Machinery's Handbook, 31st Edition
Transmission Roller Chains 2635 Cutting Standard Sprocket Tooth Form.— The proportions and seating curve data for the standard sprocket tooth form for roller chain are given in Table 11. Either formed or generating types of sprocket cutters may be employed. Hobs: Only one hob will be required to cut any number of teeth for a given pitch and roller diameter. All hobs should be marked with pitch and roller diameter to be cut. Formulas and data for standard hob design are given in Table 12. Space Cutters: Five cutters of this type will be required to cut from 7 teeth up for any given roller diameter. The ranges are, respectively, 7–8, 9–11, 12–17, 18–34, and 35 teeth and over. If less than 7 teeth is necessary, special cutters conforming to the required num ber of teeth should be used. The regular cutters are based upon an intermediate number of teeth N a , equal to 2 N 1 N 2 ÷ ( N 1 + N 2 ) in which N 1 = minimum number of teeth and N 2 = maximum number of teeth for which cutter is intended; but the topping curve radius F (see diagram in Table 13) is designed to produce adequate tooth height on a sprocket of N 2 teeth. The values of N a for the several cutters are, respectively, 7.47, 9.9, 14.07, 23.54, and 56. Formulas and con struction data for space cutter layout are given in Table 13 and recommended cutter sizes are given in Table 14. Table 13. Standard Space Cutters for Roller-Chain Sprockets
Cutter Width
M
M E
c
c ”
E
T
T
B
A
F
z ”
a
z
X
Y
y
y ”
V
V
G
G b
R R
b ”
x
X
d
W
W
Data for Laying Out Space Cutter
Range of Teeth
M
T
W
V
0.5459 D r 0.5255 D r 0.5063 D r 0.4875 D r 0.4710 D r Chord xy
1.2790 D r 1.3302 D r 1.3694 D r 1.3947 D r 1.4000 D r 0.0618 D r 0.0853 D r 0.1269 D r 0.1922 D r yz 0.2235 D r
0.5694 D r 0.4365 D r 0.2911 D r 0.1220 D r
7–8 9–11
0.5848 D r 0.6032 D r 0.6194 D r 0.6343 D r 0.6466 D r
12–17 18–34 35 up
0
Range of Teeth
Angle Yab
F
0.2384 D r + 0.0003 0.2800 D r + 0.0003 0.3181 D r + 0.0004 0.3540 D r + 0.0004 0.3850 D r + 0.0004
7–8 9–11
0.8686 D r − 0.0015 0.8554 D r − 0.0015 0.8364 D r − 0.0015 0.8073 D r − 0.0015 0.7857 D r − 0.0015
24 °
18 ° 10'
12–17 18–34 35 up
12 °
5 ° 0 °
E (same for all ranges) = 1.3025 D r + 0.0015; G (same for all ranges) = 1.4 D r See Table 14 for recommended cutter sizes.
Angle Yab is equal to 180 ° ÷ N when the cutter is made for a specific number of teeth. For the de - sign of cutters covering a range of teeth, angle Yab was determined by layout to ensure chain roller clearance and to avoid pointed teeth on the larger sprockets of each range. It has values as given below for cutters covering the range of teeth shown. The following formulas are for cutters cover- ing the standard ranges of teeth where N a equals intermediate values given on page 2635.
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