The MAZDA RX-7 86-88 technical page
The base idle speed results from: 1) air passing through internal "plumbing" in the intake manifold (adjustable with the screw on top of intake) and 2) air passing through the bypass air control (BAC) valve operating at a "default" duty cycle (obtained by setting the initial set coupler as seen below). Maintaining the proper idle as various loads are placed on the engine is the task of the (ECU controlled) BAC valve. One should obviously make sure the BAC valve is operating correctly before attempting to diagnose an idle problem. For more details on the BAC valve, check the idle control section. To make the diagnosing easier, it is of importance to make sure the grounds are good, the charging system is operating correctly, the idle speed is properly adjusted, and that there are no vacuum leaks. All these points are discussed here.
This may come as a surprise but the first thing to consider is to make sure the car has good grounds. The engine block and body should be properly grounded. The voltage between any point on the engine or body and the negative terminal post should be 0V. If this is not the case, the stock ground points should be cleaned and, if you are paranoid about it, new ground straps could be added between the negative terminal post and the engine block and/or body (although it is not necessary since the stock ground points are adequate). Note that if you don't have good grounds, the engine will not run very well in general.
The Engine Control Unit (ECU) should also be properly grounded. Pins 2C, 2R, 3A, and 3G should read 0V when tested against a known good ground. If this is not the case, the wire harness should be peeled back to have access to the soldered joint for the B (black) wires corresponding to the above pins. This joint should be resoldered and further grounded to the body near the ECU (assuming the body has been properly grounded as explained above). Note that this proper grounding of the ECU may also fix the infamous 3,800 rpm hesitation (when seconday fuel injectors kick in).
The second thing to consider is to make sure the charging system is operating correctly. Assuming the grounds are good, it only involves the alternator and the battery. A bad battery or alternator may cause idle problems since it requires the engine to work harder in most cases. Idle problems due to the charging system become more evident when electrical loads are put on the engine. Batteries and alternators can usually be tested for free in most auto parts stores. More details on the charging system can be found in the engine electrical section under charging system. The wires should also be checked for good continuity, in other words, they should not offer any significant resistance to the passage of current. A sure sign of a questionable wire is heat as current passes through it.
It is important to make sure the idle speed is properly adjusted before going further in diagnosing idle problems.
This above shows the proper way to adjust the base idle speed according to the factory service manual (FSM). In general, it is not necessary to adjust the air mixture (air/fuel ratio) so it is not discussed here (see FSM for how to adjust air/fuel mixture at idle). It is important to set the initial set coupler in order to disable any possible BAC duty cycle variation (coming from the ECU). If you turn the screw clockwise till it stops, the engine should stall. If it does not, it is very likely you have a vacuum leak. Hmmm, that is a pretty good test to figure out if you have a vacuum leak (if you ask me).
This assumes the throttle plates are closed (within specs) when idling. Be aware that the opening of the throttle plates at rest can be modified by playing with the tiny slotted bolt with an 8mm lock nut right above the throttle plates on top of intake. I have to stress that you really don't want your idle to be controlled by the opening of the throttle plates since it completely defeats the purpose of the bypass air system. So if you ask me, I would either not touch it (there is supposed to be some goo on it to prevent people from playing with it) or completely back it out if tampered with before.
To adjust the throttle position sensor, one can follow the procedure described in the FSM also mentioned in the emissions section under secondary air injection. I personally prefer to set the TPS using voltage by considering the fact that the ECU expects a voltage of 1.0V from the TPS input (pin 2G) at idle. To set the TPS using voltage, the ground voltmeter probe should be put on a known good ground and the positive probe should be inserted in the TPS plug where the G/R (green with red stripe) wire connects. When the engine is idling (and at normal operating temperature, that is, not cold), the TPS should be adjusted so that the voltmeter indicates 1.0V. While you are at it, rev the engine up and make sure the voltage goes up (until it peaks) following the throttle (this makes sure the TPS does not have any dead spots).
Vacuum leaks usually lead to a poor idle. It may also prevent you from setting the base idle speed correctly (engine idling too high no matter how much you turn the idle speed screw in). It is in my opinion the number one cause of poorly idling engines. To check for vacuum leaks on vacuum hoses, it is a good idea to spray stuff (water, carb cleaner, starting fluid, propane) on the hoses or wherever else you suspect a leak might exist and listen for changes in idle speed. Any change indicates a vacuum leak.
Once all hoses are found to be free of vacuum leaks, it is a good idea to check for possible vacuum leaks due to failing valve diaphragms, in particular the exhaust gas recirculation (EGR) valve, the anti-afterburn valve (AAV) inside the air control valve (ACV) and the purge valve (I think that's pretty much it). If a diaphragm cannot hold a vacuum (easily checked using a Mytivac type vacuum pump available at most auto parts store), there is potential for an internal vacuum leak. For details on the EGR valve, check the emissions section under egr. For details on the AAV, check the emissions section under secondary air injection. For details on the purge valve, check the emissions section under crankcase and evaporative. Another possible source of vacuum leak is the power brake booster when the diaphragm that separates engine vacuum from atmosphere (when brake pedal is depressed) has failed.
Vacuum leaks may also come from areas where gaskets are supposed to be but that is pretty obvious. Another common source of vacuum leaks are the injector grommets. They seal the injectors where they seat on the intake. Note that the upper intake and fuel rails must be removed to gain access to them.
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