Moment of inertia of the crank mechanism. Kinematic calculation of kshm. Choice l and length Lsh connecting rod

Kinematics and dynamics of the crank connecting rod mechanism. The crank mechanism is the main mechanism of a piston engine, which perceives and transmits significant loads. Therefore, the calculation of the strength of KShM is important. In turn, the calculations of many engine parts depend on the kinematics and dynamics of the crankshaft. The kinematic analysis of the crankshaft establishes the laws of motion of its links, primarily the piston and connecting rod. To simplify the study of the crankshaft, we consider that the crankshaft cranks rotate uniformly, i.e. with constant angular speed.

There are several types and varieties of crank mechanisms (Fig. 2.35). Of greatest interest from the point of view of kinematics is the central (axial), offset (de-axial) and trailer connecting rod.

The central crank mechanism (Fig. 2.35.a) is a mechanism in which the cylinder axis intersects with the axis of the engine crankshaft.

defining geometric dimensions mechanism are the radius of the crank and the length of the connecting rod. Their ratio is a constant value for all geometrically similar central crank mechanisms, for modern automotive engines .

In a kinematic study of the crank mechanism, piston stroke, crank angle of rotation, angle of deviation of the connecting rod axis in the plane of its swing from the cylinder axis are usually taken into consideration (deviation in the direction of rotation of the shaft is considered positive, and in the opposite - negative), angular velocity. The piston stroke and connecting rod length are the main design parameters of the central crank mechanism.

Kinematics of the central crankshaft. The task of the kinematic calculation is to find the analytical dependences of the displacement, speed and acceleration of the piston on the angle of rotation of the crankshaft. According to the kinematic calculation, a dynamic calculation is performed and the forces and moments acting on the engine parts are determined.

In a kinematic study of the crank mechanism, it is assumed that then the angle of rotation of the shaft is proportional to time, therefore all kinematic quantities can be expressed as a function of the angle of rotation of the crank. The position of the piston at TDC is taken as the initial position of the mechanism. The displacement of the piston depending on the angle of rotation of the crank of the engine with a central crankshaft is calculated by the formula. (one)

Lecture 7Piston movement for each of the angles of rotation can be determined graphically, which is called the Brix method. To do this, the Brix correction is deposited from the center of the circle with a radius towards the BDC. there is a new center. From the center, through certain values ​​(for example, every 30 °), a radius vector is drawn until it intersects with a circle. The projections of the intersection points on the axis of the cylinder (line TDC-BDC) give the desired positions of the piston for the given values ​​of the angle .

Figure 2.36 shows the dependence of piston displacement on the angle of rotation of the crankshaft.

piston speed. Derivative of piston displacement - equation (1) with respect to time

rotation gives the speed of the piston: (2)

Similar to the movement of the piston, the piston speed can also be represented in the form of two components: where is the component of the first order piston speed, which is determined by ; is the second-order piston velocity component, which is determined by The component is the piston speed with an infinitely long connecting rod. Component V 2 is a correction to the piston speed for the final length of the connecting rod. The dependence of the change in piston speed on the angle of rotation of the crankshaft is shown in Fig. 2.37. The speed reaches its maximum values ​​at crankshaft angles of less than 90 and more than 270°. Meaning top speed piston with sufficient accuracy can be determined as

piston acceleration is defined as the first derivative of velocity with respect to time or as the second derivative of piston displacement with respect to time: (3)

where and - harmonic components of the first and second order of the piston acceleration, respectively. In this case, the first component expresses the acceleration of the piston with an infinitely long connecting rod, and the second component expresses the acceleration correction for the finite length of the connecting rod. The dependences of the change in the acceleration of the piston and its components on the angle of rotation of the crankshaft are shown in Fig. 2.38.

Acceleration reaches maximum values ​​when the piston is at TDC, and minimum values ​​are at BDC or near BDC. These curve changes in the area from 180 to ±45° depend on the value .

Ratio of piston stroke to cylinder diameter is one of the main parameters that determines the dimensions and weight of the engine. In automotive engines, the values ​​range from 0.8 to 1.2. Engines with > 1 are called long-stroke, and with < 1 - short-stroke. This ratio directly affects the piston speed, and hence the engine power. As the value decreases, the following advantages are evident: the motor height is reduced; due to a decrease in the average piston speed, mechanical losses and wear of parts is reduced; conditions for the placement of valves are improved and prerequisites are created for increasing their size; it becomes possible to increase the diameter of the main and connecting rod journals, which increases the rigidity of the crankshaft.

However, there are also negative points: the length of the engine and the length of the crankshaft increase; the loads on the parts from the forces of gas pressure and from the forces of inertia increase; the height of the combustion chamber decreases and its shape worsens, which in carburetor engines leads to an increase in the tendency to detonation, and in diesel engines to a deterioration in the conditions of mixture formation.

It is considered advisable to decrease the value with an increase in the speed of the engine.

Values ​​for various engines: carbureted engines- ; diesel engines of medium speed -; high speed diesels.

When choosing values, it should be taken into account that the forces acting in the crankshaft depend to a greater extent on the cylinder diameter and to a lesser extent on the piston stroke.

Dynamics of the crank mechanism. When the engine is running, forces and moments act in the crankshaft, which not only affect the crankshaft parts and other components, but also cause the engine to run unevenly. These forces include: the gas pressure force is balanced in the engine itself and is not transferred to its supports; the force of inertia is applied to the center of the reciprocating masses and is directed along the axis of the cylinder, through the bearings of the crankshaft they act on the engine housing, causing it to vibrate on the supports in the direction of the axis of the cylinder; the centrifugal force from the rotating masses is directed along the crank in its middle plane, acting through the crankshaft bearings on the engine housing, causing the engine to oscillate on the supports in the direction of the crank. In addition, there are forces such as pressure on the piston from the crankcase, and gravity forces of the crankshaft, which are not taken into account due to their relatively small magnitude. All forces acting in the engine interact with the resistance on the crankshaft, friction forces and are perceived by the engine mounts. During each working cycle (720° for four-stroke and 360° for two-stroke engines), the forces acting in the crankshaft continuously change in magnitude and direction, and to establish the nature of the change in these forces from the angle of rotation of the crankshaft, they are determined every 10÷30 0 for certain positions of the crankshaft.

Gas pressure forces act on the piston, walls and cylinder head. To simplify the dynamic calculation, the gas pressure forces are replaced by a single force directed along the axis of the cylinder and applied to the axis of the piston pin.

This force is determined for each moment of time (angle of rotation of the crankshaft) according to the indicator diagram obtained on the basis of a thermal calculation or taken directly from the engine using special installation. Figure 2.39 shows detailed indicator diagrams of the forces acting in the crankshaft, in particular, the change in the gas pressure force () on the angle of rotation of the crankshaft. Forces of inertia. To determine the inertia forces acting in the crankshaft, it is necessary to know the masses of the moving parts. To simplify the calculation of the mass of moving parts, we will replace it with a system of conditional masses equivalent to real-life masses. This replacement is called mass reduction. Bringing the masses of the parts of the KShM. According to the nature of the movement of the mass of parts, the crankshaft can be divided into three groups: parts moving reciprocating (piston group and the upper head of the connecting rod); parts that perform rotational motion (crankshaft and lower connecting rod head); parts that make a complex plane-parallel movement (rod rod).

mass piston group() is considered to be concentrated on the axis of the piston pin and the point (Fig. 2.40.a). I replace the mass of the connecting rod group with two masses: - concentrated on the axis of the piston pin at the point , - on the axis of the crank at the point . The values ​​of these masses are found by the formulas:

;

where is the length of the connecting rod; - distance from the center of the crank head to the center of gravity of the connecting rod. For most existing engines is in the limit, and in the limit. The value can be determined through the structural mass obtained on the basis of statistical data. The reduced mass of the entire crank is determined by the sum of the reduced masses of the connecting rod journal and cheeks:

After bringing the masses, the crank mechanism can be represented as a system consisting of two concentrated masses connected by a rigid weightless connection (Fig. 2.41.b). Masses concentrated at a point and reciprocating wounds . Masses concentrated at a point and rotating wounds . For an approximate determination of the value , and constructive masses can be used.

