logging in or signing up UNIT IV GSANJANA Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 826 Category: Education License: All Rights Reserved Like it (3) Dislike it (0) Added: May 19, 2009 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... By: sachin1983 (4 month(s) ago) good presentation.please send me shindesms1983@gmail.com Saving..... Post Reply Close Saving..... Edit Comment Close By: GSANJANA (9 month(s) ago) Dear sir now u can download. thank u for u r comment Saving..... Post Reply Close Saving..... Edit Comment Close By: prof_panneer (9 month(s) ago) I find the presentation on Theory of gearing very useful. Please allow me to download as I want to use this for teaching my students. Prof.R.Panneer Saving..... Post Reply Close Saving..... Edit Comment Close By: devajayam (20 month(s) ago) I need to download this as i am a professor consider and allow me t o download Saving..... Post Reply Close Saving..... Edit Comment Close Premium member Presentation Transcript Slide 1: UNIT : IV Theory of gearing Gear nomenclature Law of gearing Tooth forms of gears Minimum number of teeth. Length of arc of contact Interface. Gear trains Types Velocity Ratio and Torque calculation in epicyclic gear trains 1 baburao@karunya.edu / 9790604475 Slide 2: baburao@karunya.edu / 9790604475 2 In about 2600 B.C. the Chinese used a chariot incorporating a complex series of gears, as shown in below Figure INTRODUCTION: Gears are wheels with teeth. Gears mesh together and make things turn. Gears are used to transfer motion or power from one moving part to another. Slide 3: Gears are just modified wheel and axle systems. A gear is simply a wheel with “teeth” around it’s circumference. In a simple 2-gear “train”, the direction of the motion is changed from driver to follower. The “gear ratio” is defined to be the ratio of the number of teeth on the driver to the number of teeth on the follower. Multiplies ___________ or __________________ Multiplies _________ _____ gear ratio _____ gear ratio distance Speed (rotational) force high low Slide 4: DEFINITION: Gears are defined as toothed members transmitting rotary motion from one shaft to another, and are among the oldest devices and inventions of man. 4 baburao@karunya.edu / 9790604475 Slide 5: baburao@karunya.edu / 9790604475 5 Gears – The Purpose Gears are generally used for one of four different reasons: To reverse the direction of rotation To increase or decrease the speed of rotation To move rotational motion to a different axis To keep the rotation of two axis synchronized Gears – The Purpose : Gears – The Purpose Sports cars go fast (have speed) but cannot pull any weight. Big trucks can pull heavy loads (have power), but cannot go fast. Gears cause this. Gears increase or decrease the power or speed, but you cannot generally speaking. Slide 7: baburao@karunya.edu / 9790604475 7 Limitations of Gear Drives Manufacture of gears requires special tools and equipment. Manufacturing cost is high comparatively Error in cutting teeth may cause vibrations and noise during operation. Advantages of gear drives: Exact velocity ratio is obtained , since there is no slip. Capable of transmitting large power than that of the belt and chain drives. More efficient and effective means of power transmission Requires less space a compared to belt and rope drives. Slide 8: GEARS CLASSIFICATION Gears may be classified in different manners: I. Based on the relative position of the axes of their shaft axes: Parallel Shafts Example:- b) Intersecting Shafts Example:- Straight bevel gears and Spiral Bevel Gears. c) Neither - Parallel Nor – Intersecting Example:- Crossed-helical gears Hypoid gears Rack and Pinion, Spur Gears Helical Gears Herringbone Gears (Double helical gears) Internal gears Worm and worm gear 8 baburao@karunya.edu / 9790604475 Slide 9: Bevel Gears Worm and Worm Wheel Gear Box 9 baburao@karunya.edu / 9790604475 Slide 10: II. Based on the relative motion of the shafts: Row gears Planetary and differential gears III. Based on the Peripheral Speed (v) : Low velocity gears - v < 3 m/s Medium velocity gears - v = 3 to 15 m/s High velocity gears - v > 15 m/s IV. Based on the position of Teeth on the Wheel: 1. Straight gears 2. Helical Gears 3. Herring bone Gear 4. Curved teeth gears. V. Based on the type of gearing: 1. External Gearing 2. Internal Gearing 3. Rack and Pinion. 10 baburao@karunya.edu / 9790604475 Slide 11: Planetary gears External gears Cycloidal gears 11 baburao@karunya.edu / 9790604475 Slide 12: DEFINITIONS: SPUR GEAR: A gear wheel having radial teeth parallel to the axle. BEVEL GEAR: A gear wheel meshed with another so that their shafts are at an angle less than 180 degrees CROWN GEAR: A gear wheel with teeth set in the rim perpendicular to its plane. WORM GEAR: A short rotating screw that meshes with the teeth of another gear. As a worm gear is an inclined plane, it will be the driving gear in most cases DIFFERENTIAL GEAR: A certain arrangement of gears connecting two axles in the same line and dividing the driving force between them, but allowing one axle to turn faster than the other. It is used in the rear axles of automobiles to permit a difference in axle speeds while turning. RACK GEAR: A toothed bar into which a "pinion," (worm gear, spur gear etc ) meshes. PINION: A small cogwheel, the teeth of which fit into those of a