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This paper presents a dynamic simulator of the electromechanical coupling start-up of a ball mill. The electromechanical coupling model based on the dynamic model of the ball mill, the characteristic equation of the clutch, and the dynamic model of the induction motor is established. Comparison between the simulation results of angular speed, load torque and current obtained from the model, and the experimental results is conducted to validate the correctness of these simulation results. Results show that the simulation results of the electromechanical model are highly consistent with the experimental results. Two indexes are proposed for evaluation. Finally, a 4500 kW ball mill is used to analyse the start-up process with different operation parameters of the air clutch. The effect of the engagement time and the pressure of the air clutch on the torque, current, and shock extent is analysed. Moreover, the optimum inflation time is determined.

Ball mill is an important equipment in the field of mineral size reduction. Unlike semiautogenous (SAG) mills that operate with adjustable frequency drives, the ball mills work at a fixed speed [

The establishment and validation of the tumbling mill models have been widely conducted. Morrell [

The drive motor of the large ball mill is usually required to start with a reduced-voltage method [

Figure

The schematic diagram of a ball mill driveline.

According to Figure

When the rotational speeds of the clutch are synchronised, i.e.,

The large ball mill commonly uses a double-row heavy-duty air clutch. The pressure of the friction surface is determined by the structure of the clutch. For the radial air clutch, the radial pressure generated by the compressed air can be calculated by the following formula:

After the air tube is inflated, it expands in the radial direction and overcomes the force of the return spring. As a result, the friction plate can hold the hub. Therefore, the pressing force is

Figure

Curve of pressure versus time.

The clutch inflation time is generally around 10 s, and the maximum friction torque of the clutch is generally greater than the maximum load torque of the ball mill. Therefore, this study assumes that the air pressure characteristics of the clutch are as follows:

The time from the start of the inflation to the contact (but not sliding) of the driving and driven discs is generally less than 3 s. The inflation time is usually from 6 s to 12 s. The relationship between clutch friction torque and pressing force can be expressed as

The radius and angle position of the mill charge centre of mass is commonly used for the ball mill dynamic model during start-up. This model considers that the mill load maintains its resting shape and that the mill is lifted to a certain angle depending on the mill speed and existing operating conditions during its rotation [

As shown in Figure _{load} is the mass of charge in the barrel,

Scheme of circular sector load model [

The equation of state is established in Parker’s synchronous coordinate system. When the rotor is a cage-type winding, an internal short circuit exists. The flux equation can be expressed as

The rotor current equation can be expressed as

The torque equation can be expressed as follows:

According to formulas (_{s}_{r}) is the leakage coefficient of the motor.

From the dynamic equation (

In accordance with the mechanical and induction motor dynamic models, the electromechanical coupling dynamic equation of the ball mill can be expressed as follows:

The evaluation of the start-up process of the ball mill aims to ensure successful start-up without the drive or clutch protection device that causes the mill to stop. Considering this condition, the start-up process is made as short as possible to reduce friction disc wear and heat generation. Therefore, the quantitative evaluation indexes of the start-up process of the ball mill can be set as the shock extent and motor protection to avoid vibration damage and tripping of the power.

The simulation is based on a large ball mill with the parameters shown in Table

Parameters of the ball mill.

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

The maximum diameter | mm | 5500 |

Barrel length | mm | 8500 |

Critical speed | r/min | 18.4 |

Loading mass | t | 60+340 |

Gear ratio | 14.6 | |

Effective diameter | mm | 5300 |

Working speed | r/min | 13.7 |

Filling ratio | 30%-38% | |

Mass of the tumbling parts | t | 386 |

Parameters of the drive motor.

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

Rated power | kW | 4500 |

Rated speed | r/min | 200 |

Power factor | 0.857 | |

Stator and rotor connection | Y | |

Rated frequency | Hz | 50 |

Rated voltage | V | 6000 |

Rated Current | A | 303 |

Effectiveness | 92.6% |

Parameters of the air clutch.

