How is the effective efficiency determined? Efficiency

Efficiency (coefficient of performance) is the degree of efficiency in using fuel energy in the engine; the higher it is, the more thermal energy from the combustion of fuel is converted in the engine into mechanical energy of rotation of the main shaft. The less fuel the engine consumes per unit of output power.

ARTICLE No. 1

ENGINE EFFICIENCY – TUNING GLOBAL IDEAS,
Are there any prospects for improving engines?

Modern internal combustion engines, many decades ago, with the advent of direct injection and turbocharging systems for air entering the cylinders, reached today's efficiency and fuel efficiency values. Therefore, today, global corporations - manufacturers of engines for cars and other equipment spend a lot of money and many years of effort in order to increase efficiency by only 2 - 3% at the expense of high costs and significant complication of engine design. The efforts and costs are completely incomparable with the results obtained. The result of all this is, as in the famous proverb, “the mountain gave birth to a mouse.”
By the way, this is why in all large countries There is a whole industry of “engine tuning”, i.e. a huge number of small firms, semi-handicraft workshops and individual specialists who undertake to somehow bring standard engines of mass brands of cars to higher levels of power, torque, etc. That is. subject the engine to fine-tuning, modification, boosting, etc. tricks that are popularly defined as engine tuning.

But all these events and technical actions on engines are very standard in nature and all these tuning ideas are at least half a hundred years old. Let me remind you that turbocharging the air entering the engine was successfully used back in the 20s of the last century, and the first US patent for such a device was received by Swiss engineer Alfred Büchi already in 1905... And direct fuel injection systems into cylinders were widely used in piston engines military aviation already in the initial period of the 2nd World War. Those. All modern “advanced” technical systems for improving the efficiency and fuel efficiency of engines are already about a hundred years old, or even more. With all these tricks, the overall efficiency of the best gasoline engines (with spark forced ignition) does not exceed 25-30%, and the efficiency of the best diesel engines in their most economical large-sized versions (which have many complex additional devices) for many decades cannot exceed 40 -45%. Small diesel engines have 10 percent lower efficiency.

In this article we will try to briefly and in popular language outline the main tasks and determine the theoretical possibilities of creating an internal combustion engine with a confident efficiency above 50%.

* * * So, the engine efficiency, judging by textbooks for technical universities, consists of two values: thermodynamic efficiency and mechanical efficiency .

The first value indicates which part of the heat generated in the engine is converted into useful work, and which is wasted into the surrounding space. Mechanical efficiency indicates what part of the active operation of the engine is uselessly spent on overcoming various mechanical resistances and driving additional equipment in the engine itself.

But for some reason, in all textbooks the concept of “general efficiency” is not introduced. fuel efficiency" That is, a value that will show how much fuel burns usefully and ultimately turns into heat and the volume of working gases, and how much fuel does not burn and is exhausted in the form of fuel vapor or products of its incomplete combustion. It is this unburnt part of the fuel that in modern “high-performance” cars is burned in catalysts that are installed in the exhaust pipes. Those. The exhaust due to the use of these systems turns out to be quite clean, but this system does not improve the fuel efficiency and efficiency of the engine. On the contrary, it reduces it - because in order to “pump” a portion of exhaust gases through the “dense network” of catalytic surfaces, the engine has to work like a solid pump and spend a considerable part of its power on this matter. Of course, this category is somehow present in the formulas for calculating efficiency, but it is present not clearly and timidly. For example, in a form such as, for example, in one of the general heat balance formulas there is a component “Q n.s. - heat obtained during incomplete combustion." But all these approaches suffer from some vagueness, so I will try to present everything as clearly and as systematically as possible.

So, the overall efficiency of the engine will be divided into 3 main parts:

• fuel efficiency;
• thermal efficiency;
• mechanical efficiency;

The essence of these values ​​is as follows:

Fuel efficiency- shows how much fuel was effectively burned in the engine and turned into a volume of working gases of high temperature and high pressure, and what part of the fuel was not burned and in the form of products of incomplete combustion, charred particles (in the form of smoke, soot and soot), or even practically in the form of pure fuel vapor, passed through the engine directly and flew out into the exhaust pipe. When you stand next to an old running domestic car, especially a truck, and smell a strong smell of gasoline, this is the result of this inefficient type of partial combustion of fuels;
Thermal efficiency – shows how much heat received from burning fuel is converted into useful work, and how much is uselessly dissipated in the surrounding space;
Mechanical efficiency – shows how much mechanical work is converted into torque on the main shaft and transmitted to the consumer, and how much is wasted on friction or spent on driving supporting mechanisms;

Let's take a brief look at all these positions:
Fuel efficiency – no clear data could be found on this topic, either in the old Soviet textbooks on the theory and calculation of internal combustion engines, or in the endless resources of the modern Internet.
Clear and meaningful data was found in the information on the calculation of catalytic afterburners of unburned fuel for modern cars. After all, they need to clearly calculate the performance of their afterburners for a certain volume of incoming hydrocarbons that have not been burned in the engines. So, from these data it follows that piston engines (diesels too) burn on average no more than 75% of fuel, but 25% of fuel vapor and products of incomplete combustion go into the exhaust pipe and require the services of an afterburner (so as not to poison the environment ). Those. In engines existing today, no more than 75% of the fuel is fully burned and converted into heat. For 2-stroke engines this value is even less.

Thermal efficiency– on average, piston engines have this efficiency of 35-40%. Those. about 65% of the heat generated is wastelessly released into the environment through the cooling system and exhaust gases.

Mechanical efficiency – on average, 10% of the engine’s work is spent on friction between its parts and on driving the auxiliary mechanisms of the engine.

As a result, based on the sum of thermal and mechanical losses, modern piston engines of small size and power have an efficiency of no more than 30%.
In large engines, such as marine diesel engines or large engines in railway locomotives and trucks, it is easier to save energy, but we will not talk about them.

But - the efficiency value of 30% does not take into account the share of unburned fuel, i.e. does not take into account the completeness of combustion of fuel vapors in the engine. I believe that taking this parameter into account, the real efficiency value of piston gasoline engines will not be higher than 20%, and of diesel engines - a little more, about 5-7%.

The result is better than coal-fired steam engines with their 7-8% efficiency, but still very little.
Let’s think about why the concept of efficiency did not include the specified “fuel efficiency”? Why does the concept of efficiency clearly ignore the share of fuel that does not “contribute” its part to the process of combustion and heat generation? Those. the concept of efficiency excludes most of the losses of modern engines and figures modern meanings Is the efficiency without taking these losses into account clearly overestimated?

The truth lies in the very meaning of the term “efficiency factor”. Those. this is the determination of the share of useful work - “action”, and the share of useless work. Some work or release of energy is beneficial, and some (for example, to overcome friction, or heat energy lost in the exhaust) is useless, but it exists, and this energy is tangible and taken into account. But losses from unburned fuel do not appear in the form of useless heat or inappropriate work. These “balance drawbacks” are not job losses or heat losses. This is a loss of pure fuel. Those. These losses are neither in joules nor in atmospheres, but in grams and liters. And such losses cannot be measured or accounted for in the category of lost pressure or lost heat, useless action or unnecessary work.

Therefore, purely according to the rules of formal logic, the EFFICIENCY COEFFICIENT should not take into account these losses. For this purpose there should be another indicator and qualifier, but there is no such clear and intelligible parameter in wide use. So we get a deliberately truncated and overly blissful indicator of the efficiency of modern engines - an efficiency indicator that takes into account only part of the losses...

But in fact, the total efficiency of modern internal combustion engines turns out to be noticeably lower than the universally postulated efficiency of 35-40% efficiency. After all, only the beneficial effect and wasted energy and extra work produced due to the burned part of the fuel are taken into account. But the loss of the unburned part of the fuel from the total balance of fuel entering the engine is not fully determined...

AUDIT AND INVENTORY OF LOSSES IN A PISTON ICE We will try to briefly review and analyze all the losses of energy contained in the fuel, one by one according to the positions outlined above. And then think about the possibilities of getting rid of these losses. Those. Let's try to formulate the concept and outline the general features of a perfect engine.

* * *
First level of losses– incomplete combustion of fuel in the combustion chambers of the engine. All experts know that fuel in modern engines burns incompletely and part of it is exhausted with exhaust gases. That is why modern internal combustion engines poison the air with products of incomplete combustion of hydrocarbons, and to obtain “clean exhaust” a catalytic afterburner is installed in the exhaust pipe of modern cars, which “afterburns” the fuel on the surfaces of its active elements. As a result, fuel that is not heated in the cylinders is uselessly oxidized in these catalysts. But the exhaust becomes cleaner. But the price of these catalysts with rhodium and platinum surfaces is very high and they work for a limited period.

Task– to obtain an engine that COMPLETELY burns fuel in its combustion chambers and completely converts the energy of the chemical bonds of the fuel into heat and a large volume of simple combustion gases, such as water vapor and CO2.

First, let's look at why fuel does not burn completely in traditional piston engines. What prevents the process of complete combustion?

The main difficulty in piston engines on this topic is the lack of oxygen for combustion, as well as the implementation of the combustion process in one technological stroke with the expansion of combustion gases. The last situation can be described in other words - the Working Mixture does not have enough time for complete combustion. These “generic diseases” of piston engines are practically incurable, so engineering thought, after more than 120 years of trying to get rid of them, has not found a way to do this.

Let us consider this drawback in detail: so, when the piston is at the Top Dead Center (TDC), the compressed Working Mixture (PCM) is ignited. The combustion process begins and continues for some time. The approximate combustion of the Working Mixture in a modern high-speed engine lasts about a millisecond - 0.001 seconds. In general, all 4 cycles occur in 0.02-0.04 seconds.