larger gearwheel or those of a rack. COGWHEEL: A wheel with a rim notched into teeth, which meshes with those of another wheel or a rack to transmit or receive motion. IDLER GEAR: A gear wheel placed between two other gears to transmit motion from one to the other. It does not alter the speed of the output, but it does alter the direction it turns. ( ODD number =reverse rotation, EVEN number = same rotation ) RATCHET: A toothed wheel or bar that catches and holds a PAWL, which thus prevents backward movement. PAWL: A mechanical device allowing rotation in only one direction. PLANETARY GEAR:A device allowing several gears to "orbit" about others ( very handy for robot turntables ) 12 baburao@karunya.edu / 9790604475 Slide 13: Use of Spur GearsThese gears find wide application in a number of fields including : Automobiles Textiles and Industrial engineering Use of Helical GearsThese gears are used in areas requiring high speeds, large power transmission, or where noise prevention is important. Automobiles Textile Aerospace and Conveyors Use of Bevel GearThese gears find wide application in a number of fields including : Automotive industry Textile industry Industrial engineering products Use of Rack GearThe gear is commonly used in steering mechanism of cars. Other important applications of rack gears include : Construction equipment Machine tools Conveyors and Material handling Roller feeds 13 baburao@karunya.edu / 9790604475 COMMERTIAL AVAILABLE GEARS AND THEIR USES Slide 14: Use of SprocketsThis simple gear finds application in diverse areas including : Food industry Bicycles Motorcycles Cars Tanks Industrial machines Movie projectors and cameras Use of Worm GearsThese gears find application in : Electric motors Automotive components Use of Cycloidal Gears Mechanical clocks Automobiles Use of Differential Gears The gear is extensively used in the automobile industry for effective and efficient working of vehicles. These gears do not create noise and also help in speed differential. Differential Gears 14 baburao@karunya.edu / 9790604475 Slide 15: Use of External GearsThese gears are used in diverse fields including : Coal industry Mining Steel plants Paper and pulp industry Use of Internal Gears Light duty applications Rollers Indexing Use of Pinion Gears Trucks Cars Off road applications Use of Planetary GearsThese gears are the most widely used gears having diverse applications including : Sugar industry Power industry Wind turbines Marine industry Agriculture industry Pinion Gear 15 baburao@karunya.edu / 9790604475 Slide 16: 16 baburao@karunya.edu / 9790604475 SPUR GEAR - NOMENCLATURE Slide 17: 17 baburao@karunya.edu / 9790604475 Pitch circle: An imaginary circle which by pure rolling action, would give the same motion as the actual gear. Pitch surface : The surface of the imaginary rolling cylinder (cone, etc.) WHICH meshing gears have replaced at the pitch circle. 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. 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. Tooth space: The distance between adjacent teeth measured on the pitch circle. TERMINOLOGY: Slide 18: Backlash: The difference between the circle thickness of one gear and the tooth space of the mating gear. Circular pitch (p): The width of a tooth and a space, measured on the pitch circle. (pD/T) Diametral pitch (P): The number of teeth of a gear per inch of its pitch diameter. ( T / D) Module (m): Pitch diameter divided by number of teeth. The pitch diameter is usually specified in inches or millimeters; in the former case the module is the inverse of Diametral pitch. Fillet : The small radius that connects the profile of a tooth to the root circle. Pinion: The smaller of any pair of mating gears. The larger of the pair is called simply the gear. Velocity ratio: The ratio of the number of revolutions of the driving (or input) gear to the number of revolutions of the driven (or output) gear, in a unit of time. Pitch point: The point of tangency of the pitch circles of a pair of mating gears. Common tangent: The line tangent to the pitch circle at the pitch point. Line of action: A line normal to a pair of mating tooth profiles at their point of contact. Path of contact: The path traced by the contact point of a pair of tooth profiles. Pressure angle (Ø) or Angle of Obliquity (Ø) : The angle between the common normal at the point of tooth contact and the common tangent to the pitch circles. It is also the angle between the line of action and the common tangent. Base circle : An imaginary circle used in involute gearing to generate the involutes that form the tooth profiles. 18 baburao@karunya.edu / 9790604475 Slide 19: baburao@karunya.edu / 9790604475 19 Gear Meshing Slide 20: baburao@karunya.edu / 9790604475 20 Gear Meshing Slide 21: baburao@karunya.edu / 9790604475 21 Line of action and Pressure angle The purpose of meshing gear teeth is to provide constant, instantaneous relative motion btw the engaging gears. To achieve this tooth action, the common of the curves of the two meshing gear teeth must pass through a common point, called the pitch point on the pitch circle. Slide 22: 22 A gear train is usually made up of two or more gears. The driver in this example is gear ‘A’. If a motor turns gear ‘A’ in an anticlockwise direction: Which direction does gear ‘B’ turn ? Which direction does gear ‘C’’ turn ? 