Pitch circle

Gear backlash is the play between teeth measured at the pitch circle. It is the distance between the involutes of the mating gear teeth, as illustrated in Figure 39.17. 

The elements of gear teeth common to all gears are tooth surface and profile, flank, top and bottom land, crown, root and pitch circle, gear center, line of centers, pitch point, line of action, line of contact, and point of contact. Figure 57.27 labels many of the common gear tooth elements. Figure 57.28 labels the common rack tooth elements. 

A pitch circle is illustrated in Figure 57.29. The imaginary circle can be drawn to illustrate the motion of a gear in operation. The diameters of these imaginary circles are referred to as the pitch diameters of the gears. The center distance of two correctly meshed gears, illustrated in Figure 57.30, is equal to one half the sum of the two pitch diameters. 

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 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. 

Figure 57.35 Number of teeth in 3.1416 inches on the pitch circle...

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

The mathematical relationship of the circular pitch to the pitch-circle circumference, number of teeth, and the pitch diameter is shown in the following equations ... 

C = Pitch circle circumference (jtD), inches D = Pitch diameter, inches N = Number of teeth p = Circular pitch, inches jr = pi (3.1416)... 

Approximate pitch circle dia., say, 2.2 m Circumference of bolt circle = 220()ir... 

A, must approximate the water wheel diameter, KD. (More precisely, the sum of the pitch circle diameters of the sprocket and mill must exceed KD plus the outside diameter of the mill outlet pipe.) Turning of stone in the mill exerts a resistance torque of /Ty( 1 - e) A A sin4xT2, reduced by the mechanical advantage through the drive to the water wheel by a factor of d-i-(KD), where d - sprocket pitch circle diameter. As before, the water wheel drive torque is M - 0.12 5n V-K (AT2 - 1)LD3. If A KD, the maximum sprocket diameter, d, that will provide the necessary mechanical advantage is ... 

Ultimately, the speed of a filling machine is a function of the engineering limits of metal machinability. The valves are mounted on a ring that has to be machined to very tight tolerances and mounted such that it rotates evenly, hence the overall diameter of a filler has a maximum value and so the number of valves that can be mounted on the pitch circle has a maximum. 

Because the compression characteristics of powders are time-dependent (the exact extent of this dependency depends on the primary modes of deformation), the final tablet properties depend not only on maximum compression forces but also on the rate at which these forces (rate of deformation) are applied and removed. On a rotary tablet press, the rate of deformation is determined by the tangential velocity of the punch and the compression roller diameters. The tangential velocity of the punch is a product of the press speed and the die table circumference (i.e., die table rpm x 3.14 x pitch circle diameter). As the tangential velocity increases, the rates of compression and decompression increase while the overall compression time decreases. The roller diameter affects both the rate of compression and decompression. As the diameter increases, the rates of compression and decompression decrease. 

The rate of force application should be reduced by applying the compression force as gradually as possible. This can be accomplished by lowering the press speed or using a machine with a small pitch circle diameter. 

Matching tablet press speed (rpm) of the research and production presses has, of course, no meaning, because of different number of stations and pitch circle diameter. It is vital, therefore, to translate the rpm into dwell time or contact time. 

Mechanical Definitions of dwell and contact times disregard material properties and concentrate on press and punch geometry (Fig. 17). Contact time can be defined as the time the punch is in contact with the compression wheel. Dwell time is defined as the time the flat portion of punch head is in contact with the compression wheel (time at maximum punch displacement, or time when the punch does not move in vertical direction). In dwell time calculations, the length of the punch head flat and horizontal component of punch speed (as determined by RPM and pitch circle diameter) are used. In case of a round head tooling, the dwell time, as defined here, is zero. But it should be kept in mind that mechanical definition is given here as a convention, a yardstick, or a common measure, to compare press speeds for different presses, and its absolute value is meaningless. A proposed convention to quantify linear speed of a press is to use an... 

To simulate tablet presses, compaction simulator users most frequently employ the theoretical position control profiles. Theoretical path is calculated from the geometry of the press and punches, using the radius of the compression roll, the radius of the curvature of the punch head rim, the radius of the pitch circle (distance between turret and punch axes), and the turret angular velocity. 

The rotary table can also be used to hold a work-piece requiring a series of holes spaced on a pitch circle diameter (pcd) as shown in Fig. 11.14. 

Bundle array 1+6+12+18 fuel rods on concentric pitch circles... 

Pitch circle diameter of the first ring (6 pins), cm 2.977 3.30... 

Pitch circle diameter of the second ring (12 pins), cm 5.751 6.36... 

Pitch circle diameter of the third ring (18 pins), cm 8.661 ... 

Pitch diameter, rolling elements The diameter of the pitch circle generated by the center of a rolling element as it traverses the bearing s axis of rotation. 

---