Determination of the forces of inertia. The forces of inertia acting in the KShM, in accordance with the nature of the movement of the reduced masses, are divided into the forces of inertia of translationally moving masses and the centrifugal forces of inertia of rotating masses. The force of inertia from reciprocating moving masses can be determined by formula (4). The minus sign indicates that the force of inertia is directed in the direction opposite to the acceleration. The centrifugal force of inertia of the rotating masses is constant in magnitude and directed away from the axis of the crankshaft. Its value is determined by the formula (5) A complete picture of the loads acting in the parts of the crankshaft can be obtained only as a result of the combination of the action of various forces that arise during the operation of the engine.

The total forces acting in the KShM. The forces acting in a single-cylinder engine are shown in Fig. 2.41. In KShM, the gas pressure force acts , inertia force of reciprocating masses and centrifugal force . The forces and are applied to the piston and act along its axis. Adding these two forces, we obtain the total force acting along the axis of the cylinder: (6). The displaced force in the center of the piston pin is decomposed into two components: - force directed along the axis of the connecting rod; - force perpendicular to the cylinder wall. Strength P N is perceived by the side surface of the cylinder wall and causes wear of the piston and cylinder. Strength , applied to the connecting rod journal, is decomposed into two components: (7) - tangential force tangential to the crank radius circle; (8) - normal force (radial) directed along the radius of the crank. The indicator torque of one cylinder is determined by the value: (9) The normal and tangential forces transferred to the center of the crankshaft form the resultant force, which is parallel and equal in magnitude to the force . The force loads the main bearings of the crankshaft. In turn, the force can be decomposed into two components: the force P"N, perpendicular to the axis of the cylinder, and the force R", acting along the axis of the cylinder. Forces P" N and P N form a pair of forces, the moment of which is called overturning. Its value is determined by the formula (10) This moment is equal to the indicator torque and is directed in the opposite direction: . The torque is transmitted through the transmission to the drive wheels, and the overturning moment is taken up by the engine mounts. Strength R" equal to strength R, and similarly to the latter, it can be represented as . The component is balanced by the gas pressure force applied to the cylinder head, and is a free unbalanced force transmitted to the engine mounts.

The centrifugal force of inertia is applied to the connecting rod journal of the crank and is directed away from the axis of the crankshaft. It, like the force, is unbalanced and is transmitted through the main bearings to the engine mounts.

Forces acting on the crankshaft journals. The crankpin is subjected to radial force Z, tangential force T and centrifugal force from the rotating mass of the connecting rod. Forces Z and are directed along one straight line, therefore their resultant or (11)

The resultant of all forces acting on the connecting rod journal is calculated by the formula (12) Force causes wear on the crankpin. The resulting force applied to the crankshaft journal is found graphically as the forces transmitted from two adjacent crankshafts.

Analytical and graphical representation of forces and moments. The analytical representation of the forces and moments acting in the KShM is represented by formulas (4) - (12).

More clearly, the change in the forces acting in the crankshaft depending on the angle of rotation of the crankshaft can be represented as expanded diagrams that are used to calculate the strength of the crankshaft parts, assess the wear of the rubbing surfaces of the parts, analyze the uniformity of the stroke and determine the total torque of multi-cylinder engines, as well as construction of polar diagrams of loads on the shaft neck and its bearings.

In multi-cylinder engines, the variable torques of the individual cylinders are summed along the length of the crankshaft, resulting in a total torque at the end of the shaft. The values ​​of this moment can be determined graphically. To do this, the projection of the curve on the x-axis is divided into equal segments (the number of segments is equal to the number of cylinders). Each segment is divided into several equal parts (here, 8). For each abscissa point obtained, I determine the algebraic sum of the ordinates of two curves (above the abscissa of the value with the “+” sign, below the abscissa of the value with the “-” sign). The obtained values ​​are plotted respectively in coordinates , and the resulting points are connected by a curve (Fig. 2.43). This curve is the resulting torque curve for one engine cycle.

To determine the average torque value, the area limited by the torque curve and the y-axis is calculated (above the axis is positive, below it is negative: where is the length of the diagram along the x-axis; -scale.

Since the losses inside the engine were not taken into account when determining the torque, then, expressing the effective torque through the indicator, we get where is the mechanical efficiency of the engine

The order of operation of the engine cylinders, depending on the location of the cranks and the number of cylinders. In a multi-cylinder engine, the location of the crankshaft cranks must, firstly, ensure the uniformity of the engine stroke, and, secondly, ensure the mutual balance of the inertia forces of the rotating masses and reciprocating masses. To ensure a uniform stroke, it is necessary to create conditions for alternating flashes in the cylinders at equal intervals of the angle of rotation of the crankshaft. Therefore, for a single-row engine, the angle corresponding to the angular interval between flashes in a four-stroke cycle is calculated by the formula, where i- the number of cylinders, and with a two-stroke according to the formula. The uniformity of the alternation of flashes in the cylinders of a multi-row engine, in addition to the angle between the crankshaft cranks, is also affected by the angle between the rows of cylinders. To satisfy the balance requirement, it is necessary that the number of cylinders in one row and, accordingly, the number of crankshaft cranks be even, and the cranks must be located symmetrically relative to the middle of the crankshaft. The arrangement of cranks, symmetrical relative to the middle of the crankshaft, is called "mirror". When choosing the shape of the crankshaft, in addition to the balance of the engine and the uniformity of its stroke, the order of operation of the cylinders is also taken into account. Figure 2.44 shows the sequence of operation of the cylinders of single-row (a) and V-shaped (b) four-stroke engines

The optimal order of operation of the cylinders, when the next stroke occurs in the cylinder furthest from the previous one, reduces the load on the main bearings of the crankshaft and improves engine cooling.

Engine balancingForces and moments that cause unbalance of the engine. The forces and moments acting in the KShM are continuously changing in magnitude and direction. At the same time, acting on the engine mounts, they cause vibration of the frame and the entire vehicle, as a result of which the fastening connections are weakened, the adjustments of units and mechanisms are violated, the use of instrumentation is difficult, and the noise level increases. This negative impact is reduced in various ways, in including the selection of the number and location of cylinders, the shape of the crankshaft, as well as using balancing devices, ranging from simple counterweights to complex balancing mechanisms.

Actions aimed at eliminating the causes of vibrations, i.e., unbalance of the engine, are called engine balancing.

Balancing the engine is reduced to creating such a system in which the resultant forces and their moments are constant in magnitude or equal to zero. The engine is considered to be fully balanced if, under steady-state operation, the forces and moments acting on its supports are constant in magnitude and direction. All reciprocating internal combustion engines have a reactive torque that is opposite to the torque, which is called overturning. Therefore, the absolute balance of a piston internal combustion engine cannot be achieved. However, depending on the extent to which the causes of engine imbalance are eliminated, engines are distinguished as fully balanced, partially balanced and unbalanced. Balanced engines are those in which all forces and moments are balanced.

Conditions for the balance of an engine with any number of cylinders: a) the resulting first-order forces of translationally moving masses and their moments are equal to zero; b) the resulting forces of inertia of the second order of translationally moving masses and their moments are equal to zero; c) the resulting centrifugal forces of inertia of the rotating masses and their moments are equal to zero.

Thus, the solution of balancing the engine is reduced to balancing only the most significant forces and their moments.

Balancing methods. The forces of inertia of the first and second orders and their moments are balanced by the selection of the optimal number of cylinders, their location and the choice of the appropriate crankshaft layout. If this is not enough, then the forces of inertia are balanced by counterweights located on additional shafts that have a mechanical connection with the crankshaft. This leads to a significant complication of the engine design and is therefore rarely used.

centrifugal forces the inertia of the rotating masses can be balanced in an engine with any number of cylinders by installing counterweights on the crankshaft.

The balance provided by the engine designers can be reduced to zero if the following requirements for the production of engine parts, assembly and adjustment of its components are not met: equality of the masses of the piston groups; equality of masses and the same location of the centers of gravity of the connecting rods; static and dynamic balance of the crankshaft.