3. Does gear ‘C’ revolve faster or slower than gear ’A ? An ‘idler’ gear is another important gear. In the example opposite gear ‘A’ turns in an anticlockwise direction and also gear ‘C’ turns in an anticlockwise direction. The ‘idler’ gear is used so that the rotation of the two important gears is the same. Is the speed of gears A and B the same ? Clockwise Counter-Clockwise SLOWER – SMALLER GEAR TURNS A LARGER GEAR GEAR TRAINS Slide 23: baburao@karunya.edu / 9790604475 23 Slide 24: baburao@karunya.edu / 9790604475 24 Slide 25: baburao@karunya.edu / 9790604475 25 Drawing Gears : Drawing Gears It would be very difficult to draw gears if you had to draw all the teeth every time you wanted to design a gear system. For this reason a gear can be represented by drawing two circles. CIRCLES OVERLAP WHERE TEETH MESH Gear Ratio(Velocity Ratio) : Gear Ratio(Velocity Ratio) Many machines use gears. A very good example is a bicycle which has gears that make it easier to cycle, especially up hills. Bicycles normally have a large gear wheel which has a pedal attached and a selection of gear wheels of different sizes, on the back wheel. When the pedal is revolved the chain pulls round the gear wheels at the back. Gear Ratio(Velocity Ratio) : Gear Ratio(Velocity Ratio) The reason bicycles are easier to cycle up a hill when the gears are changed is due to what is called Gear Ratio (velocity ratio). Gear ratio can be worked out in the form of numbers and examples are shown. Basically, the ratio is determined by the number of teeth on each gear wheel, the chain is ignored and does not enter the equation. But WHAT does this mean? It means that the DRIVEN gear makes TWO rotations for every ONE rotation of the Driving Gear. Gear Ratio - Examples : Gear Ratio - Examples What does this mean? For every 3 rotations of the driving gear, the driven gear makes one rotation. Gear Ratio - Examples : Gear Ratio - Examples What does this mean? For every 4 rotations of the driving gear, the driven gear makes 1 rotation. Determining RPMs (revolutions per minute) : Determining RPMs (revolutions per minute) In the example shown, the DRIVER gear is larger than the DRIVEN gear. The general rule is - large to small gear means 'multiply' the velocity ratio by the rpm of the first gear. Divide 60 teeth by 30 teeth to find the velocity ratio(1:2). Multiply this number (2) by the rpm (120). This gives an answer of 240rpm Determining RPMs (revolutions per minute) : Determining RPMs (revolutions per minute) In the example shown, the DRIVER gear is smaller than the DRIVEN gear. The general rule is - small to large gear means 'divide' the velocity ratio(3:1) by the rpm of the first gear. Divide 75 teeth by 25 teeth to find the velocity ratio. divide the 60rpm by the velocity ration (3). The answer is 20rpm. Determining RPMs (revolutions per minute) : Determining RPMs (revolutions per minute) If A revolves at 100 revs/min what is B ? (Remember small gear to large gear decreases revs) Compound Gear Ratios : Compound Gear Ratios When faced with three gears the question can be broken down into two parts. First work on Gears A and B. When this has been solved work on gears B and C. The diagram shows a gear train composed of three gears. Gear A revolves at 60 revs/min in a clockwise direction. What is the output in revolutions per minute at Gear C? In what direction does Gear C revolve ? Compound Gear Ratios : Compound Gear Ratios This means that for every THREE revolutions of GEAR A, Gear B travels once. Since we are going from a SMALLER gear to a LARGER gear we DIVIDE the Rpms. Now find the gear ratio for B & C. This means for every ONE rotation of gear B, gear C makes SIX rotations. Is there an easier way? : Is there an easier way? You can also multiply the two gear ratios together to get the TOTAL gear ratio. In the above figure we see that gear C will make TWO rotations for every one rotation of gear A. And since gear C is smaller than gear A we multiply. Compound Gear Ratios : Compound Gear Ratios Below is a question regarding 'compound gears'. Gears C and B represent a compound gear as they appear 'fixed' together. When drawn with a compass they have the same centre. Two gears 'fixed' together in this way rotate together and at the same RPM. When answering a question like this split it into two parts. Treat gears A and B as one question AND C and D as the second part. What is the output in revs/min at D and what is the direction of rotation if Gear A rotates in a clockwise direction at 30 revs/min? Compound Gear Ratios : Compound Gear Ratios Considering that Gear B is smaller than Gear A we can conclude that the RPMs for gear B is 30*3 = 90 rev/min Since Gear B is at 90rev/min and has the SAME rotational speed as gear C Multiply by 4 to get Gear D’s speed. Thus, Gear D moves at 90*4 = 360 rev/min OR Since Gear A moves at 30rpms and Gear D is SMALLER. We multiply by 12. 