4.2 Method of measurement with Over balls or Rollers

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1 m 4. Metho of measurement with Over balls or Rollers For spur gear, putting Over balls or Rollers to Spacewith. External gear is measure by outsie imension of Over ball or Rollers. Internal gear is measure by inner imension of Over balls or Rollers. Use metho of Over balls or Rollers for Helical gear. Measurement for Internal gear, this metho has avantages over others. m Fig. Metho of Over balls or Rollers m *Note for gear with small an o number of teeth an large helix angle. We recommen using metho of Over balls or Rollers ue to unstable pins causing inaccurate measurement Diameter for Over balls or Rollers Refer to Fig. to fin iameter of Over balls or Rollers. Obtain the nearest available iameter from the graph as stanar for Over balls or Rollers to measure the gear. mm 0 m,α0º, 17 x0.8 mn4,αn0º, 19, β6º4 xn0.4 x Fig. Graph to fin suitable iameter of Over balls or Rollers (for moule mn1.0 Increase proportionately by moule use. Number of teeth of Helical gear is Virtual number of teeth of Spur gear. 6

2 Dimensions of Over balls or Rollers for Spur gear. For even number of teeth, calculation is by following m For o number of teeth, calculation is by following cos m For, calculation is by following inv π xtanα φ invα m : Over balls or Rollers imension(mm : Number of teeth x : Rack shift coefficient φ : Pressure angle ( at pin centre : Diameter of Practical Over balls or Rollers (mm m : Moule (mm α : Reference pressure angle( Example 1, even number of teeth When moule m.0, Number of teeth 0, Reference pressure angle α0 an Rack shift coefficient x Calculations of Over balls or Rollers imensions is as follows, 1 Over balls or Rollers imension Refer to Fig., 1.7 multiply by moule.0.46(mm Use nearest available pin sie.5(mm instea of.46(mm Pressure angle φ at contact point between flank an Over balls or Rollers 0. 5 π inv0 cos tan (inv φ (See page164 to167 for Involutefunction charts Over balls or Rollers imension m 0 cos0 m (mm cos Example, o number of teeth Follow example 1 for calculation metho, Number of teeth is change to 9 (Other ata remains the same 1 Over balls or Rollers imension.5(mm cos inv (x Pressure angle ( at pin centre 9. 5 π inv0 cos tan φ (4 9' 5" Fig. 4 Dimension of Over balls or Rollers for Spur gear Over balls or Rollers imension m 9 cos0 m cos (mm cos

3 Dimension of Over balls or Rollers for Internal gear Calculation for even number of teeth is by following m Calculation for o number of teeth is by following cos m For, calculation is by following π xtanα invα Example 1, even number of teeth When moule m1.0, Number of teeth 80, Reference pressure angleα 0 an Rack shift coefficient x 0.1. Calculations for imensions of Over balls or Rollers is as follows, 1 Over balls or Rollers iameter Refer to Fig., 1.68 multiply by moule (mm Use nearest available pin sie 1.70(mm instea of 1.68(mm Pressure angle ( at pin centre π 1. 7 inv cos0 0 1 tan φ (19 8' 4" inv x Over balls or Rollers imension m 80 1 cos0 m (mm cos b Example, o number of teeth Number of teeth for calculation example 1 is change to 81 (other ata remains the same. 1 Over balls or Rollers imension 1.7(mm Fig. 5 Over balls or Rollers imension for Internal gear Pressure angle ( at pin centre π 1. 7 inv cos0 0 1 tan φ (19 9' " Over balls or Rollers imension m 81 1 cos0 m cos (mm cos

4 Over balls or Rollers for Straight tooth rack 1 π m m h" 1 sinα 4tan h : Datum line (mm is from Rack base to Reference line (1. Helical rack is the same as straight rack at normal section. The above can be use. For calculation of Pressure angleα an moule m, use α n an mn at normal section. Example, When moule m.0, Reference pressure angle α0 an Datum line h. Calculations of Over balls or Rollers imensions is as follows, 1 Over balls or Rollers iameter Refer to Fig., 1.68 multiply by moule (mm Use nearest available pin sie 5.0(mm instea of 5.04(mm Over balls or Rollers imension m m (mm 1 π 1 sin0 4tan0 m 1 m h" m 4tan Fig. 6 Over balls or Rollers imension for Straight rack Note: (1 Aopte the ol Stanar term. 66

