Applied calculation examples

[Example 1] Bearing service life (time) with 90 % reliability

(Conditions)
Deep groove ball bearing : 6308
Radial load F_r＝3500 N
Axial load not applied（F_a ＝ 0）
Rotational speed n＝800min^-1

①Basic dynamic load rating (C_r) is obtained from the bearing specification table.

C_r ＝ 50.9 kN

②Dynamic equivalent radial load (P_r) is calculated using equation (5-32).

P_r ＝ F_r ＝ 3500 N

③Bearing sevice life (L_10h) is calculated using equation (5-2).

[Example 2] Bearing service life (time) with 96 % reliability

(Conditions)
Deep groove ball bearing : 6308
Radial load F_r＝ 3500N
Axial load F_a＝ 1000N
Rotational speed n＝ 800min^-1

①From the bearing specification table ;

Basic load rating (C_r, C_0r) ƒ₀ factor is obtained.

C_r ＝ 50.9 kN
ƒ₀ ＝ 13.2
C_0r ＝ 24.0 kN

Values X and Y are obtained by comparing value e, calculated from value ƒ₀ F_a / C_0r via proportional interpolation, with value ƒ₀ F_a / F_r.

②Dynamic equivalent load (P_r) is obtained using equation (5-32).

P_r ＝ XF_r ＋ YF_a ＝（0.56 × 3500）＋（1.82 × 1000）＝3780 N

③Service life with 90 % reliability (L_10h) is obtained using equation (5-2).

[Example 3] Calculation of the α_ISO factor with the conditions in Example 2

(Conditions)
Oil lubrication (Oil that has been filtered by a fine filter)
Operating temperature 70℃
96% reliability

④Lubricating oil selection

From the bearing specification table, the pitch diameter D_pw = (40 + 90)/2 = 65 is obtained.
d_mn = 65 × 800 = 52 000. Therefore, select VG 68 from Table 12-8, Proper kinematic viscosities by bearing operating conditions.

⑤Calculating the α_ISO factor

The operating temperature is 70 °C, so according to Fig. 12-3, Relationship between lubricating oil viscosity and temperature (viscosity index :100), the viscosity when operating is ν ＝ 20 mm²/_s
According to Fig. A, ν₁ ＝ 21.7 mm²
κ ＝ ν / ν₁ ＝ 20/21.7 ＝ 0.92
The oil has been filtered by a fine filter, so Table 5-4 shows e_c is 0.5 to 0.6.
To stringently estimate the value, e_c = 0.5.

Therefore, according to Fig. B
α_ISO ＝ 7.7

⑥Service life with 96 % reliability (L_nm) is obtained using equation (5-8).
According to Table 5-3, α₁ = 0.55.

L_4m＝ α₁α_ISOL₁₀ ＝ 0.55× 7.7 ×50900≒ 216000 h

Fig. A

Fig. B

The α_ISO factor can also be calculated on our website.

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[Example 4] Bearing service life (total revolution)

(Conditions)
Tapered roller bearing
Bearing A：30207 JR
Bearing B：30209 JR
Radial load
F_rA＝ 5200 N
F_rB＝ 6800 N
Axial load K_a＝ 1600 N

①From the bearing specification table, the following specifications are obtained.

[Note] 1) Those values are used, where F_a/F_r＞ e.
Where F_a/F_r≦ e, X＝ 1，Y＝ 0.

②Axial load applied to shafts must be calculated, considering the fact that component force in the axial direction is generated when radial load is applied to tapered roller bearings.

(ref. equation 5-33, Table 5-9)

③Dynamic equivalent load (P_r) is obtained from Table 5-9.

④Each bearing service life (L₁₀) is calculated using equation (5-1).

[Example 5] Bearing size selection

(Conditions)
Deep groove ball bearing : 62 series
Required service life : more than 10000 h
Radial load F_r＝ 2000 N
Axial load F_a＝ 300 N
Rotational speed n ＝ 1600 min^-1

①The dynamic equivalent load (Pr) is hypothetically calculated.

The resultant value, F_a / F_r ＝ 300/2000 ＝ 0.15, is smaller than any other values of e in the bearing specification table.
Hence, JTEKT can consider that P_r ＝ F_r ＝ 2000 N.

②The required basic dynamic load rating (C_r) is calculated according to equation (5-4).

③Among those covered by the bearing specification table, the bearing of the 62 series with C_r exceeding 19730 N is 6205R, with bore diameter for 25 mm.

④The dynamic equivalent load obtained at step ① is confirmed by obtaining value e for 6205 R.

Where C_0r of 6205 R is 9.3 kN, and ƒ₀ is 12.8
ƒ₀ F_a/C_0r ＝ 12.8 × 300/9300 ＝ 0.413

Then, value e can be calculated using proportional interpolation.

As a result, it can be confirmed that
F_a / F_r ＝ 0.15 ＜ e.
Hence, P_r ＝ F_r.