It is known that for complete and complete combustion of fuel vapors, high temperature and high pressure are desirable. But immediately after the piston passes TDC, it begins to move downward with a significant increase in the volume of the space above the piston. Those. As the combustion front of the Working Mixture (WMC) spreads in the combustion chamber, the first portions of burnt WMC will burn at high temperature and high pressure. But the last portions of burning RSM find themselves in conditions of sharply decreasing pressure and falling temperature. Accordingly, the efficiency of combustion drops sharply, or even stops altogether. For this reason, part of the RSM does not have time to burn or does not burn completely. Therefore, some of the fuel vapor goes into the exhaust pipe and the exhaust gases certainly contain products of incomplete combustion of fuel hydrocarbons. The result is that part of the fuel does not burn and does not convert its energy into heat, and then into rotation of the main shaft of the engine, but only pollutes and poisons the surrounding air.

It is almost impossible to eliminate this drawback, since the very basic design of a piston engine presupposes the most important principle of combining two different processes in one technological stroke “combustion - expansion”: combustion and expansion of combustion products. It is difficult to combine these processes, since each of them optimally occurs under mutually exclusive optimal conditions for the other process.

Indeed, the combustion process of a compressed RSM charge will best occur in a locked chamber of constant volume. In thermodynamics, this process is defined as an “isochoric” process. Those. the PCM charge will burn completely and convert all the energy of the chemical bonds of fuel hydrocarbons in a closed chamber into heat and pressure under conditions of sharply increasing pressure and temperature.
And the expansion process will best occur under conditions of low temperature (to ensure lubrication of the sliding and rubbing surfaces of the working elements of the engine), with slight movement of the main working body (piston).
As we see, in piston engines both of these conditions cannot be fully met, therefore the combined process of “combustion-expansion” follows a “compromise scenario”, when less suitable conditions are created for each of the processes, but in the end they still allow somehow implement these joint processes at least 50% efficiency. As a result, the process of operation of a modern piston engine is a technology of continuous difficult compromises and significant losses.

As a result of such a “compromise marriage” with losses for both parties involved in the case, we get the following result:
— combustion occurs under conditions of a sharp expansion of the combustion chamber, and even at a significantly low temperature of the cylinder walls. As a result, the fuel burns incompletely and ineffectively, and some of the heat from the burned fuel is lost when the cold walls of the cooled cylinder are heated. Those. combustion occurs under extremely inefficient conditions.
— expansion occurs under conditions of high temperatures from the combustion process combined with expansion. That is why the cylinder walls have to be cooled, because the oil for lubricating the rubbing surfaces of the piston and cylinder at a temperature of more than 220 C° loses its “slippery properties” and friction begins to “dry”, and the charred oil sinteres into solid particles, which begin to interfere even more this process.

Part of the way out of the impasse of the “combustion-expansion” process is found by arranging “early ignition” so that the smallest possible part of the RCM combustion occurs on the line of high-speed expansion and a high increase in the volume of the combustion chamber. But this is a forced scheme and is fraught with other side troubles. Since “pre-ignition” involves igniting the RSM and creating initial stage working pressure of combustion gases even before the piston reaches TDC, i.e. at the final stage of the compression stroke. Consequently, the inertia of the crank mechanism (CPM) has to overcome this emerging pressure of the burning RCM and compress due to the inertia of rotation of the CCM or the work of other pistons, the burning RCM that has begun to expand. The result of this compromise is a sharp increase in loads on the crankshaft, pistons, connecting rods and crankshaft pins, as well as a decrease in efficiency. Those. the engine turns out to be an arena of confrontation between multidirectional forces.

Another difficult topic with piston engines is the lack of oxygen. True, it is typical only for gasoline engines (engines operating with forced spark ignition), diesel engines (engines operating with compression ignition) do not have this drawback. But instead, diesel engines acquired many other difficulties - heavy weight, bulkiness and impressive dimensions. Indeed, no one has been able to create an efficient diesel engine of acceptable dimensions with a volume of less than 1.2 liters... This is the engine of the smallest diesel car, the Audi-A2. And the reduction of diesel engines to very small dimensions has a sad result. So - small diesel engines of the Vladimir Tractor Plant D-120 (they are installed on mini-tractors) with a power of 25-30 hp. have a weight of 280-300 kg. Those. For one horsepower there is 10 kg of weight. Other manufacturers around the world have a similar situation.
So, fuel does not burn completely when the RCM is “rich”, i.e. it contains a lot of fuel vapor and little air (oxygen). Such RSM has no chance of burning completely; there is simply not enough oxygen in the fuel to oxidize hydrocarbons. The result is that fuel vapors that are not burned for this reason go to the exhaust. But such RSM burns quickly, although not fully. This means that most of the fuel vapor still burns and gives the required pressure and temperature.

You can go the other way - make a “lean mixture”, i.e. there will be a lot of air (oxygen) and little fuel vapor in the RSM. As a result, in an ideal case, such an RSM will be able to burn completely - all fuel vapors will burn 100% with full efficiency. But such RSM has a big drawback - it burns much slower than a “rich mixture” and in the conditions of a real-life piston engine, where combustion occurs on the line of rapid increase in volume, such RSM simply does not have time to burn fully. Since a significant part of the combustion of such RSM falls due to the low speed under conditions of a sharp increase in the volume of the combustion chamber and a drop in temperature. The result is that RCM again does not burn completely even in the “lean mixture” version and a noticeable part of it goes to the exhaust without being burned.

And again, the fuel efficiency of this mode of operation of a piston engine turns out to be very low.
The low supply of oxygen to the combustion process of PCM also plays a role in the method of controlling carburetor engines - the “quantitative method”. In order to reduce engine speed and reduce its “thrust”, the driver closes the throttle valve, thereby limiting the access of air to the carburetor. As a result, again there is a lack of air for fuel combustion and again poor fuel efficiency... Injection engines are partly free of this disadvantage, but the rest of the troubles of a piston engine are manifested in them “in full”.

It is necessary to separate two extremely contradictory working technological processes - “combustion - the formation of working gases of high pressure and temperature” and “expansion of working gases of high pressure and temperature”. Then both of these processes can begin to be carried out in specialized cameras and devices at the most optimal parameters. Those. combustion will occur “isochorically” - in a locked volume, with increasing pressure and increasing temperature. And expansion can be carried out at low temperatures.

In principle, the idea of ​​making such a “great division” was formulated by various inventors and engineers from different countries quite a long time ago. For example, the developments of the German company DIRO Konstruktions GmbH & Co. KG", on the topic of a piston engine with a separate combustion chamber. But so far no one has succeeded in proposing a theoretically beautiful and technically workable circuit for implementation in metal. The same German company DIRO Konstruktions GmbH & Co. KG began to receive patents for its developments about 15 years ago, but it has never heard of any real success in creating a truly functioning engine.

So, it is necessary to ensure a long-term combustion process of the RSM charge in a locked volume - an “isochoric process”. Under these conditions, it will be possible to burn a deliberately “lean mixture”, with a large excess air ratio, when the fuel vapors burn completely, produce the maximum possible amount of heat and combustion gases, and at the same time minimally toxic combustion products will be exhausted. But this can only be done by ensuring a sufficiently long burning time of the “poor” RSM charge in a locked volume under increasing pressure and significant temperature. Which is practically impossible to provide in a piston engine.

* * *
Second level of losses– significant losses of heat obtained from the combustion of “fuel assimilated by the engine.”
The thermal balance of a gasoline engine is as follows:
1) – heat converted into useful work: 35%;
2) – heat lost with exhaust gases: 35%;
3) – heat lost from losses through the cooling system: 30%;

Task– obtain an engine with minimal heat loss during external environment. Ideally, the goal would be to create an engine with a thermal efficiency of 80%. But even if we manage to achieve this figure of 65-70%, instead of 35% today, this will be a huge leap forward. Those. an engine of the same power with such efficiency will begin to consume 2 times less fuel than before.

Analysis of today's unfavorable situation: First, let's look at why there are such large heat losses "to the side" in traditional piston engines? What leads to such a sad situation?

First category of heat losses— heat loss with removal through the walls of cylinders with a cooling system. In general, to increase the thermal efficiency value, the engine should not be cooled at all. This will immediately raise the temperature of the engine parts, and this will char the oil (which creates a film for easy sliding on the friction surfaces), and the piston will stop moving easily in the cylinder and the engine will soon jam. Here we again run into the contradictions of combining two processes in one cycle - combustion and expansion. The temperature during the combustion outbreak in the initial period of ignition of the RSM reaches 3000 C°. And the maximum temperature of the oil, when it still lubricates and protects from friction, is 200 - 220 degrees. When this temperature threshold is exceeded, the oil begins to “burn” and char. To ensure high efficiency, it is not wise to cool the engine, but to ensure the movement of the main working body - the piston - lubrication is vital... That is. a cooling system that allows the piston to move in the cylinder dramatically reduces the thermal efficiency of the engine. This is a conscious and necessary reduction in efficiency.

Second category of heat losses– heat loss with exhaust gases. The temperature of the exhaust gases at the outlet of the cylinders for different sizes and engines ranges from 800 to 1100 C°. Therefore, in an engine running at high speeds, the exhaust manifolds sometimes begin to heat up to a crimson glow... This means only one thing - the energy of fuel combustion, turned into the internal energy of combustion gases in the form of their high temperature, is lost irrevocably and completely useless. It is through this channel of “thermal losses” that modern internal combustion engines lose about 35% of the fuel combustion energy. And turning this energy into useful work is extremely difficult; the most that has been done is to insert a turbine into the exhaust tract, which turns the turbocharger compressor. This achieves an increase in air pressure entering the cylinders. And this slightly increases the efficiency. But - you need to understand that the turbine does not “catch” the increased temperature, but the excess pressure of the gases leaving the cylinder. Those. This is a slightly different topic and savings of a different kind.

