# Vibration Analysis and Parameter Optimization of the Longitudinal Axial Flow Threshing Cylinder

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Structure and Working Process of a Full Feeding Rice Combine Harvester

#### 2.2. Modal Analysis and Test of Threshing Cylinder

#### 2.2.1. Free Modal Analysis of Finite Elements

^{3}, and yield strength σ

_{s}= 235 Mpa. The three-dimensional solid model of the threshing cylinder was saved in the STP format into the finite element analysis software ANSYS Workbench. The meshing was performed using the ANSYS mesh module, and the grid quality was controlled by the sizing command. In view of the thin plate structure of the screw feeding blade, the Shell 63 grid element was selected as the element type.

#### 2.2.2. Free Modal Test

_{r}and all coefficients ${\alpha}_{r}$ and ${\beta}_{r}$. The corresponding modal shapes can be obtained by substituting them into Equation (9).

#### 2.2.3. Constrained Modal Analysis of Finite Element

#### 2.3. Analysis of Excitation Source

#### 2.4. Optimization Design of Threshing Cylinder

#### 2.4.1. Optimization Method

#### 2.4.2. Test Design

#### 2.5. Characteristic Analysis of Optimized Threshing Cylinder

#### 2.5.1. Finite Element Analysis of Optimized Threshing Cylinder

_{N}at both ends of the bearing (ignoring the effect of air resistance and bearing friction), and the force is shown in Figure 4.

_{N}= 603.97 N.

^{−6}s, which is 10% of the Rayleigh time step. The total simulation time was 5 s, and the data auto-iteration save time was 0.01s. The EDEM discrete element method was used to simulate the force between crops and the threshing cylinder. Different forces were loaded on the nail teeth in ANSYS, and a rotation speed of 1300 r/min was applied to the threshing cylinder. The EDEM simulation of a threshing cylinder is shown in Figure 6.

^{6}.

#### 2.5.2. Comparative Analysis of Field Experiment

^{2}. The selected experimental field was flat. The forward distance of each test was 100 m, and 20 m was reserved in front of the test area to ensure that the harvester entered the threshing cylinder with a stable feeding rate (16.2 t/h) before each test. The 50-s test data in the test area were recorded by the signal acquisition instrument, and the sampling frequency was set at 2.56 khz. Each test was repeated three times.

## 3. Results and Discussion

#### 3.1. Threshing Cylinder Vibrational Characteristic Analysis

#### 3.1.1. The Results of the Finite Element Free Modal Analysis

#### 3.1.2. Comparison between Free Modal Analysis and Free Modal Test

#### 3.1.3. The Results of the Finite Element Constrained Modal Analysis

#### 3.2. Resonance Analysis of Threshing Cylinder

#### 3.3. Analysis of the Results of Optimization Design

_{1}, mass fraction x

_{2}, first-order natural frequency y

_{1}, maximum stress y

_{2}, and maximum deformation y

_{3}were established, respectively. The regression equation is shown in Equation (19).

#### 3.4. Analysis of Results of Threshing Cylinder Characteristics after Optimization

#### 3.4.1. Finite Element Analysis Results of Threshing Cylinder after Optimization

^{6}cycles, and the fatigue fracture did not occur in the optimized area first. According to the analysis of Figure 16b, the most vulnerable part of the threshing cylinder was the end of threshing cylinder shaft, and the minimum safety factor was 1.1; therefore, the overall design was safe. In conclusion, the reconstructed threshing cylinder met the design requirements.

#### 3.4.2. Comparative Analysis Results of Field Experiment

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Structure of a full feeding rice combine harvester. (

**a**) Overall structure; (

**b**) threshing and cleaning system. 1. Divider; 2. Cutter; 3. Reel; 4. Screw pusher; 5. Cab; 6. Tilt conveyor; 7. Grain unloading system; 8. Power chassis; 9. Threshing cylinder; 10. Concave plate; 11. Sieve; and 12. Fan.

**Figure 2.**Three-dimensional solid model of a threshing cylinder. 1. Screw feeding blade; 2. Barrel; 3. Separating bar; 4. Nail tooth; 5. Axis; and 6. Fixing plate.

**Figure 3.**Free modal test. (

**a**) Test schematic diagram; (

**b**) test field; 1. Threshing cylinder; 2. Acceleration sensor; 3. Force hammer; 4. Data acquisition instrument; 5. Computer; 6. Signal transmission line; and 7. Rubber block.

