# Railway Axle and Wheel Assembly Press-Fitting Force Characteristics and Holding Torque Capacity

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Analysis of Press-Fitting

_{i}and P

_{o}are equal and opposite at the contact surface in the wheelset because it is assumed that the axle and wheel are composed of the same material. Lame’s equation for contact pressure distribution in thick-walled cylinders [18] was used for calculating the contact pressure, P.

_{i}; outer diameter of the wheel, r

_{o}; and Young’s modulus of elasticity, E. The wheel and axle were idealized as thick-walled cylinders, and the wheel was divided into five sections (Figure 2). The average contact pressure was calculated using Equation (2).

#### 2.1. Characteristics of the Press-Fitting Curve

**d**

**d**is the mean diameter of the axle wheel seat (mm), and

**L**is the axial displacement of the fitting (mm), which must be within the range

**d**<

**L**< 1.1

**d**

- Y
_{H}= 1.3 ϕ; - Y
_{C}= 0.85 F; - Y
_{D}= Y_{E}= 1.45 F;

#### 2.2. Determination of the Press-Fitting Force

_{p}, can be calculated from

^{2}), µ = coefficient of friction, and A = contact surface area (m

^{2}). Thus, to obtain the press-fit force, the contact pressure between the two assembly parts must be known.

## 3. Finite Element Modelling and Simulation

#### 3.1. Materials

#### 3.2. Modelling and Simulation

## 4. Results and Discussion

#### 4.1. Comparison between the FEA and Theoretical Results

#### 4.2. Effect of the Interference and Friction Coefficient on Press-Fitting Curves

#### 4.3. Contact Strength Analysis

## 5. Effect of the Interference on the Holding Torque Capacity

#### 5.1. Maximum Holding Torque Capacity Theoretical Analysis

#### 5.2. Finite Element Analysis of the Holding Torque Capacity

_{E}was the maximum elastic torque, and yielding started at that point. Within the elastic torque region, the shear stress in the axle varied linearly, and the axle showed only elastic deformation. When the torque increased to the plastic region, T

_{p}, the axle rotated continuously with no further increase in the torque. The maximum elastic torque was equal to 75% of the maximum holding torque capacity at the fully plastic region [22,23]. Therefore, it was evident that the maximum holding torque capacity or plastic torque, T

_{P}, before slipping was 75 kNm at the twist angle 0.15 rad, and the maximum elastic torque T

_{E}was 56 kNm at the twist angle 0.029 rad for the interference of 240 µm. T

_{E}did not exceed the 75% of T

_{P}for 240 µm, and others were also less than 75% of the maximum holding torque capacity. When the torque increased beyond the maximum holding torque capacity, the axle started slipping. The curves for the torque capacity simulated with different interferences are shown in Figure 20. Table 3 compares the maximum holding torque capacity with theoretical and finite element results. The deviations between the estimated maximum holding torque capacities from the theory and finite element analyses were 15% for 200 μm interference, 12% for 240 μm, 8% for 280 μm, and 6% for 320 μm. Thus, the finite element results agreed with the theory.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Simplified model of a wheelset for theoretical analysis [7].

**Figure 3.**Press-fitting curve for a railway wheelset: force vs axial displacement [4].

**Figure 5.**Dimensions of the wheelset [20].

**Figure 9.**Press-fitting curves obtained from the finite element model (FEM) and Lame’s theory (straight green line).

**Figure 14.**Von Mises stress distribution during simulation (

**a**) axial displacement of 30 mm, (

**b**) axial displacement of 100 mm, and (

**c**) axial displacement of 180 mm.

**Table 1.**Chemical composition of EA4T steel [19].

Grade | C | Mn | Si | S | P | Cr | Cu | Ni | Mo | V |
---|---|---|---|---|---|---|---|---|---|---|

EA4T | 0.29 | 0.8 | 0.4 | 0.015 | 0.02 | 1.2 | 0.3 | 0.3 | 0.3 | 0.06 |

**Table 2.**Mechanical properties of EA4T steel [19].

Material | Young’s Modulus (GPa) | Poisson Ratio | Ultimate Tensile Strength (MPa) | Yield Strength (MPa) | Elongation (%) | Absorbed Energy |
---|---|---|---|---|---|---|

EA4T | 206 | 0.3 | 650–800 | ≥420 | ≥24 | ≥30 |

Interference (µm) | Maximum Holding Torque Capacity | ||
---|---|---|---|

Theory (Equation (5)) (kNm) | Finite Element Method (kNm) | Percent Deviation (%) | |

200 | 71 | 60 | 15 |

240 | 85 | 75 | 12 |

280 | 99 | 91 | 8 |

320 | 113 | 106 | 6 |

Percent Deviation was calculated as Percent Deviation = [(Theory-FEM)/Theory] × 100% |

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**MDPI and ACS Style**

Nwe, T.; Pimsarn, M.
Railway Axle and Wheel Assembly Press-Fitting Force Characteristics and Holding Torque Capacity. *Appl. Sci.* **2021**, *11*, 8862.
https://doi.org/10.3390/app11198862

**AMA Style**

Nwe T, Pimsarn M.
Railway Axle and Wheel Assembly Press-Fitting Force Characteristics and Holding Torque Capacity. *Applied Sciences*. 2021; 11(19):8862.
https://doi.org/10.3390/app11198862

**Chicago/Turabian Style**

Nwe, Theingi, and Monsak Pimsarn.
2021. "Railway Axle and Wheel Assembly Press-Fitting Force Characteristics and Holding Torque Capacity" *Applied Sciences* 11, no. 19: 8862.
https://doi.org/10.3390/app11198862