Thus, it turns out that the piston engine poorly “processes” not only the temperature, but also the high pressure of the working gases. In fact, working gases with an excess pressure of 8–10 atmospheres are exhausted. This is a lot; you just have to remember that the first steam engines at the beginning of the 19th century had a working pressure of 3 or 3.5 atmospheres and worked successfully in coal mines and in metallurgical plants, like the engines of the first steam locomotives.

The whole point here lies in the identical geometric dimensions of the compression volume and expansion volume. For a piston engine they are equal, and nothing can be done about it. Ideally, these volumes should be different. A trick like the Atkinson cycle, when in piston engines the compression volume is less than the expansion volume, is ineffective, since it sharply reduces the engine torque.

But increasing the volume of the expansion chamber will only make it possible to convert all the excess excess pressure into useful work, but the increased temperature of the hot gases of fuel combustion cannot be utilized by this method. The only thing that came to the engineers' minds was to inject water into the cylinders to turn the high temperature into work. In theory: water, turning into high-pressure steam, will sharply increase the pressure of the resulting steam-gas mixture and at the same time significantly lower its temperature. But, over more than 80 years of efforts in this direction, nothing effective and efficient could be created in a piston engine. The piston circuit of the internal combustion engine turned out to be very hostile to this idea and did not allow a steam stroke or vapor phase to be integrated into the engine operating cycle.

It must be said that according to the fundamental law of thermodynamics, formulated almost 200 years ago by S. Carnot, a heat engine with the maximum possible efficiency must have a maximum temperature of the working gases at the beginning of the operating cycle, and a minimum temperature of the working gases at the end of the cycle.
But in a piston internal combustion engine, the cooling system prevents the maximum gas temperature at the first stage of the cycle from being achieved, and the minimum excess gas temperature at the end of the cycle is prevented by the inability to build a steam component into the engine circuit. As a result, today we use engines with a thermal efficiency of about 35%, not much better than 60 or 70 years ago...

The way to get rid of this shortcoming: it is necessary to create an engine design that allows the fuel combustion process to be carried out in a thermally insulated combustion chamber (to achieve maximum temperature at the beginning of the operating cycle), and also allows the inclusion of the vapor phase at the final stage of operation of hot combustion gases (to achieve minimum temperature at the end of the working cycle). Also, this engine design will make it possible to do without a separate and bulky cooling system, which would “throw out” heat into the external environment.

At the same time, the engine will not need a bulky and heavy exhaust pipe, which in traditional piston engines dampens the roar of exhaust gases flying out in “shots” with an excess pressure of 8-10 atmospheres. Because in the proposed design, the excess pressure of the exhaust gases will be minimal.

* * *
Third level of losses– noticeable power losses to overcome friction forces, as well as inertial forces of reciprocating moving masses, as well as losses to drive auxiliary mechanisms. These losses are defined as mechanical losses. They depend on the kinematic diagram of the engine. But in addition to the mechanical losses themselves, the kinematic diagram and its design also affect another important performance indicator, which is not directly related to efficiency: this is the mode and magnitude of the torque.

The task is to obtain an engine with minimal mechanical losses. It also has a constant high torque with a small size of the engine itself. High and stable torque allows you to do without such a bulky and complex system vehicle like a gearbox. An example is transport with electric motors and steam engines.

Analysis of today's unfavorable situation: in a standard piston (trunk) engine, the reaction of the connecting rod (the transverse component of this reaction relative to the cylinder axis) to the pressure of the working gases constantly presses the piston to one side of the cylinder, then to the other. This engine operating system requires constant lubrication of highly frictional surfaces, and the cost of overcoming these frictional forces. In addition, when the crank rotates, the projection of the torque-creating arm to the piston motion vector changes all the time from “zero” to “maximum” and back every working stroke. This constantly pulsating torque mode is of little use for driving actuators. And only at high speeds of piston engines the torque increases noticeably. But high speeds (about 3-4 thousand rpm) are not needed by most consumers. Therefore, we have to make a complex and cumbersome gearbox, which is an integral part of cars, motorcycles, etc.
  In addition, mechanical efficiency is noticeably reduced due to the take-off of engine power to drive its auxiliary mechanisms - the cooling system pump, cooling fan, camshafts and timing valves, electric generator, etc. And noticeable power losses are caused by the need to compress the working mixture, and the higher the compression ratio , the higher these losses are. In addition, noticeable power losses can be caused by excessively early ignition, when the engine is forced, at the end of the 2nd “compression” stroke, to compress the combustion products that begin to expand.

The way to get rid of this shortcoming: it is necessary to create an engine design in which the pressure of the working gases does not press the main moving working body against the stationary body. In this case, the engine must have a design that would allow it to have a constant torque arm throughout the entire path of movement of the main working part of the engine. In this case, on this path, the pressure of the working gases should be maintained for as long as possible, ideally striving for 100%. Let me remind you that in 4-stroke engines, out of a full engine cycle of 2 shaft revolutions, the pressure on the piston acts only half a revolution, and even then in the mode of transmitting this pressure with an unstable torque arm.

RESULT:

SO, let’s formulate the conditions that the scientific approach puts forward in order to create an engine with high efficiency:
1) The main technological processes of the engine “combustion” and “expansion” must be separated and separated for implementation in different technological chambers. In this case, combustion must occur in a locked chamber, under conditions of increasing temperature and increasing pressure.
2) The combustion process must take place for a sufficient time and in conditions of excess air. This will allow 100% combustion of the working mixture.
3) The volume of the expansion chamber must be significantly larger than the compression chamber, at least 50%. This is necessary to fully transfer the pressure of the working gases into work on the main working body.
4) A mechanism must be created to transfer the high temperature of the exhaust gases to work on the main working body. There is only one real possibility for this - the supply of water to convert the high temperature of combustion gases into the pressure of the resulting steam.
5) The working body and the entire kinematics of the engine must be designed in such a way that the working body perceives the pressure of the working gases for as long as possible during the engine cycle, and the leverage of transferring the force of this pressure is always the maximum possible.

After careful work with these requirements of theoretical approaches of physics and mechanics on the topic of creating an engine with high efficiency, it turns out that it is completely impossible to create a piston engine for such tasks. A piston internal combustion engine does not satisfy any of these requirements. The following conclusion follows from this fact: it is necessary to look for more efficient engine designs alternative to the piston circuit. And the circuit closest to the necessary requirements turns out to be a rotary engine circuit.

In my work on the concept of a perfect rotary engine, I proceeded from an attempt to take into account, when creating a conceptual diagram of the engine, the need to implement all the above theoretical prerequisites. I hope I managed to do this.

ARTICLE No. 2-1

THINKING ABOUT COMPRESSION RATE:
EVERYTHING IS GOOD IN MODERATION

We are all accustomed to the fact that an economical and powerful engine must have a high compression ratio. Therefore, in sports cars, engines always have a high compression ratio, and engine tuning (boosting) to increase the power of standard mass-produced engines involves, first of all, increasing their compression ratio.
Therefore, the idea has taken hold in broad public opinion - the higher the engine compression ratio, the better, since this leads to an increase in engine power and an increase in its efficiency. But - unfortunately, this position is only partly true, or rather, it is no more than 50% true.
The history of technology tells us that when Lenoir's first internal combustion engine (which operated without compression) appeared in the 1860s, it was only barely superior in efficiency to steam engines, and when (15 years later) Otto's 4-stroke internal combustion engine appeared, operating with compression, the efficiency of such a model immediately surpassed all the then existing engines in terms of efficiency.
But compression is not such a simple and straightforward process. Moreover, it makes no sense to achieve very high compression ratios, and it is also very difficult technically.
First: the higher the compression ratio, the longer the piston stroke in the cylinder. Consequently, the linear speed of piston movement at high speeds is greater. Consequently, the greater the inertial alternating loads acting on all elements of the crank mechanism. At the same time, the pressure levels in the cylinder also increase. Therefore, for an engine with a high compression ratio and a long stroke, all elements and parts of the engine must be of increased strength, i.e. thick and heavy. This is why diesel engines are never small and light. That is why small diesel engines have not been created for motorcycles, outboard boat engines, light aircraft, etc. This is why standard auto engines that have undergone serious tuning have been subjected to serious tuning and have such a short service life.
Second: the higher the compression ratio, the greater the risk of detonation with all the ensuing destructive consequences. Filling with low-quality gasoline can simply destroy such an engine. Read about detonation in a special ARTICLE. Those. At a certain degree of compression, it is necessary to use increasingly more expensive and special gasoline or special additives to it. In the fifties and sixties, the main line of engine building, especially in the USA, was to increase the compression ratio, which by the early seventies on American engines often reached 11-13:1. However, this required appropriate gasoline with a high octane number, which in those years could only be obtained by adding poisonous tetraethyl lead. The introduction of environmental standards in most countries in the early seventies led to a halt in growth and even a decrease in the compression ratio on production engines.
However, there is no point in achieving the maximum possible degrees of compression. The fact is that the thermal efficiency of the engine increases with increasing compression ratio, but not linearly, but with a gradual deceleration. If when the compression ratio increases from 5 to 10 it increases by 1.265 times, then from 10 to 20 it increases only by 1.157 times. Those. after reaching a certain threshold of the compression ratio, its further increase does not make sense, because the gain will be minimal, and the growing difficulties will be enormous.

* * * With a careful analysis of job opportunities different types engines and looking for ways to improve their efficiency, there are possibilities other than constantly increasing the compression ratio. And they will be much more efficient and of higher quality than high compression ratio increases.
First, let's figure out what a high compression ratio actually gives. And she gives the following:
— gives a high working stroke length, because in a piston engine, the compression stroke is equal to the expansion stroke;
- strong pressure in the charge of the working mixture, at which the molecules of oxygen and fuel come together. This makes the combustion process better prepared and
goes faster.