**Figure 5.**EDEM 2018 simulation model. (

**a**) Discrete element model of single grain; (

**b**) discrete element model of straw.

**Figure 7.**Field experiment. A and B are the measuring points; 1. Data acquisition instrument; 2. Mobile power; 3. Computer; 4. Data transmission line; 5. Concave; and 6. Acceleration sensor.

**Figure 8.**Free modal analysis of the threshing cylinder. (

**a**) First-order modal shape (37.94 Hz); (

**b**) second-order modal shape (45.38 Hz); (

**c**) third-order modal shape (70.09 Hz); (

**d**) fourth-order modal shape (93.87 Hz); (

**e**) fifth-order modal shape (108.89 Hz); and (

**f**) sixth-order modal shape (133.71 Hz).

**Figure 9.**Constrained modal analysis of threshing cylinder. (

**a**) First-order modal shape (21.08 Hz); (

**b**) second-order modal shape (46.50 Hz); (

**c**) third-order modal shape (68.32 Hz); (

**d**) fourth-order modal shape (90.11 Hz); (

**e**) fifth-order modal shape (110.93 Hz); and (

**f**) sixth-order modal shape (131.66 Hz).

**Figure 10.**Optimization state of the fixed plate. (

**a**) Removal of 23.8% mass in the optimized area; (

**b**) Removal of 30% mass in the optimized area; (

**c**) removal of 45% mass in the optimized area; (

**d**) removal of 60% mass in the optimized area; (

**e**) removal of 66.2% mass in the optimized area.

**Figure 11.**Influence of the hollow diameter and mass fraction on the first natural frequency. (

**a**) Response surface; (

**b**) contour map.

**Figure 12.**Influence of the hollow diameter and mass fraction on the maximum stress. (

**a**) Response surface; (

**b**) contour map.

**Figure 13.**Influence of the hollow diameter and mass fraction on the maximum deformation. (

**a**) Response surface; (

**b**) contour map.

**Figure 14.**Model reconstruction. (

**a**) Optimal condition of 57.62% mass fraction of fixed plate removal; (

**b**) reconstructed threshing cylinder model.

**Figure 15.**Modal analysis and static analysis of reconstructed threshing cylinder. (

**a**) First-order modal shapes (26.06 Hz); (

**b**) stress cloud; (

**c**) deformation cloud.

**Figure 16.**Fatigue analysis. (

**a**) The life of the reconstructed threshing cylinder; (

**b**) the safety factor of the reconstructed threshing cylinder.

**Figure 17.**Spectrum analysis. (

**a**) Before optimization of measuring point A; (

**b**) after optimization of measuring point A; (

**c**) before optimization of measuring point B; (

**d**) after optimization of measuring point B.

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

Overall dimension/(mm × mm × mm) | 5130 × 2470 × 2750 |

Rated power/(kW) | 75 |

Track width/(mm) | 450 |

Header width/(mm) | 2000 |

Ground clearance of chassis/(mm) | 672 |

Threshing cylinder/(mm × mm) | Φ620 × 1960 |

Sieve/(m^{2}) | 1.24 |

Reel diameter/(mm) | Φ900 |

Feed rate/(t/h) | 16.2 |

Working speed/(km/h) | 0~4.8 |

Parameter | Values |
---|---|

Cylinder outer diameter/(mm × mm) | Φ620 × 1960 |

Separating bar/(mm × mm) | Φ30 × 1800 |

Nail tooth/(mm × mm) | Φ14 × 60 |

Nail tooth spacing/(mm) | 40 |

Fixing plate/(mm × mm) | Φ500 × 12 |

Axis/(mm × mm) | Φ45 × 2150 |

Order | Instrument | Parameter |
---|---|---|

1 | Computer | / |

2 | INV3018C 8-channel 24-bit high precision data acquisition instrument | Parallel channel: 8 Maximum sampling frequency: 102.4 kHz A/D resolution: 24 bits |

3 | LC-2D force hammer | Measuring range: 0–2 kHz Charge reference sensitivity: 4 pC/N Linearity: <1% |

4 | AY100I piezoelectric acceleration sensor | Sensitivity: 100 mV/g Maximum frequency: 10,000 Hz Resolution: 0.0002 |

