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This paper analyzes the structure and transmission principles of a modulation permanent magnet gear transmission. Its 3D data model is built based on the known optimized parameters from research team. Its structure of the harmonic response is analyzed and discussed under the software ANSYS. The displacement response and the initial 6 order response frequency and phase angle are obtained. The change rule of these responses is known under the forced vibration.

The traditional transmission method is the transmission of contacting with gears directly. It is designed based on the dynamics, hydraulics, pneumatics and mechanical transmission theory. Due to the problems of low transmission accuracy, friction loss, vibration, noise, energy loss of the action valve and many other flaws, transmission accuracy and efficiency are affected seriously [

According to the theory of classical mechanics, the general equation of object dynamics [

where: [M] is mass matrix, [C] is damping matrix, [K] is stiffness matrix,

In harmonic response analysis,

The harmonic response analysis is an analysis of the steady vibration of a structure or system under sinusoidal excitation; that’s forced vibration analysis. It can calculate the displacement response amplitude, frequency and phase. It can also do some optimization and improvement on transmission.

The magnetic field modulation technique is based on the basic structure of the internal mesh permanent magnetic gear, which can modulate the permanent magnetic field to achieve the goal of non-contact transmission [

In the structure, the internal mesh gear mainly includes:

1) A high-speed internal rotor which consists of internal rotor permanent magnet and the inner yoke.

2) A low-speed external rotor which consists of external rotor permanent magnet and the outer yoke.

3) The adjustable magnetic interleaved ring which consists of high permeability material and non-magnetic materials. Its function is modulation magnetic field of the inside and outside rotor.

4) The inner and outer layers are a air gap between the adjacent rotors. Its assembly structure is shown in

According to the theory of electromagnetic field, in the modulation permanent magnet transmission after modulated the magnetic field, the inside and outside permanent magnet ring will produce a space magnetic flux density harmonics and the magnetic flux density harmonic number is [

where: p is the number of pole pairs of rotor permanent magnet, n_{s} is the number of pole blocks of magnetic ring tone.

The angular velocity of space magnetic flux density harmonics is:

where:

In the structure the modulation magnetic ring is fixed, the internal and external permanent magnet ring rotates so as to achieve torque transmission. Therefore, in the formula (4)

where: the negative “−” represents that the rotation direction of internal and external permanent magnet rotors is opposite. n_{out} is the number of pole pairs of external permanent magnet ring, n_{in} is the number of pole pairs of internal permanent magnet ring. According to the transmission ratio formula (5), we can know that the transmission ratio of equipment only related to the number of pole pairs of inside and outside permanent magnet ring, but not to the number of pole plates of adjustable magnetic ring.

Permanent magnet material is NdFeB, which is the linear demagnetization curve (NdFe30). The main parameters and constant parameters are shown in ^{3}.

The main structural parameters of finite element model of the gear transmission are selected from the optimized parameter data by research team designing shown as

According to

Due to using the fixed adjustable magnetic ring, the internal and external permanent magnet ring rotate to transmit the torsion. The inner yoke of high speed inner rotor and inner ring permanent magnet piece are overall connected as a part as well as the external yoke of low speed external rotor and external ring permanent magnet piece. Because of the action of magnetic field force, the structure between the adjustable magnetic ring and the inner ring permanent magnet piece as well as the adjustable magnetic ring and external ring permanent magnet piece becomes a non-contact structure. So the contact type of the contact region I and IV is chosen as “bonded” and contact region II and III is chosen as “frictionless”.

Then outline shape of this structure is simple and it fits the adaptive mesh techniques. We choose tetrahedron as mesh type and mesh size is from “Sizing―Relevance Center―Fine”. The final geometry mesh model is shown as

Parameters | Number |
---|---|

Permanent magnet remanence/T | 1.10 |

Permanent magnet coercive force/KA/m | −838.00 |

Permeability of vacuum | 4π × 10^{−7 } |

Relative permeability | 1.0997 |

Magnetization/A/m | −8.9 × 10^{5 } |

Permanent magnet conductivity/S/m | 625,000 |

Symbol | Parameters | Number |
---|---|---|

n_{in} | Number of pole pairs of internal permanent magnet piece | 4 |

n_{s} | Number of pole plates of adjustable magnetic ring | 27 |

n_{out} | Number of pole pairs of external permanent magnet piece | 23 |

r_{y}_{in1} | Inner diameter of the inner yoke/mm | 45 |

r_{p}_{in1} | Inner diameter of permanent magnet piece of inner ring/mm | 54 |

r_{p}_{in2} | External diameter of permanent magnet piece of inner ring/mm | 68 |

r_{m}_{1} | Inner diameter of adjustable magnetic ring/mm | 69 |

r_{m}_{2} | External diameter of adjustable magnetic ring/mm | 75 |

r_{p}_{out1} | Inner diameter of permanent magnet piece of external ring/mm | 76 |

r_{p}_{out2} | External diameter of permanent magnet piece of external ring/mm | 82 |

r_{y}_{out2} | External diameter of the external yoke/mm | 85 |

l | Axial size/mm | 40 |

The two end planes of the adjustable magnetic ring are restricted rigidly. In the overall frame of axes, the freedom of adjustable magnetic ring is ensured as zero, that is U_{x} = 0, U_{y} = 0, U_{z} = 0. The definite function torsion is acted on the high speed inner rotor, which is the inner yoke surface. It is shown in

According to the related parameters, we can obtain the modal responses of the structure. Because the object of actual analysis is an infinite dimension, so its modality has infinite order, but the frequency of the load which acted on the gears is generally lower. The lower order modality plays a great role in the gear vibration, but higher order modality has a little effect on the gear vibration. Based on these reasons, in this paper we choose the initial six modality of vibration to analyze. The value of modal frequency is shown in

The harmonic response analysis can be used to determine the steady state response of a linear structure which is

Modality | Frequency [Hz] |
---|---|

1 | 102.62 |

2 | 203.07 |

3 | 251.06 |

4 | 256.24 |

5 | 298.46 |

6 | 457.46 |

under a changed load by the harmonic rules. In this paper, the harmonic response of a modulation NdFeB permanent magnetic transmission equipment is analyzed and its response change regularity. The maximum displacement response amplitude of the first-order modality is maximum in the entire frequency. It is 0.024501 mm and the maximum displacement response amplitude is smaller than the fit clearance of inner and external ring of the permanent magnet gear transmission. In design, according to the response change regularity, designer can better analyze the stress which corresponds to the peak frequency and predicts the operating stability and continuous dynamic of the system. Thus, we can judge the system whether it will be non-effectiveness which is caused by resonance, fatigue or other forced vibration in operation. So in practical design or application, we need to try to control the first-order modal displacement response amplitude as much as possible so that the equipment and operation system can be ensured to have better reliability and stability.

This project is supported by National Natural Science Foundation of China (No. 51305472), Natural Science Foundation of Chongqing CSTC, China (CSTC2013yykfB0184) and the Postgraduate Education Innovation Foundation of Chongqing Jiaotong University under Grant 20120108.