Introduction to Gear Trains Zhengjian XU 29th OCT 2008 Introduction to gear trains Gear Types pinion Spur gear: gear with radial teeth parallel to its axis Rack Rack & Pinion a toothed wheel (pinion) engages a notched bar (rack) to convert rotary motion into linear motion Bevel Gear Either of a pair of toothed wheels whose working surfaces are inclined to nonparallel axes. Introduction to gear trains Gear Types Helical gear: a gear that has the teeth cut at an angle to the center line of the gear. This kind of gear is useful because there is no chance of intermittent tooth-to- tooth operation because there are at least two teeth engaged at any time. It can operate quieter than spur gear. Worm gear: A worm is used to reduce speed. For each complete turn of the worm shaft the gear shaft advances only one tooth of the gear. Unlike ordinary gears, the motion is not reversible, a worm can drive a gear to reduce speed but a gear cannot drive a worm to increase it. Harmonic gear: The harmonic gear allows high reduction ratios with concentric shafts and with very low backlash and vibration. It is based on a very simple construction utilising metals elasto-mechanical property Introduction to gear trains Gear Types Herringbone gear: The two helix angle come together in the center of the gear face to form a 'V‘. Differential gear: A vehicle's wheels rotate at different speeds, especially when turning corners. The differential is designed to drive a pair of wheels with equal force, while allowing them to rotate at different speeds Input torque is applied to the ring gear (blue), which turns the If the left side gear (red) encounters resistance, the entire carrier (blue), providing torque to both side gears (red and planet gear (green) rotates about the left side gear, yellow), which in turn may drive the left and right wheels. If the in turn applying extra rotation to the right side gear resistance at both wheels is equal, the planet gear (green) does (yellow). not rotate, and both wheels turn at the same rate. Introduction to gear trains Kinematics of Gears Fundamental law of gearing: Angular velocity Ratio is constant throughout the mesh. Introduction to gear trains Gear tooth nomenclature Pitch circle: A circle the radius of which is equal to the distance from the gear axis to the pitch point. . 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. Gear tooth 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. Fillet : The small radius that connects the profile of a tooth to the root circle. Introduction to gear trains Gear tooth nomenclature Figure shows two teeth of a gear with the standard nomenclature defined. Since Tooth contact nomenclature Point of contact: any point at which two tooth profiles touch each other. Path of action: the locus of successive contact points between a pair of gear teeth, during the phase of engagement. Line of action: The line of action is the path of action for involute gears. It is the straight line passing through the pitch point and tangent to both base circles. Tooth contact nomenclature Line of contact: a line or curve along which two tooth surfaces are tangent to each other Line of contact Surface of action: the imaginary surface in which contact occurs between two engaging tooth surfaces. Plane of action: the surface of action for involute, parallel axis gears with either spur or helical teeth. It is tangent to the base cylinders. Introduction to gear trains Gear tooth nomenclature Generation of the Involute Curve This involute curve is the path traced by a point on a line as the line rolls without slipping on the circumference of a circle. It may also be defined as a path traced by the end of a string which is originally wrapped on a circle when the string is unwrapped from the circle. The circle from which the involute is derived is called the base circle. Introduction to gear trains Gear tooth nomenclature The pressure angle is the angle between the line of action and the common tangent. (has been standardized 14.50 200 250) Introduction to gear trains Gear tooth nomenclature Minimum number of Teeth Introduction to gear trains Simple gear train From the fundamental law of gearing The sign “-” is necessary to take into account the change in direction of rotation. The sign “+” is also to take into account the change in direction of rotation for internal gear. Introduction to gear trains Planar gear trains Example: Find the output angular velocity for the planetary gear train shown when the input angular velocity W4= 50 rad/sec conterclokwise. Solution: The velocity of point A Also the velocity of A can be expressed Then we get Introduction to gear trains Planar gear trains Letting r2=Pc*n2, r3=Pc*n3 Using the tooth relationship to replace the radii Substituting back into the other equation Introduction to gear trains Find the speed reductions possible for the transmission The power is transmitted through gears 0-4-5-6-10-12 for this instant status. From the fundamental law of gearings We get: If the gear 3-4 slides to the left (disengaging gear 4-5) and gear 1-2 to the left (engaging 1-9) then the power is transmitted through 0-1-9-6-10-12.
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