vrstepper - lecture 4 - Variable Reluctance Stepper Motors...

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Unformatted text preview: Variable Reluctance Stepper Motors S.D. Sudhoff Spring 2008 Spring 2008 ECE321 2 Reading Electromechanical Motion Devices Sections 8.1-8.5 Spring 2008 ECE321 3 VR Stepper Motor Characteristics U s e s Spring 2008 ECE321 4 Construction Spring 2008 ECE321 5 Physical Configuration Spring 2008 ECE321 6 Some Definitions Rotor Teeth (RT): Tooth Pitch (TP): Number of Phases (N): Step Length (SL): Spring 2008 ECE321 7 Example Rotor Teeth (RT): Tooth Pitch (TP): Number of Phases (N): Step Length (SL): Spring 2008 ECE321 8 Analysis of VR Stepper Voltage Equations Flux Linkage Equations Torque Equation Mechanical Dynamics Spring 2008 ECE321 9 VR Stepper Voltage Equations Voltage Equations (8.3-1) (8.3-2) (8.3-3) In Matrix Form (8.3-4) Where (8.3-5) dt d i r v as as s as + = dt d i r v bs bs s bs + = dt d i r v cs cs s cs + = abcs abcs s abcs p + = i r v ] [ ) ( cs bs as T abcs f f f = f Spring 2008 ECE321 10 Flux Linkage Equations Spring 2008 ECE321 11 Flux Linkage Equation (Figure 8.2-2) For any VR stepper (8.3-7) For this machine (8.3-8) (8.3-9) (8.3-10) O r = cs bs as cscs bsbs asas cs bs as i i i L L L rm B A ls asas L L L L 2 cos + + = ) 3 2 ( 2 cos + + = rm B A ls bsbs L L L L ) 3 4 ( 2 cos + + = rm B A ls cscs L L L L Spring 2008 ECE321 12 Flux Linkage Equation (Figure 8.2-2) Discussion: Spring 2008 ECE321 13 Flux Linkage Equations (Figure 8.2-3) Spring 2008 ECE321 14 Flux Linkage Equations (Figure 8.2-3) We have (8.3-12) (8.3-13) (8.3-14) O r rm B A ls asas L L L L 4 cos + + = ) 3 1 ( 4 cos + + = rm B A ls bsbs L L L L ) 3 2 ( 4 cos + + = rm B A ls cscs L L L L Spring 2008 ECE321 15 Flux Linkage Equations (Figure 8.2-4) Spring 2008 ECE321 16 Flux Linkage Equations (Figure 8.2-4) We have (8.3-12) (8.3-13) (8.3-14) O r rm B A ls asas L L L L 8 cos + + = ) 3 1 ( 8 cos + + = rm B A ls bsbs L L L L ) 3 2 ( 8 cos cscs + + = rm B A ls L L L L Spring 2008 ECE321 17 Generalized Flux Linkage Eqns Thus in general, we have (8.3-18) (8.3-19) (8.3-20) O r (8.3-21) (8.2-22) (8.2-23) ) cos( rm B A ls asas RT L L L L + + = )] ( cos[ SL RT L L L L rm B A ls bsbs + + + = )] ( cos[ SL RT L L L L rm B A ls cscs + + = ) cos( rm B A ls asas RT L L L L + + = )] ( cos[ SL RT L L L L m B A ls bsbs + + = )] ( cos[ SL RT L L L L rm B A ls cscs + + + = Spring 2008 ECE321 18 Derivation of Torque Spring 2008 ECE321 19 Electromagnetic Torque T h u s (8.3-26) (8.3-27) { } )] ( sin[ )] ( sin[ ) sin( 2 2 2 SL RT i SL RT i RT i L RT T rm 2 cs rm bs rm as B e m + + = +...
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This note was uploaded on 09/22/2011 for the course ECE 321 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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vrstepper - lecture 4 - Variable Reluctance Stepper Motors...

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