# Experimental Study, Simulation and Analysis of the Fracture Failure of the Drum Shaft of a Casting Bridge Crane

^{1}

^{2}

^{*}

## Abstract

**:**

^{5}N∙m in a period of approximately 13 s, and a residual torque about 3 × 10

^{4}N∙m was retained after braking. The torques on the drum shafts changed suddenly during the processes of starting, shifting and braking. Dynamic loading was the root cause of fatigue fracture of the drum shafts.

## 1. Introduction

## 2. Investigation of the Reasons for Fractures

#### 2.1. Fracture Appearance Analysis

#### 2.2. Material Analysis

#### 2.3. Manufacturing Process Analysis

#### 2.4. Service Condition Analysis

#### 2.5. Static Analysis of the Load Drum Group

- The coupling connecting the left and right load drum shafts can transmit torque without loss, and it was simplified to a hinged connection.
- The axial movement of the load drum group was ignored, and the bearing pedestal of the two load drum shafts was converted into a hinge support.
- The weight of the load drum and the coupling were uniform loads, the wire rope tension was the concentrated force acting on the center of the load drum, and the quality of the load drum shaft was ignored.

_{a}= 0.1T

_{max}, where T

_{max}is the maximum torque acting on the coupling. Obtained by calculations using the mechanics theory of materials science, the shearing force diagram and bending moment diagram are shown in Figure 6b,c, and the maximum absolute value of the shearing force and bending moment for the load drum and load drum shaft were calculated using Equations (1)–(3).

_{max}

_{1}is the maximum normal bending stress of the load drum body section, σ

_{max}

_{2}is the maximum normal bending stress of the load drum shaft section, I

_{1}is the cross-sectional moment of inertia of the load drum body, D is the outside diameter of the load drum body, d

_{1}is the inside diameter of the load drum body, d

_{2}is the diameter of the load drum shaft, and I

_{2}is the cross-sectional moment of inertia of the load drum shaft.

_{max}is small in the load drum group of the bilateral propelled hoisting mechanism, M

_{a}can be ignored. After calculation, the values of σ

_{max}

_{1}, τ

_{max}

_{1}, σ

_{max}

_{2}, τ

_{max}

_{2}are 1.7 MPa, 2.2 MPa, 5.2 MPa, 7.75 MPa, respectively. All of these values are far less than the ultimate strength of the load drum and load drum shaft, which are 235 MPa and 315 MPa, respectively.

#### 2.6. Dynamic Load Analysis of the Hoisting Mechanism

## 3. Dynamic Test of the Lifting Mechanism

#### 3.1. Test System Setup

#### 3.2. Test Results Analysis

## 4. Electromechanical Coupling Dynamics Model of the Bilateral Propelled Hoisting Mechanism

#### 4.1. Dynamic Simulation Process

- The vibration of the system in the horizontal plane and the swing of the weight are ignored, and only the vertical motion and the torsion of the structure are considered.
- The friction between the wire rope and the drum, and the rigid resistance of the wire rope as well are ignored.
- The contact stiffness at the connection for the reducer and the drum, which are rigidly connected, is ignored. That is, only the torque stiffness and torsional damping of the connecting shaft are considered.
- The torsional deformation of the reducer, drum and coupling are ignored.

#### 4.2. Motor and Control System

_{sd}, u

_{sq}, u

_{rd}, and u

_{rq}are the components of the stator voltage and rotor voltage on the d and q coordinate axes, respectively. i

_{sd}, i

_{sq}, i

_{rd}and i

_{rq}are the components of the stator current and rotor current on the d and q coordinate axes, respectively. R

_{s}and R

_{r}are the winding resistances of the stator and rotor, respectively. ψ

_{sd}, ψ

_{sq}, ψ

_{rd}and ψ

_{rq}are the components of the stator and rotor flux linkages in the d and q coordinate axes, respectively. L

_{s}, L

_{r}and L

_{m}are the inductance of stator and rotor and the mutual inductance between the stator and rotor. ω

_{1}is the rotational angular velocity of the d, q coordinate axis system, and, where f is the AC power frequency for the motor. ω

_{s}is the slip velocity, and ω

_{s}= (ω

_{1}− ω), where ω is the rotor speed. J

_{e}is the rotational inertia of the unit. n

_{p}is the polar number of the motor. T

_{m}is the motor load resistance torque.