5 | DASP-10 Modal analysis system | / |

Level | Hollow Diameter x_{1}/mm | Mass Fraction x_{2}/% |
---|---|---|

−1.414 | 8 | 23.8 |

−1 | 10 | 30 |

0 | 15 | 45 |

1 | 20 | 60 |

Material | Poisson Ratio | Shear Modulus/MPa | Density/kg·m^{−3} | Restitution Coefficient | Static Friction Coefficient | Dynamic Friction Coefficient |
---|---|---|---|---|---|---|

Grain | 0.33 | 2.60 | 1350 | 0.26 (Grain–Grain) | 0.93 (Grain–Grain) | 0.01 (Grain–Grain) |

0.23 (Grain–Straw) | 0.80 (Grain–Straw) | 0.01 (Grain–Straw) | ||||

Straw | 0.42 | 1.00 | 100 | 0.20 (Straw–Straw) | 0.85 (Straw–Straw) | 0.01 (Straw–Straw) |

0.30 (Straw–Threshing cylinder) | 0.76 (Straw–Threshing cylinder) | 0.01 (Straw–Threshing cylinder) | ||||

Threshing cylinder | 0.30 | 700 | 7850 | 0.50 (Grain–Threshing cylinder) | 0.52 (Grain–Threshing cylinder) | 0.01 (Grain–Threshing cylinder) |

Order | Finite Element Free Modal Analysis | Modal Test | Error/% | ||
---|---|---|---|---|---|

Calculation Frequency/Hz | Modal Shape | Test Frequency/Hz | Modal Shape | ||

1 | 37.94 | Overall bending | 38.26 | Consistent | 0.84 |

2 | 45.38 | Overall bending | 44.10 | Consistent | 2.90 |

3 | 70.09 | Bending of separating bar and nail teeth deformation | 69.37 | Consistent | 1.04 |

4 | 93.87 | Overall bending | 98.45 | Consistent | 4.65 |

5 | 108.89 | Overall bending | 111.06 | Consistent | 1.95 |

6 | 133.71 | Overall torsion | 140.23 | Consistent | 4.65 |

Rotating Parts | Speed/(r/min) | Theoretical Excitation Frequencies/(Hz) |
---|---|---|

Engine | 2200–2400 | 36.67–40 |

Fan | 1050 | 17.50 |

Tilt conveyor axis | 800 | 13.33 |

Sieve axis | 450 | 7.50 |

Screw pusher | 230 | 3.83 |

Reel | 60 | 1.00 |

Order | Test Factors | Performance Measures | |||
---|---|---|---|---|---|

Hollow Diameter x _{1}/mm | Mass Fraction x _{2}/% | First-Order Natural Frequency y _{1}/Hz | Maximum Stress y _{2}/MPa | Maximum Deformation y _{3}/mm | |

1 | −1 (10) | −1 (30) | 43.64 | 107.32 | 2.37 |

2 | 1 (20) | −1 | 36.29 | 120.48 | 2.64 |

3 | 1 | −1 | 21.34 | 310.85 | 13.98 |

4 | 1 | 1 (60) | 29.68 | 106.43 | 2.97 |

5 | −1.414 (8) | 0 (45) | 24.15 | 321.40 | 13.23 |

6 | 1.414 (22) | 0 | 33.38 | 104.15 | 3.55 |

7 | 0 | −1.414 (23.8) | 44.90 | 112.66 | 0.36 |

8 | 0 | 1.414 (66.2) | 22.66 | 274.13 | 10.92 |

9 | 0 | 0 | 43.93 | 330.78 | 13.51 |

10 | 0 | 0 | 44.18 | 332.60 | 13.41 |

11 | 0 | 0 | 43.90 | 327.31 | 12.95 |

12 | 0 | 0 | 43.74 | 324.90 | 13.36 |

13 | 0 | 0 | 43.97 | 338.46 | 13.22 |

14 | 0 | 0 | 42.62 | 332.07 | 12.89 |

15 | 0 | 0 | 43.58 | 323.56 | 13.47 |

16 | 0 | 0 | 44.28 | 331.85 | 13.33 |

Index | Source of Variance | Sum of Squares | Degree of Freedom | Mean Square Value | F-Value | p-Value |
---|---|---|---|---|---|---|

y_{1} | Model | 1120.93 | 5 | 224.19 | 89.10 | <0.0001 |

Residual | 25.16 | 10 | 2.52 | |||

Deviance | 23.29 | 3 | 7.76 | 29.06 | 0.0003 | |

Error | 1.87 | 7 | 0.27 | |||

y_{2} | Model | 152,700 | 5 | 30,545.74 | 55.25 | <0.0001 |

Residual | 5528.31 | 10 | 552.83 | |||

Deviance | 5367.24 | 3 | 1789.08 | 77.75 | <0.0001 | |

Error | 161.07 | 7 | 23.01 | |||

y_{3} | Model | 401.09 | 5 | 80.22 | 110.84 | <0.0001 |

Residual | 7.24 | 10 | 0.72 | |||

Deviance | 6.86 | 3 | 2.29 | 42.32 | <0.0001 | |

Error | 0.38 | 7 | 0.054 |

Peak Point | Measuring Point A | Peak Point | Measuring Point B | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

