Topic 5Power Transmission Elements IPulleysPulleys: CapstansWinchesBelts & CablesBelts & Cables: Stress, Tension, & Center DistanceBelts & Cables: Linear MotionBelts: Crawler TracksBelts & Cables: Rotary MotionBelts & Cables: Manufacturing & AssemblyWheelsWheels: Traction & ControllabilityWheels: Size, Torque and Contact PressureWheels: Manufacturing & MountingWheels: Steering & SuspensionsWheels: Steering & SuspensionsWheels: Clutches & DifferentialsCamsShaftsShafts: Axial LoadsShafts: Torsional loadsShafts: Bending LoadsShafts: Mounting & StabilityShafts: Component AttachmentShafts: Press-FitsCouplingsCouplings: Cheap & Easy Example© 2000 Alexander Slocum5-1Topic 5Power Transmission Elements ITopics:• Transmissions• Pulleys•Winches• Belts & Cables• Wheels• Steering & Suspensions• Clutches & Differentials•Cams• Shafts• CouplingsFW© 2000 Alexander Slocum5-2Pulley Bearing Efficie ncy70%80%90%100%2345678910Pulley/Bearing diameterEfficiencyh@m=0.05h@m=0.1h@m=0.2h@m=0.3• Pulleys (Sheaves) are a most fundamental power transmission element– Mechanical advantage–Capstans– Efficiency– Tracking– MountingFWPulleys© 2000 Alexander Slocum5-3•A capstan is typically a fixed, or controlled rotation, body-of-revolution which a cable wraps around– A capstan can also form the basis for a band brake, where a band is anchored to a structure, and then wraps around a shaft…• A cable wrapped around a capstan by θ radians with coefficient of friction m and being held with a force Fhold, can resist the pull of a cable with many times higher force Fpull• If a belt or cable runs around a fixed shaft, then there is a lot of friction between the belt and the shaft, and the efficiency is low:hold pulleFFµθ−=HoldPullAngle of wrap (degrees, radians) θ720 6.283Coefficient of friction µ0.2Holding force Fhold1Pulling force that can be resisted Fpull3.52FΓTdθT+dTN=TdθµN12345670 45 90 135 180 225 270 315 360Wrap angle (degrees)Capstan Ratio (Tout/Tin)µ = 0.3µ = 0.2µ = 0.1Pulleys: Capstans© 2000 Alexander Slocum5-4Winches• A winch is a motorized drum that controls cable tension– A single wrap of cable on the drum requires a long or large diameter drum• Effective drum diameter and winch force capability remain constant– Multiple wraps of cable on the drum allow for more cable in a smaller place• Drum diameter and winch force capability vary– A fairleader is a device to control the input/output of the cable so it winds on the drum in an orderly fashion• The simplest design just uses smooth rounded static features• Vertical and horizontal roller designs reduce cable wearLwLaLcrrθF© 2000 Alexander Slocum5-5R1Rinωout, ΓoutVbelt = RoutωoutVbelt = Rinωinωin, ΓinPowerout = PowerinspeedoutTorqueout = speedinTorqueinΓout = ωinΓin/ωout • Applications and Engineering of Belts & Cables– Linear motion– Rotary motion– Crawler tracks– Manufacturing & AssemblyBelts & Cables© 2000 Alexander Slocum5-6Belts & Cables: Stress, Tension, & Center Distance• Belts and cables are very robust elements, but they require engineering of 3 basic details:– Stress from wrapping a belt or cable around a pulley– Tension in the belt or cable– Center distance between pulleysθφACR2R1γBandstress.xlsBy Alex S locumLast modified 4/22/02by Alex S locumStress in a flat belt wrapped around a pulleyBelt parametersThickness, t (mm)0.10Width, w (mm)5Modulus, E (N/mm^2)2.00E+05Poisson ratio, n0.29ForcesLoad to be carried, F (N)10Belt stress, sigF (N/mm^2)20.0Pulley wrap stressesPulley diameter, D (mm)50stress437 Motor torque required (N-mm)250Caps tan effectcoefficient of friction, mu0.2Wrap angle, q (degrees)180required pre-tenion, pT (N)5.3Belt stress, sigT (N/mm^2)10.6Total stress 467 Total strain 0.23%Measured frequency of lateral vibration (hz)150Free-length (mm)300density (g/mm^3)7mass per unit length (g/mm)0.004Tension (N)7.1Enters numbers in BOLD, Results in REDCheck: Tension in the belt (pluck it like a guitar string)© 2000 Alexander Slocum5-7Belts & Cables: Linear Motion• Belts & Cables are a very effective way to convert rotary to linear motion• The force F in a belt with tension T on a pulley of diameter D that can be generated by the torque Γ can be conservatively estimated by:•F =2Γ/D for toothed belts, and F = TµD/2 for flat belts– A more exact model would consider the capstan effect– Play with bandstress.xls– The speed is simply•Vlinear=2ωmotor*D• Belts run on pulleys– For flat belts, the pulleys must be crowned to prevent the belt from coming off the pulley due to pulley misalignment– Timing belt pulleys must also be carefully aligned to prevent premature failureload© 2000 Alexander Slocum5-8• Treads only help when there is loose media or a surface into which they can dig• Treads DO NOT help on smooth surfaces– Smooth surfaces often are covered with a dust layer, and sharp-groove treads can help• Treads can be created by cutting angled slices from a rubber strip, and gluing them onto the belt surfaceLLn ...Belts: Crawler Tracks© 2000 Alexander Slocum5-9• Flat belts and cables (string drives) require higher tension to transmit torque– Conservatively, the belt needs to be held in tension equal to the desired torque divided by the coefficient of friction and the small pinion radius• Vee-belts use the the principle of self help:– Increased tension caused by power being transmitted, wedges the belt in a Vee-shaped pulley groove, so it can transmit more torque…• Synchronous Drives (timing or gear belts) can transmit torque between shafts and also achieve a transmission ratio– They combine the positive timing action of gears with the flexibility, speed and low noise level of belts• For an in-depth discussion on synchronous drive design, see Stock Drive Products on-line tech library:http://www.sdp-si.com/Sdptech_lib.htmTdθT+dTN=TdθµNBelts & Cables: Rotary Motion© 2000 Alexander Slocum5-10Belts & Cables: Manufacturing & Assembly• Pulleys can be grooved to provide a guide for a cable• Two pulleys’ axes of rotation can never be perfectly parallel, so a flat belt will want to drift off (tracking)– Pulleys must be crowned (round profile) to keep a belt from walking off• On a concave surface, the side with more belt in contact will cause the belt to drift further to that side until it falls off• A flat pulley is at best neutrally stable• Great, OK, bad, & horrid pulleys:–