Regarding the first position, the following comments can be made: indeed, the efficiency of diesel engines is largely due to the fact that they have a long working stroke. Those. Increasing the expansion stroke length has a much more serious effect on improving engine efficiency and economy than increasing the compression stroke length. This makes it possible to extract more benefit from the pressure of the working gases - the gases work to move the piston more. And if in “gasoline” engines the piston diameter is approximately equal to the length of the working stroke, with the corresponding “compression ratio” and “expansion ratio”, which are tied to the piston stroke length, then in diesel engines this parameter is noticeably larger. In classic low-speed diesel engines, the piston stroke is 15-30% greater than the piston diameter. In marine diesel engines, this difference becomes absolutely glaring. For example, a huge 14-cylinder diesel engine for a supertanker produced by the Finnish company Wartsila, with a displacement of 25,480 liters and a power of 108,920 hp. at 102 rpm, the cylinder diameter is 960 mm, and the piston stroke is 2500 mm.

Let me remind you that such marine diesel engines run on crude oil, which can withstand a very high compression ratio with such a huge piston stroke.

But increasing the compression ratio also has its unpleasant sides - it requires the use of expensive high-octane gasoline, increasing the weight of the engine, as well as considerable expenditure of engine power on the process of strong compression.
Let's try to figure out whether it will be possible to achieve a similar or even greater effect in increasing power and increasing engine efficiency in other ways, i.e. without excessively increasing the degree of compression with an increase in the inherent negativity of such a process. It turns out that such a path is possible. Those. All both positive aspects of increasing the compression ratio can be obtained in other ways and without the inherent troubles of increasing the compression ratio.

Consideration of the first position – long working stroke length. The main thing for efficiency is a long working stroke so that all working gases transfer maximum pressure to the piston. And in a piston engine, the working stroke is equal to the length of the compression stroke. This is how the opinion became firmly established that what is most important is the degree of compression, and not the degree of expansion. Although in a piston engine these values ​​are equal. Therefore, separating them does not make much sense.

But ideally, it is better to make these stroke lengths different. Since increasing the compression stroke leads to a lot of unpleasant consequences, make it moderate. But the expansion course, as responsible for maximum economy and efficiency, should be made as large as possible. But in a piston engine it is almost impossible to do this (or it is very difficult and complex to do - for example, the Kushul engine). But there are a lot of rotary engine designs that allow you to special labor resolve this dilemma. Those. the ability for the engine to have a moderate compression ratio and at the same time a significant stroke length.

Consideration of the second position – activation and high efficiency of the fuel combustion process. Its high speed and completeness. This is an important condition for the quality and efficiency of engine operation. But it turns out that the compression ratio (providing high pressure) is not the only one, and not even the most the best way achieving such a result.

Here I will allow myself to quote from an academic book on engine theory for universities of the Soviet period: “Automobile Engines,” ed. M.S.Hovaha. Moscow, “Mechanical Engineering”, 1967.
As can be seen from the above quote, the quality and rate of combustion depends more on the combustion temperature, and to a lesser extent on pressure. Those. if it is possible to ensure an extremely high temperature of the combustion medium, then the efficiency of combustion will be maximum, and the need for extremely high pressure before the combustion process (in the compression ratio) will disappear.

From all the theoretical approaches described above, one conclusion can be drawn - a powerful engine with high efficiency can do without a high compression ratio, with all its inherent difficulties. To do this, the expansion ratio in the engine must be noticeably higher than the compression ratio, and the combustion of the fresh working mixture charge must occur in an extremely heated combustion chamber. In this case, during the combustion process, pressure and temperature must increase due to their natural increase due to the energy of the combustion process. Those. The combustion chamber must be hermetically sealed and not change its volume during the combustion process. Consequently: there should not be a rapid increase in the volume of the combustion chamber - with a corresponding drop in pressure and temperature (as happens in a piston engine).
By the way, during the combustion of the fuel mixture, the pressure in a locked combustion chamber of a constant volume will increase, i.e. fuel portions burning in the “second series” (more than 60% of the charge mass) will burn at a very high compression ratio (pressure about 100 atm.) the pressure of which will be created by the combustion of the first part of the fuel. Here it is necessary to note that the pressure at the end of the compression stroke even for diesel engines (these current record-breakers in terms of efficiency) is no more than 45-50 atm.
But it is impossible to meet and ensure both of these above-mentioned conditions in a piston engine with a crank mechanism. That is why piston engines operate at high compression ratios, with all the ensuing difficulties, and have not been able to overcome the efficiency level of 40% for almost 100 years.

The bottom line of this article is this: – a highly efficient high-power engine with high efficiency can have a moderate compression ratio if it has an expansion stroke noticeably greater than the compression stroke. And the combustion of the working mixture will occur in a chamber that is locked for the duration of combustion and not cooled (isochoric adiabatic process) at increasing temperature and pressure from the energy of the combustion process itself.
It is impossible to create such a design within the framework of the idea of ​​a piston engine, but in the field of ideas of rotary engines it is quite possible to create such designs. This is what the author of this text and this site does.

ARTICLE No. 2-2

REFLECTION ON COMPRESSION RATE-2:
A LOOK INTO HISTORY

01/26/13

In the first part of the article, I showed that a continuous increase in the compression ratio in a piston engine with a crank mechanism is the only way to slightly increase engine efficiency, and has clear limits to its capabilities. At compression ratios approaching 16, the Working Mixture with gasoline vapors of even 100 octane begins to burn in detonation mode, and the engine parts and body become very bulky and thick-walled (as in a diesel engine) in order to withstand increased pressures and great inertial loads. But enormous forces detonation combustion destroys even such bulky and massive parts very quickly.

But there are other ways to increase engine efficiency - these are:
A) - increasing the combustion temperature of the Working Mixture (temperature in the combustion chamber) in order to achieve complete and rapid combustion of gasoline vapors. In this case, the maximum amount of heat is released and the Working Fluid will put more pressure on the piston - i.e. do a lot of work.
Piston engines with a crank-connecting rod mechanism and a combined process of “combustion-expansion” (3rd stroke) cannot follow this path, since the oil (lubricating the walls of the kinematic pair “piston-cylinder”) at a temperature of 220 degrees already begins to char and stops lubricating. That is why the engine cylinder and piston must be cooled, and this leads to a sharp decrease in the thermal efficiency of the engine.
B) – an increase in the volume (degree) of expansion of the Working Body (expansion stroke length) for the full expansion of the gases of the Working Body. This will make full use of their excess pressure. In modern piston engines, gases with a pressure of 5-8 atmospheres are exhausted, which is a significant loss. And this despite the fact that the average effective pressure of a piston engine is only 10 atmospheres. The small length of the working stroke of a piston engine with a crank mechanism (crank mechanism) prevents the increase in the “reaction” value of this pressure.
If you increase the degree of expansion of the gases of the Working Fluid in the engine, then its efficiency will increase significantly without the need to increase the compression ratio.

The first internal combustion engine in history was the Lenoir engine. 1860

So, the topic of this article: to increase efficiency, it is possible and necessary to increase the degree of expansion of the Working Body (working gases) without increasing the compression ratio. This should lead to a significant increase in engine efficiency. Let's substantiate just such a possibility in this article.

At optimum, you need to have: the degree of compression can be very small - about 3 times, this corresponds to the pressure in the charge of the compressed Working Mixture of 4 atmospheres, but the degree of expansion (the length of the working stroke line) should exceed this small degree of compression by about 6-8 once.
This formulation of the question may seem strange and unreasonable to all experts in traditional engine designs who are accustomed to high compression ratios in piston engines. But it is precisely this paradoxical state of affairs in reality that is evidenced by a careful study of the designs of internal combustion engines that were created and operated at the dawn of the appearance of such engines, i.e. in the era of the creation of the first internal combustion engines.

So, the first misconception, which works to strengthen the myth about the need to create a high compression ratio in the engine, is justified by the fact that the first internal combustion engines, which were created 150 years ago, did not pre-compress the Working Mixture before igniting it and therefore had a completely meager efficiency - almost the same as that of primitive steam engines.
Indeed, the first operational internal combustion engine designed by Jean Lenoir (patented in 1859) did not have pre-compression of the Working Mixture and operated with an efficiency of 4%. Only 4% - this is the same as the gluttonous and bulky steam engines of that time.
But the first sample of a 4-stroke engine by Nikolaus Otto, created in 1877, worked with preliminary compression of the Working Mixture and during operation showed an efficiency of 22 percent, which was a phenomenal achievement for that time. At the same time, the compression ratio and expansion ratio (like all current piston internal combustion engines with crankshafts) were equal to each other.
Based on this data:
- Lenoir engine efficiency without compression - 4%;
— Otto engine efficiency with compression – 22%;
simple and clear conclusions are drawn - an engine operating with preliminary compression of the Working Mixture operates in a fundamentally more efficient mode, and the higher the compression ratio, the better. Over the past 140 years, this conclusion has acquired the character of a truism, and over the past 100 years, engine building has been moving along the path of increasing the value of the compression ratio, which today has already reached its limit values.