30*12 = 360 rev/min Try this one : Try this one Answer : Answer If Gear A turns CCW, then gear B turns CW along with gear C as they are a compound gear. Therefore, Gear D rotates CCW. Slide 41: Spur gear geometry Addendum circle – top of teeth Dedendum circle – bottom of teeth Base circle – bottom of involute Addendum a Dedendum b Pitch circle – rolling circle Circular pitch (p) Base pitch (pb) Base radius (Rb) Pitch radius (R) Rack involute 41 baburao@karunya.edu / 9790604475 Slide 42: f f Rb – base circle radius R – pitch circle radius Spur gear geometry tooth spacing on pitch circle number of teeth Ro – addendum (outside) circle radius Ri – dedendum (inside) circle radius pressure angle Ro Ri 42 baburao@karunya.edu / 9790604475 Slide 43: Spur gear geometry 43 baburao@karunya.edu / 9790604475 Slide 44: Rb pb T teeth R p Ex A gear has 8 teeth and a pitch circle radius of 2 inches. What is the circular pitch? Spur gear geometry 44 baburao@karunya.edu / 9790604475 Pb = Base pitch P = circular pitch Slide 45: Ex Consider the spur gear with the following parameters Number of teeth 24 Pressure angle 20o Pitch circle radius 1.5" Outer radius 1.625" Find: Base circle radius Addendum (T = 24) (f = 20o) (R = 1.5”) (Ro = R+a =1.625) (Rb=?) (a = ?) Solution 45 baburao@karunya.edu / 9790604475 Slide 46: Average number of teeth in contact during motion Z mp > 1.40 ? smooth motion Note: pb is the tooth spacing along line of action: ? correct function mp > 1 Contact ratio (mp) 46 baburao@karunya.edu / 9790604475 Slide 47: Contact ratio (mp) - Calculation from gear parameters To find distance Z = AB A E1 E2 f pressure angle Ded. circle Base circle Pitch circle Add. circle Ded. circle Pitch circle Add. circle Base circle B Gear 1 (driver) Gear 2 (driven) Line of action Point A: begin contact line of action crosses addendum gear 2 Point B: end contact line of action crosses addendum gear 1 47 baburao@karunya.edu / 9790604475 Slide 48: Rb1 Ro1 A E1 E2 Ded. circle Base circle Pitch circle Add. circle Ded. circle Pitch circle Add. circle Base circle B Gear 1 (driver) Gear 2 (driven) Line of action Contact ratio (mp) - Calculation from gear parameters To find distance Z = AB 48 baburao@karunya.edu / 9790604475 Slide 49: Ro2 Rb2 Ded. circle Base circle Pitch circle Add. circle Ded. circle Pitch circle Add. circle Base circle B Gear 1 (driver) Gear 2 (driven) Line of action Contact ratio (mp) - Calculation from gear parameters To find distance Z = AB 49 baburao@karunya.edu / 9790604475 Slide 50: E1 E2 P f f E1P + E2P O1 O2 O1P sin f + O2P sin f (O1P + O2P) sin f C sin f R2 Rb2 f Ded. circle Base circle Pitch circle Add. circle Ded. circle Pitch circle Add. circle Base circle B Gear 1 (driver) Gear 2 (driven) Line of action Rb1 R1 Contact ratio (mp) - Calculation from gear parameters To find distance Z = AB C 50 baburao@karunya.edu / 9790604475 Slide 51: R = Pitch radius of pinion Rb = Base radius of pinion Ro = Outside radius of pinion a = Addendum Contact ratio (mp) - Calculation from gear parameters To find length of action Z To find length of action Z for rack and pinion 51 baburao@karunya.edu / 9790604475 Slide 52: f = 20o Pinion T1 = 24 R1 = 1.5” Ro1 = 1.625” Gear T2 = 60 R2 = 3.75” Ro2 = 3.875” EX Find a) length of action (Z) b) Contact ratio (mp) 52 baburao@karunya.edu / 9790604475 Manufacture/selection of spur gears : Manufacture/selection of spur gears Any two spur gear will mate correctly if their teeth have the same circular pitch AND The center distance is selected properly No interference occurs C = R1+R2 No backlash module (size of tooth) to mate with rack Pitch diameter 53 baburao@karunya.edu / 9790604475 Manufacture/selection of spur gears : Manufacture/selection of spur gears The basic concept of gear manufacturing is to use one gear to cut another Actually we use a cutter with the shape of a gear 2 common methods: Hobbing – cutter has same profile as gear rack Fellows method – cutter has same profile as gear (can be used to cut internal gears) 54 baburao@karunya.edu / 9790604475 Slide 55: Gear Rack A rack has a base circle radius Rb = 8 ? involute profile is a straight line So we can use a HOB with the profile of a rack to cut a gear Dedendum of gear will equal addendum of rack b = arack Gear must rotate at correct speed – matched to hob speed line of action pitch line arack brack p/2 p/2 p f Addendum of gear will depend on outer radius of gear blank a = Ro - R Ro Circular pitch of gear will equal circular pitch of rack 55 baburao@karunya.edu / 9790604475 Method of Gear Hobbing : 56 baburao@karunya.edu / 9790604475 Method of Gear Hobbing Slide 57: Fellows Method of Gear Shaping 57 baburao@karunya.edu / 9790604475 Standard tooth sizes/proportions : Standard tooth sizes/proportions There are four parameters that specify tooth shape/size Module (m) Addendum (a) 1.000 m 1.000 m Dedendum (b) 1.250 m 1.157 m or 1.167 m Pressure angle (f) 20° 20° British standard German standard Standard British modules: m = 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50 (all in mm) p t = p/2 a b pitch circle 58 baburao@karunya.edu / 9790604475 Slide 59: Tooth sizing systems U.S. System Metric system T = number of teeth D = pitch diameter, mm T = number of teeth D = pitch diameter, inches ( in inches) (in millimeters) 59 baburao@karunya.edu / 9790604475 Slide 60: Example: It is required to make a gear having 13 teeth of module 3 using the British standard system For this gear, find: a) the tooth thickness (on the pitch circle) b) the pitch circle radius c) the size of the gear blank d) the dedendum circle radius e) the base circle radius 60 baburao@karunya.edu / 9790604475 Slide 61: Lists the standard tooth system for spur gears. (Shigley & Uicker 80) 61 baburao@karunya.edu / 9790604475 Slide 62: 62 baburao@karunya.edu / 9790604475 You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
