JESS CHEN, Dept.. 62-33 Bldg. 150 DOMINIC GAEIRO, Dept.62-33 Bldg 150 ED STOECKERT, Dept 62-14 Bldg 551
Lockheed Missiles and Space Co. Inc. 1111 Lockheed Way Sunnyvale, Ca 94086 hm resistors simply prevent SPICE topological errors. Multipliers determine the desired oscillation frequency by controlling the coupling between C1and C3. The additional VCO in Figure 3 adds detent torque. Detent required an additional VCO because each stable rotor position corresponds to a positive-to-negative zero crossing in the angle versus detent torque curve. Assigning a stable equilibrium (detent) to each pole face required computing sin(2*8*P/2) where P is the number of poles and 8 = Ut =rotor angle . To include detents betweenpole faces, the model computed sin(4*8*P/2). The extra VCO generated sin(4*8*P/ 2) by running at four times the mechanical angular velocity. Figure 4 compares rotor positions with and without the detent torque as the system responds to a slew command. Without detent , load momentum moved the rotor between drive pulses such that subsequent pulses moved the rotor backwards. Because the detent torquepassed through several cycles per step, numerical errors accumulated from step to step and slowly discharged the detent VCO cosine capacitor until the detent torque became negligible. Because the VCO is a modified &oscillator, amplitude depended only on initial conditions. We tried three ways of maintaining the detent torque amplitude:
ABSTRACT This paper describes SPICE modeling of a completestepper motor system. Using a voltage controlled oscillator to track sine and cosine of rotor angle, and an electrical analog of the mechanical assembly, SPICE simulated interactions between electrical and mechanical subsystems. The simulations confirmed the effectiveness of preloading against gear backlash and dead-beating against excitation of mechanical resonances. A method for extractingfrequency domain information from this inherently time domain model is also discussed.
Electromechanical system design eventually requires analysis of the electrical and mechanical subsystems working together. In our example, an electronic subsystem controlled a mechanical load by setting a stepper motor’s step rate. We needed a model to check for uncontrolled motion resultingfrom 1)gear backlash and 2) step rates coincident with undamped mechanical resonances. Because a stepper motor employs open loop commutation ( i.e. we assume the rotor steps only on command and takes only one step), the model also had to check for slippage between electrical command and mechanical response. For example, if the pulse were too short, the rotor would not move. Furthermore, if thecurrent were not limited, the resulting torque would incorrectly guarantee rotor movement. The model therefore had to include electrical details. But a model depends on the CAE tools available, and few tools simulate electrical and mechanical systems together. Those that do either have short track records, cost a lot, runon select machines, or are too obscure. Approaching the gap from the electricalside, we developed SPICE models of the stepper motor and mechanical load. The second section explains the stepper model. Sections 3 and 4 discuss the drive and load models. The model confirmed (section 5) that dead-beat pulsing bounds the mechanical response to excitation at resonance, but also shows that dead-beat delay must change at high pulse rates to maintain forward rotation. The model alsoconfiied that preload holds backlash to tolerable limits. Because SPICE could not linearize such an inherently time domain model for frequency domain analysis, we resorted to spread sheet operations on the step response’s spectrum. Section 6 explains how we extracted loop gain from time domain SPICE simulations. 12) STEPPER MOTOR MODEL The stepper model is similar to one described in [ 11. The...