Section 17 Strength and Durability of Gears - SDP/SI

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ELEMENTS OF METRIC GEAR TECHNOLOGY PHONE: 516.328.3300 • FAX: 516.326.8827 • WWW.SDP-SI.COM Table 17-26B Surface Strength Factors of Gleason Straight Bevel Gear 164 No. Item Symbol Unit Pinion Gear 1 Allowable Hertz Stress σ H lim kgf/mm 2 21 Allowable Tangential Force on F t lim kgf 103.0 Central Pitch Circle 103.0 2 3 Pinion's Pitch Diameter Pinion's Pitch Cone Angle d 1 δ 1 mm degree 40.000 26.56505° 4 Cone Distance R e 44.721 mm 5 Tooth Width b 15 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Numbers of Teeth Ratio z 2 / z 1 Zone Factor Material Factor Contact Ratio Factor Spiral Angle Factor Life Factor Lubricant Factor Surface Roughness Factor Sliding Speed Factor Hardness Ratio Factor Dimension Factor of Root Stress Load Distribution Factor Dynamic Load Factor Overload Factor Reliability Factor u Z H Z M Z ε Z β K HL Z L Z R Z V Z W K HX K H β K V K O C R (kgf/mm 2 ) 0.5 2 2.495 60.6 1.0 1.0 1.0 1.0 0.90 0.97 1.0 1.0 2.1 1.4 1.0 1.15 17.5 Strength Of Worm Gearing This information is applicable for worm gear drives that are used to transmit power in general industrial machines with the following parameters: Axial Module: m x 1 to 25 mm Pitch Diameter of Worm Gear: d 2 less than 900 mm Sliding Speed: v s less than 30 m/sec Rotating Speed, Worm Gear: n 2 less than 600 rpm 17.5.1 Basic Formulas: Sliding Speed, v s (m/s) d 1 n v 1 s = ––––––––––– (17-48) 19100 cos γ I R T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 T-185 A
I R T 1 2 3 4 5 6 7 8 9 10 11 12 ELEMENTS OF METRIC GEAR TECHNOLOGY 17.5.2 Torque, Tangential Force and Efficiency (1) Worm as Driver Gear (Speed Reducing) PHONE: 516.328.3300 • FAX: 516.326.8827 • WWW.SDP-SI.COM F t d 2 ⎫ T 2 = –––––– 2000 ⎪ T 2 F t d 2 T 1 = –––– = ––––––––– u η R 2000 u η R ⎪ ⎬ (17-49) µ tan γ (1 – tan γ ––––––) cos α n η R = –––––––––––––––––––– µ tan γ + –––––– ⎪ cos α n ⎭ where: T 2 = Nominal torque of worm gear (kg • m) T 1 = Nominal torque of worm (kgf • m) F t = Nominal tangential force on worm gear's pitch circle (kgf) d 2 = Pitch diameter of worm gear (mm) u = Teeth number ratio = z 2 /z w η R = Transmission efficiency, worm driving (not including bearing loss, lubricant agitation loss, etc.) µ = Friction coefficient (2) Worm Gear as Driver Gear (Speed Increasing) F t d 2 ⎫ T 2 = –––––– 2000 ⎪ T 2 η I F t d 2 η I T 1 = –––– = ––––– u 2000 u ⎪ ⎬ (17-50) µ tan γ – –––––– cos α n η I = –––––––––––––––––––– µ tan γ (1 + tan γ ––––––) ⎪ cos α n ⎭ where: η I = Transmission efficiency, worm gear driving (not including bearing loss, lubricant agitation loss, etc.) 17.5.3 Friction Coefficient, µ The friction factor varies as sliding speed changes. The combination of materials is important. For the case of a worm that is carburized and ground, and mated with a phosphorous bronze worm gear, see Figure 17-12. For some other materials, see Table 17- 27. For lack of data, friction coefficient of materials not listed in Table 17-27 are very difficult to obtain. H.E. Merritt has offered some further information on this topic. See Reference 9. Metric 0 10 13 14 15 A T-186
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Section 17 Strength and Durability of Gears - SDP/SI

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