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In the datasheet of the relay OMRO G7SA from the durability curve they specify the number of operations as a function of the contact current.
Each curve is for a specific current and voltage. The curves are labeled DC13, AC15, DC1 and AC1. Can anyone tell me the meaning of these labels?

Here's the graph:

Durability Curve graph from the datasheet

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Those are just the IEC utilization categories.

Different load characteristics have different effects on contact life.

Wikipedia has a utilization categories table.

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Utilization categories: Contacts will last longer under different load characteristics. A relay/contactor that is continuously starting, reversing and stopping an AC motor , for instance, will have contact wear different than the same contactor that controls a resistive heating element. Straight resistive load vs an inductive load, etc. AC vs DC load. Switching off a large DC load is more difficult than switching off a similar size AC load. Contact material and the gap between contacts, protective circuits and space between contacts and the speed at which contacts open will all be factors in the suitability of a contactor for the job. Selecting the right contactor for the application will result in higher dependability and might save money in manufacturing cost. IEC utilization categories can be helpful in selecting a suitable contactor but real-world application data is more useful.

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