BUT in the presentation of this information there is one big BUT...
It turns out that the same Nikolaus Otto, before creating his famous 4-stroke engine with compression in 1877, a little earlier - in 1864, he created, produced and successfully sold many hundreds of his other invention - an atmospheric internal combustion engine operating without preliminary compression. The efficiency of this engine was 15%... Such a high efficiency does not fit into the theory that strong pre-compression of the Working Mixture is absolutely necessary to achieve significant engine efficiency.
Something was wrong in this topic, something was missing to understand very important facts, and I decided to study this situation. And here are the conclusions I came to:
- absolutely terrible - scanty - the efficiency of the Lenoir engine was obtained because it had absolutely unacceptably small EXPANSION RATE working gases;
- and Otto’s atmospheric engine, operating without compression, had a very decent efficiency of 15% from the fact that it had very high EXPANSION RATE working gases;
True, this Otto engine had very poor torque and a very uneven rotation mode of the main shaft, and therefore was quickly replaced by 4-stroke engines. But its efficiency value was very decent.

Let's take a close look at the dimensions of the working parts of the Lenoir engine and make some rough calculations. The piston diameter is 120 mm and the piston stroke is 100 mm. Descriptions of the engine of that time preserved data that a distance of approximately half the length of the “expansion line” was allocated for the suction of gas and air. Then the supply valve closed and the electric candle gave a spark. Those. less than half the length of the working stroke remained for the expansion process, or rather for the combined “combustion-expansion” process... The spark ignited the mixture of gas and air, a flash occurred, the temperature and pressure of the gases in the cylinder increased sharply and the working pressure forced the piston further. The maximum peak operating gas pressure on the piston was 5 atmospheres. But we must understand that the Working Mixture was ignited under conditions of an ever-deepening pressure drop - after all, the piston continued to move, creating a vacuum below atmospheric pressure... Under such conditions, only a very “rich” mixture, supersaturated with gas, could be ignited. Accordingly, combustion in this mode was extremely incomplete, and even the combustion products could hardly expand fully - after all, the length of the working stroke was extremely short. Those. for a piston with a diameter of 120 mm. the working stroke length was less than 50 mm. We can safely assume that the exhaust gases were very high pressure, and even oversaturated with unburned lighting gas. Accordingly, the engine of such parameters had a power of only 0.5 horsepower at a shaft rotation speed of 120-140 rpm. So - we look at the Lenoir engine. This engine operated on a 2-stroke cycle. Initially, along the working stroke line, the piston drew in illuminating gas and air (Working Mixture). The supply valve was then closed. An electric spark plug gave a spark - and the Working Mixture flared up, and the hot gas of increased pressure pushed the piston further. Then, during the reverse stroke, the piston pushed the combustion products out of the cylinder, and then everything was repeated again.
Those. in one working cycle - on the “expansion line” - THREE working processes were combined:
— intake of the Working Mixture;
— combustion of the Working Mixture;
— expansion of the Working Body;

CONCLUSION- the Lenoir engine had such a low efficiency and such low power primarily due to the very short length of the working stroke (when the working gases simply did not have the opportunity to work) and the very inefficient organization of work processes, when the extremely “rich” Working Mixture was ignited at a pressure noticeably lower than atmospheric under conditions of active volume expansion. Those. this engine should have been designated as an engine operating with PRE-EXPANSION (vacuum) of the Working Mixture….

NEXT - let's look at the operating diagram of another engine that operated without preliminary compression of the Working Mixture, but had an efficiency of 15%. This is a naturally aspirated Otto engine from 1864. It was a very unusual engine. In its kinematics, it seemed like something completely ugly and not suitable for work, but with a “clumsy” kinematic scheme, it operated according to a very rational scheme for organizing work processes and therefore had an efficiency of 15%.
The cylinder of this engine was mounted vertically and the engine piston moved up and down. Moreover, this engine did not have a crankshaft, and the piston had a very long toothed rack pointing upward, which engaged its teeth with the gear and rotated it.

Atmospheric engine Otto model 1864. On the right in the photo there is a piston with a long toothed rack, which gives an idea of ​​the length of the working stroke. At the same time, when the Working Mixture exploded under the piston, and the piston instantly flew up, the gear rotated idle, because a special mechanism disconnected it from the flywheel of the machine. Then, when the piston and rack reached the extreme upper point, and the pressure of the working gases in the piston ceased to act, the piston and rack, under their own weight, began to travel downward. At this moment, the gear was attached to the flywheel shaft, and the working stroke began. Thus, the engine acted in jerky impulses and had a very poor torque regime. The engine also had low power, since the force was created only by the weight of the piston and rack (i.e. gravity worked), as well as pressure atmospheric air, when cooling gases and a raised piston created a vacuum in the cylinder. That is why the engine was called atmospheric, because in it, along with the force of gravity, the force of atmospheric pressure also worked.

But on the other hand, work processes were extremely successfully organized in this engine design.
Let's look at how the work processes in this engine were organized and operated.
Initially, a special mechanism raised the piston to 1/10 of the height of the cylinder, as a result of which a rarefied space was formed under the piston and a mixture of air and gas was sucked into it. Then the piston stopped. The mixture was then ignited with an open flame through a special tube. When the flammable gas exploded, the pressure under the piston rose abruptly to 4 atm. This action threw the piston up, the volume of gas in the cylinder increased and the pressure under it dropped, since the internal volume of the piston had no connection with the atmosphere and was hermetically sealed at that moment. When the piston was thrown up by an explosion, a special mechanism disconnected the rack from the shaft. The piston, first under gas pressure, and then by inertia, rose until a significant vacuum was created under it. In this case, the working stroke turned out to be of maximum length, and continued until all the energy of the burned fuel (in the form of excess pressure of the Working Fluid) was completely spent on lifting the piston. Please note that the photograph of the engine shows that the length of the power stroke (cylinder height) is many times greater than the piston diameter. This is how long his working stroke was. While in modern piston engines the piston diameter is approximately equal to the working stroke. Only in diesel engines - these modern champions of efficiency - the stroke is approximately 20-30 percent larger than the cylinder diameter. And here - 6 or even 8 times more...
Next, the piston rushed down and the working stroke of the piston began under the load of its own weight and under the influence of atmospheric pressure. After the pressure of the gas compressed in the cylinder on the downward path of the piston reached atmospheric pressure, the exhaust valve opened and the piston, with its mass, displaced the exhaust gases. All this time, a long toothed rack was turning a gear connected by a shaft to the flywheel. This is how the engine's power was produced. After the piston returned to the lower point of the trajectory of movement, everything was repeated again - a special mechanism smoothly lifted it up and a fresh portion of the Working Mixture was sucked in.

There is one more feature - which contributed to a noticeable increase in efficiency. This feature was not found in the Lenoir engine, nor is it present in modern 2- and 4-stroke engines. In such an unusual engine design, due to the extremely complete expansion of the heated Working Fluid, the efficiency of this engine was significantly higher than the efficiency of the Lenoir engine and therefore reached 15%. In addition, the ignition of the working mixture in the Otto atmospheric engine occurred at atmospheric pressure, while in the Lenoir engine this process occurred under conditions of increasing rarefaction, i.e. under conditions of increasing drop in pressure forces, when the pressure was noticeably less than atmospheric.
It is also necessary to say that today, piledrivers - diesel hammers - operate according to a principle similar to that of this engine. True, the supply and ignition of fuel in them is arranged differently, but the general principle diagram of the movement of the working element is the same.

In the Otto atmospheric engine, at the moment the Working Mixture was ignited, the piston stood still, and when the first portions of fuel burned, an increasing pressure was created in the combustion volume, i.e. portions of fuel that burned in the second, third and subsequent stages - they burned under conditions of increasing pressure, i.e. compression of the Working Mixture occurred due to pressure increases from the flash and the release of heat from the first portions of the burning charge. At the same time, the inertia of the system pressing on the burning gas from above - a piston, a long rack and atmospheric pressure, created strong resistance to the first impulse of upward movement, which led to a noticeable increase in pressure in the burning gas environment. Those. in the atmospheric Otto engine, the combustion of the Working Mixture occurred under conditions of sharp compression of the main volume of the part of the combustible gas charge that had not yet begun to burn. Although there was no preliminary compression by the piston. It was this actual compression of a significant amount of the majority of fuel vapor that appeared during the combustion of the Working Mixture charge (together with a long working stroke) that played into the significant efficiency of the Otto atmospheric engine of the 1864 model.

But modern piston engines, like the Lenoir engine 150 years ago, are forced to ignite a fresh charge of the Working Mixture under conditions of sharply expanding volume, when the piston (and it is very powerfully moved by the connecting rod and crankshaft) desperately runs away from the bottom of the cylinder and expands the volume of the “combustion chamber” . For reference, the speed of piston movement in modern engines is 10-20 meters per second, and the speed of propagation of the flame front in a highly compressed charge of fuel vapor is 20-35 meters per second. But in modern engines, to eliminate this unpleasant situation, you can try to ignite the charge of the Working Mixture “early” - i.e. until the moving piston reaches the Top Dead Center (TDC) on the line of completion of the previous stroke, or in a position near this point. But in the Lenoir engine this was impossible, because after the piston reached TDC, the process of sucking in a fresh portion of combustible gas and air began, and its ignition was possible only under conditions of a sharply increasing volume of the “combustion chamber” and a sharp drop in pressure in a fresh portion of the Working Mixture below atmospheric. That is why the Lenoir engine had such extremely low efficiency.

It can be assumed that if the naturally aspirated Otto engine had electric spark ignition (like the earlier Lenoir engine), then its efficiency could well approach 20%. The fact is that when the charge of the Working Mixture in the cylinder was ignited with an open flame through a special tube during a flash, some part of the burning charge flew into the atmosphere through this tube and these were noticeable losses... If such losses could be eliminated, then the efficiency of this engine would be obviously higher .
But Otto did not have knowledge in the field of electrical engineering (like Lenoir), so he installed such a primitive ignition system that reduced efficiency on his naturally aspirated engine.

