4Lecture 8Gear TrainsWhenever 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 wellVariant on rolling cylinder is vee beltAlso transfers power through friction & capable of large power levelsRelatively quiet running, require no lubrication, & inexpensive vs. gears & chain drivesProblem: belts can slip if we try to transmit a lot of torque
5Lecture 8Gear TrainsPreventing 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.
6Fundamental Law of Gearing Lecture 8Fundamental Law of GearingThe angular velocity ratio between the gears of a gearset remains constant throughout the mesh.Backlash = clearance between mating teeth measured at the pitch circle
7Fundamental Law of Gearing Lecture 8Fundamental Law of GearingTo 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 cylinderCenter of curvature of involute is always at the point of tangency of the string with the cylinderA tangent to the involute is then always normal to the string
8Fundamental Law of Gearing Lecture 8Fundamental Law of GearingConsider 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 actionUsually 20 or 25 degreesThe geometry is similar to that of a cam-follower joint:Common tangent to both curves at the contact point.Common normal perpendicular to common tangent
9Fundamental Law of Gearing Lecture 8Fundamental Law of GearingIf 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.
10Fundamental Law of Gearing Lecture 8Fundamental Law of GearingThe 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.
11Fundamental Law of Gearing Lecture 8Fundamental Law of GearingAnother 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 velocityViolate fundamental law of gearing
12Lecture 8Increasing 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 torqueWhen torque changes sign, the teeth will move from contact on one side to the other can cause undesirable positional errorAntibacklash 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