Kinematic calculation of kshm. Calculation of kinematics and dynamics of kshm However, there are also negative points

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).

Everything active forces in the engine are perceived: 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).

The rebuilding of the indicator diagram into an expanded diagram according to the angle of rotation of the crankshaft is usually carried out according to the method of prof. F. Brix. For this under indicator diagram an auxiliary semicircle with 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 dynamically equivalent system concentrated masses.

Weight piston group not considered to be centered on the axis

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 wool.

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 along 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.

Kinematics of the crank mechanism

In autotractor internal combustion engines, two types of crank mechanism (KShM) are mainly used: central(axial) and displaced(deaxial) (Fig. 5.1). An offset mechanism can be created if the axis of the cylinder does not intersect the axis of the crankshaft of the internal combustion engine or is offset relative to the axis of the piston pin. A multi-cylinder internal combustion engine is formed on the basis of the indicated schemes of the crankshaft in the form of a linear (in-line) or multi-row design.

Rice. 5.1. Kinematic diagrams of the KShM of an autotractor engine: but- central linear; b- offset linear

The laws of movement of parts of the crankshaft are studied using its structure, the main geometric parameters of its links, without taking into account the forces that cause its movement, and friction forces, as well as in the absence of gaps between mating moving elements and a constant angular velocity of the crank.

The main geometric parameters that determine the laws of motion of the elements of the central KShM are (Fig. 5.2, a): Mr. crankshaft radius; / w - connecting rod length. Parameter A = g/1 w is a criterion for the kinematic similarity of the central mechanism. In autotractor internal combustion engines, mechanisms with A = 0.24 ... 0.31 are used. In de-axial crankshafts (Fig. 5.2, b) the amount of mixing of the axis of the cylinder (finger) relative to the axis of the crankshaft (but) affects its kinematics. For autotractor internal combustion engines, the relative displacement to = a/g= 0.02...0.1 - additional kinematic similarity criterion.

Rice. 5.2. Calculation scheme of KShM: but- central; b- displaced

The kinematics of the crankshaft elements is described when the piston moves, starting from TDC to BDC, and the crank rotates clockwise by the laws of time variation (/) of the following parameters:

• ? piston displacement - x;
• ? crank angle - (p;
• ? angle of deviation of the connecting rod from the axis of the cylinder - (3.

The analysis of the kinematics of the crankshaft is carried out at constancy the angular velocity of the crankshaft crank co or crankshaft speed ("), interconnected by the relation co \u003d kp/ 30.

During the operation of the internal combustion engine, the moving elements of the crankshaft make the following movements:

• ? the rotational motion of the crankshaft crank relative to its axis is determined by the dependences of the angle of rotation cp, angular velocity co and acceleration e on time t. In this case, cp \u003d w/, and with the constancy of w - e \u003d 0;
• ? the reciprocating motion of the piston is described by the dependences of its displacement x, speed v and acceleration j from the angle of rotation of the crank cf.

Moving the piston of the central KShM when turning the crank by an angle cp is determined as the sum of its displacements from the rotation of the crank by an angle cp (Xj) and from the deviation of the connecting rod by an angle p (x n) (see Fig. 5.2):

This dependence, using the ratio X = g/1 w, the relationship between the angles cp and p (Asincp = sinp), can be represented approximately as a sum of harmonics that are multiples of the crankshaft speed. For example, for X= 0.3 the first harmonic amplitudes are related as 100:4.5:0.1:0.005. Then, with sufficient accuracy for practice, the description of the piston displacement can be limited to the first two harmonics. Then for cp = co/

piston speed defined as and approximately

piston acceleration calculated according to the formula and approximately

In modern internal combustion engines, v max \u003d 10 ... 28 m / s, y max \u003d 5000 ... 20,000 m / s 2. With increasing piston speed, friction losses and engine wear increase.

For a shifted KShM, the approximate dependences have the form

These dependences, in comparison with their counterparts for the central crankshaft, differ in an additional term proportional to kk. Since for modern engines its value is kk= 0.01...0.05, then its influence on the kinematics of the mechanism is small and in practice it is usually neglected.