CONCLUSIONS from this article are as follows:

1) – a well-established opinion about the possibility of achieving extremely high engine efficiency mainly due to the maximum possible degree of pre-compression Working Mixture valid only for piston engine designs , where a piston rapidly moving from the “bottom” of the cylinder towards the crankshaft (due to forced drive from the crankshaft) at enormous speed expands the volume of the “combustion chamber” and reduces the pressure of the ignited (and also burning) charge of the Working Mixture. In the Lenoir piston engine, operating without preliminary compression of the Working Mixture, this disadvantage of piston engines was especially pronounced. Which led to its extremely low efficiency.
In modern piston engines of all types, to eliminate precisely this design “generic” defect in the organization of work processes, an extremely high degree of preliminary compression is used precisely in order to force a fresh charge of the Working Mixture to burn at sufficiently high pressures and temperatures (despite a rapid increase in the volume of the combustion chamber and a corresponding drop in pressure in this chamber), which is the key to the relatively complete combustion of the Working Mixture charge and the creation of a Working Fluid of high pressure and high temperature.
2) – in the history of technology, there are designs of engines with other kinematic schemes and a different way of organizing work processes, where even without preliminary strong compression of the fresh charge of the Working Mixture, good efficiency values ​​can be achieved even with a very primitive design. An example is an Otto atmospheric engine of the 1864 model, with an efficiency of 15%.
3) – it is possible to create a highly efficient internal combustion engine in which the processes of combustion of a fresh charge of the Working Mixture and the creation of a Working Fluid of high parameters will occur by natural compression of the burning charge due to the combustion forces themselves under conditions of a combustion chamber of constant volume. Moreover, the process of precompression to high values ​​(20-30 atmospheres), which is typical for modern piston engines, requires the expenditure of a significant amount of engine energy and the use of massive, bulky and heavy parts.
In this case, the main contribution to achieving high efficiency will be made by the large parameter of the expansion volume (long working stroke), which will be significantly larger than the compression volume.

THIS IS EXACTLY THE ENGINE, which does not require costly and cumbersome Pre-Compression of a fresh charge of the Working Mixture of high value, is what the author of this article is currently creating. In this engine, preliminary compression will be carried out to low values, and the main compression of the Working Mixture charge in a combustion chamber of constant volume will occur due to the forces of the first stage of combustion itself. Ideally, this will be detonation combustion: flash - explosion. Next, the High Pressure Working Fluid will expand to the end of its capacity in the large volume expansion sector.

Content:

In the process of moving charges inside a closed circuit, a certain amount of work is performed by the current source. It can be useful and complete. In the first case, the current source moves charges in the external circuit, while doing work, and in the second case, the charges move throughout the entire circuit. In this process great importance has the efficiency of the current source, defined as the ratio of the external and total resistance of the circuit. If the internal resistance of the source and the external resistance of the load are equal, half of the total power will be lost in the source itself, and the other half will be released at the load. In this case, the efficiency will be 0.5 or 50%.

Electrical circuit efficiency

The efficiency factor under consideration is primarily associated with physical quantities characterizing the speed of conversion or transmission of electricity. Among them, power, measured in watts, comes first. There are several formulas to determine it: P = U x I = U2/R = I2 x R.

In electrical circuits there may be different meaning voltage and charge amount, respectively, and the work performed is also different in each case. Very often there is a need to estimate the speed at which electricity is transmitted or converted. This speed represents the electrical power corresponding to the work done in a certain unit of time. In the form of a formula, this parameter will look like this: P=A/∆t. Therefore, work is displayed as the product of power and time: A=P∙∆t. The unit of work used is .

In order to determine how efficient a device, machine, electrical circuit or other similar system is in relation to power and operation, efficiency is used. This value is defined as the ratio of usefully expended energy to the total amount of energy entering the system. Efficiency is denoted by the symbol η, and is defined mathematically as the formula: η = A/Q x 100% = [J]/[J] x 100% = [%], in which A is the work performed by the consumer, Q is the energy given by the source . In accordance with the law of conservation of energy, the efficiency value is always equal to or below unity. It means that useful work cannot exceed the amount of energy expended to accomplish it.

In this way, the power losses in any system or device are determined, as well as the degree of their usefulness. For example, in conductors, power losses occur when electrical current is partially converted into thermal energy. The amount of these losses depends on the resistance of the conductor; they are not integral part useful work.

There is a difference expressed by the formula ∆Q=A-Q, which clearly shows the power loss. Here the relationship between the increase in power losses and the resistance of the conductor is very clearly visible. The most striking example is an incandescent lamp, the efficiency of which does not exceed 15%. The remaining 85% of the power is converted into thermal, that is, infrared radiation.

What is the efficiency of a current source

The considered efficiency of the entire electrical circuit allows us to better understand physical essence Efficiency of a current source, the formula of which also consists of various quantities.

In the process of moving electric charges along a closed electrical circuit, a certain amount of work is performed by the current source, which is distinguished as useful and complete. While performing useful work, the current source moves charges in the external circuit. When fully operational, charges, under the influence of a current source, move throughout the entire circuit.

They are displayed as formulas as follows:

• Useful work - Apolez = qU = IUt = I2Rt.
• Total work - Atotal = qε = Iεt = I2(R +r)t.

Based on this, we can derive formulas for the useful and total power of the current source:

• Useful power - Puse = Apoles /t = IU = I2R.
• Total power - Pfull = Afull/t = Iε = I2(R + r).

As a result, efficiency formula the current source takes the following form:

• η = Apoles/Atoll = Puse/Ptot = U/ε = R/(R + r).

Maximum useful power is achieved at a certain value of external circuit resistance, depending on the characteristics of the current source and load. However, attention should be paid to the incompatibility of maximum net power and maximum efficiency.

Study of power and efficiency of current source

The efficiency of a current source depends on many factors that should be considered in a certain sequence.

To determine, in accordance with Ohm's law, there is the following equation: i = E/(R + r), in which E is the electromotive force of the current source, and r is its internal resistance. These are constant values ​​that do not depend on the variable resistance R. Using them, you can determine the useful power consumed by the electrical circuit:

• W1 = i x U = i2 x R. Here R is the resistance of the electricity consumer, i is the current in the circuit, determined by the previous equation.

Therefore, the power value using the final variables will be shown as: W1 = (E2 x R)/(R + r).

Since it is an intermediate variable, in this case the function W1(R) can be analyzed for its extremum. For this purpose, it is necessary to determine the value of R at which the value of the first derivative of the useful power associated with the variable resistance (R) will be equal to zero: dW1/dR = E2 x [(R + r)2 - 2 x R x (R + r) ] = E2 x (Ri + r) x (R + r - 2 x R) = E2(r - R) = 0 (R + r)4 (R + r)4 (R + r)3

From this formula we can conclude that the value of the derivative can be zero only under one condition: the resistance of the electricity receiver (R) from the current source must reach the value of the internal resistance of the source itself (R => r). Under these conditions, the value of the efficiency factor η will be determined as the ratio of the useful and total power of the current source - W1/W2. Since at the maximum point of useful power the resistance of the energy consumer of the current source will be the same as the internal resistance of the current source itself, in this case the efficiency will be 0.5 or 50%.

Current power and efficiency problems

Basic theoretical information

Mechanical work

The energy characteristics of motion are introduced based on the concept mechanical work or force work. Work done by a constant force F, called physical quantity, equal to the product of the force and displacement modules multiplied by the cosine of the angle between the force vectors F and movements S:

Work is a scalar quantity. It can be either positive (0° ≤ α < 90°), так и отрицательна (90° < α ≤ 180°). At α = 90° the work done by the force is zero. In the SI system, work is measured in joules (J). A joule is equal to the work done by a force of 1 newton to move 1 meter in the direction of the force.

If the force changes over time, then to find the work, build a graph of the force versus displacement and find the area of ​​the figure under the graph - this is the work:

An example of a force whose modulus depends on the coordinate (displacement) is the elastic force of a spring, which obeys Hooke’s law ( F control = kx).

Power

The work done by a force per unit time is called power. Power P(sometimes denoted by the letter N) – physical quantity equal to the work ratio A to a period of time t during which this work was completed:

This formula calculates average power, i.e. power generally characterizing the process. So, work can also be expressed in terms of power: A = Pt(if, of course, the power and time of doing the work are known). The unit of power is called the watt (W) or 1 joule per second. If the motion is uniform, then:

Using this formula we can calculate instant power(power at a given time), if instead of speed we substitute the value of instantaneous speed into the formula. How do you know what power to count? If the problem asks for power at a moment in time or at some point in space, then instantaneous is considered. If they ask about power over a certain period of time or part of the route, then look for average power.

Efficiency - efficiency factor, is equal to the ratio of useful work to expended, or useful power to expended:

Which work is useful and which is wasted is determined from the conditions of a specific task through logical reasoning. For example, if a crane does the work of lifting a load to a certain height, then the useful work will be the work of lifting the load (since it is for this purpose that the crane was created), and the expended work will be the work done by the crane’s electric motor.

So, useful and expended power do not have a strict definition, and are found by logical reasoning. In each task, we ourselves must determine what in this task was the goal of doing work (useful work or power), and what was the mechanism or way of doing all the work (expended power or work).

In general, efficiency shows how efficiently a mechanism converts one type of energy into another. If the power changes over time, then the work is found as the area of ​​the figure under the graph of power versus time:

Kinetic energy

A physical quantity equal to half the product of a body’s mass and the square of its speed is called kinetic energy of the body (energy of movement):

That is, if a car weighing 2000 kg moves at a speed of 10 m/s, then it has kinetic energy equal to E k = 100 kJ and is capable of doing 100 kJ of work. This energy can turn into heat (when a car brakes, the tires of the wheels, the road and the brake discs heat up) or can be spent on deforming the car and the body that the car collides with (in an accident). When calculating kinetic energy, it does not matter where the car is moving, since energy, like work, is a scalar quantity.

