Module 3 Gears - Nomenclature PDF

M ACHINE ELEMENTS MODULE 3 Gears  Module 2 LEARNING OUTCOMES 1. Identify the different classification of gears and familiarize the gear nomenclature. 2. Apply gear design formulas in designing a gear....

M ACHINE ELEMENTS MODULE 3 Gears  Module 2 LEARNING OUTCOMES 1. Identify the different classification of gears and familiarize the gear nomenclature. 2. Apply gear design formulas in designing a gear. M ACHINE ELEMENTS  EXTERNAL SPUR GEAR NOMENCLATURE Pitch Circle (D) is a circle of the radius of which is equal to the distance from the gear axis to the pitch point. It is the diameter of the cylinder if the pair of gears is replaced by rolling cylinders. M ACHINE ELEMENTS  EXTERNAL SPUR GEAR NOMENCLATURE Addendum (a) is the height of tooth above pitch circle of the distances between the pitch circle and the top of the tooth. Dedendum (d) is the radial distance from the pitch circle to the root circle, that is to the bottom of the tooth space. 𝑑 =𝑎+𝑐 Clearance (c) is the distance between the outside diameter of a gear and the root diameter of its mate. This margin prevents the top of a gear tooth from interfering with the root of its mating gear tooth M ACHINE ELEMENTS  EXTERNAL SPUR GEAR NOMENCLATURE Addendum Circle (Da) is the circle that bounds the outer ends of the teeth. 𝐷𝑎 = 𝐷 + 2𝑎 𝐷 – Diameter of pitch circle Dedendum Circle (Dd) is a circle coinciding with or tangent to the bottoms of the tooth spaces. 𝐷𝑑 = 𝐷 − 2𝑑 Or, 𝐷𝑑 = 𝐷 − 2(𝑎 + 𝑐) M ACHINE ELEMENTS EXTERNAL SPUR GEAR NOMENCLATURE Root Diameter is simply the diameter of the dedendum circle. Base Circle (Db) the circle from which the involute of a gear is drawn. 𝐷𝐵 = 𝐷cos 𝜃 𝜃 – pressure angle M ACHINE ELEMENTS  EXTERNAL SPUR GEAR NOMENCLATURE Working Depth (WR) is the depth of engagement of two gears and is the sum of their addenda. 𝑊𝑅 = 2𝑎 Whole Depth (WL) is the total depth of a tooth space equal to addendum plus dedendum. It is also equal to working depth plus clearance. 𝑊𝐿 = 2𝑎 + 𝑐 𝑊𝐿 = 𝑎 + 𝑑 M ACHINE ELEMENTS  EXTERNAL SPUR GEAR NOMENCLATURE Diametral Pitch (PD) is the ratio of the number of teeth to the pitch diameter. 𝑇 𝑃𝐷 = 𝐷 Circular Pitch (PC) is the distance measured along the pitch circle from a point on one tooth to the corresponding point on an adjacent tooth. 𝜋𝐷 𝑃𝐶 = 𝑇 𝑃𝐶 𝑥 𝑃𝐷 = 𝜋 Two gears that mesh together must have the same circular pitch. The word “pitch” when not specified refers to diametral pitch. M ACHINE ELEMENTS  EXTERNAL SPUR GEAR NOMENCLATURE Pitch Point is the point of tangency of two pitch circles and is on the line of centers. Pitch Angle (α) is the angle subtended by an arc on the pitch circle equal in length to the circular pitch. 360 𝛼° = 𝑇 M ACHINE ELEMENTS  EXTERNAL SPUR GEAR NOMENCLATURE Pitch Line is the line passing through the pitch point which is perpendicular to the line of center. Tooth Flank is the surface of the tooth which is between the pitch circle and the root. Tooth Face refers to the surface of the tooth between the pitch circle and the addendum circle. Face Width is the length of the teeth in the axial plane. M ACHINE ELEMENTS  EXTERNAL SPUR GEAR NOMENCLATURE Tooth Thickness (Tt) is the width of tooth measured along the pitch circle. Tooth Space (Ts) is the space between the teeth measured along the pitch circle. Backlash (b) is the excess thickness of tooth space over the thickness of the mating tooth. 