Domestic refrigerators and freezers have single-phase compressors and are usually less than 1/2 horsepower. Small single-phase compressors have start and run windings. The purpose of the starting relay is to take the start winding out of the circuit when the compressor has reached its rated rpm. If the compressor fails to start, the problem could be internal to the compressor or in the external starting circuit. If the compressor tries to start but cannot because of a shorted or open winding, an open internal overload, or a seized bearing, one usually hears a hum followed by a clicking as the external overload in the starting circuit opens from over-current. Unfortunately, a defective starting relay can also cause the same hum and clicking. An open in the starting circuit relay or overload will prevent voltage from reaching the compressor windings and no hum or clicking will be heard since no current is flowing.
One other situation where a hum and/or clicking of the external overload will be heard (and a situation that is normal) is when a running compressor loses power and an immediate attempt is made to restart it. This might happen if the power is interrupted for a few seconds by a storm or other fault in the electrical grid. It usually takes three or four minutes for the compressor to restart under these circumstances and one may hear the clicking of the external overload more than once.
Even though compressors do fail, starting-circuits fail much more frequently. It may be worth the cost of a new relay and overload to prove that the compressor really is bad before buying a new refrigerator. Sometimes the defect in the starting circuit is obvious. Wires and terminals may be burnt or loose or parts may be melted or obviously broken.
WITH THE REFRIGERATOR UNPLUGGED inspect the wires to the compressor, remove the cover from the starting relay/overload and look for damage such as broken or loose wires or burnt connections. Gently pry the relay/overload off the compressor terminals. Shake the relay. If it sounds like a miniature baby-rattle, bad things have probably happened inside it. If it looks melted or smells burnt, it is likely damaged. A few times I have found refrigerators with good relays but defective (open) overloads. If the overload is a separate assembly, check it for continuity with a meter. The usual arrangement is for the external overload to connect to the common terminal on the compressor. The relay connects to the start and run terminals. Thus the overload sees current through both or either winding and will open if the compressor draws too much current.
WITH THE REFRIGERATOR UNPLUGGED and the relay/overload assembly removed to expose the compressor terminals check the compressor for open or shorted windings. Normally the highest resistance reading will be between the S (start) and R (run) terminals since one is reading through both windings. The next highest reading is from S to C and the lowest reading should be from C to R. The resistance from S to C and from C to R should add to equal the reading from S to R. If C to R is open (no continuity) either the windings is open or the internal thermal overload is open. The thermal overload opens to prevent damage to the compressor from heat. If there is no continuity from C to R and the compressor is cold, the winding is open or the overload is defective and the compressor will have to be replaced. If S to C is open (no continuity) the start winding is defective and the compressor is bad. If the resistance from S to R is less than the sum of the resistance from S to C and C to R, the windings are shorted and the compressor is bad. If any terminal shows a low ( or zero) resistance to the case of the compressor, the windings are shorted and the compressor is bad.
Fig 1 Most Common pin arrangement on a compressor
The above resistance checks can verify that the windings are good and not shorted and that the electrical components inside the compressor are likely good, but it does not permit us to know if there is internal mechanical damage such as a seized bearing. The good news is that starting circuits fail much more frequently than compressor bearings so if the resistance readings of the compressor look normal, I would replace the starting circuit before condemning the refrigerator.
Keep in mind that even if the starting circuit and compressor are good the compressor will not have voltage to start if the cold-control or defrost timer have failed. I have been given more than one refrigerator with a bad compressor that had a defrost-timer stuck in the defrost position. That said, if you hear the typical humming of the compressor trying to start then cold-control and timer are sending voltage to the compressor start-circuit.