What are Gear Formulas?
In gear design and drawing deciphering situations, it is necessary to understand the formulas involved in gear calculations. Here are the main formulas for gears.
Relates to tooth size:
Tooth pitch (p)
p = pitch circle diameter × circumference / number of teeth = dπ / z
Module (m)
The module is the pitch divided by the pi (omitting pi) to express the size of the teeth using a simple, rounded number.
m = p / π = d / z
Conversion formula for diametral pitch (DP) and module
m = 25.4 / DP
* The larger the DP value, the smaller the module value (tooth size).
Relates to tooth height:
Tooth height (h)
h = 2.25m (= Addendum + Dedendum)
Addendum (ha)
ha = 1.00m
Dedendum (hf)
hf = 1.25m
* In the case of tooth profile (full depth) specified by ISO and JIS
Relates to the diameter of the gear:
Pitch circle diameter (d)
d = zm (z = number of teeth)
Tip circle diameter (da)
da = d+2m
Root diameter (df)
df = d - 2.5m
Root clearance (c)
c = 1.25m - 1.00m = 0.25m
Center distance:
The center distance (a) is 1/2 of the sum of the pitch circle diameters of a pair of gears (d1+d2)
a = (d1+d2) / 2
Relates to speed transmission ratio:
Single-stage gear mechanism
For a single-stage gear mechanism with a pair of meshing gears, the speed transmission ratio i is calculated as follows.
The number of teeth of the driving gear is z1 and its rotation speed is n1, and the number of teeth of the driven gear is z2 and its rotation speed is n2.
i = z2 / z1 = n1 / n2
Two-stage gear mechanism
In the following example of a two-stage gear mechanism, the speed transmission ratio i is calculated as follows when Gear 1 is the driving gear.
i = z2 / z1 × z4 / z3 = n1 / n2 × n3 / n4
相关链接 - 齿轮计算公式