X Direction | Y Direction | Z Direction | X Direction | Y Direction | Z Direction | ||||||||

Frequency/Hz | Amplitude/(m/s^{2}) | Frequency/Hz | Amplitude/(m/s^{2}) | Frequency/Hz | Amplitude/(m/s^{2}) | Frequency/Hz | Amplitude/(m/s^{2}) | Frequency/Hz | Amplitude/(m/s^{2}) | Frequency/Hz | Amplitude/(m/s^{2}) | ||

P1 | 112.50 | 15.42 | 42.86 | 16.18 | 72.15 | 18.00 | V1 | 8.15 | 12.18 | 40.02 | 13.98 | 20.54 | 15.22 |

P2 | 119.46 | 12.80 | 55.40 | 10.20 | 28.60 | 16.85 | V2 | 38.27 | 11.23 | 42.75 | 10.20 | 52.20 | 10.18 |

P3 | 76.45 | 9.06 | 48.92 | 9.76 | 45.26 | 15.57 | V3 | 32.80 | 10.15 | 38.27 | 5.60 | 43.63 | 9.12 |

P4 | 185.00 | 7.48 | 120.10 | 5.12 | 40.20 | 11.44 | V4 | 50.58 | 8.67 | 83.00 | 3.85 | 32.06 | 7.75 |

P5 | 20.40 | 6.15 | 100.53 | 4.83 | 42.55 | 9.80 | V5 | 20.00 | 5.80 | 100.25 | 2.27 | 38.70 | 6.96 |

Q1 | 25.37 | 3.76 | 40.28 | 3.00 | 45.69 | 3.86 | W1 | 50.27 | 3.40 | 60.34 | 4.43 | 60.00 | 3.96 |

Q2 | 52.70 | 2.88 | 83.65 | 0.66 | 56.80 | 2.27 | W2 | 40.00 | 2.76 | 68.70 | 2.31 | 112.55 | 1.02 |

Q3 | 45.48 | 2.36 | 96.57 | 0.44 | 59.44 | 2.10 | W3 | 43.25 | 1.72 | 38.68 | 1.33 | 135.28 | 0.94 |

Q4 | 38.55 | 1.86 | 76.84 | 0.37 | 113.20 | 1.17 | W4 | 70.58 | 1.46 | 71.25 | 1.17 | 150.30 | 0.77 |

Q5 | 40.00 | 1.57 | 117.90 | 0.32 | 117.58 | 1.00 | W5 | 74.20 | 1.05 | 82.50 | 0.84 | 103.65 | 0.71 |

_{1–5}and Q

_{1–5}are the peak points of measuring point A before and after the optimization of threshing cylinder, V

_{1–5}and W

_{1–5}are the peak points of measuring point B before and after the optimization of the threshing cylinder.

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**MDPI and ACS Style**

Wang, J.; Xu, C.; Xu, Y.; Qi, X.; Liu, Z.; Tang, H.
Vibration Analysis and Parameter Optimization of the Longitudinal Axial Flow Threshing Cylinder. *Symmetry* **2021**, *13*, 571.
https://doi.org/10.3390/sym13040571

**AMA Style**

Wang J, Xu C, Xu Y, Qi X, Liu Z, Tang H.
Vibration Analysis and Parameter Optimization of the Longitudinal Axial Flow Threshing Cylinder. *Symmetry*. 2021; 13(4):571.
https://doi.org/10.3390/sym13040571

**Chicago/Turabian Style**

Wang, Jinwu, Changsu Xu, Yanan Xu, Xin Qi, Ziming Liu, and Han Tang.
2021. "Vibration Analysis and Parameter Optimization of the Longitudinal Axial Flow Threshing Cylinder" *Symmetry* 13, no. 4: 571.
https://doi.org/10.3390/sym13040571