Sorry, this subject is so extensive that I can’t give here a full development.
You will find below only one preliminary example for external cylindrical gear drive design.
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First of all start with estimated or imposed values for m, alpha(reference pressure angle) , z1 and z2.
1- Considering your (z1 + z2) value select the (x1 + x2) value recommended for profile shift on tables, graphics, articles or books.
For alpha = 20° you can start with:
a) If Z1>30 and z1+z2>60 than use Zero Gear Drive where a'=a=m[(z1+z2)/2)] and x1=x2=0 and so x1+x2 =0;
b) If z1<30 and z1+z2>60 than use Vzero Gear Drive where a'=a as above but x1=0,03(30-z1) and x2=-x1 and so x1+x2=0;
c) If z1<30 and z1+z2<60 than use V Gear Drive where a'>a and x1 = 0,03(30-z1) and x2 = 0,03(30-z2) and x1+x2 > 0;
d) If z1<10 use x1=0,6 and because of the insufficient tooth tip thickness in gears with small number of teeth the tooth height must be reduced to h = m (2,25 – k), where k is the tooth height reducing coefficient [k = 0,04 (10 - z1)] and adopt x2=(0,03(30-z2).
For best contact ratio (less noise) if (z1 + z2) > 60 select (x1 + x2) near zero, to improve the bending strength bring (x1 + x2) near 0,7 for increased load capacity.
2- Considering the gear ratio (z2 / z1) and also taking in account if it’s a speed reducing or speed increasing drive select separately values for x1 and x2. For this utilize information source above mentioned.
3- Compute the working pressure angle for this gear drive utilizing the under mentioned equation:
inv alpha’ = [2 tg alpha (x1 + x2) / (z1 + z2)] + inv alpha
where: inv alpha is the reference pressure angle (20° for example) involute function; inv alpha’ is the working pressure angle involute function.
4- Compute the working center distance from:
a’ = m (z1 + z2) cos alpha / 2 cos alpha’
5- Compute the working pitch diameter from:
d’1 = (2 a’ z1) / (z1 + z2) and d’2 = (2 a’ z2) / (z1 + z2)
6- Compute the root diameter resultant from the generating process and tool proportions.
df1 = m [z1 – 2 (1 + c* - x1)] and
df2 = m [z2 – 2 (1 + c* - x2)]
where c is the clearance and c* is the bottom clearance coefficient (c = m c*).
7- Compute the addendum (outside, tip) diameter from:
da1 = 2 (a’ – c) - df2 and da2 = 2 (a’ – c) - df1
8- Remember the profile shift don’t change the base diameter nor the base pitch of a gear, but change tooth thickness. For gear measurement with Wildhaber method (base tangent length) you need know the base tooth thickness:
sb1 = sb1zero + 2 x1 m sin alpha and
sb2 = sb2zero + 2 x2 m sin alpha
where: sb1 and sb2 is the base tooth thickness of gears with profile shift x1 and x2 ; sb1zero and sb2zero is the base tooth thickness of gears without profile shift (x1 = x2 = 0).
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Now eventually others geometrical parameters may be calculated like gears contact ratio, pinion tip thickness, etc. Thereafter you must check dynamics parameters like noise, bending strength, hertzian surface stress (pitting), scuffing risk (scoring), and so on. Eventually you must change pre-selected parameters like m, z1, z2 , gear material & tratment and make again the gear drive computation often and often as necessary. The gear drive design is an interactive process and for the same project there are as many different gear drives as designers.
You may find different calculation methodology and equations, for example you can employ the center distance modification coefficient
, parameters B and Bv, but here I used the most understandable.
About the Nov/Dec 2001 issue of Gear Technology magazine you probably can buy it at
I would be hope if fulfil your expectation.