𝑏 = 𝑇𝑠 − 𝑇𝑡 𝑃𝑐 = 𝑇𝑡 + 𝑇𝑠 M ACHINE ELEMENTS  EXTERNAL SPUR GEAR NOMENCLATURE Chordal Thickness is the tooth width measured along the chord at the pitch point. Gear Ratio is the number of teeth in the gear divided by the number of teeth in the pinion. Speed Ratio is the angular speed of the driver divided by the angular speed of the driven gear. M ACHINE ELEMENTS  EXTERNAL SPUR GEAR NOMENCLATURE Pressure Angle (θ) is the angle between the line of action of the force on the gear tooth and the line tangent to the pitch circles. Line of Action is the straight line passing through the pitch point and tangent to the base circles. Coincident with the pressure angle line. A large pressure angle tends to produce a large radial pressure on the bearings. M ACHINE ELEMENTS EXTERNAL SPUR GEAR NOMENCLATURE Involutes are the curve formed by path of a point on a straight line. Most gears have an involute tooth profile. Module is the reciprocal of diametral pitch. Involute gear tooth profile M ACHINE ELEMENTS  EXTERNAL SPUR GEAR NOMENCLATURE Angle of Approach is the angle through which the gear turns from the time a particular pair of teeth come into contact until they are in contact at the pitch point. Angle of Recess is the angle through which the gear turns from the time a given pair of teeth are in contact at the pitch point until they pass out of mesh. Angle of Action is the angle through which the gear turns from the time a particular pair of teeth come into contact until they go out of contact. It is equal to the angle of approach plus the angle of recess. EXTERNAL SPUR GEAR NOMENCLATURE Arc of Approach is the arc subtended by the angle of approach. Arc of Recess is the arc subtended by the angle of recess. Arc of Action is the arc of the pitch circle through which a tooth travels from the first point of contact with the mating tooth to the point where the contact ceases. EXTERNAL SPUR GEAR NOMENCLATURE M ACHINE ELEMENTS STANDARD GEAR TOOTH PROPORTIONS System 14 1/2 0 Brown and 1 1/20 Full- 200 Full Depth 200 Stub 200 Fellows Sharpe, 14 1/20 Composite and Depth Cycloidal Addendum 1/Pd 1/Pd 1/Pd 0.8/Pd 1/P2 Dedendum 1.157/Pd 1.157/Pd 1.157/Pd 1/Pd 1.25/P2 Clearance 0.157/Pd 0.157/Pd 0.157/Pd 0.2/Pd 0.25/P2 Working Depth 2/Pd 2/Pd 2/Pd 1.6/Pd 2/P2 Total Depth 2.157/Pd 2.157/Pd 2.157/Pd 1.8/Pd 2.25/P2 Outside T +2 / Pd T + 2 / Pd T + 2 / Pd T + 1.6 /Pd T/P1 + 2/P2 Diameter Tooth 1.5708/Pd 1.5708/Pd 1.5708/Pd 1.5708/Pd 1.5708/P1 thickness Tooth Space 1.5708/Pd 1.5708/Pd 1.5708/Pd 1.5708/Pd 1.5708/P1 Fillet Radius 0.209/Pd 0.209/Pd 0.236/Pd 0.3/Pd 0.25/P1 M ACHINE ELEMENTS  LAW GOVERNING THE SHAPTE OF TEETH The curves which form the profile of the teeth on a pair of gears may, in theory at least, have any form whatever, provided they conform to the fundamental law: “the line drawn from the pitch point to the point where the teeth are in contact must be perpendicular