Reaction wheels of varying sizes

General

• Primary attitude control actuators on most spacecraft
• Reaction wheel failures a common problem for many space missions
  • Extra reaction wheels for redundancy
  • Failure of one reaction wheel often followed by failure of others of same design
  • Four reaction wheels failed on the Far Ultraviolet Spectroscopy Explorer (FUSE) in 2001, 2002, 2004 and 2007

Characteristics

• Reaction wheel assembly contains:
  • Rotating flywheel (supported by ball bearings)
  • Internal brushless DC electric motor
  • Associated electronics
• Wide range of capabilities:
  • Max. torque from 0.01 to 1.0 Nm
  • Max. angular momentum from 2 to 250 Nms
  • Max. rotational speeds from 1,000 to 6,000 rpm
• Back electromotive force at high speeds
  • Difficult to provide high angular momentum and high torque in the same wheel
• Motor drives command inputs
  • Torque command
  • Internal closed-loop controller
    • Holds reaction wheel speed at commanded value
• Control electronics located in separate box or integral with the wheel unit
• Generally provided with digital and/or tachometer → reading of wheel’s rotational speed
• Wheel friction

$$ L_{drag}^w=-\tau_v\omega^w-\tau_c\space sign(\omega^w) $$

$\tau_v$ and $\tau_c$ are empirically determined, can exhibit temperature dependence

• Not a good model for friction at low speeds, especially when crossing zero speed
  • Dynamic model of friction incorporating hysteresis is required to represent these phenomena adequately
• History of friction modelling
  • 1st dynamic friction model → Dahl model (1968)
  • Many models developed since → LuGre model (developed by Lund and Grenoble)
    • Frictional forces larger at low speeds (Stribeck effect or “stiction”)

<aside> ⚠️ Increasing drag torque is often an indication of potential wheel failure. General practice to monitor drag torque on reaction wheels on orbiting spacecraft.

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Disturbances

• Reaction wheels are onw of the major sources of attitude disturbances
• 4 classifications:
  1. Radial forces
  2. Axial forces
  3. Radial moments
  4. Axial moments
• Perturb spacecraft attitude by creating an $r\times F$ torque
  • $r$ is vector from spacecraft’s centre of mass to the point of application of the force
  • Effect of reaction wheel force disturbances minimized by locating wheel close to spacecraft’s center of mass
  • Effects of disturbance moments are independent of the location of the wheel