Inertia Factor less than 5.0 is recommended, but higher reflected inertias may be used with proper testing  and analysis.  Response Rate and Torque at Low Pulse Rate Calculations The Inertia Factored Response Rate (RR JF), or No Load Speed, of a Stepper Motor Actuator is directly  effected by the Power Input at Holding (P H), the Inertia Factor, and Response Rate Constant (K RR’).  Equation 3 reflects the Inertia Factored Response Rate at the output of the Actuator, in RPM. As a note; the Response Rate Constant for redundantly wound Stepper Motors (K RR’) will be higher than a nonredundant winding, because of lower inductive losses (Ldi/dt). The Inertia Factored Response Rate calculation is presented in Equation 3. The factor of 6 converts the units to degrees per second from  RPM.  /g1844/g1844 /g3011/g3007= /g3012/g3267/g3267 /g942 /g2874./g2868 /g942 /g3493/g3017/g3257/g3118/g3121 /g3015/g1499 /g3493/g3011/g3255  …………………………………………………(3)

The Torque at Low Pulse Rate (T PPS-0), presented in Equation 4, is a function of the Holding Torque at  25ºC (T H25) and the sum of the Motor Magnetic Coulomb (f CM) Motor Bearing Friction (f BM) Gearbox  Bearing Friction (f BG) /g55/g82/g85/g84/g88/g72/g86/g15/g3/g68/g81/g71/g3/g42/g72/g68/g85/g69/g82/g91/g3/g40/g73/g73/g76/g70/g76/g72/g81/g70/g92/g3/g11/g536 G).   /g1846/g3017/g3017/g3020_/g2868 =  (/g1846/g3009/g2870/g2873/g942 0.707 ) /g3398 /g1840 ( /g1858 /g3003/g3014+/g1858 /g3004/g3014+/g1858 /g3003/g3008) ………………..…………(4) /g1846/g3009/g2870/g2873 = /g3435 /g1840/g942/g2015/g1833/g3439/g942/g1837/g3014/g2870/g2873 /g942/g3493/g1842/g3009/g2870/g2873 ………………………………………….(5) Equation 4 is a point of discrepancy to be resolved. Professionals in the aerospace industry argue that  the Magnetic Coulomb Torque (fc or Detent Torque) is a function of position and typically integrates out over a course of a step. In other words, part of the cycle, the Detent Torque is working against the  electro-magnetically generated torque, and part of the cycle, the Detent Torque /g90/g82/g85/g78/g86/g3/g90/g76/g87/g75 the generated torque. Strict interpretation of Torque Margin requirements, these components of torque should be  factored as we show in Equation 4, above [2] /g17/g3/g58/g75/g76/g79/g72/g3/g68/g81/g68/g79/g92/g93/g76/g81/g74/g3 Pull-In Torque, /g3/g87/g75/g72/g3/g71/g72/g87/g72/g81/g87/g3/g87/g82/g85/g84/g88/g72/g3/g80/g88/g86/g87/g3/g69/g72/g3 /g86/g88/g69/g87/g85/g68/g70/g87/g72/g71/g3/g73/g85/g82/g80/g3/g87/g75/g72/g3/g68/g89/g68/g76/g79/g68/g69/g79/g72/g3/g87/g82/g85/g84/g88/g72/g3/g87/g82/g3/g68/g70/g70/g72/g79/g72/g85/g68/g87/g72 . Note, torque margin factors are not applied to torque components such as f BMin this equation because it will be addressed later in the dynamic analysis. The  rationale and application of torque margin are discussed in detail in the Comprehensive Torque Margin Analysis section of this paper.  Table 2 delineates the variable values used in our simulation, shown in Figure 1. Data represented in blue herein is a reminder the values are an example. Table 2. Actuator and System Variables for Sample Simulation Parameter Units Symbol Value Load Inertia kgm2JL 5.7E-04 Holding Power (at +25ºC) Watts P H 28 Gear Ratio - N 20:1 Gearbox Efficiency % /g536G 90 Elevated Temperature ºC t 2 50

Performance at Elevated Temperatures To determine performance of voltage control systems at temperatures other than room temperature  (+25ºC) the change in DC Resistance must be determined. The example will analyze a two-phase motor. Refer to supplier catalogs for three phase calculations. For a two-phase bipolar drive, the room temperature /g39/g38/g3/g53/g72/g86/g76/g86/g87/g68/g81/g70/g72/g3/g11/g525 25) per phase may be easily calculated by using Equation 6.  377