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A power system structure composed of a brushless DC motor and a cycloidal reducer for electric balanced vehicle has been proposed, and the temperature of important components in this structure would be discussed. The loss generated by the cycloid reducer is negligible, it’s only need to analyze the thermal field of motor. Since the temperature change will affect the material properties of the target motor, the electromagnetic and temperature fields, involved in the motor, are selected for coupling calculation to determine whether the final temperature distribution can meet the requirements of vehicle for use.

Recently, with the growing concern of serious environmental problem caused by the internal combustion engine vehicles, the government is planning to forbid the manufacture of the internal combustion engine vehicles. Therefore, the cleaner, more efficient and sustainable cars have attracted much attention in recent years [

The self-balanced vehicle system can be thought as a simple robot driven by the motor [

The integrated driving system is consisted of a middle speed permanent-magnet DC motor and a cycloidal reducer. The motor is designed to have enough central space to accommodate the cycloidal reducer. The cycloidal disc, eccentric disc, roller gear pins and bushes, along with ring gear pins and bushes make up the cycloidal reducer, as shown in

Comparing with the motor used in existed electric balanced vehicle, the rotating speed of motor in this paper is relatively high to improve the power efficiency and power density. The cycloidal reducer has been adopted to convert the high speed of the motor to the low speed of the wheel and reduce the vibration, making the electric balanced vehicle more stabilized and safety. The axial length of system would not be increased by mounting the whole cycloidal reducer into the inner space of stator.

The driving force provided by motor is to overcome the resistance of vehicle during moving. The resistance is composed of air resistance F_{w}, rolling resistance F_{r} and slope resistance F_{s} [

where, T_{eq} is the output torque of drive motor; η_{r} is the transmission efficiency of reducer; i_{r} is the transmission ratio of reducer; r is the radius of vehicle wheel; C_{k} is the air resistance coefficient; A_{f} is the frontal area of the balanced vehicle and rider; ρ is the air density; v_{r} is relative air speed to unicycle; G is the gravity of balanced vehicle and rider; θ is the actual road slope angle; f is the rolling resistance coefficient.

The fundamental parameters of motor are determined by the torque and speed of vehicle under extreme driving conditions, the specific design data of electric balanced vehicle are listed in

The transmission ratio is chosen to be 11, the input rotating speed is 1500 r/min. This two data are substituted into formula 1, the function of torque with riding speed and road slope is shown in

Items | Parameters |
---|---|

Wheel size | 14 inches |

Unicycle weight | 30 kg |

Rider weight | 70 kg |

Rider height | 175 cm |

Pedal height | 15 cm |

Air temperature | 20˚C |

Max. riding slope | 20˚ |

The maximum motor torque required for unicycle approaches approximately 12 Nm at point A, when the unicycle is running on a maximum slope of 20˚. The output torque is calculated by:

where, P is the rated power of motor; n is the rated rotating speed of motor.

T_{eq} and n are substituted into formula 2 to calculate the maximum motor power. The rated power of motor is selected to be 2.2 kW, and then the fundamental parameters of motor are shown in

The magnetic circuit model is built to calculate the loss of motor according to the design parameters obtained in the front.

1) Core loss

At present, the most recognized and widely used in core loss calculation is the classical separation model of alternating loss proposed by A. Bertotti [

where B_{m} is the flux density in the core of motor; f is the alternating frequency of the magnetic field; k_{h} is the coefficient of hysteresis loss of motor; k_{c} is the coefficient of eddy current loss; and k_{e} is the coefficient of excess loss.

2) Copper loss

Copper loss is generated by the current through the stator winding, it is subscribed as:

where, m is the number of winding phase; I is the valid value of phase current; R is the phase winding resistance.

3) Eddy current loss

The eddy current loss produced by permanent magnet is:

Items | Parameters | Items | Parameters |
---|---|---|---|

Stator inner diameter (mm) | 187 | Notch width (mm) | 2 |

Stator outer diameter (mm) | 256 | Pole arc coefficient | 0.77 |

Axial length (mm) | 112 | Slot area (mm) | 726.1 |

Air-gap length (mm) | 1.5 | Notch height (mm) | 2.5 |

Rotor outer diameter (mm) | 174 | Notch slope height (mm) | 3.6 |

Rotor inner diameter (mm) | 152 | Filling ratio | 0.448 |

where, J_{c} is eddy current density; σ_{m} is permanent magnet conductivity; V is permanent magnet volume.

4) Mechanical loss

The mechanical loss is consisted of ventilation loss and friction loss, it’s usually obtained by empirical formula.

a) Ventilation loss

The ventilation loss caused by the rotational motion of rotor is expressed by:

where, C_{v} is coefficient of friction; ρ_{0} is density of surrounding medium; R_{r} is rotor radium; L_{r} is axial length of rotor.

b) Friction loss

The friction loss is generated by the rotating part with bearings, due to the friction between them, it is calculated by:

where, C_{b} is the friction coefficient of bearing; D_{b} is bearing diameter.

The core loss is always viewed as constant when the load is changeable, it only varies with the change of speed. So the loss variation of motor at different speed is studied in this paper.

