PYTHON · NUMPY

Three ways to lose the same joule

Split braking energy into recycled, exported and burnt, and show a mains meter cannot separate them.

01Challenge

When an axis brakes it returns energy to the DC link. Three things can happen to it: a sibling axis consumes it, a regeneration unit exports it to the supply, or a resistor turns it into heat. Compute all three and verify the identity that governs them.

02Model

Fanuc's US 8,040,097 writes the ledger down: Ebrg = Ebsg − Ebng − RRg. Energy genuinely recycled into sibling axes equals total regenerated, minus what went back to the source, minus what was burnt. The filing states the problem plainly — from outside, it is impossible to know which happened. That is the whole argument for fixing the measurement plane before comparing anything.

03Guided practice

Run both cells. Check that the identity closes for both regeneration paths. Then ask which of the four quantities a mains meter can observe.

04Feedback

PASS WHEN The ledger closes and you can say what a mains meter cannot see.

If your run fails, check:

A well-coupled machine and one burning its braking energy can present the same mains reading.
Exporting to the grid costs about 12% in converter and commutation losses — KUKA rejects that path on exactly this cost in EP 2 599 596 B1.
Recycling axis-to-axis is free, but it only happens if the axes overlap in time.

05Retrieve & space

Write the three-way regeneration identity from memory.
Which term is observable at the mains, and which two are not?
Why does exporting to the grid lose more than recycling to a sibling axis?

06Mastery & project

Given a mains-side energy figure, state exactly what it cannot tell you about the machine.

Sketch the instrumentation you would add to a real cell to separate all three terms. Name the sensor at each point.

GO FURTHER · THE LIVE PLAYGROUND

Open the instrument ↗ — Two axes on a shared DC link. Move the meter, slide the phase, watch the number change.

← Where you put the meter The one-volt race →

PYTHON · NUMPY

Three ways to lose the same joule

Compute the three destinations and verify the identity closes.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you