As we settle into the autumn weather, the changing of the seasons brings a sense of calm. The leaves change color, pumpkin spice is found in everything, and the cool crisp air brings a sense of peace after the hazy, hot, and humid days of summer. This peace is described by some as a sense of Zen. Some see it as a realignment of their chakras. Others say that they feel more centered at this time of year. Like people, gears also need to find their center, in order to mesh properly.
The center distance between two gears operating on parallel axes is the simplest value to determine. (Figure 1) The center distance of these gears is:
where
a = the center distance
d1 = the pitch diameter of the pinion
d2 = the pitch diameter of the driven gear
This formula is valid whenever the gears are produced without a profile shift. If a profile shift is introduced, the values of d1 and d2 must reflect the working pitch diameter instead of the normal pitch diameter for the equation to be correct.
The center distance calculation will result in a nominal value for which a tolerance will need to be applied. It is always recommended to have the tolerance range for the center distance to be at the nominal value on the lower limit and a positive range on the upper limit. When the center distance is set to a value less than the nominal value, then the gears will not perform as desired. Setting the gears at the nominal center distance allows for the teeth of each gear to engage at the proper location on the gear tooth as well as minimizes noise and permits the transfer of lubricant into the mesh. If the center distance is too large, then the gears will not transfer the torque as designed and will be very noisy.
For gears that have intersecting axes, such as bevel gears, the center distance is known as the mounting distance. The mounting distance is measured from the back of the hub of a bevel gear to the point of intersection of the pitch diameters (Figure 2). This value is typically set by the manufacturer as it is not defined by the gear geometry itself.
The tooth of a bevel gear is defined as having a toe and a heel. The heel is the backmost portion of the tooth and the tip of the tooth at the heel is the point at which the gear’s outer diameter is measured (Figure 3). This is a known point and can be used to set the mounting distance value.
As with parallel axes gears, it is recommended to set bevel gears at the nominal mounting distance or slightly larger. Forcing the gears into the mesh will cause premature wear as there will be a buildup of heat due to the excess friction and the lack of lubricant in the mesh.
For gears with non-intersecting and non-parallel axes, such as worm gear pairs, the center distance is also measured as one half of the sum of the pitch diameters (Figure 4).
Worm gear pairs operate best when the center distance is set to the nominal value on the lower limit and a positive value on the upper limit.
Unique to all the center distance calculations is that of a gear rack meshing with a profile shifted pinion (Figure 5). The formula for this value is:
where
a = the center distance
z = the number of teeth on the pinion
m = the module (pitch of the gear)
H = the height of the rack from the base to the pitch line
x = the coefficient of profile shift
If the pinion is not profile shifted, then the center distance for the rack and pinion is equal to one half of the pinion pitch diameter plus the height of the rack from the base to the pitch line.
For each of these gear styles, it is important to know what the nominal center distance value is and apply a suitable tolerance. Doing so will allow for a proper mesh, an acceptable amount of backlash, and the opportunity for lubricant to flow through the teeth. This will keep both you and your gears centered.
