Determination of Factors in Surface Strength Equations

Product catalog summary

Determination of Factors in Surface Strength

1. Tooth Width, b (mm): Defined as the tooth width on the pitch cone. For a meshed pair, the narrower gear's width is used for strength calculations.

2. Zone Factor, ZH: Calculated using central spiral angle (βm), normal pressure angle (αn), central radial pressure angle (αt), and βb. If αn is 20º, 22.5º, or 25º, ZH can be obtained from a specific figure.

3. Material Factor, ZM: Obtainable from a designated table.

4. Contact Ratio Factor, Zε: For straight bevel gears, Zε = 1.0. For spiral bevel gears, it involves radial contact ratio (εα) and overlap ratio (εβ).

5. Spiral Angle Factor, Zβ: Typically assumed to be unity (Zβ = 1.0).

6. Life Factor, KHL: Obtainable from a specific table.

7. Lubricant Factor, ZL: Found in a designated figure.

8. Surface Roughness Factor, ZR: Based on average roughness, calculated from the roughness of pinion and gear, and center distance.

9. Sliding Speed Factor, Zv: Obtained from a figure based on pitch circle linear speed.

10. Hardness Ratio Factor, Zw: Applies to gears meshed with quenched and ground pinions. Calculated by a specific equation, with Zw assumed to be unity if hardness is outside 130 ≤ HB2 ≤ 470.

11. Dimension Factor, KHX: Often assumed to be unity (KHX = 1.0).

Catalog excerpts

The Hertz stress, sH (kgf/mm2) is calculated from Equation (17-40). 17.4.3 Determination of Factors In Surface Strength Equations 17.4.3.A Tooth Width, b (mm) This term is defined as the tooth width on the pitch cone. For a meshed pair, the narrower gear's "b" is used for strength calculations. 17.4.3.B Zone Factor, ZH The zone factor is defined as: where: bm = Central spiral angle an = Normal pressure angle at = Central radial pressure angle bb = tan-1(tanbm cosat) If the normal pressure angle an is 20º, 22.5º or 25º, the zone factor can be obtained from Figure 17-10. 17.4.3.C Material Factor, ZM The material factor, ZM, is obtainable from Table 17-9. 17.4.3.D Contact Ratio Factor, Ze The contact ratio factor is calculated from the equations below. Straight bevel gear: Ze = 1.0 Spiral bevel gear: where: ea = Radial Contact Ratio eb = Overlap Ratio 17.4.3.E Spiral Angle Factor, Zb Little is known about these factors, so usually it is assumed to be unity. Zb = 1.0 (17-43) 17.4.3.F Life Factor, KHL The life factor for surface strength is obtainable from Table 17-10. 17.4.3.G Lubricant Factor, ZL The lubricant factor, ZL, is found in Figure 17-3. 17.4.3.H Surface Roughness Factor, ZR The surface roughness factor is obtainable from Figure 17-11 on the basis of average roughness, Rmaxm, in mm The average surface roughness is calculated by Equation (17-44) from surface roughnesses of the pinion and gear (Rmax1 and Rmax2), and the center distance, a, in mm. 17.4.3.I Sliding Speed Factor, Zv The sliding speed factor is obtained from Figure 17-5 based on the pitch circle linear speed. 17.4.3.J Hardness Ratio Factor, Zw The hardness ratio factor applies only to the gear that is in mesh with a pinion which is quenched and ground. The ratio is calculated by Equation (17-45). where Brinell hardness of the gear is: 130 £ HB2 £ 470 If the gear's hardness is outside of this range, Zw is assumed to be unity. Zw = 1.0 (17-46) 17.4.3.K Dimension Factor, KHX Since, often, little is known about this factor, it is assumed to be unity. KHX = 1.0 (17-47) 417

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