Understanding Eccentricity Effects on Stator Tooth Forces for eNVH Analysis

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HOME / Applications / Double-Sided Flat PM Linear Synchronous Motor Analysis Using EMWorks2D

The increase in the demand of linear motors is principally driven by the replacement of traditional mechanical (ball screws, gear trains, cams), hydraulic, or pneumatic linear motion systems in manufacturing processes with direct electromechanical drives. Linear motors are also used in various applications such as high-speed maglev transport and elevator hoisting.

Linear synchronous motors (LSMs) can be classified as follows,- Flat (planar) or Tubular (cylindrical)
- Single-sided or Double-sided
- Slotted or Slotless
- Iron-cored or Air-cored
- Transverse-flux or Longitudinal-flux

In this application note a 3-phase double-sided FLSM motor prototype, illustrated in Figure 1, will be analyzed using EMWorks2D inside Solidworks.

Fig. 1. Flat Slotted Iron Cored Linear Synchronous Motor (FLSM) Model

The materials used in the FLSM model are shown in Table 1. The stainless steel 1010 is used for the core ferromagnetic material and the rare-earth sintered NdFeB grade-35 characterized with high coercivity and remanence are used as magnets. Hence, this would highly improve the performance of the motor.

Motor Componen | Material |
---|---|

Armature coil | Copper |

Flat ferromagnetic bar | Stainless steel 1010 |

Ferromagnetic core | Stainless steel 1010 |

Permanent magnet (PM) | N35 |

Non ferromagnetic core | Aluminum |

Table 1. FLSM Material

As shown in Figure 2, the coercivity direction is chosen so that the magnetic flux will be longitudinal from the magnets, the ferromagnetic flat bars will play the role of a magnetic flux conducting material so they will transform the direction of flux to be transversal if a ferromagnetic core is sufficiently close to them.

Fig. 2. Coercivity Direction and Winding Layout

The distance is defined as a mate between the mover (magnets + ferromagnetic bars) and the stationary component, which is in this case the armature (ferromagnetic core + armature winding) as shown in Figure 3.

Fig. 3. Distance Definition

To perform an open circuit or no-load simulation, the armature winding should be set to current-driven mode inside the EMWorks2D winding editor and set the current magnitude to zero, the simulation time and time step are chosen so that the mover displacement is equal to two times the pole pitch. The other parameters are listed as shown in Table 2.

Parameter | Value |
---|---|

Simulation time | 0.03 s |

Time step | 0.0005 s |

Velocity | 1 m/s |

Distance | 30 mm |

Initial position | 0 mm |

Number of turns per phase | 280 |

Table 2. Open Circuit Simulation Settings

Fig. 4. Detent Force

Fig. 5. Flux Linkage

Fig. 6. Induced Voltage

Fig. 7. Flux Density

Fig. 5. Flux Linkage

Fig. 6. Induced Voltage

Fig. 7. Flux Density

For the on-load test, the applied current values depend on the distance value(x) of the mover, the moving range will be set to a pole pitch value of 15 mm and the peak current value is 8 A, linear velocity will be set to 1 m/s. The current equations for all three phases are as shown below,

Where is the load angle, to get the maximum thrust, different simulations were performed with

Linear velocity depends only on frequency and pole pitch value according to the equation,

Similarly, the values of the current are obtained at a 33Hz frequency.

Fig. 8. Input Current Versus Distance

Fig. 9. Thrust

The simulation results obtained are tabulated as shown in Table 3.

Parameter | Value |
---|---|

Maximum force, f_{max} |
241.34 N |

Minimum force, f_{min} |
160.01 N |

Average force, f_{av} |
196.10 N |

Force ripple coefficient, k_{r} |
0.414 |

Maximum detent cogging force | 25.66 N |

Table 3. Simulation Results

The force ripple coefficient is computed as:

Fig. 10. On- Load Flux Density Plot

The FLSM dynamic simulation parameters are shown in Table 4. The armature currents are the same as the on-load simulation and the speed values are computed using the dynamic Newtonian equation

Parameter | Value |
---|---|

Mover mass (kg) | 1 |

Dumping Factor (N-s/m) | 0.001 |

Initial velocity (m/s) | 0 |

Initial position (m) | 0 |

Table 4. FLSM Dynamic Simulation Parameters

Fig. 11. Dynamic Speed

Fig. 12. Dynamic Force

Fig. 11. Dynamic Speed

Fig. 12. Dynamic Force

The simulation results obtained are tabulated as shown in Table 5.

Parameter | Value |
---|---|

Maximum force, f_{max} |
237 N |

Minimum force, f_{min} |
132 N |

Average force, f_{av} |
194.04 N |

Force ripple coefficient, k_{r} |
0.5411 |

Table 5. Simulation Results

[1] Gieras, Jacek F., Zbigniew J. Piech, and Bronislaw Tomczuk. Linear synchronous motors: transportation and automation systems. CRC press, 2016.