UNIT IV GSANJANA Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 826 Category: Education License: All Rights Reserved Like it (3) Dislike it (0) Added: May 19, 2009 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... By: sachin1983 (4 month(s) ago) good presentation.please send me shindesms1983@gmail.com Saving..... Post Reply Close Saving..... Edit Comment Close By: GSANJANA (9 month(s) ago) Dear sir now u can download. thank u for u r comment Saving..... Post Reply Close Saving..... Edit Comment Close By: prof_panneer (9 month(s) ago) I find the presentation on Theory of gearing very useful. Please allow me to download as I want to use this for teaching my students. Prof.R.Panneer Saving..... Post Reply Close Saving..... Edit Comment Close By: devajayam (20 month(s) ago) I need to download this as i am a professor consider and allow me t o download Saving..... Post Reply Close Saving..... Edit Comment Close Premium member Presentation Transcript Slide 1: UNIT : IV Theory of gearing Gear nomenclature Law of gearing Tooth forms of gears Minimum number of teeth. Length of arc of contact Interface. Gear trains Types Velocity Ratio and Torque calculation in epicyclic gear trains 1 baburao@karunya.edu / 9790604475 Slide 2: baburao@karunya.edu / 9790604475 2 In about 2600 B.C. the Chinese used a chariot incorporating a complex series of gears, as shown in below Figure INTRODUCTION: Gears are wheels with teeth. Gears mesh together and make things turn. Gears are used to transfer motion or power from one moving part to another. Slide 3: Gears are just modified wheel and axle systems. A gear is simply a wheel with “teeth” around it’s circumference. In a simple 2-gear “train”, the direction of the motion is changed from driver to follower. The “gear ratio” is defined to be the ratio of the number of teeth on the driver to the number of teeth on the follower. Multiplies ___________ or __________________ Multiplies _________ _____ gear ratio _____ gear ratio distance Speed (rotational) force high low Slide 4: DEFINITION: Gears are defined as toothed members transmitting rotary motion from one shaft to another, and are among the oldest devices and inventions of man. 4 baburao@karunya.edu / 9790604475 Slide 5: baburao@karunya.edu / 9790604475 5 Gears – The Purpose Gears are generally used for one of four different reasons: To reverse the direction of rotation To increase or decrease the speed of rotation To move rotational motion to a different axis To keep the rotation of two axis synchronized Gears – The Purpose : Gears – The Purpose Sports cars go fast (have speed) but cannot pull any weight. Big trucks can pull heavy loads (have power), but cannot go fast. Gears cause this. Gears increase or decrease the power or speed, but you cannot generally speaking. Slide 7: baburao@karunya.edu / 9790604475 7 Limitations of Gear Drives Manufacture of gears requires special tools and equipment. Manufacturing cost is high comparatively Error in cutting teeth may cause vibrations and noise during operation. Advantages of gear drives: Exact velocity ratio is obtained , since there is no slip. Capable of transmitting large power than that of the belt and chain drives. More efficient and effective means of power transmission Requires less space a compared to belt and rope drives. Slide 8: GEARS CLASSIFICATION Gears may be classified in different manners: I. Based on the relative position of the axes of their shaft axes: Parallel Shafts Example:- b) Intersecting Shafts Example:- Straight bevel gears and Spiral Bevel Gears. c) Neither - Parallel Nor – Intersecting Example:- Crossed-helical gears Hypoid gears Rack and Pinion, Spur Gears Helical Gears Herringbone Gears (Double helical gears) Internal gears Worm and worm gear 8 baburao@karunya.edu / 9790604475 Slide 9: Bevel Gears Worm and Worm Wheel Gear Box 9 baburao@karunya.edu / 9790604475 Slide 10: II. Based on the relative motion of the shafts: Row gears Planetary and differential gears III. Based on the Peripheral Speed (v) : Low velocity gears - v < 3 m/s Medium velocity gears - v = 3 to 15 m/s High velocity gears - v > 15 m/s IV. Based on the position of Teeth on the Wheel: 1. Straight gears 2. Helical Gears 3. Herring bone Gear 4. Curved teeth gears. V. Based on the type of gearing: 1. External Gearing 2. Internal Gearing 3. Rack and Pinion. 10 baburao@karunya.edu / 9790604475 Slide 11: Planetary gears External gears Cycloidal gears 11 baburao@karunya.edu / 9790604475 Slide 12: DEFINITIONS: SPUR GEAR: A gear wheel having radial teeth parallel to the axle. BEVEL GEAR: A gear wheel meshed with another so that their shafts are at an angle less than 180 degrees CROWN GEAR: A gear wheel with teeth set in the rim perpendicular to its plane. WORM GEAR: A short rotating screw that meshes with the teeth of another gear. As a worm gear is an inclined plane, it will be the driving gear in most cases DIFFERENTIAL GEAR: A certain arrangement of gears connecting two axles in the same line and dividing the driving force between them, but allowing one axle to turn faster than the other. It is used in the rear axles of automobiles to permit a difference in axle speeds while turning. RACK GEAR: A toothed bar into which a "pinion," (worm gear, spur gear etc ) meshes. PINION: A small cogwheel, the teeth of which fit