## [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}) *ƒ*_{0} factor is obtained.

*C*_{r} ＝ 50.9 kN

*ƒ*_{0} ＝ 13.2

*C*_{0r} ＝ 24.0 kN

#### Values *X* and *Y* are obtained by comparing value *e*, calculated from value *ƒ*_{0} *F*_{a} / *C*_{0r} via proportional interpolation, with value *ƒ*_{0} *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 mm^{2}/_{s}

According to **Fig. A**, *ν*_{1} ＝ 21.7 mm^{2}

*κ* ＝ *ν* / *ν*_{1} ＝ 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, *α*_{1} = 0.55.

*L*_{4m}＝ *α*_{1}*α*_{ISO}*L*_{10} ＝ 0.55× 7.7 ×50900≒ 216000 h

Fig. A

Fig. B

The *α*_{ISO} factor can also be calculated on our website.

Click here to WEB based technical calculation tool

## [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.

Basic dynamic load rating （ C_{r}） | e | X^{1)} | Y^{1)} | |
---|---|---|---|---|

Bearing A | 68.8 kN | 0.37 | 0.4 | 1.60 |

Bearing B | 83.9 kN | 0.40 | 0.4 | 1.48 |

[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 (*L*_{10}) 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 *ƒ*_{0} is 12.8

*ƒ*_{0} *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 *ƒ*_{0}*F*_{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*_{m}*n* ＝ 80 × 1500 ＝ 12 × 10_{4}, 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*_{m}^{2} ＝ 9.8 × 2 × 1.0 × 0.062 × 80^{2} ≒ 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 *α*_{1} ＝ *α*_{2} ＝ 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 *α*_{1} ＝ 95 mm ，*α*_{2} ＝ 265 mm ，*b*_{1} ＝ 245 mm ，*b*_{2} ＝ 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.

Basic dynamic load rating （ C_{r}） | e | X^{1)} | Y^{1)} | |
---|---|---|---|---|

Bearing A | 183 kN | 0.35 | 0.4 | 1.74 |

Bearing B | 221 kN |

[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}/2*Y*_{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 :