During the operation of the engine, it is necessary that identical working processes in all its cylinders proceed in the same way. And this depends on the composition of the mixture, ignition timing or fuel injection, cylinder filling, thermal conditions, even distribution of the mixture over the cylinders, etc.

Crankshaft balancing. The crankshaft, like the flywheel, being a massive moving part of the crank mechanism, must rotate evenly, without beats. To do this, its balancing is performed, which consists in identifying the unbalance of the shaft relative to the axis of rotation and the selection and fastening of balancing weights. Balancing of rotating parts is divided into static and dynamic. Bodies are considered statically balanced if the center of mass of the body lies on the axis of rotation. Static balancing is performed on rotating disk-shaped parts, the diameter of which is greater than the thickness.

Dynamic balancing is ensured subject to the condition of static balancing and the fulfillment of the second condition - the sum of the moments of the centrifugal forces of the rotating masses relative to any point of the shaft axis must be equal to zero. When these two conditions are met, the axis of rotation coincides with one of the principal axes of inertia of the body. Dynamic balancing is carried out when the shaft rotates on special balancing machines. Dynamic balancing provides greater accuracy than static balancing. Therefore, crankshafts, which are subject to increased requirements regarding balance, are subjected to dynamic balancing.

Dynamic balancing is performed on special balancing machines.

Balancing machines are equipped with special measuring equipment - a device that determines the desired position of the balancing weight. The mass of the cargo is determined by successive samples, focusing on the readings of the instruments.

During engine operation, continuously and periodically changing tangential and normal forces act on each crankshaft crank, causing variable torsion and bending deformations in the elastic system of the crankshaft assembly. Relative angular oscillations of masses concentrated on the shaft, causing twisting of individual sections of the shaft, are called torsional vibrations. Under certain conditions, alternating stresses caused by torsional and bending vibrations can lead to fatigue failure of the shaft.

Torsional vibrations of the crankshafts are also accompanied by a loss of engine power and adversely affect the operation of the mechanisms associated with it. Therefore, when designing engines, as a rule, the crankshafts are calculated for torsional vibrations and, if necessary, the design and dimensions of the crankshaft elements are changed so as to increase its rigidity and reduce the moments of inertia. If these changes do not give the desired result, special torsional vibration dampers can be used - dampers. Their work is based on two principles: the energy of vibrations is not absorbed, but is damped due to dynamic action in antiphase; vibrational energy is absorbed.

On the first principle, pendulum torsional vibration dampers are based, which are also made in the form of counterweights and are connected to bandages installed on the cheeks of the first knee using pins. The pendulum damper does not absorb the energy of vibrations, but only accumulates it during the twisting of the shaft and releases the stored energy when it unwinds to the neutral position.

Torsional vibration dampers operating with energy absorption perform their functions mainly through the use of friction force and are divided into the following groups: dry friction dampers; liquid friction dampers; absorbers of molecular (internal) friction.

These absorbers are usually a free mass connected to the shaft system in the zone of greatest torsional vibrations by a non-rigid connection.

When studying the kinematics of the crankshaft, it is assumed that the engine crankshaft rotates at a constant angular velocity ω , there are no gaps in the mating parts, and the mechanism is considered with one degree of freedom.

In reality, due to the non-uniformity of the motor torque, the angular velocity is variable. Therefore, when considering special issues of dynamics, in particular, torsional vibrations of the crankshaft system, it is necessary to take into account the change in angular velocity.

The independent variable is the angle of rotation of the crankshaft crank φ. In kinematic analysis, the laws of motion of the crankshaft links, and primarily the piston and connecting rod, are established.

The initial position of the piston is taken at top dead center (point IN 1) (Fig. 1.20), and the direction of rotation of the crankshaft is clockwise. At the same time, to identify the laws of motion and analytical dependencies, the most characteristic points are established. For the central mechanism, such points are the axis of the piston pin (point AT), reciprocating along with the piston along the axis of the cylinder, and the axis of the connecting rod journal of the crank (point BUT) rotating around the axis of the crankshaft O.

To determine the dependences of the kinematics of the crankshaft, we introduce the following notation:

l- the length of the connecting rod;

r- radius of the crank;

λ - the ratio of the crank radius to the length of the connecting rod.

For modern automobile and tractor engines, the value λ = 0.25–0.31. For high-speed engines, in order to reduce the forces of inertia of reciprocating masses, longer connecting rods are used than for low-speed ones.

β - the angle between the axes of the connecting rod and the cylinder, the value of which is determined by the following relationship:

The largest angles β for modern automobile and tractor engines are 12–18°.

Move (path) piston will depend on the angle of rotation of the crankshaft and is determined by the segment X(see Fig. 1.20), which is equal to:

Rice. 1.20. Scheme of the central KShM

From triangles A 1 AB and OA 1 A follows that

Given that , we get:

From right triangles A 1 AB and A 1 OA we establish that

Where

then, substituting the obtained expressions into the formula for piston displacement, we obtain:

Since then

The resulting equation characterizes the movement of parts of the crankshaft depending on the angle of rotation of the crankshaft and shows that the piston path can be conditionally represented as consisting of two harmonic movements:

where is the path of the piston of the first order, which would take place in the presence of a connecting rod of infinite length;

- the path of the piston of the second order, i.e. additional movement, depending on the final length of the connecting rod.

On fig. 1.21 curves of the piston path along the angle of rotation of the crankshaft are given. It can be seen from the figure that when the crankshaft is rotated through an angle equal to 90 °, the piston travels more than half of its stroke.

Rice. 1.21. Changing the piston path depending on the angle of rotation of the crankshaft

Speed

where is the angular velocity of rotation of the shaft.

The piston speed can be represented as the sum of two terms:

where is the harmonically changing speed of the piston of the first order, i.e., the speed with which the piston would move in the presence of a connecting rod of infinitely long length;

- harmonically changing piston speed of the second order, i.e., the speed of additional movement that occurs due to the presence of a connecting rod of finite length.

On fig. 1.22 curves of piston speed are given according to the angle of rotation of the crankshaft. The values ​​of the angles of rotation of the crankshaft, where the piston reaches its maximum speed, depend on? and its increase are shifted towards the dead spots.

For practical estimates of engine parameters, the concept is used average piston speed:

For modern car engines Vav= 8–15 m/s, for tractors - Vav= 5–9 m/s.

Acceleration piston is defined as the first derivative of the piston path with respect to time:

Rice. 1.22. Variation in piston speed depending on the angle of rotation of the crankshaft

Piston acceleration can be represented as the sum of two terms:

where is the harmonically changing acceleration of the piston of the first order;

– harmonically changing second-order piston acceleration.

On fig. 1.23 curves of acceleration of the piston on an angle of rotation of a cranked shaft are given. The analysis shows that the maximum value of acceleration occurs when the piston is at TDC. When the piston is in BDC, the acceleration value reaches the minimum (maximum negative) value opposite in sign and its absolute value depends on ?.

Figure 1.23. Change in piston acceleration depending on the angle of rotation of the crankshaft

Lecture 4. KINEMATICS AND DYNAMICS OF INTERNAL COMBUSTION PISTON ENGINES 1. Kinematics and dynamics of the crank mechanism 2. Engine balancing heat engine final converter. The sensitive element of this converter is piston 2 (see Fig. 1), the bottom of which perceives the pressure of gases. The reciprocating and rectilinear movement of the piston (under the action of gas pressure) is converted into rotational movement of the output crankshaft using connecting rod 4 and crank 5.

The moving parts of the crankshaft also include a flywheel mounted on the rear end of the crankshaft. The mechanical energy of a rotating crankshaft is characterized by a torque M and a rotation frequency n. The fixed parts of the crankshaft include cylinder block 3, block head 1 and pan 6. Fig. 1. Scheme of a piston internal combustion engine: 1 block head; 2 piston; 3 cylinder block; 4 connecting rod; 5 crankshaft crank; used sump (oil sump)

Working conditions of KShM parts modern engines, associated with the impact of gas forces on the piston, are characterized by significant and rapidly variable speeds and accelerations. The connecting rod and crankshaft perceive and transmit significant loads. An analysis of all the forces acting in the engine crankshaft is necessary to calculate the strength of the engine elements, determine the loads on the bearings, assess the engine balance, and calculate the engine supports. The magnitude and nature of the change in mechanical loads falling on these parts is determined on the basis of a kinematic and dynamic study of the crankshaft. The dynamic calculation is preceded by a thermal calculation, which provides the possibility of choosing the main dimensions of the engine (cylinder diameter, piston stroke) and finding the magnitude and nature of the change in forces under the influence of gas pressure.