into those of a larger gearwheel or those of a rack. COGWHEEL: A wheel with a rim notched into teeth, which meshes with those of another wheel or a rack to transmit or receive motion. IDLER GEAR: A gear wheel placed between two other gears to transmit motion from one to the other. It does not alter the speed of the output, but it does alter the direction it turns. ( ODD number =reverse rotation, EVEN number = same rotation ) RATCHET: A toothed wheel or bar that catches and holds a PAWL, which thus prevents backward movement. PAWL: A mechanical device allowing rotation in only one direction. PLANETARY GEAR:A device allowing several gears to "orbit" about others ( very handy for robot turntables ) 12 baburao@karunya.edu / 9790604475 Slide 13: Use of Spur GearsThese gears find wide application in a number of fields including : Automobiles Textiles and Industrial engineering Use of Helical GearsThese gears are used in areas requiring high speeds, large power transmission, or where noise prevention is important. Automobiles Textile Aerospace and Conveyors Use of Bevel GearThese gears find wide application in a number of fields including : Automotive industry Textile industry Industrial engineering products Use of Rack GearThe gear is commonly used in steering mechanism of cars. Other important applications of rack gears include : Construction equipment Machine tools Conveyors and Material handling Roller feeds 13 baburao@karunya.edu / 9790604475 COMMERTIAL AVAILABLE GEARS AND THEIR USES Slide 14: Use of SprocketsThis simple gear finds application in diverse areas including : Food industry Bicycles Motorcycles Cars Tanks Industrial machines Movie projectors and cameras Use of Worm GearsThese gears find application in : Electric motors Automotive components Use of Cycloidal Gears Mechanical clocks Automobiles Use of Differential Gears The gear is extensively used in the automobile industry for effective and efficient working of vehicles. These gears do not create noise and also help in speed differential. Differential Gears 14 baburao@karunya.edu / 9790604475 Slide 15: Use of External GearsThese gears are used in diverse fields including : Coal industry Mining Steel plants Paper and pulp industry Use of Internal Gears Light duty applications Rollers Indexing Use of Pinion Gears Trucks Cars Off road applications Use of Planetary GearsThese gears are the most widely used gears having diverse applications including : Sugar industry Power industry Wind turbines Marine industry Agriculture industry Pinion Gear 15 baburao@karunya.edu / 9790604475 Slide 16: 16 baburao@karunya.edu / 9790604475 SPUR GEAR - NOMENCLATURE Slide 17: 17 baburao@karunya.edu / 9790604475 Pitch circle: An imaginary circle which by pure rolling action, would give the same motion as the actual gear. Pitch surface : The surface of the imaginary rolling cylinder (cone, etc.) WHICH meshing gears have replaced at the pitch circle. 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. 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. Tooth space: The distance between adjacent teeth measured on the pitch circle. TERMINOLOGY: Slide 18: Backlash: The difference between the circle thickness of one gear and the tooth space of the mating gear. Circular pitch (p): The width of a tooth and a space, measured on the pitch circle. (pD/T) Diametral pitch (P): The number of teeth of a gear per inch of its pitch diameter. ( T / D) Module (m): Pitch diameter divided by number of teeth. The pitch diameter is usually specified in inches or millimeters; in the former case the module is the inverse of Diametral pitch. Fillet : The small radius that connects the profile of a tooth to the root circle. Pinion: The smaller of any pair of mating gears. The larger of the pair is called simply the gear. Velocity ratio: The ratio of the number of revolutions of the driving (or input) gear to the number of revolutions of the driven (or output) gear, in a unit of time. Pitch point: The point of tangency of the pitch circles of a pair of mating gears. Common tangent: The line tangent to the pitch circle at the pitch point. Line of action: A line normal to a pair of mating tooth profiles at their point of contact. Path of contact: The path traced by the contact point of a pair of tooth profiles. Pressure angle (Ø) or Angle of Obliquity (Ø) : The angle between the common normal at the point of tooth contact and the common tangent to the pitch circles. It is also the angle between the line of action and the common tangent. Base circle : An imaginary circle used in involute gearing to generate the involutes that form the tooth profiles. 18 baburao@karunya.edu / 9790604475 Slide 19: baburao@karunya.edu / 9790604475 19 Gear Meshing Slide 20: baburao@karunya.edu / 9790604475 20 Gear Meshing Slide 21: baburao@karunya.edu / 9790604475 21 Line of action and Pressure angle The purpose of meshing gear teeth is to provide constant, instantaneous relative motion btw the engaging gears. To achieve this tooth action, the common of the curves of the two meshing gear teeth must pass through a common point, called the pitch point on the pitch circle. Slide 22: 22 A gear train is usually made up of two or more gears. The driver in this example is gear ‘A’. If a motor turns gear ‘A’ in an anticlockwise direction: Which direction does gear ‘B’ turn ? Which direction does gear ‘C’’ turn ? 