The kinematics of the complex plane-parallel movement of the connecting rod in the plane of its swing consists of the movement of its upper head with the kinematic parameters of the piston and rotational movement relative to the point of articulation of the connecting rod with the piston.

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 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 (LMP) 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 were 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) Assuming that atmospheric pressure acts on the reverse side of the piston, we find the excess gas pressure 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

We 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%.

3.1.1. Correction of the indicator chart

The indicator diagram should be rebuilt for other coordinates: along the abscissa axis - at the angle of rotation of the crankshaft φ and under the corresponding piston movement S . The indicator diagram is then used to graphically find the current value of the cycle pressure acting on the piston. To rebuild under the indicator diagram, a crank mechanism diagram is built (Fig. 3), where the straight line AC corresponds to the length of the connecting rod L in mm, straight line AO ​​- crank radius R in mm. For various crank angles φ graphically determine the points on the axis of the cylinder ОО / , corresponding to the position of the piston at these angles φ . For the origin, i.e. φ=0 accept top dead center. From the points on the OO / axis, vertical straight lines (ordinates) should be drawn, the intersection of which with the polytropes of the indicator diagram gives points corresponding to the absolute values ​​of gas pressure R c . When determining R c it is necessary to take into account the direction of the flow of processes according to the diagram and their correspondence to the angle φ pkv.

The modified indicator diagram should be placed in this section of the explanatory note. In addition, to simplify further calculations of the forces acting in the crankshaft, it is assumed that the pressure R c =0 at the inlet ( φ =0 0 -180 0) and release ( φ =570 0 -720 0).

Fig.3. Indicator chart, combined

with kinematics of the crank mechanism

3.1.2 Kinematic calculation of the crank mechanism

The calculation consists in determining the displacement, speed and acceleration of the piston for various angles of rotation of the crankshaft, at a constant speed. The initial data for the calculation are the radius of the crank R = S /2 , connecting rod length L and kinematic parameter λ = R / L - constant KShM. Attitude λ = R / L depends on the type of engine, its speed, the design of the crankshaft and is within
=0.28 (1/4.5…1/3). When choosing, it is necessary to focus on a given engine prototype and take the nearest value according to table 8.

crank angular velocity

The determination of kinematic parameters is carried out according to the formulas:

Piston movement

S = R [(1-
) + (1-
)]

piston speed

W P = R ( sin
sin 2)

piston acceleration

j P = R
(
+
)

An analysis of the piston velocity and acceleration formulas shows that these parameters obey a periodic law, changing positive values ​​to negative ones during the movement. Thus, the acceleration reaches its maximum positive values ​​at pkv φ = 0, 360 0 and 720 0 , and the minimum negative at pkv φ = 180 0 and 540 0 .

The calculation is performed for the angles of rotation of the crankshaft φ from 0º to 360º, every 30º the results are entered in table 7. In addition, the current angle of deviation of the connecting rod is found from the indicator diagram for each current angle value φ . Injection it is considered with a sign (+) if the connecting rod deviates in the direction of rotation of the crank and with a sign (-) if in the opposite direction. Biggest connecting rod deflection ±
≤ 15º ... 17º will correspond to pkv. =90º and 270º.

Table 7

Kinematic parameters of KShM

When the engine is running in the crankshaft, the following main force factors act: gas pressure forces, inertia forces of the moving masses of the mechanism, friction forces and the moment of useful resistance. In dynamic analysis KShM forces friction is usually neglected.

Rice. 8.3. Impact on KShM elements:

but - gas forces; b - inertial forces P j ; c - centrifugal force of inertia K r

Gas pressure forces. The force of gas pressure arises as a result of the implementation of the working cycle in the cylinders. This force acts on the piston, and its value is determined as the product of the pressure drop and its area: P g = (r g - p 0) F p (here p g is the pressure in the engine cylinder above the piston; p 0 is the pressure in the crankcase; F n is the area of ​​the piston). To assess the dynamic loading of the KShM elements, the dependence of the force P g on time is important

The force of gas pressure acting on the piston loads the moving elements of the crankshaft, is transferred to the main bearings of the crankcase and is balanced inside the engine due to the elastic deformation of the bearing elements of the crankcase by the force acting on the cylinder head (Fig. 8.3, a). These forces are not transmitted to the engine mounts and do not cause it to become unbalanced.