Abc Fig. 2. The main design schemes of the crank mechanisms of automobile engines: a central; b shifted; c V-shaped 1. Kinematics and dynamics of the crank mechanism In automobile piston engines, crankshafts of three design schemes are mainly used (Fig. 2): a) the central, or axial, axis of the cylinder intersects with the axis of the crankshaft; b) displaced, or deaxial, the axis of the cylinder is displaced by some distance relative to the axis of the crankshaft; c) with a trailer connecting rod, two or more connecting rods are placed on one crankshaft journal.

The most widespread in automobile engines is the central crankshaft. Let us analyze the kinematics and dynamics of its work. The task of the kinematic analysis of the crankshaft is to establish the laws of motion of the piston and connecting rod with a known law of motion of the crankshaft crank. When deriving the main regularities, the uneven rotation of the crankshaft is neglected, assuming that its angular velocity is constant. The position of the piston corresponding to TDC is taken as the initial one. All quantities characterizing the kinematics of the mechanism are expressed as a function of the angle of rotation of the crankshaft. Piston path. It follows from the diagram (see Fig. 2, a) that the displacement of the piston from TDC, corresponding to the rotation of the crankshaft by an angle φ, is equal to Sn = ОА1 - ОА = R(l - cos φ) + Lш (I - cosβ) (1 ) where R is the crankshaft radius, m; L w is the length of the connecting rod, m. It is known from trigonometry that cosβ = (l - sin2 φ) 2, and from fig. 2, and it follows that (2)

Denoting The expression is Newton's binomial, which can be expanded into a series, you can write For automobile engines λ = 0.24 ... 0.31. (3) Neglecting the terms of the series above the second order, we accept with sufficient accuracy for practice Substituting the obtained value of cosβ into expression (1) and taking into account that we obtain the final expression describing the movement of the piston

(4) Piston speed. The formula for determining the piston speed v n is obtained by differentiating expression (4) with respect to time, (5) where is the angular velocity of the crankshaft. For a comparative assessment of the design of engines, the concept of average piston speed (m / s) is introduced: where n is the crankshaft speed, rpm. For modern automobile engines, the value of vp.sr varies within m/s. The higher the average piston speed, the faster the guiding surfaces of the cylinder and piston wear out.

Piston acceleration. The expression for the piston acceleration j p is obtained by differentiating expression (5) with respect to time (6) Figure 2 shows the curves of the change in the path, speed and acceleration of the piston depending on the angle of rotation of the crankshaft φ, constructed according to formulas (4) ... (6) for one complete rotation of the crankshaft. Curve analysis allows us to note the following: when turning the crank from starting position on the first quarter of a turn (from φ = 0 to φ = 90°), the piston travels a longer distance Rλ than when turning on the second quarter of a turn, which causes a greater average piston speed in the first quarter and greater wear on the upper part of the cylinder; the piston speed is not constant: it is equal to zero at dead points and has a maximum value at φ close to 75° and 275°; piston acceleration reaches the highest absolute values ​​at TDC and BDC, i.e. at those moments when the direction of movement of the piston changes: in this case, the acceleration at TDC is greater than at BDC; at v nmax = 0 (acceleration changes its sign).

The task of dynamic analysis of the crankshaft is to obtain calculation formulas for determining the magnitude and nature of the change in the forces acting on the piston, connecting rod and crankshaft, and the moments of forces arising in the crankshaft during engine operation. Knowledge of the forces acting on the parts of the crankshaft is necessary to calculate the strength of the engine elements and determine the loads on the bearings. When the engine is running, forces from the gas pressure in the cylinder and the inertia forces of the moving masses of the mechanism, as well as friction forces and useful resistance forces on the engine shaft, act on the parts of the crankshaft. The gas pressure force Р g, acting on the piston along the axis of the cylinder, is calculated by the formula (7) where Рi is the indicator gas pressure (pressure above the piston) at a given angle of rotation of the crank, MPa; p 0 pressure in the engine crankcase (under the piston), MPa; A p area of ​​the piston bottom, m 2.

The curves of dependence of the pressure force of the RG on the angle of rotation of the crank φ are shown in fig. 3. When constructing a graph, it is considered that the force is positive if it is directed towards the crankshaft, and negative if it is directed away from the shaft. Rice. 3. Change in gas pressure forces, inertia and total force depending on the angle of rotation of the crankshaft

The forces of inertia, depending on the nature of the movement of the moving parts of the KShM, are divided into the forces of inertia of the reciprocating masses P j and the forces of inertia of the rotating masses P a. The mass mw of the connecting rod, which simultaneously participates in reciprocating and rotational movements, is replaced by two masses m 1 and m 2, concentrated in cents A and B, respectively, of the piston and crank heads (Fig. 4, b). For approximate calculations, t x \u003d 0.275 t w and t 2 \u003d 0.725 t w. The inertia force of reciprocating masses (piston with rings and pin m p, as well as mass m w, connecting rod) acts along the axis of the cylinder and is equal to (8) The nature of the change in this force is similar to the nature of the change in the acceleration of the piston j n. The minus sign shows that the directions of force and acceleration are different. The graph of the dependence of Р j on the angle of rotation of the crank cp is shown in fig. 3. The force of inertia of the rotating masses, which is the centrifugal force, is directed along the radius of the crank from its axis of rotation and is equal to (9)

Where t k is the unbalanced mass of the crank, which is considered to be concentrated on the axis of the crank at point B (Fig. 4, b); m sh.sh. - the mass of the connecting rod journal with the parts of the cheeks adjacent and located concentrically to it; t y is the mass of the middle part of the cheek enclosed in the contour a-b-c-d-a, the center of gravity of which is located at a distance p from the axis of rotation of the shaft (Fig. 4, a). Rice. 4. The system of concentrated masses, dynamically equivalent to the crank mechanism: a scheme for reducing the masses of the crank; b is a diagram of the crank mechanism

Total strength. The gas pressure force P g and the inertia force of the reciprocating masses P j act together along the axis of the cylinder. To study the dynamics of the CSM, the sum of these forces is important (P = P t + P j). The force P for different angles of rotation of the crank is obtained by algebraic addition of the ordinates of the points of the curves P t and P j (see Fig. 3). To investigate the effect of the total force P on the parts of the crankshaft, we decompose it into two components of the force: R w, directed along the axis of the connecting rod, and N, acting perpendicular to the axis of the cylinder (Fig. 5, a): We transfer the force R w along the line of its action to the center crank pin (point B) and replace with two component forces tangential (7) and radial (K): (10) (11)

To the center O of the crank, we apply two mutually opposite forces T "and T", equal and parallel to the force T. The forces T and T" are paired with a shoulder equal to the radius R of the crank. The moment of this pair of forces, which rotates the crank, is called the torque of the engine M D \u003d TR. We transfer the radial force to the center O and find the resulting Р w forces K and T "(Fig. 5, b). The force R w is equal and parallel to the force R w. The expansion of the force P w in directions along the axis of the cylinder and perpendicular to it gives two components of the force P "and N". The force P" is equal in magnitude to the force P, which is composed of the forces P t and P. The first of the two terms of the force is balanced by the pressure force of the gases on the cylinder head, the second is transmitted to the engine mounts. This unbalanced force of inertia of the reciprocating parts P j is usually represented in the form of the sum of two forces (12) which are called inertia forces of the first (PjI) and second (PjII) orders.These forces act along the axis of the cylinder.

