中國石油大(北京)機械原理考研習題Chapter 6

1、6-17. How many teeth would an external standard spur involute gear have when its dedendum circle and its base circle coincide? Which one is bigger as the number of teeth increases ?mchZhddaff)22(2*20coscosmZddbfbddmchZmZa)22(20cos*mchZmZa)22(20cos*4145.4120cos122*chZacos)22(*mZmchZddabf*22cos1chZmaI

2、f Z41, then df-db0So, df is bigger as the number of teeth increases6-18. For a pair of external standard spur gears = =20 , m=5mm , Z1=19, Z2=42, calculate the contact ratio .8502. 0121920cos192coscos11111aabahZmmZdd7666.318502. 0cos11a89698. 0124220cos42cos222abadd2478.2689698. 0cos11a) tan(tan) ta

3、n(tan212211aaZZ6352. 1) 20tan2478.26(tan42) 20tan7666.31(tan19216-22. A pair of standard external helical gears have the following parameters: Z1 =20, Z2 =118, mn =5mm, n =20, han*=1, B=30mm, a=350mm. Find the helix angle , total contact ratio and the virtual numbers of teeth Zv1, Zv2. Solution:soco

4、s212121zzmddan9857. 035021182052cos21azzmn70. 99857. 0cos136925. 070. 9cos20tancostantanntmmmmnt0725. 570. 9cos5cosmmzmrt725.502200725. 5211mmzmrt2775.29921180725. 52222667.2036925. 0tan1tmmmhrhrrnanaa725.551111mmmhrhrrnanaa2775.304222236.31coscoscos1111111atabatrrrr68.22coscoscos2212212atabatrrrr121122ZZattatt(tantan)(tantan)6771. 1) 2667.20tan68.22(tan118) 2667.20tan36.31(tan20213218.057 .9si