MEASURING INSTRUMENTS CATALOG No.E2019

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B-72BMitutoyo reserves the right to change any or all aspects of any product specication, including prices, designs and service content, without notice.B-72BFor a gear with an even number of teeth:dm = dp + cosø = dp + cosøFor a gear with an odd number of teeth:dm = dp + cosø·cos = dp + cosø ·coshowever,invø = dg – 2 = z·m·cos0 – 2z – inv0 + z ·Xdgz·m·cos 0 dgXz·m·cos0( z )90°90°2tan0dpdpOver-pin methodObtain ø(invø) from the involute function table.dpdpdm(a)(b)90º Zdm: Number of teeth: Pressure angle teeth: Module: Addendum modification coefficient z 0 m X Gear MeasurementRoot Tangent Lengthinv 20° 0.014904inv 14.5° 0.0055448ZFormula for calculating a root tangent length (Sm): Sm = m cos 0 { (Zm − 0.5) + Z inv 0 } + 2Xm sin 0Formula for calculating the number of teeth within the root tangent length (Zm): 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}and, f = XSmm0ZXSmZm: Module: Pressure angle: Number of teeth: Addendum modification coefficient: Root tangent length: Number of teeth within the root tangent lengthMajor Measurement Errors of the Screw MicrometerError causePrecautions for eliminating errorsPossible errorError that might not be eliminated even with precautionsPitch error (workpiece)1. Correct the pitch error (p = E)2. Measure several points and adopt their average.3. Reduce single pitch errors.±18 µm assuming that the pitch error is 0.02 mm.±3 μmError of half angle (workpiece)1. Use the optimal wire diameter.2. No correction is needed.±0.3 μm±0.3 μmDue to anvil difference1. Use the optimal wire diameter.2. Use the wire which has a diameter close to the average at the one wire side.±8 μm±1 μmWire diameter error1. Use the predetermined measuring force appropriate for the pitch.2. Use the predetermined width of measurement edge.3. Use a stable measuring force.−3 μm−1 μmCumulative errorIn the worst case+ 20 μm− 35 μmWhen measured carefully+ 3 μm− 5 μmScrew Pitch Diameter Measurement• Three-wire methodThe screw pitch diameter can be measured with the three-wire method as shown in the gure.Calculate the pitch diameter (E) with equations (1) and (2).Metric thread or unied screw (60°)E=M−3d+0.866025P .......(1)Whitworth thread (55°)E=M−3.16568d+0.960491P .......(2)d=Wire diameterE=Screw pitch diameterM=Micrometer reading including three wiresP=Screw pitch (Convert inches to millimeters for unied screws.)Thread typeOptimal wire size at DMetric thread or unied screw (60°)0.577PWhitworth thread (55°)0.564Pd (×3)SpindlePAnvilScrewME• One-wire methodThe pitch diameter of odd-uted tap can be measured using the V-anvil micrometer with the one-wire method. Obtain the measured value (M1) and calculate M with equation (3) or (4).M1=Micrometer reading during one-wire measurementD=Odd-uted tap diameterTap with three utes:M=3M1−2D ···························(3)Tap with ve utes:M=2.2360M1−1.23606D ·······(4)Then, assign the calculated M to equation (1) or (2) to calculate the pitch diameter (E).AnvilSpindleOdd-fluted tapWireError causeMaximum possible errorPrecautions for eliminating errorsError that might not be eliminated even with precautionsMicrometer feed error3 μm1. Correct the micrometer before use.±1 μmAnvil angle error±5 μm assuming the error of a half angle is 15 minutes1. Measure the angle error and correct the micrometer.2. Adjust the micrometer using the same thread gage as the workpiece.±3 μm expected measurement error of half angleMisalignedcontact points+10 μm+3 μmInuence of measuring force±10 μm1. Use a micrometer with a low measuring force if possible.2. Always use the ratchet stop.3. Adjust the micrometer using a thread gage with the same pitch.+3 μmAngle error of thread gage±10 μm1. Perform correction calculation (angle).2. Correct the length error.3. Adjust the micrometer using the same thread gage as the workpiece.+3 μmLength error of thread gage±(3+ L 25) μm1. Perform correction calculation.2. Adjust the micrometer using the same thread gage as the workpiece.±1 μmWorkpiece thread angle errorJIS 2 grade error of half angle ±229 minutes−91 μm+71 μm1. Minimize the angle error as much as possible.2. Measure the angle error and perform correction calculation.3. Use the three-wire method for a large angle error.±8 μm assuming the error of half angle is ±23 minutesCumulative error(±117+40) μm+26 μm−12 μm( z )( )Major Measurement Errors of the Three-wire Method

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