WORM GEARING - Quality Transmission Components - #5

This is a very complex method, both theoretically and practically. Usually, the crowning is done to the worm gear, but in this method the modification is on the worm. That is, to change the pressure angle and pitch of the worm without changing the pitch line parallel to the axis, in accordance with the relationships shown in Equations 9-4:

0.6 0.55 0.5 4

k

0.45 0.4 -f 0.35

14° 15° 16° 17° 18° 19° 20° 21° 22° 23° Axial Pressure Angle oc_X

Fig. 9-10 The Value of Factor (k)

Self-locking is a unique characteristic of worm meshes that can be put to advantage. It is the feature that a worm cannot be driven by the worm gear. It is very useful in the design of some equipment, such as lifting, in that the drive can stop at any position without concern that it can slip in reverse. However, in some situations it can be detrimental if the system requires reverse sensitivity, such as a servomechanism.

Self-locking does not occur in all worm meshes, since it requires special conditions as outlined here. In this analysis, only the driving force acting upon the tooth surfaces is considered without any regard to losses due to bearing friction, lubricant agitation, etc. The governing conditions are as follows:

Let F_u1 = tangential driving force of worm Then, F_u1 = F_n (cosoc_n siny- ji cosy) (9-6)

where:

oc_n = normal pressure angle

y = lead angle of worm

ji = coefficient of friction

F_n = normal driving force of worm

If F_u1 > 0 then there is no self-locking effect at all. Therefore, F_u1 < 0 is the critical limit of self-locking.

Let oc_n in Equation (9-6) be 20°, then the condition:

Fu1 < 0 will become:

(cos20° siny - jicosy) < 0

p_xcosoc_x = p_x'cosa_x'

In order to raise the pressure angle from before change, oc_x, to after change, oc_x, it is necessary to increase the axial pitch, p_x, to a new value, p_x, per Equation (9-4). The amount of crowning is represented as the space between the worm and worm gear at the meshing point A in Figure 9-9. This amount may be approximated by the following equation:

Amount of Crowning

2

An example of calculating worm crowning is shown in Table 9-6.

Because the theory and equations of these methods are so complicated, they are beyond the scope of this treatment. Usually, all stock worm gears are produced with crowning.

Figure 9-11 shows the critical limit of self-locking for lead angle y and coefficient of friction ji. Practically, it is very hard to assess the exact value of coefficient of friction ji. Further, the bearing loss, lubricant agitation loss, etc. can add many side effects. Therefore, it is not easy to establish precise self-locking conditions. However, it is true that the smaller the lead angle y, the more likely the self-locking condition will occur.

0.20

C

O

o

0.15

o

0.10

c

CD O

it

CD O O

0.05

0

0

3°

6°

9°

12°

Lead angle y

Fig. 9-11 The Critical Limit of Self-locking of Lead Angle y and Coefficient of Friction ji

*It should be determined by considering the size of tooth contact surface.