湖南工业大学本科生毕业设计（论文）
shown in Fig.1.The inductances and electromagnetic flux distributions were calculated by 3-D FEA in[5],and the results indicated that the generated machine side-force would eventually enhance the operational stability of this machine.However,these FEA investigations were only obtained in certain operational conditions.
The largest normal force will be generated in linear switched-reluctance machine when its energized primary poles ahd its secondary counterparts are aligned.By proper structure arrangement,this normal force can be utilized to alleviate the machine gravity applied to the track.Hence the system friction will be reduced and a smaller propulsive force will be required to drive the machine.For practical consideration,the system dynamic behavior and operational stabilities of the proposed machine will be evaluated in detail.By using 3-D FEA and eigenvalue analyze,this paper will investigate both the machine performance and the machine guidance force stability enhancements.Results from the system electronmagnetic forces and root loci of the mechanical oscillation modes show that a well-designed TFLSRM structure can eventually provide a fully stabe operating region.
Ⅱ.FORMULATION OF SYSTEM STATE-SPAVE MODEL
湖南工业大学本科生毕业设计（论文）
A. Calculations of Inductance and Forces
The required system 3-D finite element governing equation is
??B??(??A)??J (1)
where
B is the flux density, A is the vector potential, is the permeability,and J is the current density.
Since the experimental machine is designed to operate in the magnetic linear region,the system electromagnetic co-energy can be generally written as[6]
N1Bi21Bi21W???Vi??Vi?L(x,y,z)I2 (2)
2i?12?r?oi?m?12?om where
N is the total number of system elements, m is the number of core region elements, Vi is the volume of element i, Bi is the flux density of element I,
L is the equivalent system inductance matrix,and I is the current verctor.
The machine generated 3-D electromagnetic forces can be obtained by manipulating the numberical data of co-energy in their associated directions as[7]
FX?[W?(x,y,z)?W?(x??x,y,z)]/?x (3) FY?[W?(x,y,z)?W?(x,y??y,z)]/?y (4) Fz?[W?(x,y,z)?W?(x,y,z??z)]/?z (5)
?zare displacement of two adjacment nodes in the associated Where ?x,?yanddirections.
B. Modeling of System Equations
The machine system inductances and forces were calculated in Section Ⅱ-A.Curve fitting technique is applied to derive the approximate position-dependent forms of these
湖南工业大学本科生毕业设计（论文）
variables.By selecting the machine winding currents,
positions,and speeds as state variables,the system model can be written in closed forms as
V?RI?[(?L(x,y,z)/?x)vsx?(?L(x,y,z)/?y)vsy?(?L(x,y,z)/vsz]I?L(x,y,z)?dI/dt(6)
Vs?[vsxvsyvsz]t?[dx/dtdy/dtdz/dt]t (7)
FP?FLP?M(dvsp/dt)?BPvsp?KP?p(p?x,y,z) (8)
where
V is the input voltage vector, R is the winding resistance matrix, Vs is the machine speed vector, FLp is the p-axis load force, M is the machine bogie mass,
Bp is the machine p-axis viscous friction coefficient,and Kp is the machine p-axis spring constant.
By solving the above state-space equations,we can determine the system eigenvalues and hence the associated oscillation modes of the TFLSRM system at certain operational conditions.If all the real parts of these modes are located in the left-half plane,a stable operation can be guaranteed.
Ⅲ.3-D FORCE AND INDUCTANCE PATTERNS
湖南工业大学本科生毕业设计（论文）
湖南工业大学本科生毕业设计（论文）
Ⅲ.3-D Force AND lnducatance patterns
Since the designed TFLSRM has 3 degrees of freedom(3-DOF)in its operation,the force and inductance patterns at all the three Cartesian axes must be derived in advance for the system stability analyze.By using the machine parameters as provided in Table Ⅰ and the 3-D FEA as described above,the associated patterns can be obtained.Some of the patterns are illustrated in Figs.2 and 3.Evidently these patterns are position-dependent,and some curve fitting techniques can be easily introduced to derive the approximate expressions of those required variables in (6)-(8).
Ⅳ.OPERATIONAL STABILITY ANALYSIS
Sinces the track-guided transverse flux type linear machine system is designed to