Forces of inertia of moving masses. KShM is a system with distributed parameters, the elements of which move non-uniformly, which leads to the occurrence of inertial loads.

A detailed analysis of the dynamics of such a system is possible in principle, but involves a large amount of calculations. Therefore, in engineering practice, to analyze the dynamics of the engine, lumped parameter models created on the basis of the replacement mass method are used. In this case, for any moment of time, the dynamic equivalence of the model and the considered real system must be satisfied, which is ensured by the equality of their kinetic energies.

Usually, a model is used of two masses interconnected by an absolutely rigid inertialess element (Fig. 8.4).

Rice. 8.4. Formation of a two-mass dynamic model of KShM

The first replacement mass m j is concentrated at the junction point of the piston with the connecting rod and reciprocates with the kinematic parameters of the piston, the second m r is located at the junction point of the connecting rod with the crank and rotates uniformly with an angular velocity ω.

The parts of the piston group perform a rectilinear reciprocating motion along the axis of the cylinder. Since the center of mass of the piston group practically coincides with the axis of the piston pin, then to determine the force of inertia P j p it is enough to know the mass of the piston group m p, which can be concentrated at a given point, and the acceleration of the center of mass j, which is equal to the acceleration of the piston: P j p = - m p j.

The crankshaft crankshaft performs a uniform rotational movement. Structurally, it consists of a combination of two halves of the main journal, two cheeks and a connecting rod journal. With uniform rotation, each of these elements of the crank is affected by a centrifugal force proportional to its mass and centripetal acceleration.

In the equivalent model, the crank is replaced by a mass m k, spaced from the axis of rotation at a distance r. The value of the mass m k is determined from the condition of equality of the centrifugal force created by it to the sum of the centrifugal forces of the masses of the crank elements: K k \u003d K r w.w + 2K r w or m k rω 2 \u003d m w.w rω 2 + 2m w ρ w ω 2 , whence we get m k \u003d m w.w + 2m w ρ w ω 2 /r.

The elements of the connecting rod group perform a complex plane-parallel movement. In the two-mass KShM model, the mass of the connecting rod group m w is divided into two replacement masses: m w. n, concentrated on the axis of the piston pin, and m sh.k, referred to the axis of the connecting rod journal of the crankshaft. In this case, the following conditions must be met:

1) the sum of the masses concentrated at the replacing points of the connecting rod model must be equal to the mass of the replaced KShM link: m sh. p + m w.k = m w

2) the position of the center of mass of the element of the real KShM and replacing it in the model must be unchanged. Then m sh. p \u003d m w l w.k / l w and m w.k \u003d m w l w.p / l w.

The fulfillment of these two conditions ensures the static equivalence of the replacement system to the real KShM;

3) the condition of dynamic equivalence of the replacement model is provided when the sum of the moments of inertia of the masses located at the characteristic points of the model is equal. This condition for two-mass models of connecting rods of existing engines is usually not performed, it is neglected in calculations due to its small numerical values.

Finally, by combining the masses of all links of the CVL at the replacement points of the dynamic model of the CVL, we obtain:

a mass concentrated on the axis of the finger and reciprocating along the axis of the cylinder, m j \u003d m p + m w. P;

a mass located on the axis of the connecting rod journal and performing rotational motion around the axis of the crankshaft, m r \u003d m k + m sh.k. For V-shaped internal combustion engines with two connecting rods located on one connecting rod journal of the crankshaft, m r \u003d m k + 2m sh.k.

In accordance with the adopted model of the KShM, the first replacement mass mj, moving unevenly with the kinematic parameters of the piston, causes an inertia force P j = - mjj, and the second mass mr, rotating uniformly with the angular velocity of the crank, creates a centrifugal force of inertia K r = K r w + K k \u003d - mr rω 2.

The force of inertia P j is balanced by the reactions of the supports on which the engine is installed. Being variable in value and direction, if no special measures are provided for, it can be the cause of external unbalance of the engine (see Fig. 8.3, b).