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

The maximum friction torque | Nm | 246645 |

Rated pressure | MPa | 0.56 |

Moment of inertia | kg·m^{2} | 852.3 |

Friction plate thickness | mm | 17 |

The minimum hub diameter | mm | 1518 |

The maximum speed | r/min | 520 |

Mass | kg | 4854 |

Friction area | cm^{2} | 18060 |

Air tube volume | dm^{3} | 32.8 |

Centrifugal loss | bar/rpm^{2} | 10.01×10-6 |

The inflation time range of the air clutch is generally from 6 s to 12 s. In accordance with the actual situation, this section sets the inflation time (

Figure

The angular speeds versus time.

The angular speeds of different

Figure

The rotation angle of the barrel versus time.

Figure

Effect of

The theoretical friction toque and the load torque versus time.

Figure

Figure

Effect of

Figure ^{3} (

Effect of

The simulation results show that

The angular speed of the clutch engagement too fast.

Figure

The barrel rotation angle of the too short inflation time.

Figure

The electromagnetic torque of the too short inflation time.

Figure

The theoretical friction torque and the load torque of the too short inflation time.

Figure

The current of the too short inflation time.

Figure ^{3} (^{3} at 1.1 s. The second peak is 41 rad/s^{3} at 2.3 s. The shock extent is twice as large as

The shock extent of the too short inflation time.

The angular speed of the too long inflation time.

Figure

The barrel rotation angle of the too long inflation time.

Figure

The theoretical friction torque and load torque of the too long inflation time.

Figure

The current of the too long inflation time.

Figure ^{3}. When ^{3}. When ^{3}. Compared with those in

The shock extent of the too long inflation time.

The results of this section show that the inflation time significantly affects the heat generation of the friction discs and the duration of the current. The change in the operation parameters of the clutch should be strictly avoided after the optimal inflation time of the air clutch is determined.

This section assumes that the pressure of the air tank has changed. Therefore, the maximum friction torque (

Figure

Effect of

Figure

The rotation angle of the barrel versus time.

Figure

The theoretical friction torque and the load torque versus time.

Figure

Effect of

Effect of

Figure

In this study, the electromechanical coupling dynamic model of a single-motor edge-driven ball mill is established. Then, the start-up process of a large-scale ball mill is simulated. The electromechanical performance of the ball mill is evaluated in terms of the shock extent and current. The conclusions based on the observations, calculations, and analyses are as follows.

Changes in the parameters of the air clutch can cause the changes in the clutch engagement. In the friction process, the angular speed of the driven disc may decrease during the increase of the synchronous rotational speed. The reason for the fluctuation can be explained as follows: at this moment, the friction torque that the air clutch can transmit is smaller than the torque generated by the rotation of the ball mill. However, as long as the barrel does not reverse and the rotation angle keep increasing, the angular speed of the driven disc fluctuation will not cause failure of the ball mill start-up.

The shock extent is too large when

When the air pressure of the clutch increases, which is similar to the decrease in

The surface area of friction

The width of the air tube

The sum of the centrifugal forces

Reduction ratio

The moment of inertia of motor rotor and clutch driving disc

The moment of inertia of the pinion shaft

The moment of inertia of the rotary sections and materials of the ball mill

Shock extent

The isentropic exponent

A constant which is related to the inflation speed

The mass of charge in the barrel

The pressing force

The number of pole pairs

The air tank pressure

The initial pressure

The radial pressure generated by the compressed air

The minimum working pressure

The force of the return spring

The minimum radius of the air tube

The distance between mill centre and the centroid of the charge

The rotation resistance coefficient of the drive motor

The effective cross-sectional area of the inflation valve

Rotation direction of the ball mill

Inflation time of the air clutch

Friction torque

Load torque

The electromagnetic time constant of the rotor

The electromagnetic torque

The air tube volume

The deflection angle of the mill

The coefficient of frictional torque

The leakage coefficient of the motor

Time constant.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this article.

This work was supported by the National Natural Science Foundation of China (Grant no. 51775225) and the Shanxi Province Coal Basic Key Technologies Research and Development Program (Grant no. MJ2014-02).