The forces N "and N (Fig. 5, c) are a pair of forces with a moment M opr \u003d -NH, tending to overturn the engine. The overturning moment, also called the reactive moment of the engine, is always equal to the engine torque, but has the opposite direction. This moment through the external engine mounts is transmitted to the vehicle frame.Using the formula (10), as well as the dependence M D \u003d TR, it is possible to plot the indicator torque M d of a single-cylinder engine depending on the angle φ (Fig. 6, a). located above the abscissa axis, represent a positive, and located under the abscissa axis, the negative work of the torque.Dividing the algebraic sum of these areas A by the length of the graph l, we obtain the average value of the moment where M m is the scale of the moment

To assess the degree of uniformity of the indicator torque of the engine, we introduce the coefficient of unevenness of the torque where M max ; M min ; M avg, respectively, the maximum, minimum and average indicator moments. With an increase in the number of engine cylinders, the coefficient μ decreases, i.e. the uniformity of the torque increases (Fig. 6). Torque unevenness causes changes in the angular velocity from the crankshaft, which is estimated by the stroke unevenness coefficient: where: ω max ; ω min ; ω cf respectively the largest, smallest and average angular velocity of the crankshaft per cycle,

The given stroke unevenness δ is ensured by using a flywheel with a moment of inertia J, using the following relations: - scale of the angle of rotation of the crankshaft, 1 rad / mm i ab - (i number of cylinders, segment ab in mm); n speed, rpm Excess work is determined graphically, the values ​​of δ and J are set during design. For automobile engines δ = 0.01...0.02.

2. Balancing the engine The engine is considered to be balanced if, in the steady state of operation, the forces and moments acting on its supports are constant in magnitude and direction or equal to zero. In an unbalanced engine, the variables in magnitude and direction of force transmitted to the suspension cause vibrations in the under-engine frame and body. These fluctuations are often the cause of additional breakdowns of vehicle components. In the practical solution of problems of balancing engines, the following forces and moments acting on the piston engine supports are usually taken into account: a) the inertia forces of the reciprocating masses of the crankshaft of the first P jI and second order P jII; b) centrifugal force of inertia of rotating unbalanced masses of KShM R c; c) longitudinal moments M jI and M jII of inertia forces P jI and P jII ; d) longitudinal centrifugal moment M c of the centrifugal force of inertia R c.

The engine balance conditions are described by the following system of equations: (13) Balancing is carried out in two ways, applied separately or simultaneously: 1. choosing such a crankshaft crank scheme, in which the indicated forces and moments arising in different cylinders are mutually balanced; 2. the use of counterweights, i.e. additional masses, the force of inertia of which is equal in magnitude and opposite in direction to the balanced forces. Consider the balancing of a single-cylinder engine, in which the inertia forces P jI, P jII, P c are unbalanced. The forces of inertia of the first P jI and the second P jII order can be completely balanced using a system of additional counterweights.

The force P jI \u003d m j Rω 2 cos φ is balanced when two counterweights with a mass m pr 1 are installed on two additional shafts parallel to the crankshaft axis and symmetrically located relative to the cylinder axis, rotating in opposite directions with the crankshaft angular velocity ω. The counterweights are installed so that at any moment the direction of their suspension makes an angle with the vertical equal to the angle of rotation of the crankshaft φ (Fig. 7). During rotation, each counterweight creates a centrifugal force where p j is the distance from the axis of rotation of the counterweight to its center of gravity. By decomposing the vectors of two forces into horizontal Y I and vertical X I components, we are convinced that for any φ the forces Y I are mutually balanced, and the forces X I give the resultant Force R) can completely balance the force P l subject to the condition

Whence Similarly, the force P and is balanced, only the counterweights in this case rotate with a doubled angular velocity 2ω (Fig. 7). The centrifugal force of inertia R c can be completely balanced with the help of counterweights, which are installed on the cheeks of the crankshaft from the side opposite to the crank. The mass of each counterweight m pr is selected subject to the condition where where p is the distance from the center of gravity of the counterweight to the axis of rotation.

The scheme of inertial forces acting in a 4-cylinder single-row engine is shown in fig. 8. It can be seen from it that with a given shape of the crankshaft, the first-order inertia forces are balanced by Σ PjI \u003d 0. In the longitudinal plane of the engine, the forces form two pairs, the moment P jI of which M jI \u003d P jI a. Since the directions of these moments are opposite, they are also balanced (Σ M jI = 0). Rice. 8. Scheme of inertia forces acting in a 4-cylinder single-row engine

The centrifugal forces and their moments and moments of inertia forces of the second order are also balanced, which means that in a 4-cylinder engine the forces P jII remain unbalanced. They can be balanced using rotating counterweights, as mentioned above, but this will complicate the design of the engine. In a 6-cylinder in-line four-stroke engine, the crankshaft cranks are evenly spaced at 120° intervals. In this engine, both inertia forces and their moments are completely balanced. A single-row 8-cylinder four-stroke engine can be considered as two single-row four-cylinder engines in which the crankshafts are rotated 90° relative to each other. In such an engine scheme, all inertia forces and their moments are also balanced. A diagram of a V-shaped 6-cylinder four-stroke engine with an angle between the rows of 90 ° (cylinder camber angle) and three twin cranks at an angle of 120 ° is shown in fig. 9.

In each 2-cylinder section, the resultant of the first-order inertia forces and the resultant of the inertia forces of the rotating masses of the left and right cylinders are constant in magnitude and directed along the radius of the crank. The resulting second-order inertia forces in the section are variable in magnitude and act in the horizontal plane. On fig. 9 forces P jI, P jII, P c - resultant inertial forces for each section of paired cylinders, dashes in the designation of forces in the figure indicate the number of the cylinder section. For the entire engine (for three pairs of cylinders), the sum of the forces of inertia is zero, i.e. The total moments of the first-order inertia forces and centrifugal forces are equal, respectively, and act in one rotating plane passing through the axis of the crankshaft and making an angle of 30 with the plane of the first crank °. To balance these moments, counterweights are installed on the two extreme cheeks of the crankshaft (see Fig. 9). The mass of the counterweight t pr is determined from the condition

Where b is the distance between the centers of gravity of the counterweights. The total moment of inertia forces of the second order acts in the horizontal plane. Usually, ΣM jII is not balanced, as this is associated with a significant complication of the design. To approximate the actual balance to the theoretical one in the production of engines, a number of design and technological measures are provided: - the crankshaft is made as rigid as possible; - during assembly, reciprocating moving parts are selected as a set with the smallest difference in the masses of the sets in different cylinders of the same engine; - allowable deviations in the dimensions of the KShM parts are set as small as possible; - rotationally moving parts are carefully balanced, and crankshafts and flywheels are dynamically balanced.

Balancing consists in identifying the imbalance of the shaft relative to the axis of rotation and in balancing itself by removing metal or by attaching balancing weights. Balancing of rotating parts is divided into static and dynamic. A body is considered statically balanced if the center of mass of the body lies on the axis of rotation. Static balancing is performed on rotating disk-shaped parts, the diameter of which is greater than the thickness. The part is mounted on a cylindrical shaft, which is placed on two parallel horizontal prisms. The part self-adjusts by turning its heavy part down. This imbalance is eliminated by attaching a counterweight at a point diametrically opposite the bottom (heavy) part of the part. In practice, for static balancing, devices are used that allow you to immediately determine the mass of the balance weight and the place of its installation. Dynamic balancing is provided under the condition of static balancing and the fulfillment of the second condition, the sum of the moments of the centrifugal forces of the rotating masses relative to any point of the shaft axis must be equal to zero. When these two conditions are met, the axis of rotation coincides with one of the principal axes of inertia of the body.

Dynamic balancing is carried out when the shaft rotates on special balancing machines. GOST establishes balancing accuracy classes for rigid rotors, as well as balancing requirements and methods for calculating unbalances. So, for example, an engine crankshaft assembly for a passenger car and truck it is estimated by the 6th class of accuracy, the imbalance should be within the limits of mm rad/s. During engine operation, continuously and periodically changing tangential and normal forces act on each crankshaft crank, causing variable torsion and bending deformations in the elastic system of the crankshaft assembly. Relative angular vibrations of masses concentrated on the shaft, causing twisting of individual sections of the shaft, are called torsional vibrations. Under certain conditions, alternating stresses caused by torsional and bending vibrations can lead to fatigue failure of the shaft. Calculations and experimental studies show that bending vibrations are less dangerous for crankshafts than torsional vibrations.

