1(a) A pair of spur gears with involute tooth form have a module of
m and equal addenda of
m. Show that involute interference will occur if the number of teeth on the pinion is less than
(2)/(\sqrt(G^(2)+(1+2G)sin^(2)\psi )-G)
(b) A pair of spur gears is required to give a ratio of
2.5:1. A module of 3 is to be used and a pressure angle of
20\deg . Determine:
i. suitable number of teeth for the wheel and pinion; and
ii. the exact centre distance.
2(a) Explain the term interference as it applied to gearing with involute profiles.
(b) Derive expression for the minimum number of teeth required on the pinion in order to avoid interference in involute teeth when it meshes with:
i. wheel; and
ii. rack.
3(a) State and prove the law of gearing.
(b) Derive an expression for the velocity of sliding between a pair of involute teeth.
4(a) What condition must be satisfied if two wheels in gearing are to have a constant velocity ratio? Show that this condition is satisfied by teeth of involute profile.
(b) Discuss the effect of increasing the centre distance of a pair of spur wheel having involute teeth upon the following:
i. effective addenda; ii. working depth; iii. arc of contact; and iv. backlash.
(c) Derive an expression for the length of arc of contact in a pair of meshed spur gears.
5(a) Show that the maximum addendum for a rack engaging with pinion of diameter,
d, without interference is
(1)/(2)dsin^(2)\psi ;where
\psi is angle of obliquity.
(b) List three types of gears used to transmit rotation between shafts with crossed axes.
(c) Suggest gears used to convert rotary motion into translational motion.
6(a) A pair of involute spur gears with
16\deg pressure angle and pitch in module 6 mm is in mesh. The number of teeth on pinion is 16 and its rotational speed is
240re(v)/(m)in. When the gear ratio is 1.75 , find in order that the interference is just avoided, the:
(i) addenda on pinion and gear wheel;
