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9.0 DRIVE RATIO TABLES DEFINITION:

TABLE 22 Drive Ratio (Transmission Ratio) is the ratio of number of teeth of the input and output pulley. If the input pulley is larger than the output, the Drive Ratio will be larger than one and we have a step-up-drive. If the input pulley is smaller than the output pulley the Drive Ratio will be smaller than one and we have a step-down-drive. N1 Number of teeth of large pulley N2 Number of teeth of small pulley N1/N2 Step-up Drive ratio N2/N1 Step-down Drive ratio N1-N2 Pulley tooth differential needed for the Center Distance Table Cmin Minimum center distance for particular pulley combination expressed in belt pitches 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 25, 28, 30, 32, 36, 40, 48, 60, 72, 84, 96, 120, 156 These pulley sizes reflect the preferred sizes per ISO Standard 5294 for synchronous belt drives--Pulleys (First edition-1979-07-15).

NOMENCLATURE USED:

PULLEY SIZES INCLUDED: NOTE:

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TABLE 22

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TABLE 22

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TABLE 22

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l. Nomenclature and basic equations. Figure 11 illustrates the notation involved. The following nomenclature is used: C center distance, inches. = BL belt length, inches = PNB. = p circumferential pitch of belt, inches. = NB number of teeth on belt = LIP. = N1 number of teeth (grooves) on larger pulley. = N2 number of teeth (grooves) on smaller pulley. = one half angle of wrap on smaller pulley, radians. =

R1 R2

= = = =

=angle between straight portion of belt and line of centers, radians. pitch radius of larger pulley, inches =(N1)p/2. pitch radius of smaller pulley, inches =(N2)p/2. 3.14159 (ratio of circumference to diameter of circle).

The basic equation for the determination of center distance is: 2Csin = L- (R1 + R2) - ( - 2) (R1 - R2) [1] where C cos = R1 - R2 [2] These equations can be combined in different ways to yield various equations for the determination of center distance. We have found the formulations which follow useful. 526

ll. Exact center distance determination -- unequal pulleys. The exact equation is as follows: C = (1/2)p [(NB - N1) + k(N1 - N2)] where k = (1/)

[3] [4a]

and is determined from: (1/) (tan - ) = (NB-N1)/(N1-N2) = Q (say) [4b] The value of k varies within the range (1/, 1/2) depending on the number of teeth on the belt. All angles in equations [3,4] are in radians. The procedure for center distance determination is as follows: 1. Select values of N1, N2(in accordance with desired transmission ratio) and NB. 2. Compute Q = (NB-N1)/(N1-N2). 3. Compute by solving equation [4b] numerically. 4. Compute k from equation. [4a]. 5. Compute C from equation [3]. lll. Exact center distance determination -- equal pulleys. For equal pulleys, N1 = N2 and equation [3] becomes [5] lV. Approximate center distance determination. Approximate formulas are used when it is desirable to minimize computation time and when an approximate determination of center distance suffices. An alternative to equation [1] for the exact center distance can be shown to be the following: [6] where S varies between 0 and 0.1416, depending on the angle of wrap of the smaller pulley. The value of S is given very nearly by the expression: S = (cos²)/12 [7] 527

In the approximate formulas for center distance, it is customary to neglect S and thus to obtain following approximation for C: [8] The error in equation [8] depends on the speed ratio and the center distance. The accuracy is greatest for speed ratios close to unity and for large center distances. The accuracy is least at minimum center distance and high transmission ratios. in many cases the accuracy of the approximate formula is acceptable. V. Number of teeth in mesh (TIM). It is generally recommended that the number of teeth in mesh be not less than 6. The number, TIM, teeth in mesh is given by: TIM = N2 [9] where = /(3.1416) when (see equation [4b]) is given in radians (See also the derivation given for TIM in this Handbook). Vl. Determination of belt size for given pulleys and center distance. Occasionally the center distance of a given installation is prescribed and the belt length is to be determined. For given pitch, number of teeth on pulleys and center distance, the number of teeth on the belt can be found from the equation: [10] where the arc sin is given in radians and lies between 0 and /2. Since NB in general will not be a whole number, the nearest whole number less than NB can be used, assuming a slight increase in belt tension is not objectionable. An approximate formula can be used to obtain the belt length: [11]

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Catalog D757

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