K eV V= w Ke Vin = Vemf + IR w T Vin = + R Ke Kt Kt Ke ME14 Introduction to Mechanical Engineering Design Electric Motors For a given voltage 6000 80 70 5000 60 Speed (rpm) 50 3000 40 30 2000 20 1000 10 0 0 0.05 0.1 0.15 0.2 Torque (Nm) 0.25 ME14 Introduction to Mechanical Engineering Design 0.3 0 0.35 Efficiency (%) 4000 Electric Motor Power Can’t always operate here due to heat 50 6000 45 5000 40 Speed (rpm) 30 3000 25 20 2000 15 10 1000 5 0 0 0.05 0.1 0.15 0.2 Torque (Nm) 0.25 ME14 Introduction to Mechanical Engineering Design 0.3 0 0.35 Power Output (W) 35 4000 Continuous Operating Range ME14 Introduction to Mechanical Engineering Design