How to avoid damaging relay used for controlling motors?
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Figure 1. Snubbers on reversible motor.

Provided your relay contacts are break-before-make you shouldn't be causing a direct short. The problem is likely to be the inductive kick causing arcing of the contacts when they open.

One solution is to put diodes on the motor to shunt the current to the PSU. This may look a little strange but is really just a rearrangement of the standard H-bridge protection as shown in Figure 2.







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Figure 2. The same circuit in H-bridge configuration.







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Figure 3. Redrawn to use relay configuration on OP's schematic.