Presets
Playback
Governor
Heavier flyballs need more speed to lift; a heavier sleeve raises the speed at which the balls swing out.
Actions
Model checks
The science
What is modelled
Two flyballs of mass m hang from hubs on a spinning spindle by upper links of length Lu and are joined to a sliding sleeve of mass M by lower links of length Ll. As the spindle speeds up the balls swing outward and the sleeve rises; in an engine the sleeve closes the throttle. Link lengths, hub offsets and pivot height are the numbers used by the 3D page; the ball and sleeve masses are assumptions of this 2D page (the 3D page animates the motion kinematically).
Equations
- Equilibrium by virtual work:
ω² = g [(2m + M) tanα + M tanβ] / (2 m r), withsinα = (r - h)/Luandsinβ = (r - s)/Ll. - Radial dynamics:
Meff(r) r'' = 2 m ω² r - g[(2m+M) tanα + M tanβ] - c r'with the generalised mass of balls and sleeve and the damping chosen from the damping ratio. - Drive: the spindle speed relaxes to the set speed, reduced by the applied load (a simple droop model).
Checks run in the page
- A governor started off-equilibrium settles at the closed-form radius.
- Link-tension force balance and virtual work give the same speed.
- With no sleeve and the hubs on the axis the formula collapses to the Watt governor, h = g/ω².
Simplifications: massless links, frictionless joints, the sleeve load is only its weight; a real governor also has friction and a spring.
What to try
- Raise the sleeve mass: the whole characteristic shifts to higher speed.
- Press Kick with low damping and watch the hunting oscillation.
- Compare the speed gain in the bottom-right graph: a governor is most sensitive where the curve is steep.