# Profile Rail Life

All of the following factors should be taken into consideration when selecting a NOOK Precision Profile Rail System:

The rolling elements and raceways of a NOOK Precision Profile Rail System that support a load are always subject to cyclic stress. Eventually, part of the raceway may spall due to metal fatigue. The life of a linear motion system is defined as the total distance of the travel reached by the time that first fatigue spalling occurs, either from a rolling element or raceway.

## 1. Definition of Rated Load

### Dynamic load ratings C

- C (kN) is the operating load which specifies 50km of travel.
- (1 kgf=9.81 Newtons=0.2248 lbf)

### Static load ratings C

_{0}- C
_{0}(kN) is the load that causes a permanent deformation equal to 1/10000 of the ball diameter at the contact point between the ball groove and the steel ball.

### Static moment ratings M

- M (kN-m) is the moment which causes a permanent deformation equal to 1/10000 of the ball diameter at the contact point between the ball groove and the steel ball when a moment load is applied.
For C, C

_{0}, M of each model refer to dimensional table.

(See Image 1 in Figure 1 Below)

## 2. Static Safety Factor

Generally, the maximum permitted static load on the runner block
is equivalent to static load ratings C_{0}. However, in repeated linear
motion applications, unexpected load is caused by the inertia when
the system starts or stops. Therefore, the safety factor fs should be
calculated in order to determine the allowable load.

C_{0} |
≥ fs | |

P_{0} |

- C
_{0}= static load ratings - P
_{0}= equivalent load (static load, impact load) - fs = static safety factor

The value of fs for general use is indicated in the table below:

OPERATING CONDITION | MINIMUM Fs |

Normal operation | 1 ~ 3 |

Smooth running required | 3 ~ 4 |

Operation with impact or vibration | 4 ~ 5 |

## 3. Determination of Rated Fatigue Life

Dynamic load ratings C (kN), number of strokes per minute and rated fatigue life L (km) are related as follows:

L = 50 × ( | C | )^{3} |

P |

- L = expected life
- C = basic load ratings
- P = equivalent load

Where the stroke L_{s} (m) and the number of cycles per minute n_{1} (cpm) are constant, the rated fatigue life L_{h} (hr) is calculated
by the following formula:

L_{h}= |
50 × 10^{3} |
× ( | C | )^{3} |

120 × L_{s} × n_{1} |
P |

- L
_{h}= expected life (hr) - L
_{s}= stroke length (m) - n
_{1}= number of strokes per minute

## 4. Calculation of Runner Block Load

### Driving factor and contact factor

The load acting upon the runner block is the sum of all of the loads applied such as the weight of the table, the cutting force and the inertia force caused by the change of speed or by heavy impact or vibration.

- Loads other than the weight of the table are often difficult to calculate. If in doubt, the applied load should be multiplied by a driving factor fd (table below) to give the effective external load.

## Driving Factor fd

OPERATING CONDITION | MINIMUM FD |

Smooth running wihtout impact (Speed under 15m/min.) | 1.0 ~ 1.5 |

Running with light impact (Speed under 60m/min.) | 1.5 ~ 2.0 |

Running with heavy impact (Speed over 60m/min.) | 2.0 ~ 4.0 |

In most installations each rail is fitted with at least two runner blocks. The distribution of load across each runner block is very much influenced by the mounting accuracy or machining accuracy of the table. Therefore, the contact factor in the table below should be taken into account.

## Contact Factor FC

NUMBER OF RUNNER BLOCKS ON ONE RAIL | FC |

1 | 1.00 |

2 | 0.86 |

3 | 0.74 |

4 | 0.66 |

### Effect of preload on internal load of runner block

- Internal load P
_{A}is determined by external force F and preload of runner block P_{PL}

### Resultant force of vertical load and horizontal load

- Resultant force of vertical load P
_{v}and horizontal load P_{H}is determined as seen in Image 3.1 in Figure 1 Below.

### Resultant force of radial load and moment load

- Resultant force of radial load F and moment load M is determined as seen in Image 3.2 in Figure 1 Below.

- C
_{0}= rated static load - M
_{c}= rated static torque on M direction - M = applied moment

### Mean load vs. load variation

- In applications where the load onto the runner block varies, mean load should be considered instead of discrete load variations P
_{1}, P_{2}, ... P_{n}.

- 1) For cases where the load and travel vary gradually:

P_{e}= ∛ |
(1/L) (P_{1}^{3}L_{1} + P_{2}^{3}L_{2} +.........+ P_{n}^{3}L_{n}) |

- P
_{e}= mean load (kN) - P
_{n}= load step (kN) - L = total travel (m)
- L
_{n}= distance traveled by P_{n}(m)

(See Image 4.1 in Figure 1 Below)

- 2) For cases where the load vary abruptly:

P_{e} = |
2P_{max} + P_{min} |

3 |

- P
_{min}: min. load (kN) - P
_{max}: max. load (kN)

(See Image 4.2 in Figure 1 Below)

- 3) Sinusoidal load change

- P
_{e}≈ 0.65 P_{max}(See Image 4.3.A in Figure 1 Below) - P
_{e}≈ 0.75 P_{max}(See Image 4.3.B in Figure 1 Below)

### Frictional resistance

- For correct load calculation, frictional resistance of the runner block must be included. Frictional resistance is calculated using the following formula.

F = | µW + f |

- F = frictional resistance force (kN)
- W = slide load (kN)
- µ = coefficient of friction
- f = seal resistance force (kN)

- The coefficient of friction for NOOK Precision Profile Rails is typically 0.003~0.005 with no preload. Seal resistance force per runner block is typically .00196~.002942 kN.
Example: For a slide load (W) of 15.69 kN on 4 runner blocks of NH-TR model, the frictional resistance (F) is calculated:

### Load on the runner block

- The loads acting on a linear motion system vary according to the location of the center of gravity, the thrust, position, moment, loading speed changes by acceleration and deceleration, cutting forces and other external forces. It is important that all of these parameters are considered at the design stage.
### Determination of RUNNER BLOCK LIFE

- A sample calculation of runner block life is shown in Image 6 in Figure 1 Below.
### Selection of a suitable Profile Rail Assembly as a function of required life

- A sample selection is shown below using the following criteria shown in Image 7 in Figure 1 Below.
### Determination of runner block life (single axis)

- A sample selection is show below using the following criteria shown in Image 8 in Figure 1 Below.

F = | µW + f |

= (0.004 × 15.69) + (0.3 × 4) = .0745 kN |

(See Image 4.4 in Figure 1 Below)

(See Image 5 in Figure 1 Below)