L.C. Institute Of Technology Mechanical Eng. Department Subject: Kinematics of Machines Topic Name: Gear tooth Terminology and Law of Gearing & Interference Guided by: Prof. B T Patel Prepared by: Roll No. 53 to 56 3 rd Semester Mech. A Year Year

Name Enrollment No Patel Laukik J Patel Lav G Patel Meet A Patel Montu I /7/2016S.K.AYYAPPAN,LECT.MECH2

3 Terminology Spur Gears 7/7/2016S.K.AYYAPPAN,LECT.MECH

4 Terminology 7/7/2016S.K.AYYAPPAN,LECT.MECH

5 Definitions Addendum: The radial distance between the Pitch Circle and the top of the teeth. Arc of Action: Is the arc of the Pitch Circle between the beginning and the end of the engagement of a given pair of teeth. Arc of Approach: Is the arc of the Pitch Circle between the first point of contact of the gear teeth and the Pitch Point. Arc of Recession: That arc of the Pitch Circle between the Pitch Point and the last point of contact of the gear teeth. Backlash: Play between mating teeth. 7/7/2016S.K.AYYAPPAN,LECT.MECH

6 Definitions Base Circle: The circle from which is generated the involute curve upon which the tooth profile is based. Center Distance: The distance between centers of two gears. Chordal Addendum: The distance between a chord, passing through the points where the Pitch Circle crosses the tooth profile, and the tooth top. Chordal Thickness: The thickness of the tooth measured along a chord passing through the points where the Pitch Circle crosses the tooth profile. Circular Pitch: Millimeter of Pitch Circle circumference per tooth. 7/7/2016S.K.AYYAPPAN,LECT.MECH

7 Definitions Circular Thickness: The thickness of the tooth measured along an arc following the Pitch Circle Clearance: The distance between the top of a tooth and the bottom of the space into which it fits on the meshing gear. Contact Ratio: The ratio of the length of the Arc of Action to the Circular Pitch. Dedendum: The radial distance between the bottom of the tooth to pitch circle. Diametral Pitch: Teeth per mm of diameter. 7/7/2016S.K.AYYAPPAN,LECT.MECH

8 Definitions Face: The working surface of a gear tooth, located between the pitch diameter and the top of the tooth. Face Width: The width of the tooth measured parallel to the gear axis. Flank: The working surface of a gear tooth, located between the pitch diameter and the bottom of the teeth Gear: The larger of two meshed gears. If both gears are the same size, they are both called "gears". Land: The top surface of the tooth. 7/7/2016S.K.AYYAPPAN,LECT.MECH

9 Definitions Line of Action: That line along which the point of contact between gear teeth travels, between the first point of contact and the last. Module: Millimeter of Pitch Diameter to Teeth. Pinion: The smaller of two meshed gears. Pitch Circle: The circle, the radius of which is equal to the distance from the center of the gear to the pitch point. Diametral pitch: Teeth per millimeter of pitch diameter. Pitch Point: The point of tangency of the pitch circles of two meshing gears, where the Line of Centers crosses the pitch circles. 7/7/2016S.K.AYYAPPAN,LECT.MECH

10 Definitions Pressure Angle: Angle between the Line of Action and a line perpendicular to the Line of Centers. Profile Shift: An increase in the Outer Diameter and Root Diameter of a gear, introduced to lower the practical tooth number or acheive a non-standard Center Distance. Ratio: Ratio of the numbers of teeth on mating gears. Root Circle: The circle that passes through the bottom of the tooth spaces. Root Diameter: The diameter of the Root Circle. Working Depth: The depth to which a tooth extends into the space between teeth on the mating gear. 7/7/2016S.K.AYYAPPAN,LECT.MECH

11 Formulae 7/7/2016S.K.AYYAPPAN,LECT.MECH

12 Formulae 7/7/2016S.K.AYYAPPAN,LECT.MECH

13 Forumulae Specific to Gears with Standard Teeth Addendum= 1 ÷ Diametral Pitch = × Circular Pitch Dedendum= ÷ Diametral Pitch = × Circular Pitch Working Depth= 2 ÷ Diametral Pitch = × Circular Pitch Whole Depth= ÷ Diametral Pitch = × Circular Pitch 7/7/2016S.K.AYYAPPAN,LECT.MECH

14 Forumulae Specific to Gears with Standard Teeth Clearance= ÷ Diametral Pitch = 0.05 × Circular Pitch Outside Diameter= (Teeth + 2) ÷ Diametral Pitch = (Teeth + 2) × Circular Pitch ÷ π Diametral Pitch= (Teeth + 2) ÷ Outside Diameter 7/7/2016S.K.AYYAPPAN,LECT.MECH

15 Law of Gearing  N 2 is the foot of the perpendicular from O 2 to N 1 N 2. Tooth profile 1 drives tooth profile 2 by acting at the instantaneous contact point K. N 1 N 2 is the common normal of the two profiles. N 1 is the foot of the perpendicular from O 1 to N 1 N 2 7/7/2016S.K.AYYAPPAN,LECT.MECH

16 Law of Gearing  Although the two profiles have different velocities V 1 and V 2 at point K, their velocities along N 1 N 2 are equal in both magnitude and direction. Otherwise the two tooth profiles would separate from each other. Therefore, we have 7/7/2016S.K.AYYAPPAN,LECT.MECH

17 Law of Gearing  We notice that the intersection of the tangency N 1 N 2 and the line of center O 1 O 2 is point P, and from the similar triangles 7/7/2016S.K.AYYAPPAN,LECT.MECH

18 Law of Gearing  Therefore, velocity ratio 7/7/2016S.K.AYYAPPAN,LECT.MECH

19 Law of Gearing  From the equations 4.2 and 4.4, we can write, -ratio of the radii of the two base circles and also given by; 7/7/2016S.K.AYYAPPAN,LECT.MECH

20 Law of Gearing  -centre distance between the base circles  = pressure angle or the angle of obliquity. It is angle between the common normal to the base circles and the common tangent to the pitch circles. 7/7/2016S.K.AYYAPPAN,LECT.MECH

21 Constant Velocity Ratio  A common normal (the line of action) to the tooth profiles at their point of contact must, in all positions of the contacting teeth, pass through a fixed point on the line-of-centers called the pitch point Any two curves or profiles engaging each other and satisfying the law of gearing are conjugate curves, and the relative rotation speed of the gears will be constant (constant velocity ratio). 7/7/2016S.K.AYYAPPAN,LECT.MECH

22 Conjugate Profiles  To obtain the expected velocity ratio of two tooth profiles, the normal line of their profiles must pass through the corresponding pitch point, which is decided by the velocity ratio. The two profiles which satisfy this requirement are called conjugate profiles. 7/7/2016S.K.AYYAPPAN,LECT.MECH

23 Conjugate action It is essential for correctly meshing gears, the size of the teeth ( the module ) must be the same for both the gears. Another requirement - the shape of teeth necessary for the speed ratio to remain constant during an increment of rotation; this behaviour of the contacting surfaces (ie. the teeth flanks) is known as conjugate action. 7/7/2016S.K.AYYAPPAN,LECT.MECH

7/7/2016S.K.AYYAPPAN,LECT.MECH24

7/7/2016S.K.AYYAPPAN,LECT.MECH25