22.322 Mechanical Design II

22.322 Mechanical Design II Spring 2013

Lecture 10 Gear Types • Spur gears teeth are parallel to the axis of the gear. • Simplest and least expensive form of gear to make. • Spur gears can only be meshed if their axes are parallel. • A spur gearset can be 98 to 99% efficient (Power Out/Power In).

Lecture 10 Gear Types • Helical gears are ones in which the teeth are at a helix angle with respect to the axis of the gear. • Helical gears are quieter and smoother than spur gears because of the gradual contact between the angled surfaces as the teeth mesh together. • They are better suited for applications of high speed, large power transmission, or where noise abatement is important. • A helical gearset will be 96 to 98% efficient due to the sliding friction along the helix angle. • Helical gears also have a reaction force along the axis of the gear and so they require thrust and radial bearings.

Lecture 10 Gear Types • When a pair of meshing helical gears are mounted on parallel shafts, they must be of opposite hand. • When meshing helical gears are mounted on nonparallel shafts, they are known as crossed helical gears • Crossed helical gears are only 50 to 90% efficient. • Herringbone gears are two helical gears of identical pitch and diameter but of opposite hand on the same shaft. There is a cancellation of the thrust load and so no thrust bearing is needed. This type of gear is expensive. Side-thrust of one half is balanced by that of the other half

Lecture 10 Gear Types • A worm gear has one tooth wrapped continuously around its circumference (similar to a screw thread). • A large speed ratio (200 to 1) could not be reasonably achieved in one reduction because of the size of the gear required. • If a spur gear pinion had 20 teeth, the larger spur gear would have 4000 teeth. • A better solution is to use a worm gear. They are designed not to backdrive and can only be driven from the worm. Driven Driving

Lecture 10 Gear Types • A rack and pinion has teeth that are trapezoids but are still involutes (no slipping). • They are typically used in steering of automobiles.

Lecture 10 Gear Types • Bevel gears are based on rolling cones and are used for non-parallel intersecting shafts Straight bevel gears Spiral bevel gears • The advantages and disadvantages of straight bevel and spiral bevel gears are similar to those of the spur and helical gears.

Lecture 10 Gear Types • Hypoid gears are used if the axes between the gears are non-parallel and nonintersecting. They are based on rolling hyperboloids of revolution. Be able to identify different types of gears on the final exam!

Lecture 10 Simple Gear Trains • Two gears can mesh if and only if they have the same circular pitch or diameteral pitch • Let’s consider the motion of point A for the following gears 

Lecture 10 Simple Gear Trains A single gearset of spur, helical, or bevel gears is usually limited to a ratio of about 10:1 because of cost, size, manufacturing, and packaging.

Lecture 10 Example • a) Two spur gears are meshed together. The pinion has 15 teeth while the gear has 60 teeth. If the pinion is driven at 100 rpm, what is the speed of the gear? N1 = 15 (input) N2=60 (output) Assume an external mesh (w1/w2) = (-N2/N1) = (-60/15) = -4  w2 = (w1/-4)  w2 = 100 rpm/-4 = -25 rpm • b) If the gear is driven at 100 rpm what is the speed of the pinion? N1 = 60 N2=15 (w1/w2) = (-15/60) = -1/4  w2 = -4w1  w2 = -4(100 rpm) = -400 rpm • What is the angular velocity of the gear in part b? w1 = 100 rot/min * (2p rad/1 rot) * (1 min/60 sec) = 10.47 rad/s

22.322 Mechanical Design II