It can be found that the core loss, eddy current loss and mechanical loss are proportional to the speed, and the infection is bigger when the speed is higher. The copper loss changes little while the rotating speed is increasing, it implies that the speed changing has almost no effect on the value of copper loss.

It’s difficult to calculate the heat transfer according to the actual situation because of the irregular shape of conductor in solving domain [

The convection coefficient of different parts in motor is displayed in

The loss brought by cycloidal reducer mechanism is mainly through fiction, the friction loss of motor is small, and the speed of reducer is relatively little. Therefore, the loss generated by reducer is ignored in the thermal calculation. Setting the environment temperature to be 295.13 K, the thermal field of motor at rated state is displayed in

Speed (rpm) | 300 | 600 | 900 | 1200 | 1500 | 1800 |
---|---|---|---|---|---|---|

Core loss (W) | 20.07 | 41.21 | 66.44 | 91.76 | 104.08 | 151.16 |

Copper loss (W) | 316.25 | 334.47 | 323.92 | 361.13 | 192.28 | 287.61 |

Eddy current loss (W) | 0.48 | 1.77 | 3.90 | 6.91 | 10.37 | 14.42 |

Mechanical loss (W) | 0.023 | 0.186 | 0.629 | 1.490 | 2.911 | 5.030 |

Items | Thermal conductivity (W/m・K) | Items | Thermal conductivity (W/m・K) |
---|---|---|---|

Air | 0.02524 | Slot insulation | 0.21 |

Copper | 386 | Axial direction of core | 8.05 |

Permanent magnet | 9 | Radial direction of core | 38.81 |

Slot wedge | 0.2 | Circular direction of core | 38.81 |

Speed (rpm) | 300 | 600 | 900 | 1200 | 1500 | 1800 |
---|---|---|---|---|---|---|

End face of stator | 24.65 | 27.08 | 29.51 | 31.94 | 34.37 | 36.80 |

End face of rotor | 59.05 | 71.92 | 81.79 | 90.11 | 97.44 | 104.06 |

End face of winding | 29.34 | 34.59 | 38.62 | 42.01 | 44.22 | 47.71 |

the highest, the second is stator core, and the lowest is rotor. Because the copper loss is the largest, the eddy current loss and core loss in rotor is small, and the convection coefficient of rotor is the maximum of all parts.

When the rotating speed is changing, the one-way coupled field results are shown in

Speed (rpm) | 300 | 600 | 900 | 1200 | 1500 | 1800 |
---|---|---|---|---|---|---|

Stator winding | 38.97 | 39.03 | 39.39 | 44.60 | 24.03 | 34.25 |

Stator core | 18.96 | 22.68 | 25.09 | 30.07 | 15.20 | 20.59 |

Rotor core | 9.93 | 10.30 | 10.68 | 12.27 | 7.41 | 9.54 |

Permanent magnet | 10.71 | 11.17 | 11.62 | 13.44 | 8.41 | 10.51 |

Taking the influence of temperature change to material property into consideration, the copper is chosen to discuss the difference between this analytic way and the former one. The influence of temperature in the copper is:

where, R is the resistance value when the temperature is t; R_{c} is the resistance value when the temperature is t_{c}; t_{c} is the initial temperature, it’s set to be 295.13 K; α_{c} is the resistance coefficient when the temperature is t_{c}.

Based on the one-way coupled field, changing the material properties of winding according to formula 8. The two-way interaction analysis is carried out when the motor is rotating at rated speed, the result is shown in

It can be found that the temperature of each part has increased considering the influence of temperature on the resistance value. In the two-way coupled field, the temperature of winding rises 1.8 K, stator rises 0.53 K, rotor and permanent magnet rises 0.2 K. Because the copper loss of winding increases, the rest has no obvious variation at rated condition.

Then

It can be found that the trend of temperature variation in

A power structure consisting of a cycloidal reducer and a permanent magnet brushless DC motor has been proposed in paper, and this structure is applied in

Speed (rpm) | 300 | 600 | 900 | 1200 | 1500 | 1800 |
---|---|---|---|---|---|---|

Stator winding | 41.11 | 45.08 | 45.08 | 51.03 | 25.88 | 38.31 |

Stator core | 21.09 | 24.97 | 27.43 | 32.56 | 18.73 | 22.10 |

Rotor core | 11.07 | 11.32 | 11.71 | 13.20 | 7.61 | 10.32 |

Permanent magnet | 11.93 | 12.26 | 12.68 | 14.51 | 8.64 | 11.13 |

grade | A | E | B | F | H |
---|---|---|---|---|---|

Allowed temperature rising (K) | 105 | 120 | 130 | 155 | 180 |

the electric balanced vehicle. The permanent magnet brushless DC motor is chosen as object to analyze and calculate the basic loss. The coupled field analysis method is used to analyze the electromagnetic field and temperature field inside the motor to obtain the motor temperature. The results show that the temperature of motor is in the safety range, won’t do damage to the motor.

The authors declare no conflicts of interest regarding the publication of this paper.

Wang, B.G., Li, J.G. and Ai, D. (2019) Temperature Research of Permanent Magnet Brushless DC Motor for Electric Balanced Vehicle. World Journal of Engineering and Technology, 7, 1-9. https://doi.org/10.4236/wjet.2019.74B001