A body has energy if it can do work. For example, a moving body has kinetic energy, i.e. energy of motion, and is capable of doing work to deform bodies or impart acceleration to bodies with which a collision occurs.

The physical meaning of kinetic energy: in order for a body at rest with a mass m began to move at speed v it is necessary to do work equal to the obtained value of kinetic energy. If the body has a mass m moves at speed v, then to stop it it is necessary to do work equal to its initial kinetic energy. When braking, kinetic energy is mainly (except for cases of impact, when the energy goes to deformation) “taken away” by the friction force.

Theorem on kinetic energy: the work of the resultant force is equal to the change in the kinetic energy of the body:

The theorem on kinetic energy is also valid in the general case, when a body moves under the influence of a changing force, the direction of which does not coincide with the direction of movement. It is convenient to apply this theorem in problems involving acceleration and deceleration of a body.

Potential energy

Along with kinetic energy or energy of motion in physics important role plays concept potential energy or energy of interaction of bodies.

Potential energy is determined by the relative position of bodies (for example, the position of the body relative to the surface of the Earth). The concept of potential energy can be introduced only for forces whose work does not depend on the trajectory of the body and is determined only by the initial and final positions (the so-called conservative forces). The work done by such forces on a closed trajectory is zero. This property is possessed by gravity and elastic force. For these forces we can introduce the concept of potential energy.

Potential energy of a body in the Earth's gravity field calculated by the formula:

The physical meaning of the potential energy of a body: potential energy is equal to the work done by gravity when the body is lowered zero level (h– distance from the center of gravity of the body to the zero level). If a body has potential energy, then it is capable of doing work when this body falls from a height h to zero level. The work done by gravity is equal to the change in the potential energy of the body, taken from opposite sign:

Often in energy problems one has to find the work of lifting (turning over, getting out of a hole) the body. In all these cases, it is necessary to consider the movement not of the body itself, but only of its center of gravity.

The potential energy Ep depends on the choice of the zero level, that is, on the choice of the origin of the OY axis. In each problem, the zero level is chosen for reasons of convenience. What has a physical meaning is not the potential energy itself, but its change when a body moves from one position to another. This change is independent of the choice of zero level.

Potential energy of a stretched spring calculated by the formula:

Where: k– spring stiffness. An extended (or compressed) spring can set a body attached to it in motion, that is, impart kinetic energy to this body. Consequently, such a spring has a reserve of energy. Tension or compression X must be calculated from the undeformed state of the body.

The potential energy of an elastically deformed body is equal to the work done by the elastic force during the transition from a given state to a state with zero deformation. If in the initial state the spring was already deformed, and its elongation was equal to x 1, then upon transition to a new state with elongation x 2, the elastic force will do work equal to the change in potential energy, taken with the opposite sign (since the elastic force is always directed against the deformation of the body):

Potential energy during elastic deformation is the energy of interaction of individual parts of the body with each other by elastic forces.

The work of the friction force depends on the path traveled (this type of force, whose work depends on the trajectory and the path traveled is called: dissipative forces). The concept of potential energy for the friction force cannot be introduced.

Efficiency

Efficiency factor (efficiency)– characteristic of the efficiency of a system (device, machine) in relation to the conversion or transmission of energy. It is determined by the ratio of usefully used energy to the total amount of energy received by the system (the formula has already been given above).

Efficiency can be calculated both through work and through power. Useful and expended work (power) are always determined by simple logical reasoning.

In electric motors, efficiency is the ratio of the performed (useful) mechanical work to the electrical energy received from the source. In heat engines, the ratio of useful mechanical work to the amount of heat expended. In electrical transformers, the ratio of the electromagnetic energy received in the secondary winding to the energy consumed by the primary winding.

Due to its generality, the concept of efficiency makes it possible to compare and evaluate such different systems as nuclear reactors, electric generators and engines, thermal power plants, semiconductor devices, biological objects, etc.

Due to inevitable energy losses due to friction, heating of surrounding bodies, etc. Efficiency is always less than unity. Accordingly, the efficiency is expressed in shares of the energy expended, that is, in the form proper fraction or as a percentage, and is a dimensionless quantity. Efficiency characterizes how efficiently a machine or mechanism operates. The efficiency of thermal power plants reaches 35-40%, internal combustion engines with supercharging and pre-cooling - 40-50%, dynamos and high-power generators - 95%, transformers - 98%.

A problem in which you need to find the efficiency or it is known, you need to start with logical reasoning - which work is useful and which is wasted.

Law of conservation of mechanical energy

Total mechanical energy is called the sum of kinetic energy (i.e. the energy of motion) and potential (i.e. the energy of interaction of bodies by the forces of gravity and elasticity):

If mechanical energy does not transform into other forms, for example, into internal (thermal) energy, then the sum of kinetic and potential energy remains unchanged. If mechanical energy turns into thermal energy, then the change in mechanical energy is equal to the work of the friction force or energy losses, or the amount of heat released, and so on, in other words, the change in total mechanical energy is equal to the work of external forces:

The sum of the kinetic and potential energy of the bodies that make up a closed system (i.e. one in which there are no external forces acting, and their work is correspondingly zero) and the gravitational and elastic forces interacting with each other remains unchanged:

This statement expresses law of conservation of energy (LEC) in mechanical processes. It is a consequence of Newton's laws. The law of conservation of mechanical energy is satisfied only when bodies in a closed system interact with each other by forces of elasticity and gravity. In all problems on the law of conservation of energy there will always be at least two states of a system of bodies. The law states that the total energy of the first state will be equal to the total energy of the second state.

Algorithm for solving problems on the law of conservation of energy:

1. Find the points of the initial and final position of the body.
2. Write down what or what energies the body has at these points.
3. Equate the initial and final energy of the body.
4. Add other necessary equations from previous physics topics.
5. Solve the resulting equation or system of equations using mathematical methods.

It is important to note that the law of conservation of mechanical energy made it possible to obtain a relationship between the coordinates and velocities of a body at two different points of the trajectory without analyzing the law of motion of the body at all intermediate points. The application of the law of conservation of mechanical energy can greatly simplify the solution of many problems.

In real conditions, moving bodies are almost always acted upon, along with gravitational forces, elastic forces and other forces, by friction forces or environmental resistance forces. The work done by the friction force depends on the length of the path.

If friction forces act between the bodies that make up a closed system, then mechanical energy is not conserved. Part of the mechanical energy is converted into internal energy of bodies (heating). Thus, energy as a whole (i.e., not only mechanical) is conserved in any case.

During any physical interactions, energy neither appears nor disappears. It just changes from one form to another. This experimentally established fact expresses a fundamental law of nature - law of conservation and transformation of energy.

One of the consequences of the law of conservation and transformation of energy is the statement about the impossibility of creating a “perpetual motion machine” (perpetuum mobile) - a machine that could do work indefinitely without consuming energy.

Various tasks for work

If the problem requires finding mechanical work, then first select a method for finding it:

1. A job can be found using the formula: A = FS∙cos α . Find the force that does the work and the amount of displacement of the body under the influence of this force in the chosen frame of reference. Note that the angle must be chosen between the force and displacement vectors.
2. Job external force can be found as the difference in mechanical energy in the final and initial situations. Mechanical energy is equal to the sum of the kinetic and potential energies of the body.
3. The work done to lift a body at a constant speed can be found using the formula: A = mgh, Where h- height to which it rises body center of gravity.
4. Work can be found as the product of power and time, i.e. according to the formula: A = Pt.
5. The work can be found as the area of ​​the figure under the graph of force versus displacement or power versus time.

Law of conservation of energy and dynamics of rotational motion

The problems of this topic are quite complex mathematically, but if you know the approach, they can be solved using a completely standard algorithm. In all problems you will have to consider the rotation of the body in the vertical plane. The solution will come down to the following sequence of actions:

1. You need to determine the point you are interested in (the point at which you need to determine the speed of the body, the tension force of the thread, weight, and so on).
2. Write down Newton’s second law at this point, taking into account that the body rotates, that is, it has centripetal acceleration.
3. Write down the law of conservation of mechanical energy so that it contains the speed of the body at that very interesting point, as well as the characteristics of the state of the body in some state about which something is known.
4. Depending on the condition, express the squared speed from one equation and substitute it into the other.
5. Carry out the remaining necessary mathematical operations to obtain the final result.

When solving problems, you need to remember that:

• The condition for passing the top point when rotating on a thread at a minimum speed is the support reaction force N at the top point is 0. The same condition is met when passing the top point of the dead loop.
• When rotating on a rod, the condition for passing the entire circle is: the minimum speed at the top point is 0.
• The condition for the separation of a body from the surface of the sphere is that the support reaction force at the separation point is zero.

Inelastic collisions

The law of conservation of mechanical energy and the law of conservation of momentum make it possible to find solutions to mechanical problems in cases where the acting forces are unknown. An example of this type of problem is the impact interaction of bodies.

By impact (or collision) It is customary to call a short-term interaction of bodies, as a result of which their speeds experience significant changes. During a collision of bodies, short-term impact forces act between them, the magnitude of which, as a rule, is unknown. Therefore, it is impossible to consider the impact interaction directly using Newton's laws. The application of the laws of conservation of energy and momentum in many cases makes it possible to exclude the collision process itself from consideration and obtain a connection between the velocities of bodies before and after the collision, bypassing all intermediate values ​​of these quantities.

We often have to deal with the impact interaction of bodies in everyday life, in technology and in physics (especially in the physics of the atom and elementary particles). In mechanics, two models of impact interaction are often used - absolutely elastic and absolutely inelastic impacts.

Absolutely inelastic impact They call this impact interaction in which bodies connect (stick together) with each other and move on as one body.

