Lecture 07 Gears PDF

Lecture 07 Gears 1 Hedaya, M. Gears:- are fundamental mechanical components with several important functions in machinery. 1. Transmit Motion Gears transfer rotational motion from one shaft to another. They enable machines to perform tasks where motion needs to be convey...

Lecture 07 Gears 1 Hedaya, M. Gears:- are fundamental mechanical components with several important functions in machinery. 1. Transmit Motion Gears transfer rotational motion from one shaft to another. They enable machines to perform tasks where motion needs to be conveyed between components. Example: In a car, gears transmit motion from the engine to the wheels 2. Change Speed Gears can increase or decrease rotational speed depending on their size (number of teeth). This is achieved through the gear ratio. Speed increase: When a smaller gear drives a larger gear. Speed decrease: When a larger gear drives a smaller gear. 3. Change Torque Torque is inversely related to speed in gear systems. Gears can amplify torque to overcome resistance or reduce it for faster motion. Example: In a car, low gears provide high torque for climbing hills, while higher gears reduce torque for higher speeds on flat roads. 4. Change Direction of Motion Gears can reverse the direction of rotation or transmit motion at an angle. Reversing direction: Meshing two gears results in opposite rotation directions. Changing angles: Bevel gears or worm gears can change motion direction, such as 90° in a drill 5. Synchronize Motion Gears help synchronize the motion of connected shafts or components, ensuring consistent and precise timing. Example: In clocks, gears synchronize the motion of the hour, minute, and second. 6. Power Transmission Across Distances Gear trains can transmit power over short or long distances by connecting multiple shafts. Example: In conveyor belts, gears transmit power from the motor to the rollers. 7. Reduce Wear and Improve Efficiency By providing smooth motion transmission, gears reduce wear and tear in machinery compared to systems like belts and chains. This improves efficiency and durability 7.1. Types of Gears ❑ Spur gears [parallel axes] Straight Helical Double helical 4 7.1. Types of Gears (cont.) ❑ Spur gears [parallel axes] Straight Helical Double helical 5 7.1. Types of Gears (cont.) ❑ Spur gears [parallel axes] Straight Helical Double helical ❑ Bevel gears [intersecting axes] 6 7.2. Definitions ❑ Pitch circle (diameter d) Imaginary circle representing the friction wheel, transmits the same motion as gears ❑ Pitch point The point of contact of the two pitch circles of mating gears. 7 7.2. Definitions (cont.) ❑ Circular pitch: 𝑝𝑐 = 𝜋𝑑 𝑇 Pc is the space between the teeth ❑ Diameteral pitch: 𝑝𝑑 = 𝑇 𝑑 Pd is a unit to express the size of gear teeth ❑ Module: 𝑚 = 𝑑 𝑇 ❑ Pinion: the smaller gear of two mating gears ❑ Rack: a portion of a gear with infinity radius Pitch circle → pitch line Gears will only mesh with each other if they have teeth of the same module ❑ Meshing condition The two meshing gears should have the same module and the same circular pitch 8 7.3. Gear Trains ❑ Simple gear train ❑ Compound gear train ❑ Planetary (epicyclical) gear train 9 7.4. Gear Trains ❑ Kinematic Diagram of Gear Mechanism Kinematic diagram Kinematic diagram 1 7.4.1. Simple Gear Train ❑ Each gear is fixed to a separate shaft. External meshing ◼ 𝑆𝑝𝑒𝑒𝑑 𝑟𝑎𝑡𝑖𝑜 = 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑑𝑟𝑖𝑣𝑒𝑛 = 𝑁 𝐵 = − 𝑇 𝐴 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑑𝑟𝑖𝑣𝑒𝑟 𝑁𝐴 𝑇𝐵 ◼ N: speed, T: number of teeth A B 11 7.4.1. Simple Gear Train ❑ Each gear is fixed to a separate shaft. Internal meshing ◼ 𝑆𝑝𝑒𝑒𝑑 𝑟𝑎𝑡𝑖𝑜 = 𝑁 𝐵 = 𝑇 𝐴 𝑁𝐴 𝑇𝐵 A B 12 7.4.2. Compound Gear Train ❑ More than one gear are fixed on the same shaft 13 7.4.2. Compound Gear Train ❑ 𝑆𝑝𝑒𝑒𝑑 𝑟𝑎𝑡𝑖𝑜 = 𝑁𝐷 = 𝑁 𝐷 × 𝑁 𝐵 , where 𝑁𝐶 = 𝑁𝐵 D 𝑁𝐴 𝑁𝐶 𝑁𝐴 A 𝑆𝑝𝑒𝑒𝑑 𝑟𝑎𝑡𝑖𝑜 = 𝑁𝐷 = (− 𝑇𝐶 )(− 𝑇𝐴 ) 𝑁𝐴 𝑇𝐷 𝑇𝐵 𝑇 𝑇 𝑆𝑝𝑒𝑒𝑑 𝑟𝑎𝑡𝑖𝑜 = 𝑁 𝐷 = 𝐴 𝐶 C 𝑁𝐴 𝑇𝐵𝑇𝐷 B 14 Problem 1: Speed Ratio In a simple gear train, Gear A has 20 teeth and is meshed with Gear B, which has 40 teeth. If Gear A rotates at 100 RPM (revolutions per minute), what is the rotational speed of Gear B? Solution: 𝑁𝐵 𝑇𝐴 Speed ratio = = 𝑁𝐴 𝑇𝐵 20 1 𝑁𝐵 Speed ratio = = = 40 2 100 100 𝑁𝐵 = = 50 𝑅𝑃𝑀 2 Problem 2 : Torque Transmission Problem 3: Direction of Rotation In a simple gear train, Gear A is rotating clockwise. It meshes with Gear B. What is the direction of rotation of Gear B? Solution: In a simple gear train, when two gears mesh, they rotate in opposite directions. If Gear A rotates clockwise, Gear B will rotate counterclockwise. Problem 4: Compound Calculation Gear A (driver) with 30 teeth drives Gear B with 45 teeth. Gear B is mounted on the same shaft as Gear C (with 20 teeth), which drives Gear D with 60 teeth. If Gear A rotates at 180 RPM, what is the speed of Gear D? Solution 𝑇𝐴 = 30 teeth. 𝑇𝐵 =45 teeth 𝑇𝑐 = 20 𝑡𝑒𝑒𝑡ℎ , 𝑇𝐷 = 60 𝑡𝑒𝑒𝑡ℎ , 𝑁𝐴 =180 RPM Req. 𝑁𝐷 𝑁 𝑁 𝑁 Speed ratio = 𝐷 = 𝐷 ∗ 𝐵 where 𝑁𝐶 = 𝑁𝐵 𝑁𝐴 𝑁𝐶 𝑁𝐴 𝑇𝐶 TA 20 30 1∗2 2 =- *- = * = = 𝑇𝐷 TB 60 45 3∗3 9 2 𝑁𝐷 𝑁𝐷 2 Speed ratio = = = = 9 𝑁𝐴 180 9 180∗2 𝑁𝐷 = = 40 𝑅𝑃𝑀 9