Diametrical pitch

The ratio between the pitch diameter and the number of teeth is called the diametral pitch, and for two gears to mesh, they must have the same diametral pitch. The diametral pitch is standardized and is always an integer. For gears used in process machineiy, the diametral pitch varies between 6 (coarse) and 20 (fine). 

As with spur gears, the tooth size of bevel gears is established by the diametrical pitch. Because the tooth size varies along its length, measurements must be taken... 

Linear and circular measurements that define gears and are used in their specification and design are center distance, offset, pitch diameter, diametric pitch, axial pitch, base pitch, and axial base pitch, lead, and backlash. 

Circular Circular pitch is the distance from a point on one tooth to the corresponding point on the next tooth measured along the pitch circle as shown in Figure 57.32. Its value is equal to the circumference of the pitch circle divided by the number of teeth in the gear. While most common-size gears are based on diametric pitch, large-diameter gears are frequently made to circular pitch dimensions. 

Diametric The most commonly used method of gear specification is based on diametric pitch. Practically all common-size gears are made to diametric pitch specifications, which also designate the size and proportions of gear teeth. 

Diametric pitch is a whole number used to specify the ratio of the number of teeth in a gear to its pitch diameter. Stated another way, it specifies the number of teeth in a gear per inch of pitch diameter. For each inch of pitch-circle diameter, there are pi (jr = 3.1416) inches of pitch-circle circumference. Therefore, the diametric pitch provides the number of teeth for each 3.1416 inches of circumference along the pitch circle. 

The pitch-circle diameter and the diametric pitch of a 4-inch pitch-circle diameter gear are illustrated in Figure 57.33. For this 4-inch gear, there are four 3.1416-inch circumference segments. Note that for a 3-inch gear, there are three 3.1416-inch segments. 

These concepts may be better visualized and dimensions more easily obtained with the rack teeth presented in Figure 57.34. This clearly shows that there are 10 teeth in 3.1416 inches and, therefore, the rack illustrated is a 10 diametric-pitch rack. 

Figure 57.35 illustrates a similar measurement along the pitch circle of a 10 diametric-pitch gear. 

Figure 57.37 Using Method 2 to approximate the diametric pitch...

This section presents the equations used to make circular and diametric pitch calculations as well as tooth proportion calculations. 

The mathematical relationship of pitch diameter, diametric pitch, and number of teeth is shown in the equations below. As with any equation, one of the variables can be calculated if any two are known. 

D = Pitch diameter, inches P = Diametric pitch, inches N = Number of teeth... 

Example 1 What is the diametric pitch of a 40-tooth gear with a 5-inch pitch diameter ... 

Example 2 What is the pitch diameter of a 12 diametric-pitch gear with 36 teeth ... 

Example 3 How many teeth are there in a 16 diametric-pitch gear with a pitch diameter of 3 inches ... 

Figure 14.11 illustrates that the diametrical pitch number specifying the number of teeth per inch of pitch diameter must also specify the number of teeth per 3.1416 inches of pitch-line distance. This maybe more easily visualized and specifically dimensioned when applied to the rack in Figure 14.12. 

A similar measurement is illustrated in Figure 14.13, along the pitch line of a gear. The diametrical pitch being the number of teeth in 3.14l6 inches of pitch line, the gear in this illustration is also a 10 diametrical pitch gear. 

In many cases, particulariy on machine repair work, it may be desirable for the mechanic to determine the diametrical pitch of a gear. This may be done very easily without the use of precision measuring tools, templates, or gauges. Measurements need not be exact because diametrical pitch numbers... 

The following two methods may be used to determine the approximate diametrical pitch of a gear. A common steel rule, preferably flexible, is adequate to make the required measurements. 

Figure 14.15 illustrates a gear with 56 teeth. The pitch diameter measured from the bottom of the tooth space to the top of the opposite tooth is 5 inches. Dividing 56 by 5g gives an answer of 9-jg inches, or approximately 10. This method also indicates that the gear is a 10 diametrical pitch gear. 

Figure 14.14 Using method 1 to approximate the diametrical pitch. In this method the outside diameter of the gear is measured.

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