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Major Measurement Errors of the Screw One-wire method
Micrometer The pitch diameter of odd-fluted tap can be measured using the V-anvil
micrometer with the one-wire method. Obtain the measured value (M1)
Error cause Maximum possible Precautions for eliminating errors Error that might and calculate M with equation (3) or (4).
error not be eliminated
even with
precautions M1 = Micrometer reading during one-wire measurement
D = Odd-fluted tap diameter
Micrometer feed 3 m 1. Correct the micrometer before use. ±1 m
error
Anvil angle error ±5 m assuming 1. Measure the angle error and correct ±3 m expected Tap with three flutes : M = 3M1-2D ···························(3) B
Misaligned the error of a half the micrometer. measurement Tap with five flutes : M = 2.2360M1-1.23606D ·······(4)
contact points angle is 15 minutes error of half Then, assign the calculated M to equation (1) Anvil
2. Adjust the micrometer using the same angle or (2) to calculate the pitch diameter (E).
thread gauge as the workpiece.
+10 m +3 m
1. Use a micrometer with a low
measuring force if possible.
Influence of ±10 m 2. Always use the ratchet stop. +3 m Spindle
measuring force
3. Adjust the micrometer using a thread
gauge with the same pitch.
Odd-fluted tap
1. Perform correction calculation (angle). Wire
Angle error of 2. Correct the length error. Root Tangent Length
thread gauge ±10 m 3. Adjust the micrometer using the same +3 m
Length error of
thread gauge ( )± 3+25L m thread gauge as the workpiece.
Workpiece thread
angle error JIS 2 grade error 1. Perform correction calculation.
Cumulative error of half angle ±229 2. Adjust the micrometer using the same ±1 m
minutes thread gauge as the workpiece.
-91 m 1. Minimize the angle error as much as
+71 m possible. ±8 m assuming
(±117+40) m 2. Measure the angle error and perform the error of half
correction calculation. angle is ±23
3. Use the three-wire method for a large minutes
angle error.
+26 m
-12 m Sm
Screw Pitch Diameter Measurement Formula for calculating a root tangent length (Sm):
Sm = m cos 0 { (Zm - 0.5) + Z inv 0 } + 2Xm sin 0
Three-wire method
Screw pitch diameter can be measured with the three-wire method as Formula for calculating the number of teeth within the root tangent length (Zm):
shown in the figure.
Calculate the pitch diameter (E) with equations (1) and (2). Zm' = Z·K (f) + 0.5 ( Zm is the integer closest to Zm'.)
where, K (f) = 1 { sec 0 (1 + 2f) 2 - cos2 0 - inv 0 - 2f tan 0}
Metric thread or unified screw (60°) Spindle d (3) and, f= X m : Module
E = M-3d+0.866025P .......(1) EM Z 0 : Pressure angle
Whitworth thread (55°) Z : Number of teeth
E = M-3.16568d+0.960491P .......(2) P Anvil inv 20° 0.014904 X : Addendum modification coefficient
inv 14.5° 0.0055448 Sm : Root tangent length
Zm : Number of teeth within the root
Screw Gear Measurement
tangent length
d = Wire diameter
E = Screw pitch diameter Over-pin method dp
M = Micrometer reading including three wires
P = Screw pitch dp
(Convert inches to millimetres for unified threads.)
Thread type Optimal wire size at D dm
Metric thread or unified screw (60°) 0.577P dm
Whitworth thread (55°) 0.564P
90
Major Measurement Errors of the Three-Wire Method Z
Error cause Precautions for eliminating errors Possible error Error that might (a) (b)
not be eliminated
even with For a gear with an even number of teeth:
precautions
Pitch error 1. Correct the pitch error ( p = E) their ±18 µm assuming ±3 m dm = dp + dg = dp + z·m·cos 0
(workpiece) 2. Measure several points and adopt that the pitch error ±0.3 m cos cos
3. average. is 0.02 mm. ±1 m
Reduce single pitch errors.
Error of half angle 1. Use the optimal wire diameter. -1 m For a gear with an odd number of teeth:
(workpiece) 2. No correction is needed. ±0.3 m
( ) ( )dm dg
Due to anvil 1. Use the optimal wire diameter. = dp + cos · cos 90° = dp + z·m·cos 0 · cos 90°
difference 2. Use the wire which has a diameter z cos z
close to the average at the one wire ±8 m
side. however,
1. Use the predetermined measuring
( )inv dp
force appropriate for the pitch. = dg – X = dp – 2z – inv 0 + 2tan 0 ·X
Wire diameter error 2. Use the predetermined width of -3 m 2 z·m·cos z
measurement edge. 0
3. Use a stable measuring force. Obtain (inv) from the involute function table. z : Number of teeth
0 : Pressure angle teeth
Cumulative error In the worst case When measured m : Module
+20 m carefully
-35 m X : Addendum modification coefficient
+3 m
-5 m
B-78
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