GEAR….. Power transmission is the movement of energy from its place of generation to a location where it is applied to performing useful work A gear is a component within a transmission device that transmits rotational force to another gear or device

TYPES OF GEARS 1. According to the position of axes of the shafts. a.Parallel 1.Spur Gear 2.Helical Gear 3.Rack and Pinion b. Intersecting Bevel Gear c. Non-intersecting and Non-parallel worm and worm gears

Applications of Gears Control gears – long life, low noise, precision gears kinematic & stress analysis Aerospace gears – light weight, moderate to high load kinematic & stress analysis Power transmission – long life, high load and speed kinematic & stress analysis Appliance gears – long life, low noise & cost, low to moderate load kinematic & some stress analysis Toys and Small Mechanisms – small, low load, low cost kinematic analysis

Types of Gears Spur gears – tooth profile is parallel to the axis of rotation, transmits motion between parallel shafts. Pinion (small gear) Gear (large gear) Internal gears – teeth are inclined to the axis of rotation, the angle provides more gradual engagement of the teeth during meshing, transmits motion between parallel shafts. Helical gears

SPUR GEAR Teeth is parallel to axis of rotation Transmit power from one shaft to another parallel shaft Used in Electric screwdriver, oscillating sprinkler, windup alarm clock, washing machine and clothes dryer

Herringbone gears To avoid axial thrust, two helical gears of opposite hand can be mounted side by side, to cancel resulting thrust forces Herringbone gears are mostly used on heavy machinery.

Rack and pinion Rack and pinion gears are used to convert rotation (From the pinion) into linear motion (of the rack) A perfect example of this is the steering system on many cars

Bevel gears Bevel gears are useful when the direction of a shaft's rotation needs to be changed They are usually mounted on shafts that are 90 degrees apart, but can be designed to work at other angles as well The teeth on bevel gears can be straight, spiral or hypoid locomotives, marine applications, automobiles, printing presses, cooling towers, power plants, steel plants, railway track inspection machines, etc.

Straight and Spiral Bevel Gears

WORM AND WORM GEAR Worm gears are used when large gear reductions are needed. It is common for worm gears to have reductions of 20:1, and even up to 300:1 or greater Many worm gears have an interesting property that no other gear set has: the worm can easily turn the gear, but the gear cannot turn the worm Worm gears are used widely in material handling and transportation machinery, machine tools, automobiles etc

WORM AND WORM GEAR

Types of Gears Bevel gears – teeth are formed on a conical surface, used to transfer motion between non-parallel and intersecting shafts. Straight bevel gear Spiral bevel gear

Types of Gears Worm gear sets – consists of a helical gear and a power screw (worm), used to transfer motion between non- parallel and non-intersecting shafts. Rack and Pinion sets – a special case of spur gears with the gear having an infinitely large diameter, the teeth are laid flat. Rack Pinion

Gear Design and Analysis Kinematics of gear teeth and gear trains. Force analysis. Design based on tooth bending strength. Design based on tooth surface strength.

Mechanical Engineering Dept. 16 Nomenclature of Spur Gear Teeth = (tooth spacing) driven gear – (tooth thickness) driver, measured on the pitch circle. Backlash Pitch circle gear diam. Fillet radius Clearance Base Circle

Useful Relations P = N / d P = diametral pitch, teeth per inch N = number of teeth d = pitch diameter (gear diameter) m (module, mm) = d / N Metric system p ( circular pitch ) = πd / N Pp = π

Standard Tooth Specifications Pressure angle Two mating gears must have the same diametral pitch, P, and pressure angle, φ. Pitch line Line of centers Line of action Base circle Pitch circle Pressure angle φ Standard pressure angles, 14.5 o (old), 20 o, and 25 o

Kinematics ( ω p / ω g ) = (d g / d p ) = (N g / N p ) = VR (velocity ratio) P = (N g / d g ) = (N p / d p ) Spur, helical and bevel gears ωgωg dgdg ωpωp dpdp Rack and pinion Velocity of the rack Displacement of the rack Δθ is in radians,

Kinematics of Gear Trains Conventional gear trains ω3ω3 ω2ω2 = N2N2 N3N3 ω3ω3 ω4ω4 =, ω5ω5 ω4ω4 = N4N4 N5N5, m V = e = train value Speed ratio ω5ω5 ω2ω2 = output input = Reverted gear train – output shaft is concentric with the input shaft. Center distances of the stages must be equal.

