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I'm wondering whether there are any notable losses in a typical automobile clutch when fully engaged.

Only losses that come to mind:

  • material twisting with torque changes
  • slipping due to imperfect friction

Are these even significant and are there any more? What is a typical energy efficiency of a fully-engaged clutch?

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The effects the OP mentioned do exist and would probably be measurable in controlled conditions in a test rig. However they are negligible, because they only dissipate a tiny amount of energy as the torque through the clutch changes with driving conditions.

Nearly all of the strain energy in the components that is stored as they twist up under torque load is recovered when the load is removed at they return to their undeformed shape. The amount of energy lost in one cycle of loading and unloading (independent of how long the cycle takes) is of the order of 0.001% to 0.01%, for metal components.

If the clutch is continuously slipping as it transmits power, it will quickly fail because that is not how it is designed to operate.

The analogous effects in bolted joints between components can dissipate a significant amount of energy and affect the mechanical damping of the system, but only if the load in the joint is continually changing at high frequency - e.g. something like a cylinder head bolt where the loads are changing in sync with the engine RPM, hundreds of times per second.

Any energy losses in the clutch will be tiny compared with losses in the gearbox, for example.

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