3. Does gear ‘C’ revolve faster or slower than gear ’A ? An ‘idler’ gear is another important gear. In the example opposite gear ‘A’ turns in an anticlockwise direction and also gear ‘C’ turns in an anticlockwise direction. The ‘idler’ gear is used so that the rotation of the two important gears is the same. Is the speed of gears A and B the same ? Clockwise Counter-Clockwise SLOWER – SMALLER GEAR TURNS A LARGER GEAR GEAR TRAINS Slide 23: baburao@karunya.edu / 9790604475 23 Slide 24: baburao@karunya.edu / 9790604475 24 Slide 25: baburao@karunya.edu / 9790604475 25 Drawing Gears : Drawing Gears It would be very difficult to draw gears if you had to draw all the teeth every time you wanted to design a gear system. For this reason a gear can be represented by drawing two circles. CIRCLES OVERLAP WHERE TEETH MESH Gear Ratio(Velocity Ratio) : Gear Ratio(Velocity Ratio) Many machines use gears. A very good example is a bicycle which has gears that make it easier to cycle, especially up hills. Bicycles normally have a large gear wheel which has a pedal attached and a selection of gear wheels of different sizes, on the back wheel. When the pedal is revolved the chain pulls round the gear wheels at the back. Gear Ratio(Velocity Ratio) : Gear Ratio(Velocity Ratio) The reason bicycles are easier to cycle up a hill when the gears are changed is due to what is called Gear Ratio (velocity ratio). Gear ratio can be worked out in the form of numbers and examples are shown. Basically, the ratio is determined by the number of teeth on each gear wheel, the chain is ignored and does not enter the equation. But WHAT does this mean? It means that the DRIVEN gear makes TWO rotations for every ONE rotation of the Driving Gear. Gear Ratio - Examples : Gear Ratio - Examples What does this mean? For every 3 rotations of the driving gear, the driven gear makes one rotation. Gear Ratio - Examples : Gear Ratio - Examples What does this mean? For every 4 rotations of the driving gear, the driven gear makes 1 rotation. Determining RPMs (revolutions per minute) : Determining RPMs (revolutions per minute) In the example shown, the DRIVER gear is larger than the DRIVEN gear. The general rule is - large to small gear means 'multiply' the velocity ratio by the rpm of the first gear. Divide 60 teeth by 30 teeth to find the velocity ratio(1:2). Multiply this number (2) by the rpm (120). This gives an answer of 240rpm Determining RPMs (revolutions per minute) : Determining RPMs (revolutions per minute) In the example shown, the DRIVER gear is smaller than the DRIVEN gear. The general rule is - small to large gear means 'divide' the velocity ratio(3:1) by the rpm of the first gear. Divide 75 teeth by 25 teeth to find the velocity ratio. divide the 60rpm by the velocity ration (3). The answer is 20rpm. Determining RPMs (revolutions per minute) : Determining RPMs (revolutions per minute) If A revolves at 100 revs/min what is B ? (Remember small gear to large gear decreases revs) Compound Gear Ratios : Compound Gear Ratios When faced with three gears the question can be broken down into two parts. First work on Gears A and B. When this has been solved work on gears B and C. The diagram shows a gear train composed of three gears. Gear A revolves at 60 revs/min in a clockwise direction. What is the output in revolutions per minute at Gear C? In what direction does Gear C revolve ? Compound Gear Ratios : Compound Gear Ratios This means that for every THREE revolutions of GEAR A, Gear B travels once. Since we are going from a SMALLER gear to a LARGER gear we DIVIDE the Rpms. Now find the gear ratio for B & C. This means for every ONE rotation of gear B, gear C makes SIX rotations. Is there an easier way? : Is there an easier way? You can also multiply the two gear ratios together to get the TOTAL gear ratio. In the above figure we see that gear C will make TWO rotations for every one rotation of gear A. And since gear C is smaller than gear A we multiply. Compound Gear Ratios : Compound Gear Ratios Below is a question regarding 'compound gears'. Gears C and B represent a compound gear as they appear 'fixed' together. When drawn with a compass they have the same centre. Two gears 'fixed' together in this way rotate together and at the same RPM. When answering a question like this split it into two parts. Treat gears A and B as one question AND C and D as the second part. What is the output in revs/min at D and what is the direction of rotation if Gear A rotates in a clockwise direction at 30 revs/min? Compound Gear Ratios : Compound Gear Ratios Considering that Gear B is smaller than Gear A we can conclude that the RPMs for gear B is 30*3 = 90 rev/min Since Gear B is at 90rev/min and has the SAME rotational speed as gear C Multiply by 4 to get Gear D’s speed. Thus, Gear D moves at 90*4 = 360 rev/min OR Since Gear A moves at 30rpms and Gear D is SMALLER. We multiply by 12. 