Kinematics of Gear Trains Planetary gear trains  gear =  arm +  gear/arm  F/arm =  F -  arm,  L/arm =  L -  arm = e (train value)

Kinematics of Gear Trains Determine the speed of the sun gear if the arm rotates at 1 rpm. Ring gear is stationary. 2 degrees of freedom, two inputs are needed to control the system

Planetary Gear Trains - Example For the speed reducer shown, the input shaft a is in line with output shaft b. The tooth numbers are N 2 =24, N 3 =18, N 5 =22, and N 6 =64. Find the ratio of the output speed to the input speed. Will both shafts rotate in the same direction? Gear 6 is a fixed internal gear. Train value = (- N 2 / N 3 )(N 5 / N 6 ) = (-24/18)(22/64) = = ( ω L – ω arm ) / ( ω F – ω arm ) = ( 0 – ω arm ) / ( 1 – ω arm ) ω arm =.125, reduction is 8 to 1 Input and output shafts rotate in the same direction d 2 + d 3 = d 6 – d 5

Harmonic Drive The mechanism is comprised of three components: Wave Generator, Flexspline, and Circular Spline. Wave Generator Consists of a steel disk and a specially design bearing. The outer surface has an elliptical shape. The ball bearing conforms to the same elliptical shape of the wave generator. The wave generator is usually the input. Flexspline The Flexspline is a thin-walled steel cup with gear teeth on the outer surface near the open end of the cup. Flexspline is usually the output. Circular Spline Rigid internal circular gear, meshes with the external teeth on the Flexspline.

Harmonic Drive Teeth on the Flexspline and circular spline simultaneously mesh at two locations which are 180 o apart. As the wave generator travels 180 o, the flexspline shifts one tooth with respect to circular spline in the opposite direction. ω Circular Spline = 0 ω Flexspline = output ω Wave Generator = input The flexspline has two less teeth than the circular spline. Gear Ratio = - ( N flex spline )/ 2,,

NOMENCLATURE…. Pitch surface: The surface of the imaginary rolling cylinder (cone, etc.) that the toothed gear may be considered to replace. Pitch circle: A right section of the pitch surface. Addendum circle: A circle bounding the ends of the teeth, in a right section of the gear. Root (or dedendum) circle: The circle bounding the spaces between the teeth, in a right section of the gear. Addendum: The radial distance between the pitch circle and the addendum circle. Dedendum: The radial distance between the pitch circle and the root circle. Clearance: The difference between the dedendum of one gear and the addendum of the mating gear.

NOMENCLATURE…. Face of a tooth: That part of the tooth surface lying outside the pitch surface. Flank of a tooth: The part of the tooth surface lying inside the pitch surface. Circular thickness (also called the tooth thickness): The thickness of the tooth measured on the pitch circle. It is the length of an arc and not the length of a straight line. Tooth space: pitch diameter The distance between adjacent teeth measured on the pitch circle. Backlash: The difference between the circle thickness of one gear and the tooth space of the mating gear. Circular pitch (Pc) : The width of a tooth and a space, measured on the pitch circle.

NOMENCLATURE…. Diametral pitch (Pd): The number of teeth of a gear unit pitch diameter. The diametral pitch is, by definition, the number of teeth divided by the pitch diameter. That is, Where Pd = diametral pitch N = number of teeth D = pitch diameter Module (m): Pitch diameter divided by number of teeth. The pitch diameter is usually specified in inches or millimeters; in the former case the module is the inverse of diametral pitch. m = D/N

VELOCITY RATIO OF GEAR DRIVE d= Diameter of the wheel N =Speed of the wheel ω = Angular speed velocity ratio (n) =

GEAR TRAINS A gear train is two or more gear working together by meshing their teeth and turning each other in a system to generate power and speed It reduces speed and increases torque Electric motors are used with the gear systems to reduce the speed and increase the torque

Types of Gear Trains Simple gear train Compound gear train Planetary gear train Simple Gear Train The most common of the gear train is the gear pair connecting parallel shafts. The teeth of this type can be spur, helical or herringbone. Only one gear may rotate about a single axis

Simple Gear Train

Compound Gear Train For large velocities, compound arrangement is preferred Two or more gears may rotate about a single axis

Planetary Gear Train (Epicyclic Gear Train)

Planetary Gear Train … In this train, the blue gear has six times the diameter of the yellow gear The size of the red gear is not important because it is just there to reverse the direction of rotation In this gear system, the yellow gear (the sun) engages all three red gears (the planets) simultaneously All three are attached to a plate (the planet carrier), and they engage the inside of the blue gear (the ring) instead of the outside.

Planetary Gear Train… Because there are three red gears instead of one, this gear train is extremely rugged. planetary gear sets is that they can produce different gear ratios depending on which gear you use as the input, which gear you use as the output, and which one you hold still.

Planetary Gear Train… They have higher gear ratios. They are popular for automatic transmissions in automobiles. They are also used in bicycles for controlling power of pedaling automatically or manually. They are also used for power train between internal combustion engine and an electric motor