# Research on the Bending Fatigue Property of Quenched Crankshaft Based on the Multi-Physics Coupling Numerical Simulation Approaches and the KBM Model

^{*}

## Abstract

**:**

## 1. Introduction

^{th}degree type of fit can be obtained [7]. Aliakbari analyzed the unusual failure in the crankshaft of the heavy-duty truck engine. The results showed that although the stress field in stress concentration zones with the lubricating hole was much less than the web-crankpin fillet, the presence of cluster impurities, low hardness, and downshifting has caused the growth of primary cracks [8]. Fonte analyzed a failed crankshaft from a diesel motor engine and discovered that the main reason for the failure may not be attributed to the part itself, but to the misalignment of the main journals and a weakness of design close to the gear at the region where the crack was initiated [9]. Infante analyzed a failure crankshaft from a helicopter engine based on various kinds of professional test. The results showed that the crankshaft itself had no obvious surface or inside initiation of the crack. However, the damaged shell bearings applied to the main journal revealed significant damage, which was considered to be the main reason [10]. Karim Aliakbari conducted the fatigue failure analysis of a ductile iron crankshaft based on different experiments and tests. The result showed that the main reasons for the failure may be attributed to the low nodularity of the material and the low crankpin hardness [11]. For the second type, the aim of the research was to discover one or more effective models to predict the fatigue property (such as the fatigue life under a given load condition, the fatigue strength under a specified fatigue life, or the fatigue safety factor) of a given type of crankshaft. Among these works, M. Leitner investigated the fatigue strength of multi-axially loaded gas engine crankshafts and pointed out that the model proposed by Spagnoli provided the best accuracy in both fatigue strength and crack angle [12]. Venicius also applied multi-axial fatigue criteria to motor crankshafts in thermoelectric power plants to provide guidance for the selection of the material in the production [13]. Bulut proposed a new fatigue safety factor model to analyze the fatigue life of the crankshaft from a single cylinder diesel engine under variable forces and speeds; in this way, the comprehensive evaluation of the safety of the crankshaft during the whole working period can be achieved [14]. Khameneh extracted the standard specimens from the crankshaft and examined them with a four-point rotary-bending high-cycle fatigue testing machine; the results indicated that the high-cycle fatigue lifetimes were lower than the S-N curve from the FEMFAT data bank, and that the standard specimens extracted from the crankshaft could be used to consider the manufacturing effects [15]. Singh conducted the fatigue life analysis of a diesel locomotive crankshaft and proposed a 3D finite element model to research the relationship between the fillet radius and the least life of the crankshaft. Based on this, the optimum structural design of the crankshaft can be proposed [16]. Fonseca analyzed the influence of the manufacturing process on the residual stress, which was caused by deep rolling with the combination of the finite element analysis and the corresponding fatigue tests. The research results could provide the theoretical basis for the optimization design of the process [17,18]. Antunes analyzed the finite element meshes for optimal modeling of plasticity-induced crack closure and proposed the analytical expression of the most refined region along the crack propagation area. The results showed that there may be an optimum value for the plasticity-induced crack closure [19]. At present, most of the crankshafts applied in powerful engines are made of high strength steel and are treated with surface strengthening techniques before being arranged in the engine. One of the most commonly used techniques is electromagnetic induction quenching [20,21]. Stephanie compared the mechanical and microstructure property of the 42CrMo steel after electromagnetic induction quenching and conventional heat treatment processes through the standard tensile experiment and pyramid hardness test. The result showed that yield strength and hardness of the steel after electromagnetic induction quenching were a little lower than those of the steel after conventional heat treatment processes, which can be attributed to the size effect [22]. Umberto researched the microstructures and mechanical properties of the hardening layer and proposed that the main influencing factors were the heating and cooling speeds during the electromagnetic induction quenching, as well as the peak value of the temperature [23]. Cajner proposed a 2D simplified axial symmetrical model to conduct the numerical simulation of the electromagnetic induction quenching approach on a 42CrMo steel crankshaft. The experimental verification showed that this model can provide accurate surface hardness and hardness layer depth results [24]. Dietmar applied the adaptive finite element analysis approach in simulating the electromagnetic induction quenching of the gear and got accuracy in the temperature and hardening curve [25]. Dmitry carried out the technological parameter influence analysis of this approach and proposed a corresponding model to accurately simulate the process [26]. Akram proposed the novel alternate magnetic field treatments in EN8 steel and discovered that this approach could improve the wear resistance and reduce the coefficient of friction of the material, which could be explained by the increase of the compressive residual stress and the microhardness. This method can also be applied in fatigue property research of similar metal materials [27]. Mohan proposed a new optimal design method based on a satisfactory function, which was established during the electromagnetic induction quenching process [28].

