Page 215 - Gear Technology Solutions

15.4 Example

In the following example, for a realistic design, the required crowning and relief
motion of the manufacturing machine are calculated.

Given: Wanted:
L = 12mm - Spline face radius on blank
=

e 0.2° - Crowning relief of hobbing or grinding machine
a = 30°

Relief required: a = tan0.2° • 12/2 = 0.02094mm

Required face radius: R1 =[6² – 0.02094²] /(2 • 0.02094) = 859.58mm

Required crowning advance: b = 0.02094/tan30° = 0.03627mm

Crowning radius
orthogonal to root: R2 =[6² – 0.03627²] /(2 • 0.03627) = 496.26mm

15.5 The Increase of the Interference Problem

The apparent disadvantage of the barrel design is the severe increase in inter-
ference fit if the misalignment is applied. The reason is that the radii R1 do not
have their origin at the centerline of the spline shaft but are, for example
400mm to 800mm away from the centerline (see Figure 2). However, the pivot
point of the misalignment is the centerline of the spline tooth as shown in Fig-
ure 3. Vector P in Figure 3 rotates about the pivot point by the misalignment
angle e resulting in vector P*. Vector R1 also rotates about the pivot point by
,
angle e resulting in vector R1*. To reach the point of maximal interference,
,
vector R1* is now rotated in a vertical position, resulting in vector R1**. For the
interference calculation, only the vertical (Y) components of the vectors are
required. For the parameters given in the example in Figure 3, the Interference
results in .01mm which is a significant amount, especially at higher RPM’s.

With the radii R1 and R2, calculated by the crowning amount “a” approximately
50% of the misalignment is compensated and the remaining 50% leads to the
discussed increase in interference. A possibility to reduce the interference is to
increase the crowning by using only half the crowning radius.

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