5 Over balls or Rollers imension for Helical gear Calculation for even number of teeth is by following m cosα t t m p Calculation for o number of teeth is by following m cosα t t m cos For inv φ, calculation is by following inv π xn tanα n φ invα t mncosα n mn : Normal moule (mm αn : Normal pressure angle( xn : Normal rack shift coefficient mt : Transverse moule αt : Transverse pressure angle( p Transverse moule mt mn m cosβ cos15 t (mm 4 Transverse pressure angle α t -1 tanα n -1 tan0 α t tan tan cosβ cos15 0. (0 8' 48" 5 Pressure angle ( at pin centre. 5 π inv φ inv0. 6 cos tan (inv φ. 77 ( 461 ' " See page164 to167 for Involute function charts 6 Over balls or Rollers imension m m (mm cos. 77 Example, o number of teeth Number of teeth for calculation example 1 is change to 5 (other ata remains the same. cosc (xn 1 (1 Virtual Number of teeth of Spur gear υ 5 υ cos β cos 15 9 t inv Over balls or Rollers iameter Refer to Fig., 1.7 multiply by moule.0.4 (mm Use nearest available pin sie.5(mm instea of.4(mm Fig. 7 Over balls or Rollers imension for Helical gear (shown in axis section Transverse moule mt mt.07055(mm Calculations is the same as above in even number of teeth part Example 1, even number of teeth When moule m.0, Number of teeth 6, helix angle β 15, Normal pressure angleα n 0 an Normal rack shift coefficient xn Calculations of Over balls or Rollers imensions is as follows, 1 (1 Virtual Number of teeth of Spur gear υ 6 υ cos β cos 15 Note: (1 Aopte the ol Stanar term. Over balls or Rollers iameter Refer to Fig., 1.7 multiply by moule.0.4 (mm Use nearest available pin sie.5(mm instea of.4(mm 40 4 Transverse pressure angle α t α t 0. ( Calculations is the same as Example 1, even number of teeth part 4 5 Pressure angle at pin centre (. 5 π inv φ inv0. 5 cos tan (inv φ ( 50' 47" See page164 to167 for Involute function charts 6 Over balls or Rollers imension m cos cos cos m (mm 67

6 Over balls or Rollers imension for Worm gear To obtain Over balls or Rollers imension for Worm gear, introuce following methos, 1 Substitute three wire metho from threa screw use for measurement. Use same calculation metho of Rack for Worm gear. Use same calculation metho of Helical gear for Worm gear. However, only is introuce. m 1 4 ( 1 A Ae e A (1 A 8 e 1 px px A cosγ b e cotγ b sinγ b π π mn -1 tanγ px γ b tan cos cosα t - tanα n α t tan 1 sin : Pitch iameter of Worm gear (mm : Number of threa of Worm gear px : Axial pitch of Worm gear (mm γ : Reference cyliner lea angle ( γb : Base cyliner lea angle ( Example When moule mn.0, Number of threa 1, Pitch iameter of Worm gear 1, Normal pressure angle α n0 an Reference cyliner lea angle γ 4 (.7. Calculations of Over balls or Rollers imensions of Worm gear is as follows. 1 Over balls or Rollers iameter Refer to Number of teeth(10 to in Fig., 1.68 an multiply by moule.0.6 (mm Use nearest available pin sie.4 (mm instea of.6(mm Transverse pressure angle α t α t - tan0 tan sin. 7 Base cyliner lea angle γ b -1 tanα n -1 tan0 α t tan tan cosβ cos15 4 Axial pitch cos. 7 px A A. 4 cos0. 1sin e e cot0. 56 π Over balls or Rollers imension m 5.71 (mm (Substitution metho omitte Fig. 8 Over balls or Rollers imension of Worm gear 68

1.8 Rack shift of the gear

1.8 Rack shift of the gear Undercut When Number of teeth is belo minimum as shon in Fig. 3, part of dedendum is no longer an Involute curve but ill look like a shape scooped out by cutter tool. Refer to