_{p}is the pole pair of the motor, U

_{s}and ω

_{1}are the stator phase voltage and supply angular frequency of the motor, s is the slip ratio, R

_{s}and R

_{r}’ are the resistance of each phase of the stator and the resistance of each phase of the rotor is converted to the stator side, L

_{ls}and L

_{lr}’ are the leakage inductance of each phase of the stator and the leakage inductance of each phase of the rotor is converted to the stator side.

#### 4.3. Mass-Stiffness-Damping a Model of Transmission Mechanisms

**C**, the damping matrix, is a symmetric matrix; thus, ${\mathit{C}}_{12}={\mathit{C}}_{21}{}^{T}$, ${\mathit{C}}_{13}={\mathit{C}}_{31}{}^{T}$, ${\mathit{C}}_{23}={\mathit{C}}_{32}{}^{T}$, ${\mathit{C}}_{24}={\mathit{C}}_{42}{}^{T}$, and ${\mathit{C}}_{34}={\mathit{C}}_{43}{}^{T}$.

_{e1}and T

_{e6}are the driving torque of motors 1 and 6, respectively, and T

_{2}and T

_{7}are the braking torque of brakes 2 and 7, respectively.

_{m1}and T

_{m6}are the load torque of the motor 1 and motor 6, respectively.

#### 4.4. Calculation of the Structural Parameters of the Hoisting Mechanism

#### 4.4.1. Calculation of Equivalent Mass of the Main Girder

#### 4.4.2. Calculation of the Equivalent Moment of Inertia

_{1}= E

_{2}, the equivalent inertia moment of load is:

#### 4.4.3. Calculation of the Damping Coefficient

_{i}, ζ, c

_{ci}, k

_{i}and mi are the actual damping coefficient, damping ratio, critical damping coefficient, stiffness and mass of the part, respectively. The damping ratio ζ is taken as 0.1.

#### 4.4.4. Calculation of Stiffness Coefficient

_{p}is the length of the torsion shaft.

_{z}is the elastic coefficient of the wire rope, E

_{z}= 110 × 109 N

^{2}/m, A is the area of the wire rope cross-section, A = 6.154 × 10

^{−4}m

^{2}, L

_{0}is the initial length of the wire rope, L

_{0}= 6 m, and $\sum {y}_{i}$ is the displacement of the shortened length of the unilateral wire rope.

#### 4.5. Comparison of Dynamic Simulation and Experiment

## 5. Simulation Results and Application Analysis

#### 5.1. Effects of the Motor and Its Controls

#### 5.2. Effects of Nonsynchronous Control

#### 5.2.1. Single-motor Towing

#### 5.2.2. Motor startup Time Difference

^{4}N∙m to 2.5 × 10

^{3}N∙m. The torque decreased slowly with running time increased.

#### 5.2.3. Brake starting Time Difference

^{4}N∙m.

^{5}N∙m, causing shock and fatigue damage to the structure and reducing the service life of the spool shaft.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Appearance of the fracture of a load drum shaft: (