30*12 = 360 rev/min Try this one : Try this one Answer : Answer If Gear A turns CCW, then gear B turns CW along with gear C as they are a compound gear. Therefore, Gear D rotates CCW. Slide 41: Spur gear geometry Addendum circle – top of teeth Dedendum circle – bottom of teeth Base circle – bottom of involute Addendum a Dedendum b Pitch circle – rolling circle Circular pitch (p) Base pitch (pb) Base radius (Rb) Pitch radius (R) Rack involute 41 baburao@karunya.edu / 9790604475 Slide 42: f f Rb – base circle radius R – pitch circle radius Spur gear geometry tooth spacing on pitch circle number of teeth Ro – addendum (outside) circle radius Ri – dedendum (inside) circle radius pressure angle Ro Ri 42 baburao@karunya.edu / 9790604475 Slide 43: Spur gear geometry 43 baburao@karunya.edu / 9790604475 Slide 44: Rb pb T teeth R p Ex A gear has 8 teeth and a pitch circle radius of 2 inches. What is the circular pitch? Spur gear geometry 44 baburao@karunya.edu / 9790604475 Pb = Base pitch P = circular pitch Slide 45: Ex Consider the spur gear with the following parameters Number of teeth 24 Pressure angle 20o Pitch circle radius 1.5" Outer radius 1.625" Find: Base circle radius Addendum (T = 24) (f = 20o) (R = 1.5”) (Ro = R+a =1.625) (Rb=?) (a = ?) Solution 45 baburao@karunya.edu / 9790604475 Slide 46: Average number of teeth in contact during motion Z mp > 1.40 ? smooth motion Note: pb is the tooth spacing along line of action: ? correct function mp > 1 Contact ratio (mp) 46 baburao@karunya.edu / 9790604475 Slide 47: Contact ratio (mp) - Calculation from gear parameters To find distance Z = AB A E1 E2 f pressure angle Ded. circle Base circle Pitch circle Add. circle Ded. circle Pitch circle Add. circle Base circle B Gear 1 (driver) Gear 2 (driven) Line of action Point A: begin contact line of action crosses addendum gear 2 Point B: end contact line of action crosses addendum gear 1 47 baburao@karunya.edu / 9790604475 Slide 48: Rb1 Ro1 A E1 E2 Ded. circle Base circle Pitch circle Add. circle Ded. circle Pitch circle Add. circle Base circle B Gear 1 (driver) Gear 2 (driven) Line of action Contact ratio (mp) - Calculation from gear parameters To find distance Z = AB 48 baburao@karunya.edu / 9790604475 Slide 49: Ro2 Rb2 Ded. circle Base circle Pitch circle Add. circle Ded. circle Pitch circle Add. circle Base circle B Gear 1 (driver) Gear 2 (driven) Line of action Contact ratio (mp) - Calculation from gear parameters To find distance Z = AB 49 baburao@karunya.edu / 9790604475 Slide 50: E1 E2 P f f E1P + E2P O1 O2 O1P sin f + O2P sin f (O1P + O2P) sin f C sin f R2 Rb2 f Ded. circle Base circle Pitch circle Add. circle Ded. circle Pitch circle Add. circle Base circle B Gear 1 (driver) Gear 2 (driven) Line of action Rb1 R1 Contact ratio (mp) - Calculation from gear parameters To find distance Z = AB C 50 baburao@karunya.edu / 9790604475 Slide 51: R = Pitch radius of pinion Rb = Base radius of pinion Ro = Outside radius of pinion a = Addendum Contact ratio (mp) - Calculation from gear parameters To find length of action Z To find length of action Z for rack and pinion 51 baburao@karunya.edu / 9790604475 Slide 52: f = 20o Pinion T1 = 24 R1 = 1.5” Ro1 = 1.625” Gear T2 = 60 R2 = 3.75” Ro2 = 3.875” EX Find a) length of action (Z) b) Contact ratio (mp) 52 baburao@karunya.edu / 9790604475 Manufacture/selection of spur gears : Manufacture/selection of spur gears Any two spur gear will mate correctly if their teeth have the same circular pitch AND The center distance is selected properly No interference occurs C = R1+R2 No backlash module (size of tooth) to mate with rack Pitch diameter 53 baburao@karunya.edu / 9790604475 Manufacture/selection of spur gears : Manufacture/selection of spur gears The basic concept of gear manufacturing is to use one gear to cut another Actually we use a cutter with the shape of a gear 2 common methods: Hobbing – cutter has same profile as gear rack Fellows method – cutter has same profile as gear (can be used to cut internal gears) 54 baburao@karunya.edu / 9790604475 Slide 55: Gear Rack A rack has a base circle radius Rb = 8 ? involute profile is a straight line So we can use a HOB with the profile of a rack to cut a gear Dedendum of gear will equal addendum of rack b = arack Gear must rotate at correct speed – matched to hob speed line of action pitch line arack brack p/2 p/2 p f Addendum of gear will depend on outer radius of gear blank a = Ro - R Ro Circular pitch of gear will equal circular pitch of rack 55 baburao@karunya.edu / 9790604475 Method of Gear Hobbing : 56 baburao@karunya.edu / 9790604475 Method of Gear Hobbing Slide 57: Fellows Method of Gear Shaping 57 baburao@karunya.edu / 9790604475 Standard tooth sizes/proportions : Standard tooth sizes/proportions There are four parameters that specify tooth shape/size Module (m) Addendum (a) 1.000 m 1.000 m Dedendum (b) 1.250 m 1.157 m or 1.167 m Pressure angle (f) 20° 20° British standard German standard Standard British modules: m = 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50 (all in mm) p t = p/2 a b pitch circle 58 baburao@karunya.edu / 9790604475 Slide 59: Tooth sizing systems U.S. System Metric system T = number of teeth D = pitch diameter, mm T = number of teeth D = pitch diameter, inches ( in inches) (in millimeters) 59 baburao@karunya.edu / 9790604475 Slide 60: Example: It is required to make a gear having 13 teeth of module 3 using the British standard system For this gear, find: a) the tooth thickness (on the pitch circle) b) the pitch circle radius c) the size of the gear blank d) the dedendum circle radius e) the base circle radius 60 baburao@karunya.edu / 9790604475 Slide 61: Lists the standard tooth system for spur gears. (Shigley & Uicker 80) 61 baburao@karunya.edu / 9790604475 Slide 62: 62 baburao@karunya.edu / 9790604475