Question

3- For a spur gearset with Q= 25°, while avoiding interference, find: (a) The smallest pinion tooth count that will run with itself (b) The smallest pinion tooth count at a ratio mg = 3, and the largest gear tooth count possible with this pinion (c) The smallest pinion that will run with a rack

Answer 1

At pressure angle 25⁰ for full depth the value of K is 1.

For every question there will be formula to find the minimum teeth explained in detail in below images:

mga 3) Given, Pressure Angle $ = 25° for full depth Spor Gear, K=1 a.) Smallest Pinion tooth count that run itself. we know that, 2K Np > + 1+ 3sine 3 sinzo = > Np z 2 [+ 11 + 3sin?as? 3 sin² 25 * .; Nup > 8.35 The value should be integer therefore Yound nearest integer ie, INp 9 teeth it to the nearest : The smallest Pinion that count will run itself is a teeth. 16.) Smallest Pinion tooth count at ratio : Given 3.

we know that, Np z m+m²+(1+2m) Sin²6 (1+2m) sino No 2 f IV 3+ [+ (1+2(3) sinks +19+(1+2(3)) sin22,50 INp = 9.92 :. The value should be integes, therefore round it to the nearest Integer i.es 10 teeth :. The smallest Pinion tooth count at ratio mg = 3 is lo teeth 16) The Largest - Gear-tooth Count possible to Mesh with this Pinion 19; 2 .G < No sinag - 4k 4K - 2 Np sin²0 (10)’sin? 2550 4(0)2 4(0) - 2010) Sin2250 AT N G 32-39 The value should the nearest integes i.e. be integer, therefore Yound it to ING 3ę teeth! i The largest Gear- Tooth Count possible to Mesh 132 Teeth. with this Pinion is

G., The Smallest Pinion that will run with a rack in ak Ne z Sin²0 Np IV Sin225° ok INp z 11:19 : The value should value it be be integer, Therefore Yound the ito nearest integer . Np = 12 teeth : The smallest Pinion that will run with a rack is 12 teeth и X -THE END