**a**) cross-section of the left load drum shaft; (

**b**) cross-section of the right load drum shaft.

**Figure 6.**The force and flexural moment analysis of drum: (

**a**) static model of the bilateral drive drum; (

**b**) the shear force diagram; (

**c**) bending moment diagram.

**Figure 9.**Crane lifting weight fast and frequent starting-braking test: (

**a**) The motor speed and gear of the hoisting mechanism; (

**b**) frequent starting-braking drum shaft torque change.

**Figure 10.**Torque change of the drum shaft before and after braking of the bilateral drive lifting mechanism: (

**a**) lifting brake in 1st gear when lifting 40.44 t; (

**b**) lowering brake in 1st gear when lifting 40.44 t.

**Figure 12.**Vertical translational-torsional dynamic model of the bilaterally driven lifting mechanism.

**Figure 17.**Current curves of motor: (

**a**) three-phase current of stator; (

**b**) three-phase current of rotor.

**Figure 21.**Drum speed and lifting speed when a single motor is driving: (

**a**) left and right drum speeds; (

**b**) lifting speed.

Location | Surface | 1/2R | Core | Required | |
---|---|---|---|---|---|

Elements | |||||

C | 0.37 | 0.34 | 0.35 | 0.32–0.39 | |

Mn | 0.59 | 0.58 | 0.59 | 0.50–0.80 | |

Si | 0.22 | 0.22 | 0.22 | 0.17–0.37 | |

P | 0.018 | 0.017 | 0.017 | ≤0.035 | |

S | 0.002 | 0.002 | 0.002 | ≤0.035 | |

Cr | 0.01 | 0.01 | 0.01 | ≤0.10 | |

Ni | 0.01 | 0.01 | 0.01 | ≤0.30 |

Items | Work Level | Use Level | Loads Level |
---|---|---|---|

Crane | A7 | U5 | Q4 |

Hoisting mechanism | M8 | T7 | L4 |

**Table 3.**Values and meanings of the codes in Figure 5.

Codes | Values |
---|---|

Load drum length L/mm | 1331 |

Load drum shaft length L_{1}/mm | 220 |

Coupling length L_{2}/mm | 838 |

Load drum group quality G_{1}/kN | 44 |

Coupling quality G_{2}/kN | 8 |

Unilateral lifting weight G_{3}/kN | 250 |

Pulley set magnification N | 2 |

Single load drum load F/kN | 125 |

Properties | Lifting Capacity | Length | Beam Weight | Trolley Weight | Motor Power | Rated Speed |
---|---|---|---|---|---|---|

Units | t | m | t | t | kW | rpm |

Values | 50 | 22.5 | 183 | 29 | 75 | 750 |

No. | Instrument Model | Application |
---|---|---|

1 | KFW-2-120-D16-11 L1M2S | Strain test |

2 | TQ201 No. 2126 | Torque and speed test |

3 | BS903 | Wireless receiving gateway |

4 | BeeData | Software for signal acquisition and processing |

Type | Object Weight | Speed and Direction | Operation Method |
---|---|---|---|

Type 1 | None | Static | The hook is static without weights, and the sensor is set to zero |

Type 2 | None | 4th gear and dropping | After the hook falls a certain vertical distance, quickly decelerate from the 4th gear to the 1st gear and finally stop in the air |

Type 3 | 4th gear and lifting | After the hook lifts a certain vertical distance, quickly decelerate from the 4th gear to the 1st gear and finally stop in the air | |

Type 4 | 40.44 t | 4th gear and lifting | After the object is lifted a certain vertical distance, quickly decelerate from the 4th gear to the 1st gear and finally stop in the air |

Type 5 | 4th gear and dropping | After the object falls a certain vertical distance, quickly decelerate from the 4th gear to the 1st gear and finally stop in the air | |

Type 6 | ≤40.44 t | 4th gear and dropping or lifting | The heavy object is always placed on the ground, and the hoisting mechanism repeatedly lifts and descends in 1 block |

Type 7 | 40.44 t | 4th gear and dropping | After the object falls a certain vertical distance, quickly decelerate from the 4th gear to the 1st gear and finally stop on the ground |

Gear | Percentage of Maximum Speed | Motor Speed | Load Drum Speed |
---|---|---|---|

Units | % | r/min | r/min |

4 | 100 | 745 | 4.3 |

3 | 30 | 223.5 | 1.29 |

2 | 20 | 149 | 0.86 |

1 | 10 | 74.5 | 0.43 |

**Table 8.**The parameters for the bilateral driven crane mechanisms and their meanings are shown in Figure 12.

Parameters | Object Weight | Parameters | Operation Method |
---|---|---|---|

${m}_{1}$ | Equivalent weight of the hoisting mechanism | ${m}_{2}+{m}_{3}$$,{m}_{5}+{m}_{6}$ | Weight of the hooks |

${m}_{4}$$,{m}_{7}$ | Weight of the objects | ${m}_{8}$ | Weight of the crane girder |

${J}_{1}$$,{J}_{6}$ | Moment of the motor | ${J}_{2}$$,{J}_{7}$ | Moment of the brake |

${J}_{3}$$,{J}_{8}$ | Moment of the reducer | ${J}_{4}$$,{J}_{9}$ | Moment of the load drum |

${J}_{5}$ | Moment of the coupling | ${J}_{10}$$~{J}_{15}$ | Moment of the pulley block |

${k}_{i}$ i = 1,10,11,12…20 | Translational stiffness coefficient | ${k}_{i}$ i = 2,3,…9 | Rotational stiffness coefficient |

c_{i}i = 1,10,11,12…20 | Translation damping coefficient | c_{i}i = 2,3,…9 | Rotational damping coefficient |

${r}_{4}$$,{r}_{9}$ | Radius of the load drum | ${r}_{i}$ i = 10,11,…15 | Radius of the pulley |

y_{i}i = 1,2…8 | Displacement of the crane masses | θ_{i}i = 1,2,3…15 | Rotation angle of the crane parts |

