## Change Gear Calculations

In the absence of an index chart showing gear combinations for various threads, it is necessary to calculate the proper gears to use for cutting threads. On lathes equipped with tumbler reverse gears, it must first be determined whether the lathe is even-geared or odd-geared.

On an even-geared lathe, the stud gear revolves at the same speed as the spindle gear (that is, the two gears are equal in size). If the stud gear revolves at any other speed, the lathe is an odd-geared lathe.

### Change Gears

Change gears are either simple or compound in form. In simple gearing, an idler gear is used to transmit motion from the stud gear to the lead screw gear (Figure 8-8). In compound gearing, the idler is combined with another gear of different size. As the two gears are keyed together, the assembly no longer functions as an idler, but as a first-stage ratio reduction between the stud gear and the lead screw gear (Figure 8-9). This "compound gear assembly" is necessary when a large ratio between the stud gear and lead screw gear is required to cut extra-fine threads.

### Simple Gearing

The ratio between the number of teeth on the stud gear and the lead screw gear must be determined. The ratio depends on the pitch of the lead screw and the number of teeth to be cut. This is expressed as the following formula:

number of threads to be cut Figure 8-8 Simple gearing for cutting screw threads on a change-gear lathe. Figure 8-9 Compound gearing for cutting screw threads on a change-gear lathe.

For example, to determine the size of the stud gear and the lead screw gear required to cut 12 threads per inch in a lathe having a lead screw with 8 threads per inch, use the following formula:

To cut 12 threads per inch, the spindle (or stud gear on an even-geared lathe) must make 12 revolutions to 8 revolutions of the lead screw. Thus, if gears of 12 teeth were available, they would cut the required thread. Because these gears are impossible, multiply each by a common number to obtain the desired gears available in the change-gear set as follows:

1. Stud gear =8x3=24 teeth

Because change gears of various sizes are used, the distance between gears will vary. Therefore, an idler gear must be used to transmit the motion (Figure 8-10). The idler gear does not change the gear ratio. Figure 8-10 Diagram of simple change gearing.

Compound Gearing

When the gears are arranged in a train, they are said to be compounded. As in simple gearing, the gear ratio must be determined between the stud gear and the lead screw gear. To illustrate the necessity for compound gearing, suppose that it is desired to cut 80 threads per inch in a lathe having a lead screw with 8 threads per inch. Use the following formula:

Gear ratio =

To cut 80 threads per inch, the spindle (or stud gear in an even-geared lathe) must make 80 revolutions to 8 revolutions of the lead screw. It is impossible to use gears with 8 and 80 teeth to cut the required thread. Multiply the number of teeth by a common number to obtain gears within the range of the change-gear set. Because a 16-tooth gear is usually the lowest number of teeth furnished in the set, multiply by 2 as follows:

1. Stud gear =8X2=16 teeth

2. Lead screw gear = 80X2 = 160 teeth

Because a 160-tooth gear is entirely out of range of most equipment, and the required diameter would probably be too large to mesh with the stud gear, compound gearing is necessary so that smaller gears can be used.

For example, to determine the compound gears necessary to cut 80 threads per inch on a lathe having a lead screw with 8 threads per inch, the following procedure can be used:

1. The ratio between the stud gear and the lead screw gear is as follows:

2. Because this is a 10 to 1 ratio, the stud gear must make 10 revolutions to 1 revolution of the lead screw. Factor the total ratio as follows:

3. Multiply each term by a common number (8, for example), and obtain the required gears as follows:

4. Place these gears in the following order: 16, 64, 32, and 80.

Use the 16-tooth gear as the stud gear, use the 64- and 32-

tooth gears for the compound gear assembly, and place the 80-tooth gear on the lead screw (Figure 8-11). This gear setup will provide a 10 to 1 ratio or speed reduction between the lathe spindle and the lead screw.

STUD GEAR

STUD GEAR SCREW GEAR

COMPOUND GEAR ASSEMBLY

Figure 8-11 Diagram of compound change gearing.

SCREW GEAR

COMPOUND GEAR ASSEMBLY

Figure 8-11 Diagram of compound change gearing.

Compound gearing actually consists of two ratios whose product is equivalent to the total ratio as follows:

Total ratio = first ratio X second ratio

When compound gearing is used, the ratio of the compound gears is usually 2 to 1, so that the threads are twice the number per inch as when simple gearing is used. Therefore, the following procedure can be used:

I. Calculate as in simple gearing:

Gear ratio =

40 (lead screw gear)

2. Doubling these figures results in 16 teeth for the stud gear and 80 teeth for the lead screw gear, respectively. Selecting, for example, 18- and 36-tooth gears for the compound assembly, the setup would be as follows: A 16-tooth gear for the stud gear, 36- and 18-tooth gears for the compound assembly, and an 80-tooth gear for the lead screw (Figure 8-12). Thus, the following ratios are:

80 5

36 2 1 revolution

Figure 8-12 Diagram showing use of total ratio in a compound change-gear setup.

1 revolution

Figure 8-12 Diagram showing use of total ratio in a compound change-gear setup.

### Quick-Change Gear Lathes

The quick-change gearbox permits the operator to obtain the various pitches of threads without using loose gears. All lathes equipped with quick-change gearboxes have index plates or charts for setting up the lathe to cut various threads. It is necessary only to arrange the levers on the gearbox for the various threads per inch, as indicated on the index plate.

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