Condition
No. 3: (13-9)Satisfying this condition insures that adjacent planet gears can operate without interfering with each other. This is the condition that must be met for standard gear design with equal placement of planet gears. For other conditions, the system must satisfy the relationship: dab < 2 ax sinq (13-10) |
 |
where:
dab = outside diameter of the planet gears
ax = center distance between the sun and planet gears
Besides the above three basic conditions, there can be an
interference problem between the internal gear C and the planet gears B.
See SECTION 5 that discusses more about this problem.
13.3.2 Speed Ratio of Planetary Gear System
In a
planetary gear system, the speed ratio and the direction of rotation
would be changed according to which member is fixed. Figures
13-6(a), 13-6(b) and 136(c) contain three typical types of planetary
gear mechanisms, depending upon which member is locked. |
 |
(a) Planetary Type
In this type, the internal gear is fixed. The input is the sun gear and
the output is carrier D. The speed ratio is calculated as in Table
13-1.
(13-11)
Note that the direction of rotation of input and output axes are the
same.
Example: Za=16, Zb=16, Zc=48, then speed ratio=1/4.
(b) Solar Type
In this type, the sun gear is fixed. The internal gear C is the input,
and carrier D axis is the output. The speed ratio is calculated as in
Table 13-2.
(13-12)Note that the directions of rotation of input and output axes are the same.
Example: Za = 16, zb = 16, zc = 48, then the speed ratio = 1/1.3333333.
(c) Star Type
This is the type in which Carrier D is fixed. The planet gears rotate only on fixed axes. In a strict definition, this train, loses the features of a planetary system and it becomes an ordinary gear train. The sun gear is an input axis and the internal gear is the output. The speed ratio is:
Speed Ratio = - za (13-13)
zc
Referring to Figure 13-6(c), the planet gears are merely idlers. Input and output axes have opposite rotations.
Example: Za = 16, Zb = 16, Zc = 48;
then speed ratio = - 1/3.
13.4 Constrained Gear System
A planetary gear system which has four gears, as in
Figure 13-5, is an
example of a constrained gear system. It is a closed loop system in which
the power is transmitted from the driving gear through other gears and
eventually to the driven gear. A closed loop gear system will not work if
the gears do not meet specific conditions.
Let z1, z2 and z3 be the numbers of gear teeth, as in
Figure 13-7. Meshing cannot function if the length of the heavy line (belt)
does not divide evenly by circular pitch. Equation (13-14) defines this
condition.
z1q1+Z2(180+zq1+q2)+z3q2=Integer
(13-14)
180
180 180
where q1 and
q2 are in degrees.
Figure 13-8 shows a constrained gear system in which a rack is meshed.
The heavy line in Figure 13-8 corresponds to the belt in Figure
13-7. If
the length of the belt cannot be evenly divided by circular pitch then the
system does not work. It is described by Equation (13-15).
z1q1
+ z2(180+q1)
+ a = integer (13-15)
180 180
pm
