This document presents the calculations for finding out the Gear Ratio of a 3 stage (Bevel-Helical-Planetary) gearbox for Vertical Roller Mill (VRM-3700) of a Cement plant. The capacity of this VRM is 260tons/hour and is used limestone grinding.

1. GEAR RATIO CALCULATIONS OF VERTICAL ROLLER MILL (LINE-2)
Syed Fahad Ahmed
SMT - Mechanical
Ratio in 1st
Stage (Bevel Stage)
Input Speed = N1 = 990 rpm
Output Speed = N2 =?
Teeth of Input pinion = T1 = 26
Teeth of output gear = T2 = 41
𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝐷𝑟𝑖𝑣𝑖𝑛𝑔 𝑔𝑒𝑎𝑟 𝑁1
𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝐷𝑟𝑖𝑣𝑒𝑛 𝐺𝑒𝑎𝑟 (N2)
=
𝑇𝑒𝑒𝑡 𝑕 𝑜𝑓𝐷𝑟𝑖𝑣𝑒𝑛 𝑔𝑒𝑎𝑟 𝑇2
𝑇𝑒𝑒𝑡 𝑕 𝑜𝑓 𝐷𝑟𝑖𝑣𝑖𝑛𝑔 𝑔𝑒𝑎𝑟 (T1)
N2 =
N1 x T1
T2
= (990 x 26)/41 = 627.81 rpm
Ratio in 2nd
Stage (Helical Stage)
Input Speed = N1 = 627.81 rpm
Output Speed = N2 =?
Teeth of Input gear = T1 = 19
Teeth of output gear = T2 = 71
𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝐷𝑟𝑖𝑣𝑖𝑛𝑔 𝑔𝑒𝑎𝑟 𝑁1
𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝐷𝑟𝑖𝑣𝑒𝑛 𝐺𝑒𝑎𝑟 (N2)
=
𝑇𝑒𝑒𝑡 𝑕 𝑜𝑓𝐷𝑟𝑖𝑣𝑒𝑛 𝑔𝑒𝑎𝑟 𝑇2
𝑇𝑒𝑒𝑡 𝑕 𝑜𝑓 𝐷𝑟𝑖𝑣𝑖𝑛𝑔 𝑔𝑒𝑎𝑟 (T1)
N2 =
N1 x T1
T2
= (627.81 x 19)/71 = 168.27 rpm
Ratio in 3rd
Stage (Planetary Stage)
Input Speed = Ns = 168.27 rpm
Output Speed = Nc =?
Teeth of Sun gear = Ts = 20
Teeth of Ring gear = Tr = 92
𝐼𝑛𝑝𝑢𝑡 𝑆𝑝𝑒𝑒𝑑 𝑁𝑠
𝑂𝑢𝑡𝑝𝑢𝑡 𝑆𝑝𝑒𝑒𝑑 (Nc)
=
𝑇𝑒𝑒𝑡 𝑕 𝑜𝑓 𝑆𝑢𝑛 𝑔𝑒𝑎𝑟 𝑇𝑠 + 𝑇𝑒𝑒𝑡 𝑕 𝑜𝑓 𝑅𝑖𝑛𝑔 𝐺𝑒𝑎𝑟 (𝑇𝑟)
𝑇𝑒𝑒𝑡 𝑕 𝑜𝑓 𝑆𝑢𝑛 𝑔𝑒𝑎𝑟 (Ts)
Nc =
Ns x Ts
Ts+ Tr
= (168.27 x 20)/(20 + 92) = 30.0 rpm
Therefore, the rotational speed of VRM grinding table is 30rpm
3 Stage Gearbox for VRM