Therefore, in the first approximation, bending vibrations can be neglected in calculations. Torsional vibrations of the crankshaft are dangerous not only for the parts of the crankshaft, but also for the drives of various engine assemblies and for the vehicle's power transmission units. Usually, the calculation for torsional vibrations is reduced to determining the stresses in the crankshaft at resonance, i.e. when the frequency of the exciting force coincides with one of the frequencies of the natural oscillations of the shaft. If there is a need to reduce the resulting stresses, then torsional vibration dampers (dampers) are installed on the crankshaft. In autotractor engines, internal (rubber) and liquid friction dampers are most widely used. They work on the principle of absorbing vibrational energy and then dissipating it in the form of heat. The rubber damper consists of an inertial mass, when vulcanized through a rubber seal to the disc. The disc is rigidly connected to the crankshaft. In resonant modes, the inertial mass begins to oscillate, deforming the rubber gasket. The deformation of the latter contributes to the absorption of vibration energy and "unsets" the resonant vibrations of the crankshaft.

In fluid friction dampers, the free inertial mass is placed inside a hermetically sealed housing rigidly connected to the crankshaft. The space between the body walls and the mass is filled with a special high viscosity silicone fluid. When heated, the viscosity of this liquid changes slightly. Torsional vibration dampers should be installed in the place of the shaft where there is the greatest vibration amplitude.

2.1.1 Selection l and length Lsh of the connecting rod

In order to reduce the height of the engine without a significant increase in inertial and normal forces, the value of the ratio of the radius of the crank to the length of the connecting rod was taken in the thermal calculation of l = 0.26 of the prototype engine.

Under these conditions

where R is the radius of the crank - R = 70 mm.

The results of the calculation of the piston displacement, carried out on a computer, are given in Appendix B.

2.1.3 Angular speed of rotation of the crankshaft u, rad/s

2.1.4 Piston speed Vp, m/s

2.1.5 Piston acceleration j, m/s2

The results of calculating the speed and acceleration of the piston are given in Appendix B.

Dynamics

2.2.1 General information

The dynamic calculation of the crank mechanism is to determine the total forces and moments arising from the pressure of gases and from the forces of inertia. These forces are used to calculate the main parts for strength and wear, as well as to determine the unevenness of the torque and the degree of unevenness of the engine.

During engine operation, the parts of the crank mechanism are affected by: forces from gas pressure in the cylinder; inertia forces of reciprocating moving masses; centrifugal forces; pressure on the piston from the crankcase (approximately equal to atmospheric pressure) and gravity (these are usually not taken into account in the dynamic calculation).

All acting forces in the engine are perceived by: useful resistances on the crankshaft; friction forces and engine mounts.

During each operating cycle (720 for a four-stroke engine), the forces acting in the crank mechanism continuously change in magnitude and direction. Therefore, to determine the nature of the change in these forces by the angle of rotation of the crankshaft, their values ​​are determined for a number of individual shaft positions, usually every 10 ... 30 0 .

The results of the dynamic calculation are summarized in tables.

2.2.2 Gas pressure forces

The forces of gas pressure acting on the area of ​​the piston, to simplify the dynamic calculation, are replaced by one force directed along the axis of the cylinder and close to the axis of the piston pin. This force is determined for each moment of time (angle u) according to the actual indicator diagram, built on the basis of a thermal calculation (usually for normal power and the corresponding number of revolutions).

Rebuilding indicator chart in an expanded diagram for the angle of rotation of the crankshaft is usually carried out according to the method of prof. F. Brix. To do this, under the indicator diagram, an auxiliary semicircle with a radius R = S / 2 is built (see the drawing on sheet 1 of A1 format called “Indicator diagram in P-S coordinates”). Further from the center of the semicircle (point O) towards N.M.T. Brix correction equal to Rl/2 is postponed. The semicircle is divided by rays from the center O into several parts, and lines parallel to these rays are drawn from the center of Brix (point O). The points obtained on the semicircle correspond to certain rays q (in the drawing of format A1, the interval between the points is 30 0). From these points, vertical lines are drawn until they intersect with the lines of the indicator diagram, and the obtained pressure values ​​are taken down on the vertical

corresponding angles c. The development of the indicator diagram usually starts from V.M.T. during the intake stroke:

a) an indicator diagram (see the figure on sheet 1 of A1 format), obtained in a thermal calculation, is deployed according to the angle of rotation of the crank using the Brix method;

Brix correction

where Ms is the scale of the piston stroke on the indicator diagram;

b) scales of the expanded diagram: pressure Mp = 0.033 MPa/mm; angle of rotation of the crank Mf \u003d 2 gr p c. / mm;

c) according to the expanded diagram, every 10 0 of the angle of rotation of the crank, the values ​​\u200b\u200bof Dr g are determined and entered in the dynamic calculation table (in the table, the values ​​​​are given through 30 0):

d) according to the expanded diagram, every 10 0 it should be taken into account that the pressure on the collapsed indicator diagram is measured from absolute zero, and the expanded diagram shows the excess pressure above the piston

MN/m2 (2.7)

Therefore, the pressures in the engine cylinder, which are less than atmospheric pressure, will be negative on the expanded diagram. Gas pressure forces directed to the axis of the crankshaft are considered positive, and from the crankshaft - negative.

2.2.2.1 Gas pressure force on the piston Рg, N

P g \u003d (r g - p 0) F P * 10 6 N, (2.8)

where F P is expressed in cm 2, and p g and p 0 - in MN / m 2,.

From equation (139, ) it follows that the curve of the gas pressure forces Р g according to the angle of rotation of the crankshaft will have the same character of change as the gas pressure curve Dr g.

2.2.3 Bringing the masses of the parts of the crank mechanism

According to the nature of the mass movement of the parts of the crank mechanism, it can be divided into masses moving reciprocatingly (piston group and upper connecting rod head), masses performing rotational movement (crankshaft and lower connecting rod head): masses performing complex plane-parallel motion ( connecting rod).

To simplify the dynamic calculation, the actual crank mechanism is replaced by a dynamically equivalent system of concentrated masses.

The mass of the piston group is not considered concentrated on the axle

piston pin at point A [2, Figure 31, b].

The mass of the connecting rod group m Ш is replaced by two masses, one of which m ШП is concentrated on the axis of the piston pin at point A - and the other m ШК - on the axis of the crank at point B. The values ​​of these masses are determined from the expressions:

where L SC is the length of the connecting rod;

L, MK - distance from the center of the crank head to the center of gravity of the connecting rod;

L ШП - distance from the center of the piston head to the center of gravity of the connecting rod

Taking into account the diameter of the cylinder - the S / D ratio of the engine with an in-line arrangement of cylinders and a sufficiently high value of p g, the mass of the piston group (piston made of aluminum alloy) is set t P \u003d m j

2.2.4 Forces of inertia

The forces of inertia acting in the crank mechanism, in accordance with the nature of the movement of the reduced masses R g, and the centrifugal forces of inertia of the rotating masses K R (Figure 32, a;).

Force of inertia from reciprocating masses

2.2.4.1 From the calculations obtained on the computer, the value of the inertia force of reciprocating moving masses is determined:

Similarly to the acceleration of the piston, the force P j: can be represented as the sum of the inertial forces of the first P j1 and second P j2 orders

In equations (143) and (144), the minus sign indicates that the force of inertia is directed in the direction opposite to the acceleration. The forces of inertia of reciprocating masses act along the axis of the cylinder and, like the forces of gas pressure, are considered positive if they are directed towards the axis of the crankshaft, and negative if they are directed away from the crankshaft.

The construction of the inertia force curve of reciprocating masses is carried out using methods similar to the construction of the acceleration curve

piston (see Figure 29,), but on a scale of M p and M n in mm, in which a diagram of gas pressure forces is plotted.

Calculations P J should be made for the same positions of the crank (angles u) for which Dr r and Drg were determined

2.2.4.2 Centrifugal force of inertia of rotating masses

The force K R is constant in magnitude (when w = const), acts along the radius of the crank and is constantly directed from the axis of the crankshaft.

