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3.21 Contact Ratio    To assure smooth continuous tooth action, as one pair of teeth ceases contact a succeeding pair of teeth must already have come into engagement. It is desirable to have as much overlap as possible. The measure of this overlapping is the contact ratio. This is a ratio of the length of the line-of-action to the base pitch. Figure 3-3 shows the geometry. The length-of-action is determined from the intersection of the line-of-action and the outside radii. For the simple case of a pair of spur gears, the ratio of the length of-action to the base pitch is determined from:    It is good practice to maintain a contact ratio of 1 .2 or greater. Under no circumstances should the ratio drop below 1.1, calculated for all tolerances at their worst-case values.    A contact ratio between 1 and 2 means that part of the time two pairs of teeth are in contact and during the remaining time one pair is in contact. A ratio between 2 and 3 means 2 or 3 pairs of teeth are always in contact. Such a high contact ratio generally is not obtained with external spur gears, but can be developed in the meshing of an internal and external spur gear pair or specially designed nonstandard external spur gears.    More detail is presented about contact ratio, including calculation equations for specific gear types, in SECTION 11. 3.3 The Involute Function    Figure 3-4 shows an element of involute curve. The definition of involute curve is the curve traced by a point on a straight line which rolls without slipping on the circle. The circle is called the base circle of the involutes. Two opposite hand involute curves meeting at a cusp form a gear tooth curve. We can see, from Figure 3-4, the length of base circle arc ac equals the length of straight line bc.    tana = bc = rbq = q (radian)              (3-5)               Oc   rb   The q in Figure 3-4 can be expressed as inva + a, then Formula (3-5) will become:     inva = tana - a                                (3-6)

Function of a, or inva, is known as involute function. Involute function is very important in gear design. Involute function values can be obtained from appropriate tables. With the center of the base circle 0 at the origin of a coordinate system, the involute curve can be expressed by values of x and y as follows: SECTION 4 SPUR GEAR CALCULATIONS 4.1 Standard Spur Gear    Figure 4-1 shows the meshing of standard spur gears. The meshing of standard spur gears means pitch circles of two gears contact and roll with each other. The calculation formulas are in Table 4-1.

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