## 2. Materials and Methods

#### 2.1. Research Object and Material

#### 2.2. The Prediction Method

#### 2.3. The Experiment Method

## 3. Results

#### 3.1. Heating Stage Analysis

#### 3.1.1. Mesh Model and Material Parameter

#### 3.1.2. Load and Boundary Conditions

_{S}is the temperature of the crankshaft surface, and T

_{f}is the temperature of the air. During the heating stage, the main styles of heat transfer on the surface are convective and radiative heat transfer. The corresponding transfer coefficients are 100 W/(m

^{2}∙°C) and 0.8. The symmetrically cut planes are the thermal insulation.

^{8}A/m

^{2}and the heating time is 9 s. While for the crankpin, the values of these two parameters are 6.5 × 10

^{7}A/m

^{2}and 3 s.

#### 3.1.3. Temperature Field Results

#### 3.2. Cooling Process Analysis

^{2}∙°C). Based on these parameters and the temperature field obtained in the previous step, the evolution process of the temperature field during the cooling stage can be carried out based on the same mesh model. Figure 9 shows the cooling result of this crankshaft. It can be discovered that the location of the maximum temperature point has moved from the surface to the central part of the crankpin. The value of the maximum temperature is 212 °C.

#### 3.3. Prediction and Experimental Verification

^{7}. In this paper, the shear fatigue strength of the material under this condition is 226 MPa, and the shear modulus of the material is 80,000 MPa.

## 4. Conclusions and Further Work Plans

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${A}_{\mathrm{st}}$ | the strengthening factor of a given surface treatment approach |

${M}_{\mathrm{t}}$ | the median value of the fatigue limit load of the crankshaft after the surface treatment |

${M}_{\mathrm{u}}$ | the median value of the fatigue limit load of the crankshaft before the surface treatment |

${\epsilon}_{er}$ | the equivalent shear strain caused by the residual stress field |

${\epsilon}_{ea}$ | the equivalent shear strain caused by the alternating stress field |

${\epsilon}_{et}$ | the total amount of the equivalent shear strain |

${M}_{a}$ | the applied bending moment load on the crankshaft |

${M}_{e}$ | the prediction of the fatigue limit load |

$h$ | the equivalent heat transfer coefficient |

$\lambda $ | the thermal conductivity |

${T}_{s}$ | the temperature of the crankshaft surface |

${T}_{f}$ | the temperature of the crankshaft surface |

${\gamma}_{\mathrm{max}}$ | the maximum shear strain in the critical plane |

$\Delta {\epsilon}_{n}$ | the amplitude of the normal strain in the critical plane |

${\sigma}_{n}$ | the normal stress in the critical plane |

${\sigma}_{s}$ | the yield strength of the material |

${N}_{f}$ | the fatigue life of the component |

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**Figure 6.**The finite element model of the crankshaft; (

**a**) the quarter model in the far field; (

**b**) the quarter model of the crankpin and the coil.

**Figure 13.**The finite element model of the crankpin. (

**a**) The boundary condition on the symmetrical plane; (

**b**) the load and boundary condition on the right face.

**Figure 15.**The fitting results of the fatigue limit load based on the Gaussian distribution function.

Composition | Percentage/% |
---|---|

C | 0.38–0.45 |

Si | 0.17–0.37 |

Mn | 0.50–0.80 |

S | ≤0.035 |

P | ≤0.035 |

Cr | 0.9–1.2 |

Ni | ≤0.3 |

Cu | ≤0.3 |

Mo | 0.15–0.25 |

Temperature (°C) | Relative Permeability (Mur) | Volumetric Heat Capacity $(\mathbf{J}\xb7{\mathbf{m}}^{-3}\xb7\xb0\mathbf{C})$ | Heat Conductivity $(\mathbf{W}/(\mathbf{m}\xb7\xb0\mathbf{C}))$ | Electrical Resistivity $(\mathbf{\Omega}\xb7\mathbf{m})$ |
---|---|---|---|---|

