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 No. Item Symbol Unit Pinion Gear 1 Allowable Hertz Stress kgf/mm 2 164 2 Pitch Diameter of Pinion 40 mm 3 Effective Tooth Width 20 4 Teeth Ratio (z 2 /z 1 ) 2 5 Zone Factor 2.495 6 Material Factor (kgf/mm 2 ) 0.5 60.6 7 Contact Ratio Factor 1.0 8 Helix Angle Factor 1.0 9 Life Factor 1.0 10 Lubricant Factor 1.0 11 Surface Roughness Factor 0.90 Sliding Speed Factor 0.97 Hardness Ratio Factor 1.0 Dimension Factor of Root Stress 1.0 12 13 14 15 16 17 18 19 Load Distribution Factor Dynamic Load Factor Overload Factor Safety Factor for Pitting Allowable Tangential Force on Standard Pitch Circle 17.3 Bending Strength Of Bevel Gears Table 17-16B Surface Strength Factors Calculation δ H lim d 1 b H 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 S H This information is valid for bevel gears which are used in power transmission in general industrial machines. The applicable ranges are: F t lim Module: m 1.5 to 25 mm Pitch Diameter: d less than 1600 mm for straight bevel gears less than 1000 mm for spiral bevel gears Linear Speed: v less than 25 m/sec Rotating Speed: n less than 3600 rpm 17.3.1 Conversion Formulas In calculating strength, tangential force at the pitch circle, F tm , in kgf; power, P , in kW, and torque, T , in kgf • m, are the design criteria. Their basic relationships are expressed in Equations (17-23) through (17-25). 102 P 1.95 x 10 6 P 2000 T F tm = –––– = –––––––– = ––––– (17-23) v m d m n d m F tm v m P = –––– = 5.13 x 10 –7 F tm d m n (17-24) 102 F tm d m 974 P T = –––– = –––– (17-25) 2000 n kgf 1.025 1.4 1.0 1.15 251.9 I R T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 T-171 A
I R T 1 2 3 4 5 6 7 8 9 10 11 12 13 ELEMENTS OF METRIC GEAR TECHNOLOGY 17.3.2 Bending Strength Equations PHONE: 516.328.3300 • FAX: 516.326.8827 • WWW.SDP-SI.COM The tangential force, F tm , acting at the central pitch circle should be equal to or less than the allowable tangential force, F tm lim , which is based upon the allowable bending stress σ F lim . That is: F tm ≤ F tm lim (17-26) The bending stress at the root, σ F , which is derived from F tm should be equal to or less than the allowable bending stress σ F lim . σ F ≤ σ F lim (17-27) The tangential force at the central pitch circle, F tm lim (kgf), is obtained from Equation (17-28). R a – 0.5 b 1 K L K FX 1 F tm lim = 0.85 cos β m σ F lim mb –––––––– ––––––– (–––––––) ––– (17-28) R a Y F Y ε Y β Y C K M K V K O K R where: β m : Central spiral angle (degrees) m : Radial module (mm) R a : Cone distance (mm) And the bending strength σ F (kgf/mm 2 ) at the root of tooth is calculated from Equation (17-29). Y F Y ε Y β Y C R a K M K V K O σ F = F tm ––––––––––– –––––––– (–––––––)K R (17-29) 0.85 cos β m mb R a – 0.5 b K L K FX 17.3.3 Determination of Factors in Bending Strength Equations 17.3.3.A Tooth Width, b (mm) The term b is defined as the tooth width on the pitch cone, analogous to face width of spur or helical gears. For the meshed pair, the narrower one is used for strength calculations. 17.3.3.B Tooth Profile Factor, Y F The tooth profile factor is a function of profile shift, in both the radial and axial directions. Using the equivalent (virtual) spur gear tooth number, the first step is to determine the radial tooth profile factor, Y FO , from Figure 17-8 for straight bevel gears and Figure 17-9 for spiral bevel gears. Next, determine the axial shift factor, K, with Equation (17-33) from which the axial shift correction factor, C, can be obtained using Figure 17-7. Finally, calculate Y F by Equation (17-30). Y F = CY FO (17-30) Metric 0 10 14 15 A T-172
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Section 17 Strength and Durability of Gears - SDP/SI

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