Specify suitable materials for the pinion and the gear from Example Problem 9-3 based on contact stress. Application conditions are described in Example Problems 9-1 and 9-2.

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In Example Problem 9-3, we found that the expected contact stress number is [latex]s_e = 156000[/latex] psi. This should be modified as indicated in Equation (9-27).

[latex]\frac{K_R(SF)}{Z_NC_H} S_e\lt S_{ac}[/latex] (9-27)

In Example Problem 9-2, we determined that a carburized, case-hardened steel would be used for the pinion, and a through-hardened steel should be used for the gear.
We must complete the material selection for pitting resistance independently from the bending stress analysis. However, we could not specify a material with lower properties than those specified in Example Problem 9-2 because then the bending strength would be inadequate.

In Example Problem 9-2, we used [latex] K_R = 1.50[/latex] for the desired reliability of fewer than one failure in 10 000. We decided to use [latex]S_F= 1.00[/latex] because we anticipated no unusual factors
in the application that have not already been taken into account by other factors. We can find [latex]Z_N[/latex] from Figure 9-24 using [latex] 2.10×10^9[/latex] cycles of loading on the pinion and [latex] 6.00×10^8[/latex] cycles for the gear as computed in Example Problem 9-2. We find, then, that

[latex]Z_{NP} = 0.88[/latex] [latex]Z_{NG}= 0.91 [/latex]

Let's complete the analysis for the pinion first. The hardness ratio factor does not apply to the pinion. Then Equation (9-27) gives

[latex]\frac{K_R(SF)}{Z_N}S_e=\frac{(1.50)(1.00)}{(0.88)} =(156 000 \ psi) = 265 900 \ psi\lt s_{ac}[/latex]

This value is quite high. Referring to Table 9-3, note that the only suitable listed material is a Grade 3 carburized and case-hardened steel having an allowable contact stress number of 275 ksi. Let's complete the calculations for the gear material and then discuss the results.

TABLE 9-3 Allowable stress numbers for case-hardened steel gear materials
	Allowable bending stress number, [latex]s_{ac}[/latex](ksi)			Allowable contact stress number, [latex]s_{ac}[/latex] (ksi)
Hardness at surface	Grade 1	Grade 2	Grade 3	Grade 1	Grade 2	Grade 3
Flame- or induction-hardened:
50 HRC	45	55		170	190
54 HRC	45	55		175	195
Carburized and case-hardened
55-64 HRC	55			180
58-64 HRC	55	65	75	180	225	275
Nitrided, through-hardened steels:
83.5 HR 15N		See Figure 9-14.		150	163	175
84.5 HR 15N		See Figure 9-14.		155	168	180
Nitrided nitralloy 135 [latex]M^a[/latex]
87.5 HR 15N		See Figure 9-15.
90.0 HR 15N		See Figure 9-15.		170	183	195
Nitrided, nitralloy [latex]N^a[/latex]:
87.5 HR 15N		See Figure 9-15.
90.0 HR 15N		See Figure 9-15.		172	188	205
Nitrided. 2.5% chrome (no aluminum):
87.5 HR 15N		See Figure 9-15.		155	172	189
90.0 HR 15N		See Figure 9-15.		176	196	216
Source: Extracted from AGMA Standard 2001 -C95. Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth, with the permission of the publisher. American Gear Manufacturers Association, 1500 King Street. Suite 201. Alexandria. VA 22314. Nitralloy is a proprietary family of steels containing approximately 1 .0% aluminum which enhances the formation of hard nitrides

Assume an initial value for the hardness ratio factor [latex]C_H = 1.00.[/latex] Then Equation (9-27) gives

[latex]\frac{K_R(SF)}{Z_N}S_e=\frac{(1.50)(1.00)}{(0.91)(1.00)} =(156 000 \ psi) = 257 100 \ psi\lt s_{ac}[/latex]

This value is also quite high, requiring the same Grade 3 carburized and case-hardened steel to provide adequate pitting resistance.

Comments and Design Decisions Specifying the Grade 3 carburized and case-hardened steel would be expected to provide adequate strength and pitting resistance for this pair of gears. However, the design is marginal, and it would be expensive because of the special requirements of cleanliness for the material and other guarantees related to material composition and microstructure.
Most designs are executed using Grade 1 steel. It is recommended that the gears be redesigned to produce a lower bending stress and contact stress. In general, that can be achieved by using larger teeth (a smaller value for diametral pitch, [latex]P_d[/latex]), a larger diameter for each gear, and a larger face width. Greater precision in the manufacture
of the gears, producing a higher quality number, [latex]Q_v,[/latex] would lower the dynamic factor and therefore reduce the bending stress number and the contact stress number. See section 9-15.

Question 9.4: Specify suitable materials for the pinion and the gear from ...

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