When analyzing the dynamics and especially the balance of the engine, taking into account the previously obtained dependence of acceleration y on the angle of rotation of the crank φ, the force P j is represented as the sum of the inertial forces of the first (P jI) and second (P jII) order:

where С = - m j rω 2 .

The centrifugal force of inertia K r = - m r rω 2 from the rotating masses of the crankshaft is a vector of constant magnitude, directed along the radius of the crank and rotating at a constant angular velocity ω. The force K r is transferred to the engine mounts, causing variables in terms of the magnitude of the reaction (see Fig. 8.3, c). Thus, the force K r , as well as the force P j , can be the cause of the external imbalance of the internal combustion engine.

The total forces and moments acting in the mechanism. The forces Р g and Р j having a common point of application to the system and a single line of action, in the dynamic analysis of the KShM, are replaced by the total force, which is an algebraic sum: Р Σ \u003d Р g + Р j (Fig. 8.5, a).

Rice. 8.5. Forces in KShM: a - design scheme; b - dependence of forces in the crankshaft on the angle of rotation of the crankshaft

To analyze the action of the force P Σ on the elements of the crankshaft, it is decomposed into two components: S and N. The force S acts along the axis of the connecting rod and causes repeated-variable compression-tension of its elements. The force N is perpendicular to the axis of the cylinder and presses the piston against its mirror. The action of the force S on the connecting rod-crank interface can be estimated by transferring it along the connecting rod axis to the point of their articulation (S ") and decomposing it into a normal force K directed along the crank axis and a tangential force T.

Forces K and T act on the main bearings of the crankshaft. To analyze their action, the forces are transferred to the center of the main support (forces K, T "and T"). A pair of forces T and T "on the shoulder r creates a torque M k, which is then transferred to the flywheel, where it performs useful work. The sum of the forces K" and T" gives the force S", which, in turn, is decomposed into two components: N" and .

It is obvious that N" = - N and = P Σ. The forces N and N" on the shoulder h create an overturning moment M def = Nh, which is then transferred to the engine mounts and balanced by their reactions. M def and the reactions of the supports caused by it change with time and can be the cause of the external unbalance of the engine.

The main relations for the considered forces and moments have the following form:

On the crank neck the crank is acted by the force S "directed along the axis of the connecting rod, and the centrifugal force K r w acting along the radius of the crank. The resulting force R w. w (Fig. 8.5, b), loading the connecting rod journal, is determined as the vector sum of these two forces.

Indigenous necks crank of a single-cylinder engine are loaded with force and centrifugal force of inertia of the masses of the crank. Their resultant strength , acting on the crank, is perceived by two main bearings. Therefore, the force acting on each main journal is equal to half of the resulting force and is directed in the opposite direction.

The use of counterweights leads to a change in the loading of the root neck.

The total torque of the engine. In a single cylinder engine, torque Since r is a constant value, the nature of its change in the angle of rotation of the crank is completely determined by the change in the tangential force T.

Let us imagine a multi-cylinder engine as a set of single-cylinder engines, the working processes in which proceed identically, but are shifted relative to each other by angular intervals in accordance with the accepted order of engine operation. The moment twisting the main journals can be defined as the geometric sum of the moments acting on all the cranks preceding the given crankpin.

Consider, as an example, the formation of torques in a four-stroke (τ \u003d 4) four-cylinder (i \u003d 4) linear engine with an operating order of cylinders 1 -3 - 4 - 2 (Fig. 8.6).

With a uniform alternation of flashes, the angular shift between successive working strokes will be θ = 720°/4 = 180°. then, taking into account the order of operation, the angular momentum shift between the first and third cylinders will be 180°, between the first and fourth - 360°, and between the first and second - 540°.

As follows from the above diagram, the moment twisting the i-th main journal is determined by summing the force curves T (Fig. 8.6, b) acting on all i-1 cranks preceding it.

The moment twisting the last main journal is the total engine torque M Σ , which is then transferred to the transmission. It changes according to the angle of rotation of the crankshaft.

The average total torque of the engine at the angular interval of the working cycle M k. cf corresponds to the indicator moment M i developed by the engine. This is due to the fact that only gas forces produce positive work.

Rice. 8.6. Formation of the total torque of a four-stroke four-cylinder engine: a - design scheme; b - the formation of torque