2.2.4.3 Centrifugal force of inertia of the rotating masses of the connecting rod

2.2.4.4 Centrifugal force acting in the crank mechanism

2.2.5 Total forces acting in the crank mechanism:

a) the total forces acting in the crank mechanism are determined by algebraic addition of the pressure forces of gases and the forces of inertia of reciprocating moving masses. The total force concentrated on the axis of the piston pin

P \u003d P G + P J, N (2.17)

Graphically, the curve of the total forces is built using diagrams

Rg \u003d f (c) and P J \u003d f (c) (see Figure 30,

The total force Р, as well as the forces Р g and Р J, is directed along the axis of the cylinders and is applied to the axis of the piston pin.

The impact from the force P is transmitted to the walls of the cylinder perpendicular to its axis, and to the connecting rod in the direction of its axis.

The force N acting perpendicular to the axis of the cylinder is called the normal force and is perceived by the walls of the cylinder N, N

b) the normal force N is considered positive if the moment it creates relative to the axis of the crankshaft of the journals has a direction opposite to the direction of rotation of the engine shaft.

The values ​​of the normal force Ntgv are determined for l = 0.26 according to the table

c) the force S acting along the connecting rod acts on it and is then transferred * to the crank. It is considered positive if it compresses the connecting rod, and negative if it stretches it.

Force acting along the connecting rod S, N

S = P(1/cos in),H (2.19)

From the action of the force S on the crankpin, two components of the force arise:

d) force directed along the crank radius K, N

e) tangential force directed tangentially to the crank radius circle, T, N

The force T is considered positive if it compresses the cheeks of the knee.

2.2.6 Average tangential force per cycle

where P T - average indicator pressure, MPa;

F p - piston area, m;

f - cycle rate of the prototype engine

2.2.7 Torques:

a) according to the value e) the torque of one cylinder is determined

M cr.c \u003d T * R, m (2.22)

The curve of the change in force T depending on q is also the curve of change in M ​​cr.c, but on a scale

M m \u003d M p * R, N * m in mm

To plot the curve of the total torque M kr of a multi-cylinder engine, a graphical summation of the torque curves of each cylinder is performed, shifting one curve relative to the other by the angle of rotation of the crank between flashes. Since the magnitude and nature of the change in torques in terms of the angle of rotation of the crankshaft are the same for all engine cylinders, they differ only in angular intervals equal to the angular intervals between flashes in individual cylinders, then to calculate the total engine torque, it is enough to have a torque curve of one cylinder

b) for an engine with equal intervals between flashes, the total torque will change periodically (i is the number of engine cylinders):

For a four-stroke engine through O -720 / L deg. In the graphical construction of the curve M cr (see sheet of paper 1 of format A1), the curve M cr.c of one cylinder is divided into a number of sections equal to 720 - 0 (for four-stroke engines), all sections of the curve are reduced to one and summarized.

The resulting curve shows the change in the total engine torque depending on the angle of rotation of the crankshaft.

c) the average value of the total torque M cr.av is determined by the area enclosed under the curve M cr.

where F 1 and F 2 are, respectively, the positive area and the negative area in mm 2, enclosed between the M cr curve and the AO line and equivalent to the work done by the total torque (for i ? 6, there is usually no negative area);

OA is the length of the interval between flashes on the diagram, mm;

M m is the scale of the moments. H * m in mm.

The moment M cr.av is the average indicator moment

engine. The actual effective torque taken from the motor shaft.

where s m - mechanical efficiency of the engine

The main calculated data on the forces acting in the crank mechanism for the angle of rotation of the crankshaft are given in Appendix B.

The crankshaft during engine operation is subjected to the following forces: gas pressure on the piston, inertia of the moving masses of the mechanism, gravity of individual parts, friction in the links of the mechanism and resistance of the energy receiver.

The calculation of the friction forces is very difficult and is usually not taken into account when calculating the forces of the loading crankshafts.

In WOS and SOD, the forces of gravity of parts are usually neglected due to their insignificant magnitude compared to other forces.

Thus, the main forces acting in the KShM are the forces from the pressure of gases and the inertia forces of moving masses. The forces from the pressure of gases depend on the nature of the course of the working cycle, the forces of inertia are determined by the magnitude of the masses of the moving parts, the size of the piston stroke and the rotational speed.

Finding these forces is necessary for calculating engine parts for strength, identifying loads on bearings, determining the degree of uneven rotation of the crankshaft, and calculating the crankshaft for torsional vibrations.

Bringing the masses of parts and links of KShM

To simplify the calculations, the actual masses of the moving parts of the crankshaft are replaced by the reduced masses concentrated at the characteristic points of the crankshaft and dynamically or, in extreme cases, statically equivalent to the real distributed masses.

For the characteristic points of the crankshaft, the centers of the piston pin, connecting rod journal, a point on the axis of the crankshaft are taken. In crosshead diesels, instead of the center of the piston pin, the center of the crosshead cross member is taken as a characteristic point.

Translational-moving masses (LMM) M s in trunk diesel engines include the mass of the piston with rings, piston pin, piston rings and part of the mass of the connecting rod. In crosshead engines, the reduced mass includes the mass of the piston with rings, rod, crosshead and part of the mass of the connecting rod.

The reduced LHD M S is considered to be concentrated either in the center of the piston pin (trunk ICE) or in the center of the crosshead crosshead (crosshead engines).

The unbalanced rotating mass (NVM) M R consists of the remaining part of the mass of the connecting rod and part of the mass of the crank, reduced to the axis of the connecting rod journal.

The distributed mass of the crank is conditionally replaced by two masses. One mass located in the center of the connecting rod journal, the other - located on the axis of the crankshaft.

The balanced rotating mass of the crank does not cause inertia forces, since the center of its mass is located on the axis of rotation of the crankshaft. However, the moment of inertia of this mass is included as a component in the reduced moment of inertia of the entire KShM.

In the presence of a counterweight, its distributed mass is replaced by a reduced concentrated mass located at a distance of the crank radius R from the axis of rotation of the crankshaft.

Replacing the distributed masses of the connecting rod, knee (crank) and counterweight with concentrated masses is called mass reduction.

Bringing the masses of the connecting rod

The dynamic model of a connecting rod is a straight line segment (a weightless rigid rod) having a length equal to the length of the connecting rod L with two masses concentrated at the ends. On the axis of the piston pin is the mass of the translational-moving part of the connecting rod M shS, on the axis of the connecting rod journal - the mass of the rotating part of the connecting rod M shR.

Rice. 8.1

M w - the actual mass of the connecting rod; c.m. - center of mass of the connecting rod; L is the length of the connecting rod; L S and L R - distances from the ends of the connecting rod to its center of mass; M shS - the mass of the translational-moving part of the connecting rod; M shR - mass of the rotating part of the connecting rod

For complete dynamic equivalence of a real connecting rod and its dynamic model, three conditions must be met

To satisfy all three conditions, a dynamic model of a connecting rod with three masses would have to be made.

To simplify the calculations, the two-mass model is retained, limited to the conditions of only static equivalence

In this case

As can be seen from the obtained formulas (8.3), in order to calculate M wS and M wR, it is necessary to know L S and L R , i.e. location of the center of mass of the connecting rod. These values ​​can be determined by calculation (graph-analytical) method or experimentally (by swinging or weighing). You can use the empirical formula of prof. V.P. Terskikh

where n is the engine speed, min -1.

You can also roughly take

M wS ? 0.4M w; M wR ? 0.6M w.

Bringing the masses of the crank

The dynamic model of the crank can be represented as a radius (weightless rigid rod) with two masses at the ends M to and M to 0 .

Static equivalence condition

where is the mass of the cheek; - part of the mass of the cheek, reduced to the axis of the connecting rod journal; - part of the mass of the cheek, reduced to the axis of the rudder; c - distance from the center of mass of the cheek to the axis of rotation of the crankshaft; R is the radius of the crank. From formulas (8.4) we obtain

As a result, the reduced masses of the crank will take the form

where is the mass of the connecting rod journal;

The mass of the frame neck.

Rice. 8.2

Bringing the masses of the counterweight

The dynamic counterweight model is similar to the crank model.

Fig.8.3

Reduced unbalanced counterweight mass

where is the actual mass of the counterweight;

c 1 - distance from the center of mass of the counterweight to the axis of rotation of the crankshaft;

R is the radius of the crank.