**Table 9.**Relationship between the parameters in Table 7.

Number | Name | Relationship |
---|---|---|

1 | Weight | m_{2} = m_{3} = m_{5} = m_{6} = m_{h}, m_{2} + m_{3}= m_{5} + m_{6}= m_{j} |

2 | Displacement | y_{2} = y_{3} = y_{l}, y_{5} = y_{6} = y_{r} |

3 | Radius | r_{10} = r_{11} = r_{12} = r_{13} = r_{14} = r_{15} = r_{h} |

4 | Moment | J_{1} = J_{6}, J_{2} = J_{7}, J_{3} = J_{8}, J_{4} = J_{9} |

5 | Stiffness | J_{10} = J_{11} = J_{12} = J_{13} = J_{14} = J_{15} = J_{h} |

6 | Damping | k_{2} = k_{6}, k_{3} = k_{7}, k_{4} = k_{8}, k_{5} = k_{9}, k_{18} = k_{19} |

**Table 10.**The values of the parameters in Table 7.

Parameters | Value | Unit | Parameters | Value | Unit |
---|---|---|---|---|---|

m_{1} | 44,800 | kg | m_{j} | 3500 | kg |

m_{4} | 25,000 | kg | m_{7} | 25,000 | kg |

m_{8} | 90,000 | kg | J_{2},J_{7} | 0.049 | kg∙m^{2} |

J_{1},J_{6} | 7.22 | kg∙m^{2} | J_{4},J_{9} | 2158 | kg∙m^{2} |

J_{3},J_{8} | 0.1633 | kg∙m^{2} | J_{10}~J_{15} | 0.04 | kg∙m^{2} |

J_{5} | 26.45 | kg∙m^{2} | k_{1} | 8 × 106 | N/m |

k_{20} | 9 × 106 | N/m | k_{3},k_{7} | 4.26 × 104 | N/m |

k_{2},k_{6} | 1.26 × 104 | N/m | k_{4},k_{8} | 2 × 105 | N/m |

k_{r},k_{l} | 4.1 × 105 | N/m | k_{5},k_{9} | 2 × 105 | N/m |

k_{18},k_{19} | 2.5 × 105 | N/m | c_{1} | 80,000 | N∙s/m |

c_{20} | 90,000 | N∙s/m | c_{3},c_{7} | 5000 | N∙s/m |

c_{2},c_{6} | 5000 | N∙s/m | c_{4},c_{8} | 5000 | N∙s/m |

c_{r},c_{l} | 4080 | N∙s/m | c_{5},c_{9} | 2000 | N∙s/m |

r_{4},r_{9} | 0.7 | m | c_{18},c_{19} | 6.5 × 104 | N∙s/m |

r_{i} (i = 10,11,…,15) | 0.09 | m | N | 173.03 |

Performance | Value | Performance | Value |
---|---|---|---|

Phase voltage/V | 380 | Rotor resistance/Ω | 0.027 |

Power frequency/Hz | 50 | Rotor leakage inductance/H | 0.000462 |

DC voltage/V | 15 | Mutual inductance/H | 3.6 |

Rotor resistance at startup/Ω | 0.873 | Pole pairs | 4 |

Rotor resistance at steady state/Ω | 0.209 | Rotor moment/kg·m^{2} | 7.22 |

Stator resistance/Ω | 0.042 | Friction coefficient | 0.0 |

Stator leakage inductance/H | 0.0000296 |

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## Share and Cite

**MDPI and ACS Style**

Xiang, D.; Li, Y.; Zhang, Y.; Xu, F.
Experimental Study, Simulation and Analysis of the Fracture Failure of the Drum Shaft of a Casting Bridge Crane. *Electronics* **2022**, *11*, 3043.
https://doi.org/10.3390/electronics11193043

**AMA Style**

Xiang D, Li Y, Zhang Y, Xu F.
Experimental Study, Simulation and Analysis of the Fracture Failure of the Drum Shaft of a Casting Bridge Crane. *Electronics*. 2022; 11(19):3043.
https://doi.org/10.3390/electronics11193043

**Chicago/Turabian Style**

Xiang, Dong, Yan Li, Yuqing Zhang, and Feng Xu.
2022. "Experimental Study, Simulation and Analysis of the Fracture Failure of the Drum Shaft of a Casting Bridge Crane" *Electronics* 11, no. 19: 3043.
https://doi.org/10.3390/electronics11193043