Let's note right away: the operating instructions for many modern cars say: "the car does not require running-in." But whether to believe this - let's try to figure it out.
Why was car running-in needed
Since the advent of the automobile, engines, gearboxes, chassis components, etc., needed a long and tedious running-in procedure. Differing in details, in general terms this procedure boiled down to the fact that for the first 5-10 thousand kilometers of mileage, the driver was strictly forbidden to accelerate sharply, brake sharply, shift to a higher gear, drive uphill and over bumps, and was prescribed to change the oil almost every thousand kilometers, and much more.

All this was done so that all rubbing surfaces of the car's parts would wear in, and the metal shavings that appeared as a result would be washed out by the replaced oil.
Since "lapping of parts" is accompanied by increased heat, the car must operate under low loads and low speeds.
Is running-in needed now
Technical progress does not stand still, and over time, car parts began to be manufactured with ever-decreasing tolerances and high accuracy classes.
Moreover, procedures such as "cold engine running-in" and "hot running-in" began to be used.

Running-in is performed on special machines by the manufacturer. Oil, coolant, and fuel are supplied to the engine. Each engine model has its own modes, and during running-in, the load on the parts being worn in gradually increases.
Cold running-in is also carried out after a major engine overhaul.
The "garage" version of this procedure looks like this:
Increasing the accuracy class of parts, improving production culture, additional technological procedures - all this led to the appearance in the operating instructions of the phrase "the car does not require running-in." And this would indeed be the case, if not for a few "buts."
Currently, car parts are manufactured not only at automotive brand factories. A huge number of contractors around the world are engaged in this, and they have their own subcontractors. During assembly, brands, of course, control quality, but mass production imposes its own limitations. And, as you know, the longer the chain - the more likely an error (remember "broken telephone"?).
Also, during assembly, the tiniest dust could get into the engine.
The high production culture of German and Japanese car brands reduces this probability to a negligible value. But it still remains.
Moreover, not only the car's engine needs running-in - even tires, brake pads, etc., require running-in.

As arguments in favor of running-in, let's quote several operating instructions:
Hyundai
To extend the service life of your vehicle, it is recommended to observe the following precautions:
First 300 km: avoid sudden braking.
First 1000 km:
- avoid exceeding the vehicle's speed limit.
- avoid sudden accelerations.
- do not drive constantly in lower gears.
- do not drive at a constant speed for a long time.
Opel Astra G
To ensure the reliability and durability of the vehicle in operation, during the first 600 km of mileage, the following rules must be followed:
- Do not start off at full throttle, avoid sudden accelerations.
- Do not brake too sharply. Normal wear-in of new brake pads occurs over a mileage of 300 km, during which, if possible, you should brake smoothly and with moderate intensity.
- After repair or replacement of the engine, as well as after replacing brake pads, similar restrictions and recommendations must be observed.
Recommendations for BMW are especially strict:

BMW 3 Series E46 (from 1998 model year)
Follow the recommendations below to help extend the service life and ensure the efficiency of your vehicle.
Engine and rear axle differential
Mileage up to 2000 km
Engine speed and speed may vary, but their values should not exceed the following limits:
Vehicles with petrol engines:
4-cylinder: 4500 rpm, 150 km/h
6-cylinder: 4500 rpm, 160 km/h
Vehicles with diesel engines: 3500 rpm, 150 km/h
Do not press the accelerator pedal to a position corresponding to full throttle opening or maximum acceleration mode.
After the first 2000 km, you can gradually increase the speed and engine speed.
The running-in rules must also be observed if the engine or rear axle differential is replaced during subsequent operation.
Tires
Tire manufacturing technology does not guarantee optimal grip of new tires with the road. Therefore, during the first 300 km, it is recommended to drive more restrainedly.
Brake system
Optimal wear-in and load perception by brake pads and discs is achieved only after a mileage of approximately 500 km.

So what happens - even BMW is not confident in the quality of their cars? And those manufacturers who write "the car does not need running-in" are, to put it mildly, being disingenuous?
How it actually happens
In reality, everything is more complicated. BMW is confident in quality (but at the same time recommends running in the car), and the phrase "does not need running-in" is also legitimate.
The fact is that the classic running-in of a car, which was necessary in the times of the Soviet Union, has indeed become a thing of the past. There is no longer a need to change the oil every thousand kilometers (it is enough to do the "zero maintenance"), there is no need to restrain yourself from shifting to a higher gear, etc.
Such running-in is no longer needed. Modern equipment makes it possible to produce mating pairs of parts of such quality that allows the engine to do without running-in. And manufacturers using such equipment can not fear for their cars.
Nevertheless, even they advise operating the car in a gentle mode (which is reflected in the quotes above).
But whether full running-in is needed for cars manufactured using less precise equipment (we won't name brands) - the question remains open.
Therefore, let's give some general rules for running in a car.

Car running-in rules
- Be sure to warm up the engine (at least 4-5 minutes at idle).
- Do not start sharply, brake sharply, overload the car, drive off-road, uphill, or brake with the engine.
- Do not exceed a speed of 100-110 km/h.
- Do not drive at one speed for a long time (the engine must change operating modes).
- The engine should operate at optimal speeds for it (see the operating instructions).
- Handle the gearbox and clutch very carefully.
- All of the above should be observed for at least the first 1.5-2 thousand km.
- Be sure to carry out the "zero maintenance" at which the oil and filters will be replaced.
It should be noted that for European cars in Europe, "zero maintenance" is often not scheduled, but they offer to come immediately for the first maintenance - after 15 or 20 thousand km. Moreover, they also increase the oil change interval to 20-25 thousand km.
All this is due both to confidence in the quality of the car and to confidence in the quality of oil, fuel, and more gentle operating conditions. In our realities, however, greater caution is still needed.

Conclusion
European and Japanese cars practically do not need running-in - it is enough to observe the gentle mode prescribed in the owner's manual.
Even if the owner's manual says that "the car does not need running-in" - still, for the first thousand kilometers, operate the car in a gentle mode.
The need for running-in is directly proportional to the quality of the car's manufacture. And if running-in is not carried out for a car of inadequate quality - nothing good will come of it.








