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Dividing circle

Dimension reference

This entry is made by Compilation and application of scientific encyclopedia entries of "Science Popularization China" to examine.

The dividing circle is a dimension reference selected for the convenience of gear design and manufacturing radius , diameter, tooth thickness, tooth slot width and tooth pitch are respectively expressed in r, d, s, e and p.

Chinese name: Dividing circle
Foreign name: Dividing circle

Painting: The drawing method of cylindrical gear is specified as dotted line
Calculation formula: Diameter of reference circle=module * number of teeth

catalog

four modulus
five Modified gear
six Measurement of chord tooth thickness

concept

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Figure 1 Symbols of Gear Parts^[1]

The dividing circle is a dimension reference selected for the convenience of gear design and manufacturing. The gear reference circle has standard modulus and standard pressure angle, so it is taken as the calculation basis of the size of each part of the gear. The radius of the dividing circle is shown as r in Figure 1.^[2]

Calculation of diameter

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Calculation of the diameter of the dividing circle
classification	Code	Calculation formula	Supplementary notes
Involute standard cylindrical gear			—— modulus —— Number of teeth
Helical cylindrical gear			—— End face modulus ——Normal modulus —— Helix angle
Standard straight bevel gear			Axis angle

Size property

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Figure 2

On the reference circle of standard gear Tooth thickness

And slot width

Equal (as shown in Figure 2).

And the arc length between the corresponding points of two adjacent feet on the dividing circle is called Pitch of indexing circle

, i.e

。^[3]

The pressure angle on the dividing circle is the standard value,

。

modulus

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When the number of teeth of the gear is known, the diameter of the reference circle

、 Pitch

And Number of teeth

The relationship of is as follows:

Or:

Irrational number in factor

In order to make the diameter of the dividing circle an integer or a simple decimal for calculation or measurement

，

be called modulus , in

。 be

。

Modulus is the basic parameter for calculating the geometric dimensions of gears. The size of the module reflects the thickness, thickness, size and bearing capacity of the gear. Modulus is now standardized.^[3]

Modified gear

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In order to improve some shortcomings of the standard gear, it is necessary to break through the limitation of the standard gear and make necessary corrections to the gear. The most widely used is Displacement correction method 。

Figure 3 Correction Method of Displacement

If it is necessary to manufacture gears with the number of teeth less than 17 and without undercutting, the addendum height coefficient can be reduced

And the method of increasing the pressure angle. But decrease

It will reduce the coincidence degree, and increase the pressure angle and use non-standard tools. In addition to these two methods, the best way to solve the above problem is to move the rack tool outward from the standard position relative to the center of the gear blank for a certain distance when machining the gear

It is called radial displacement (as shown in Figure 3), where

by Radial deflection coefficient ，

Is modulus, so that undercutting will not occur. This method of cutting gears by changing the relative position of the cutter is called Displacement correction method 。 At this time, the dividing line of the tool and the dividing circle of the gear wheel blank No longer tangent , the gear thus processed is due to

It is no longer a standard gear, so it is called Modified gear 。

Fig. 4 Comparison between modified gear and standard gear^[1]

See Figure 4 for the comparison between the modified gear and the standard gear. What is tangent to the indexing circle of the modified gear is no longer the centerline of the tool, but the pitch line of the tool.

Measurement of chord tooth thickness

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Tooth thickness of dividing circle chord

Figure 5

As shown in Figure 5, the tooth thickness on the gear reference circle is arc length, which is inconvenient to measure; The chord length AB is easy to measure, which is represented by S, called Tooth thickness of dividing circle chord 。 During machining and measurement, the radial height from the tooth tip to chord AB shall be based on the tooth tip

It is called pitch circle chord tooth height. Standard gear

and

The calculation formula of is:

Where

，

Module, number of teeth and Addendum height coefficient 。^[4]

measuring method

Fig. 6 Measurement of the thickness of the indexing circular chord tooth

Figure 7 Measurement of Common Normal Length

Measuring the tooth thickness of the dividing circle chord requires a special measuring instrument (Figure 6), and the measurement must be based on the addendum circle. The measurement result is undoubtedly affected by the accuracy of the addendum circle. So for

>For 10 mm gears, the method of measuring the length of common normal is often preferred to detect the machining accuracy of gears. As shown in Figure 7, use a micrometer (or precision Vernier caliper ）The two feet of span the gear

A tooth is tangent to the tooth profile at two points A and B. The distance AB (or AC) between the two tangent points is called the common normal length