22.322 Mechanical Design II

22.322 Mechanical Design II Spring 2013

Lecture 8 Quiz Solution

Lecture 8 Gear Trains • Whenever a change in the speed or torque of a rotating device is needed, a gear train or one of its cousins, the belt or chain drive mechanism, will usually be used. • The simplest means of transferring rotary motion from one shaft to another is a pair of rolling cylinders: • Provided that sufficient friction is available at the rolling interface  will work well • Variant on rolling cylinder is vee belt • Also transfers power through friction& capable of large power levels • Relatively quiet running, require nolubrication, & inexpensive vs. gears& chain drives • Problem: belts can slip if we try totransmit a lot of torque

Lecture 8 Gear Trains • Preventing slip usually means adding some meshing teeth to the rolling cylinders. • They then become gears and are together called a gearset. • Conventional to refer to smaller of two gears as pinion and the other as the gear.

Lecture 8 Fundamental Law of Gearing • The angular velocity ratio between the gears of a gearset remains constant throughout the mesh. Backlash = clearance between mating teeth measured at the pitch circle

Lecture 8 Fundamental Law of Gearing • To solve these problems we can design the gear teeth to be shaped such that the gear tooth surface is always parallel to another surface, always in contact, and have no sliding between teeth. • Such a curve is called an “involute”. • Curve can be generated by unwrapping a taut string from a cylinder: • String is always tangent to cylinder • Center of curvature of involute is always at the point of tangency of the string with the cylinder • A tangent to the involute is then always normal to the string

Lecture 8 Fundamental Law of Gearing • Consider two involutes on separate cylinders in contact: • These represent gear teeth. • The cylinders from which the strings are unwrapped are the base circles of the respective gears. • Note the pressure angle is formed by the velocity at the pitch point and the line of action • Usually 20 or 25degrees • The geometry issimilar to that of a cam-followerjoint: • Common tangentto both curvesat the contactpoint. • Common normalperpendicular tocommon tangent

Lecture 8 Fundamental Law of Gearing • If we look at the line of action of the teeth while they are at two different locations (just beginning contact & about to leave contact), you can notice that the line of action (axis of transmission) always passes through the pitch point.

Lecture 8 Fundamental Law of Gearing • The common normal of the tooth profiles, at all contact points within the mesh, must always pass through a fixed point on the line of centers, called the pitch point.

Lecture 8 Fundamental Law of Gearing • Another important property of involute gears is that the center distance errors do not affect the velocity ratio. • The velocity ratio of involute gears is fixed by the ratio of base circle diameters. • The pressure angle will change and the pitch point will shift but the line of action will still be tangent to both base circles. • If the gear tooth form is not an involute, then there will be a variation, or “ripple” in the output velocity. • Output angular velocity will not be constant for a constant input velocity • Violate fundamental law of gearing

Lecture 8 • Increasing the center distance between gears will also increase the backlash(clearance between mating teeth measured at pitch circle) • Backlash is not an issue if the gearset is run with a nonreversing torque • When torque changes sign, the teeth will move from contact on one side to the other  can cause undesirable positional error • Antibacklash gears are two gears back to back on the same shaft that are rotated slightly in opposite direction and then fixed to take up the backlash

22.322 Mechanical Design II