to a line drawn through the point of contact tangent to the curves of the teeth; that is, the common normal to the tooth curves at all points of contact must pass through the pitch point” M ACHINE ELEMENTS LAW GOVERNING THE SHAPTE OF TEETH The teeth in full-line position on the figure, touch each other at point a; that is, the curves are tangent to each other at this point. The line ST is drawn tangent to the two curves at point a. The curves must be made so that this tangent line is perpendicular to the line drawn from point a to P. M ACHINE ELEMENTS THE INVOLUTE OF A CIRCLE Suppose that the involute is to be drawn starting at any point p on the circle whose center is C. Set the dividers at any convenient short spacing; a distance which is about one- eight the diameter of the circle will give good result. Place one of the points of the dividers at point p and space along on the circumference a few times, getting equal distance m, n, r and s M ACHINE ELEMENTS THE INVOLUTE OF A CIRCLE At each of these points draw radial lines and construct lines perpendicular to these radii as shown in the figure. Each of these perpendiculars will then be tangent to the circle at one of the points. Taking care that the setting of the dividers remain unchanged, lay off one space m1(=mp) on the tangent point m. M ACHINE ELEMENTS THE INVOLUTE OF A CIRCLE On the next line, which is tangent at point n, lay off from point n the same distance twice (making n2 = np) , getting the point 2. From point r, lay off the distance three times (making r3 = rp), getting the point 3; and so on until points are found as far out as desired. A smooth curve drawn through these points with a French curve will be a very close approximation to the true involute. M ACHINE ELEMENTS EXAMPLE 1 Find the distance between centers of a pair of gears one of which has 12 teeth and the other 37 teeth. The diametral pitch is 7. Given: 𝑇1 = 12 𝑇2 = 37 𝑃𝐷 = 7 𝐷1 + 𝐷2 Required: Center distance 𝐶= 2 Solution: 𝑇1 12 𝑃𝐷 = → 7= → 𝐷1 = 1.714 𝑖𝑛 𝐷1 𝐷1 𝑇2 37 𝑃𝐷 = → 7= → 𝐷2 = 5.286 𝑖𝑛 𝐷2 𝐷2 𝐷1 + 𝐷2 1.714 + 5.286 𝐶= = = 𝟑. 𝟓 𝒊𝒏 (𝑨𝒏𝒔. ) 2 2 M ACHINE ELEMENTS EXAMPLE 2 Two shafts are 15 in. on centers. One of the shafts carries a 40-tooth, 2-in diametral pitch gear which drives a gear on the other shaft at a speed of 150 rpm. How fast is the 40- tooth gear turning? Given: 𝐶 = 15 𝑇1 = 40 𝑃𝐷 = 2 𝑁2 = 150 Required: 𝑁1 → 𝑁1 𝐷1 = 𝑁2 𝐷2 Solution: 𝑇1 40 𝑃𝐷 = →2= → 𝐷1 = 20 𝑖𝑛 𝑁1 𝐷1 = 𝑁2 𝐷2 𝐷1 𝐷1 𝑁1 (20) = (150)(10) 𝐷1 + 𝐷2 𝑵𝟏 = 𝟕𝟓 𝒓𝒑𝒎 (𝑨𝒏𝒔) 𝐶= 2 𝐷2 = 2𝐶 − 𝐷1 = 2 15 − 20 = 10 M ACHINE ELEMENTS EXAMPLE 3 A gearset consists of a 16-tooth pinion driving a 40-toothe gear. The diametral pitch is 2, and the addendum and dedendum are 1/P and 1.25/P, respectively. The gears are cut using a pressure angle of 20°. Compute the circular pitch, the center distance, and the radii of the base circles. Solution: 𝜋 𝜋 𝑃𝐶 = = = 1.571 𝑖𝑛. 𝑃𝐷 2 The pitch diameters of the pinion and gear are The base circle radii are 𝑇 16 𝑇𝐺 40 𝐷𝐵 = 𝐷cos 𝜃 𝑑𝑃 = = = 8 𝑖𝑛. 𝑑𝐺 = = = 20 𝑖𝑛. 𝑃𝐷 2 𝑃𝐷 2 8 𝑟𝑃 = 𝑐𝑜𝑠20° = 3.759 𝑖𝑛 Therefore, the center distance is 2 𝐷𝑃 + 𝐷𝐺 8 + 20 20 𝐶= = = 14 𝑖𝑛 𝑟𝐺 = 𝑐𝑜𝑠20° = 9.379 𝑖𝑛 2 2 2