Example 2: Gear Shift
- Basic system:
- manual transmission in a car
- allows to change the ratio of rotational speeds from
motor and drive shaft
- usually provides a few fixed ratios (gears)
- complex internal structure
- Model in Modelica:
- basic component GearWithExternalRatio
- two connectors (flanges) and external input ratio
r
- equations
- gear shift model
- table to compute ratio from gear
- additional inertias
- complete model
- run in Dymola with changing gear →
- Failed to reduce the DAE index.
- Mathematical problem:
- event at gear shift r1 → r2
- rotational speeds before event
- rotational speeds after event
- start values of ωi, ωo 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
- result
- one new parameter for shifting time