The reduced mass of the counterweight is considered to be located at a point at a distance R towards the center of mass relative to the axis of the crankshaft.

Dynamic model of KShM

The dynamic model of the KShM as a whole is based on the models of its links, while the masses concentrated at the same points are summed up.

1. Reduced translational mass concentrated in the center of the piston pin or crosshead

M S \u003d M P + M PC + M KR + M WS , (8.9)

where M P is the mass of the piston set;

M PCS - mass of the rod;

M CR - crosshead mass;

M ШS - PDM part of the connecting rod.

2. Reduced unbalanced rotating mass concentrated in the center of the crankpin

M R = М К + М ШR , (8.10)

where M K - unbalanced rotating part of the mass of the knee;

M SHR - HBM parts of the connecting rod;

Usually, for the convenience of calculations, absolute masses are replaced by relative ones.

where F p - piston area.

The fact is that the forces of inertia are summed up with the pressure of gases, and in the case of using masses in relative form, the same dimension is obtained. In addition, for the same type of diesel engines, the values ​​of m S and m R vary within narrow limits and their values ​​are given in special technical literature.

If it is necessary to take into account the gravity forces of parts, they are determined by the formulas

where g is the free fall acceleration, g = 9.81 m/s 2 .

Lecture 13. 8.2. Forces of inertia of one cylinder

When the KShM moves, inertia forces arise from the translational-moving and rotating masses of the KShM.

Forces of inertia LDM (referred to F П)

marine engine thermodynamic piston

q S = -m S J. (8.12)

Sign "-" because the direction of inertial forces is usually inversely directed to the acceleration vector.

Knowing that we get

At TDC (b = 0).

B BDC (b = 180).

Let us denote the amplitudes of the inertial forces of the first and second orders

P I \u003d - m S Rsh 2 and P II \u003d - m S l Rsh 2

q S = P I cosb + P II cos2b, (8.14)

where P I cosb - inertia force of the first order PDM;

P II cos2b - inertia force of the second order LDM.

The inertia force q S is applied to the piston pin and is directed along the axis of the working cylinder, its value and sign depend on b.

The first-order inertia force PDM P I cosb can be represented as a projection onto the axis of the cylinder of a certain vector directed along the crank from the center of the crankshaft and acting as if it is a centrifugal force of inertia of the mass m S located in the center of the crankpin.

Rice. 8.4

The projection of the vector onto the horizontal axis represents a fictitious value P I sinb, since in reality such a value does not exist. In accordance with this, the vector itself, which resembles the centrifugal force, also does not exist and therefore is called the fictitious first-order inertia force.

Introduction to the consideration of fictitious inertial forces, which have only one real vertical projection, is a conditional technique that makes it possible to simplify the calculations of the LDM.

The first-order fictitious inertia force vector can be represented as the sum of two components: the real force P I cosb directed along the cylinder axis and the fictitious force P I sinb directed perpendicular to it.

The second-order inertia force P II cos2b can be similarly represented as the projection onto the cylinder axis of the vector P II of the fictitious second-order PDM inertia force, which makes an angle of 2b with the cylinder axis and rotates with an angular velocity of 2sh.

Rice. 8.5

The fictitious force of inertia of the second order PDM can also be represented as the sum of two components of which one is the real P II cos2b, directed along the axis of the cylinder, and the second fictitious P II sin2b, directed perpendicular to the first.

Forces of inertia HBM (referred to F П)

The force q R is applied to the axis of the connecting rod journal and is directed along the crank away from the axis of the crankshaft. The inertial force vector rotates together with the crankshaft in the same direction and at the same speed.

If you move it so that the beginning coincides with the axis of the crankshaft, then it can be decomposed into two components

vertical;

Horizontal.

Rice. 8.6

Total inertial forces

The total inertia force of the LDM and NVM in the vertical plane

If we consider separately the inertia forces of the first and second orders, then in the vertical plane the total inertia force of the first order

Force of inertia of the second order in the vertical plane

The vertical component of the first order inertia forces tends to lift or press the engine against the foundation once per revolution, and the second order inertia force - twice per revolution.

The first order inertia force in the horizontal plane tends to move the motor from right to left and back once during one revolution.

The combined action of the force from the pressure of gases on the piston and the forces of inertia of the crankshaft

The gas pressure that occurs during engine operation acts on both the piston and the cylinder head. The law of change P = f(b) is determined by a detailed indicator diagram obtained experimentally or by calculation.

1) Considering that on reverse side atmospheric pressure acts on the piston, we find the excess pressure of gases on the piston

P g \u003d P - P 0, (8.19)

where Р is the current absolute gas pressure in the cylinder, taken from the indicator diagram;

P 0 - ambient pressure.

Fig.8.7 - Forces acting in the KShM: a - without taking into account the forces of inertia; b - taking into account the forces of inertia

2) Taking into account the forces of inertia, the vertical force acting on the center of the piston pin is determined as the driving force

Pd = Rg + qs. (8.20)

3) We decompose the driving force into two components - the normal force P n and the force acting on the connecting rod P w:

P n \u003d R d tgv; (8.21)

The normal force P n presses the piston against the cylinder sleeve or the crosshead slider against its guide.

The force acting on the connecting rod P W compresses or stretches the connecting rod. It acts along the axis of the connecting rod.

4) We transfer the force P w along the line of action to the center of the crankpin and decompose into two components - the tangential force t directed tangentially to the circle described by the radius R

and radial force z directed along the radius of the crank

In addition to the force P w, the inertia force q R will be applied to the center of the connecting rod journal.

Then the total radial force

Let us transfer the radial force z along the line of its action to the center of the frame neck and apply at the same point two mutually balanced forces and, parallel and equal to the tangential force t. A pair of forces t and rotates the crankshaft. The moment of this pair of forces is called torque. Absolute torque value

M cr = tF p R. (8.26)

The sum of the forces and z applied to the crankshaft axis gives the resulting force that loads the crankshaft frame bearings. Let us decompose the force into two components - vertical and horizontal. The vertical force, together with the force of gas pressure on the cylinder cover, stretches the details of the skeleton and is not transferred to the foundation. Oppositely directed forces and form a pair of forces with a shoulder H. This pair of forces tends to rotate the frame around the horizontal axis. The moment of this pair of forces is called the overturning or reverse torque M def.

The overturning moment is transmitted through the engine skeleton to the foundation frame supports, to the ship's foundation hull. Therefore, M ODA must be balanced by the external moment of reactions r f of the ship foundation.

The procedure for determining the forces acting in the KShM

These forces are calculated in tabular form. The calculation step should be selected using the following formulas:

For two-stroke; - for four-stroke,

where K is an integer: i is the number of cylinders.

Driving force per piston area

P d \u003d R g + q s + g s + P tr. (8.20)

The friction force P tr is neglected.

If g s ? 1.5% P z , then we also neglect.

The values ​​of P g are determined using the pressure of the indicator diagram P.

P g \u003d P - P 0. (8.21)

The force of inertia is determined analytically

Rice. 8.8

The driving force curve Pd is the starting point for plotting force diagrams Pn = f(b), Psh = f(b), t = f(b), z = f(b).

To verify the correctness of the construction of the tangential diagram, it is necessary to determine the tangential force t cf. averaged over the angle of rotation of the crank.

It can be seen from the diagram of the tangential force that t cf is defined as the ratio of the area between the line t \u003d f (b) and the abscissa axis to the length of the diagram.

The area is determined by a planimeter or by trapezoidal integration

where n 0 is the number of sections into which the required area is divided;

y i - ordinates of the curve at the boundaries of the plots;

Having determined t cp in cm, using the scale along the y-axis, convert it to MPa.

Rice. 8.9 - Diagrams of tangential forces of one cylinder: a - two-stroke engine; b - four-stroke engine

The indicator work per cycle can be expressed in terms of the average indicator pressure Pi and the average value of the tangential force tcp as follows

P i F p 2Rz = t cp F p R2р,

where the cycle factor z = 1 for two-stroke internal combustion engines and z = 0.5 for four-stroke internal combustion engines.

For two stroke engines

For four stroke engines

The allowable discrepancy should not exceed 5%.