In a completely inelastic collision, mechanical energy is not conserved. It partially or completely turns into the internal energy of bodies (heating). To describe any impacts, you need to write down both the law of conservation of momentum and the law of conservation of mechanical energy, taking into account the heat released (it is highly advisable to make a drawing first).

Absolutely elastic impact

Absolutely elastic impact called a collision in which the mechanical energy of a system of bodies is conserved. In many cases, collisions of atoms, molecules and elementary particles obey the laws of absolutely elastic impact. With an absolutely elastic impact, along with the law of conservation of momentum, the law of conservation of mechanical energy is satisfied. A simple example A perfectly elastic collision can be a central impact of two billiard balls, one of which was at rest before the collision.

Central strike balls is called a collision in which the velocities of the balls before and after the impact are directed along the line of centers. Thus, using the laws of conservation of mechanical energy and momentum, it is possible to determine the velocities of the balls after a collision if their velocities before the collision are known. Central impact is very rarely implemented in practice, especially when it comes to collisions of atoms or molecules. In a non-central elastic collision, the velocities of particles (balls) before and after the collision are not directed in one straight line.

A special case of an off-central elastic impact can be the collision of two billiard balls of the same mass, one of which was motionless before the collision, and the speed of the second was not directed along the line of the centers of the balls. In this case, the velocity vectors of the balls after an elastic collision are always directed perpendicular to each other.

Conservation laws. Complex tasks

Multiple bodies

In some problems on the law of conservation of energy, the cables with which certain objects are moved can have mass (that is, not be weightless, as you might already be used to). In this case, the work of moving such cables (namely their centers of gravity) also needs to be taken into account.

If two bodies connected by a weightless rod rotate in a vertical plane, then:

1. choose a zero level to calculate potential energy, for example at the level of the axis of rotation or at the level of the lowest point of one of the weights and be sure to make a drawing;
2. write down the law of conservation of mechanical energy, in which on the left side we write the sum of the kinetic and potential energy of both bodies in the initial situation, and on the right side we write the sum of the kinetic and potential energy of both bodies in the final situation;
3. take into account that the angular velocities of the bodies are the same, then the linear velocities of the bodies are proportional to the radii of rotation;
4. if necessary, write down Newton's second law for each of the bodies separately.

Shell burst

When a projectile explodes, explosive energy is released. To find this energy, it is necessary to subtract the mechanical energy of the projectile before the explosion from the sum of the mechanical energies of the fragments after the explosion. We will also use the law of conservation of momentum, written in the form of the cosine theorem (vector method) or in the form of projections onto selected axes.

Collisions with a heavy plate

Let us meet a heavy plate that moves at speed v, a light ball of mass moves m with speed u n. Since the momentum of the ball is much less than the momentum of the plate, after the impact the speed of the plate will not change, and it will continue to move at the same speed and in the same direction. As a result of the elastic impact, the ball will fly away from the plate. It is important to understand here that the speed of the ball relative to the plate will not change. In this case, for the final speed of the ball we obtain:

Thus, the speed of the ball after impact increases by twice the speed of the wall. Similar reasoning for the case when before the impact the ball and the plate were moving in the same direction leads to the result that the speed of the ball decreases by twice the speed of the wall:

In physics and mathematics, among other things, three most important conditions must be met:

1. Study all topics and complete all tests and assignments given in the educational materials on this site. To do this, you need nothing at all, namely: devote three to four hours every day to preparing for the CT in physics and mathematics, studying theory and solving problems. The fact is that CT is an exam where it is not enough just to know physics or mathematics, you also need to be able to solve a large number of problems quickly and without failures. different topics and of varying complexity. The latter can only be learned by solving thousands of problems.
2. Learn all the formulas and laws in physics, and formulas and methods in mathematics. In fact, this is also very simple to do; there are only about 200 necessary formulas in physics, and even a little less in mathematics. In each of these subjects there are about a dozen standard methods for solving problems of a basic level of complexity, which can also be learned, and thus, completely automatically and without difficulty solving most of the CT at the right time. After this, you will only have to think about the most difficult tasks.
3. Attend all three stages of rehearsal testing in physics and mathematics. Each RT can be visited twice to decide on both options. Again, on the CT, in addition to the ability to quickly and efficiently solve problems, and knowledge of formulas and methods, you must also be able to properly plan time, distribute forces, and most importantly, correctly fill out the answer form, without confusing the numbers of answers and problems, or your own last name. Also, during RT, it is important to get used to the style of asking questions in problems, which may seem very unusual to an unprepared person at the DT.

Successful, diligent and responsible implementation of these three points will allow you to show an excellent result at the CT, the maximum of what you are capable of.

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Efficiency is a characteristic of the operating efficiency of a device or machine. Efficiency is defined as the ratio of the useful energy at the output of the system to the total amount of energy supplied to the system. Efficiency is a dimensionless value and is often determined as a percentage.

Formula 1 - efficiency

Where- A useful work

—Q total work that was spent

Any system that does any work must receive energy from outside, with the help of which the work will be done. Take, for example, a voltage transformer. A mains voltage of 220 volts is supplied to the input, and 12 volts is removed from the output to power, for example, an incandescent lamp. So the transformer converts the energy at the input to the required value at which the lamp will operate.

But not all the energy taken from the network will reach the lamp, since there are losses in the transformer. For example, the loss of magnetic energy in the core of a transformer. Or losses in the active resistance of the windings. Where electrical energy will be converted into heat without reaching the consumer. This thermal energy is useless in this system.

Since power losses cannot be avoided in any system, the efficiency is always below unity.

Efficiency can be considered for the entire system, consisting of many individual parts. So, if you determine the efficiency for each part separately, then the total efficiency will be equal to the product of the efficiency coefficients of all its elements.

In conclusion, we can say that efficiency determines the level of perfection of any device in the sense of transmitting or converting energy. It also indicates how much energy supplied to the system is spent on useful work.

General provisions

Efficiency is defined as the ratio of useful, or delivered, power P 2 to power consumption P 1:

Modern electric machines have a high efficiency factor (efficiency). Thus, for DC machines with a power of 10 kW, the efficiency is 83 - 87%, with a power of 100 kW - 88 - 93% and with a power of 1000 kW - 92 - 96%. Only small machines have relatively low efficiency; for example, a 10 W DC motor has an efficiency of 30 - 40%.

Electric machine efficiency curve η = f(P 2) first increases rapidly with increasing load, then efficiency reaches its maximum value (usually at a load close to the rated load) and decreases at high loads (Figure 1). The latter is explained by the fact that certain types of losses (electrical I a 2 r and additional ones) grow faster than the useful power.

Direct and indirect methods for determining efficiency

Direct method for determining efficiency from experimental values P 1 and P 2 according to formula (1) can give a significant inaccuracy, since, firstly, P 1 and P 2 are close in value and, secondly, their experimental determination is associated with errors. The greatest difficulties and errors are caused by measuring mechanical power.

If, for example, the true power values P 1 = 1000 kW and P 2 = 950 kW can be determined with an accuracy of 2%, then instead of the true value of efficiency.

η = 950/1000 = 0,95

available

Therefore, GOST 25941-83, “Rotating electric machines. Methods for determining losses and efficiency,” prescribes for machines with η% ≥ 85% an indirect method for determining efficiency, in which the amount of losses is determined from experimental data p Σ .

Substituting into formula (1) P 2 = P 1 - pΣ , we get

(3)

Using the substitution here P 1 = P 2 + pΣ, we get another form of the formula:

(4)

Since it is more convenient and accurate to measure electrical power (for motors P 1 and for generators P 2), then formula (3) is more suitable for engines and formula (4) for generators. Methods for experimental determination of individual losses and the amount of losses pΣ are described in standards for electrical machines and in manuals for testing and researching electrical machines. Even if pΣ is determined with significantly less accuracy than P 1 or P 2, when using formulas (3) and (4) instead of expression (1), significantly more accurate results are obtained.

Conditions for maximum efficiency

Different types of losses depend on the load in different ways. It can generally be assumed that some types of losses remain constant as the load changes, while others are variable. For example, if a DC generator operates at a constant rotation speed and a constant excitation flux, then the mechanical and magnetic losses are also constant. On the contrary, electrical losses in the windings of the armature, additional poles and compensation windings change proportionally I a ², and in brush contacts - proportionally I A. The generator voltage is also approximately constant, and therefore with a certain degree of accuracy P 2 ∼ I A.

Thus, in a general, somewhat idealized case, we can assume that

Where p 0 – constant losses, independent of load; p 1 – value of losses depending on the first degree k ng at rated load; p 2 – value of losses depending on the square k ng, at rated load.

Let's substitute P 2 of (5) and pΣ from (7) into the efficiency formula.

(8)

Let us establish at what value k ng efficiency reaches its maximum value, for which we determine the derivative dη/ dk ng according to formula (8) and equate it to zero:

This equation is satisfied when its denominator is equal to infinity, that is, when k ng = ∞. This case is not of interest. Therefore, it is necessary to set the numerator equal to zero. In this case we get

Thus, the efficiency will be maximum at a load at which variable losses k ng ² × p 2, depending on the square of the load, become equal to the constant losses p 0 .

The value of the load factor at maximum efficiency, according to formula (9),

(10)

If a machine is designed for a given value η max, then since the losses k ng × p 1 are usually relatively small, we can assume that

p 0 + p 2 ≈ pΣ = const.

Changing the loss ratio p 0 and p 2, the maximum efficiency can be achieved at different loads. If the machine operates mostly at loads close to the rated load, then it is advantageous that the value k ng [see formula (10)] was close to unity. If the machine operates mainly under light loads, then it is advantageous for the value k ng [see formula (10)] was correspondingly less.