[Example 6] Bearing size selection

(Conditions)
Deep groove ball bearing : 63 series
Required service life : more than 15 000 h
Radial load F_r = 4000 N
Axial load F_a＝ 2400 N
Rotational speed n ＝ 1000 min^-1

①The hypothetic dynamic equivalent load (P_r) is calculated :

Since F_a/F_r ＝ 2400/4000 ＝ 0.6 is much larger than the value e specified in the bearing specification table, it suggests that the axial load affects the dynamic equivalent load.
Hence, assuming that X ＝ 0.56, Y ＝ 1.6
(approximate mean value of Y), using equation (5-32),
P_r ＝ XF_r ＋ XF_a ＝ 0.56 × 4000 ＋ 1.6 × 2400 ＝ 6080 N

②Using equation (5-4), the required basic dynamic load rating (C_r) is :

③From the bearing specification table, a 6309 with a bore diameter of 45 mm is selected as a 63 series bearing with C_r exceeding 58700 N.

④The dynamic equivalent load and basic rating life are confirmed, by calculating the value e for a 6309.
Values obtained using the proportional interpolation are :

where ƒ₀F_a/C_0r ＝ 13.3 × 2400/29500 ＝ 1.082
e ＝ 0.283, Y ＝ 1.54.

Thus, F_a / F_r ＝ 0.6 ＞ e.
Using the resultant values, the dynamic equivalent load and basic rating life can be calculated as follows :

⑤The basic rating life of the 6308, using the same steps, is :
L_10h ≒ 11500 h, which does not satisfy the service life requirement.

[Example 7] Calculation of allowable axial load for cylindrical roller bearings

(Conditions)
Single-row cylindrical roller bearing : NUP 310
Rotational speed n ＝ 1500 min^-1
Oil lubrication
Axial load is intermittently applied.

①Using the bearing specification table, the value d_m for the NUP 310 can be calculated as follows :

②Each coefficient used in equation (5-45).

From values listed in Table 5-11, coefficient ƒ_a related to intermittent load is : ƒ_a ＝ 2
From values listed in Table 5-12, coefficient ƒ_b related to diameter series 3 is : ƒ_b ＝ 1.0
According to Fig. 5-13, coefficient ƒ_p for allowable rib surface pressure, related to
d_mn ＝ 80 × 1500 ＝ 12 × 10₄, is : ƒ_p ＝ 0.062

③Using equation (5-45), the allowable axial load
F_ap is :

F_ap ＝ 9.8 ƒ_a・ƒ_b・ƒ_p・d_m² ＝ 9.8 × 2 × 1.0 × 0.062 × 80² ≒ 7780 N

[Example 8] Calculation of service life of spur gear shaft bearings

(Conditions)
Tapered roller bearing
Bearing A：32309 JR
Bearing B：32310 JR
Gear type : spur gear (normally machined)
Gear pressure angle α₁ ＝ α₂ ＝ 20°
Gear pitch circle diameter
D_p1＝ 360 mm
D_p2＝ 180 mm
Transmission power W ＝ 150 kW
Rotational speed n ＝ 1000 min^-1
Operating condition: accompanied by impact
Installation locations α₁ ＝ 95 mm ，α₂ ＝ 265 mm ，b₁ ＝ 245 mm ，b₂ ＝ 115 mm ，c ＝ 360 mm

①Using equations (5-14) and (5-15), theoretical loads applied to gears (tangential load, K_t; radial load, K_r) are calculated.

[Gear 1]

[Gear 2]

②The radial load applied to the bearing is calculated,

where the load coefficient is determined as ƒ_w = 1.5 from Table 5-6, and the gear coefficient as ƒ_g = 1.2 from Table 5-8.

[Bearing A]

Load consisting of K_t1 and K_t2 is :

Load consisting of K_r1 and K_r2 is :

Combining the loads of K_tA and em>K_rA, the radial load (F_rA) applied to bearing A can be calculated as follows :

[Bearing B]

*Load consisting of K_t1 and K_t2 is :

Load consisting of K_r1 and K_r2 is :

The radial load (F_rB) applied to bearing B can be calculated using the same steps as with bearing A.

③The following specifications can be obtained from the bearing specification table.

[Note] 1) Those values are used, where F_a/F_r＞ e.
Where F_a/F_r≦ e, X = 1, Y = 0.

④When an axial load is not applied externally, if the radial load is applied to the tapered roller bearing, an axial component force is generated.
Considering this fact, the axial load applied from the shaft and peripheral parts is to be calculated :

(Equation 5-33, Table 5-9)

According to the result, it is clear that the axial component force (F_rB/2Y_B) applied to bearing B is also applied to bearing A as an axial load applied from the shaft and peripheral parts.

⑤Using the values listed in Table 5-9, the dynamic equivalent load is calculated, where K_a ＝ 0 :

⑥Using equation (5-2), the basic rating life of each bearing is calculated :

[Bearing A]

[Bearing B]

Reference

Using equation (5-11), the system service life (L_10hs) using a pair of bearings is :