Example 2: Gear Shift (2)

• Mathematical problem:
  • event at gear shift r₁ → r₂
  • rotational speeds before event
    • 
  • rotational speeds after event
    • 
  • start values of ω_i, ω_o after event undefined
  • simple solution
    • fix one ω and compute the other
    • → often unrealistic behaviour
• Reality check:
  • problem appears in reality as well!
  • modern transmissions use synchronizer rings
    • adapt rotational speeds using friction
    • basically simple clutches
    • ω's adapt dynamically (according to connected inertias)
• Extended Model:
  • new gear shift model
    • 
    • one clutch per gear
  • shift logic component
    • detects gear change and opens/closes corresponding clutches
    • clutch of current gear is closed
    • other clutches are open
  • works with one new parameter for shifting time