25 | 200 | 3,685,270 | 38.5 | 1.8 × 10^{−7} |

100 | 194 | 3,795,044 | 35.5 | 2.0 × 10^{−7} |

200 | 188 | 4,085,161 | 35.0 | 3.2 × 10^{−7} |

300 | 181 | 4,390,960 | 33.5 | 4.2 × 10^{−7} |

400 | 170 | 4,759,487 | 32.5 | 5.0 × 10^{−7} |

500 | 158 | 5,237,788 | 31.0 | 6.2 × 10^{−7} |

600 | 141 | 5,842,545 | 28.0 | 7.7 × 10^{−7} |

700 | 100 | 6,845,193 | 24.5 | 9.7 × 10^{−7} |

760 | 1 | 8,429,075 | 20.0 | 1.0 × 10^{−6} |

800 | 1 | 6,241,436 | 21.0 | 1.2 × 10^{−6} |

900 | 1 | 5,363,244 | 23.0 | 1.2 × 10^{−6} |

1000 | 1 | 5,308,357 | 22.5 | 1.2 × 10^{−6} |

Parameter | Value |
---|---|

$\alpha $ | 8.45 |

$E$ | 210,000 MPa |

${\sigma}_{f}^{\prime}$ | 1725 MPa |

$b$ | −0.0833 |

Stress Component | Value | Strain Component | Value |
---|---|---|---|

${S}_{11}$ | 41.8 MPa | ${\epsilon}_{11}$ | −1.14 × 10^{−5} |

${S}_{22}$ | 73 MPa | ${\epsilon}_{22}$ | 1.8 × 10^{−4} |

${S}_{33}$ | 72.5 MPa | ${\epsilon}_{33}$ | 1.78 × 10^{−4} |

${S}_{12}$ | 0.015 MPa | ${\epsilon}_{12}$ | −1.84 × 10^{−7} |

${S}_{13}$ | 0.038 MPa | ${\epsilon}_{13}$ | 4.9 × 10^{−8} |

${S}_{23}$ | 74.2 MPa | ${\epsilon}_{23}$ | 9.2 × 10^{−4} |

Source | The Residual Stress Field | The Given Load |
---|---|---|

Shear strain | −7.54 × 10^{−4} | 9.3 × 10^{−4} |

Normal stress | −199 MPa | 74 MPa |

Normal strain | −7.56 × 10^{−4} | −1.78 × 10^{−4} |

Load Value/N·m | Load Cycle |
---|---|

5352 | 2,201,350 |

5988 | 868,299 |

6074 | 543,448 |

5207 | 5,464,627 |

6017 | 779,762 |

5988 | 1,043,235 |

6278 | 575,953 |

6133 | 327,416 |

6104 | 402,108 |

5497 | 3,318,128 |

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**MDPI and ACS Style**

Sun, S.; Gong, X.; Xu, X. Research on the Bending Fatigue Property of Quenched Crankshaft Based on the Multi-Physics Coupling Numerical Simulation Approaches and the KBM Model. *Metals* **2022**, *12*, 1007.
https://doi.org/10.3390/met12061007

**AMA Style**

Sun S, Gong X, Xu X. Research on the Bending Fatigue Property of Quenched Crankshaft Based on the Multi-Physics Coupling Numerical Simulation Approaches and the KBM Model. *Metals*. 2022; 12(6):1007.
https://doi.org/10.3390/met12061007

**Chicago/Turabian Style**

Sun, Songsong, Xiaolin Gong, and Xiaomei Xu. 2022. "Research on the Bending Fatigue Property of Quenched Crankshaft Based on the Multi-Physics Coupling Numerical Simulation Approaches and the KBM Model" *Metals* 12, no. 6: 1007.
https://doi.org/10.3390/met12061007