2.1.1 Choice of l and length L 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 l = 0.26 of the prototype engine.
Under these conditions
where R is the radius of the crank - R = 70 mm.
The results of calculating the displacement of the piston, carried out on a computer, are given in Appendix B.
2.1.3 Angular speed of rotation crankshaft u, rad / s
2.1.4 Piston speed Vп, 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
The dynamic calculation of the crank mechanism consists in determining the total forces and moments arising from the pressure of gases and from the forces of inertia. These forces are used to calculate the strength and wear of the main parts, as well as to determine the unevenness of the torque and the degree of unevenness of the engine stroke.
During engine operation, the parts of the crank mechanism are affected by: forces from the pressure of gases in the cylinder; forces of inertia of reciprocating moving masses; centrifugal forces; pressure on the piston from the side of the crankcase (approximately equal to atmospheric pressure) and gravity (they are usually not taken into account in the dynamic calculation).
All acting forces in the engine are perceived: by useful resistances on the crankshaft; frictional forces and engine mounts.
During each operating cycle (720 for a four-stroke engine), the forces acting in the crank mechanism are continuously changing 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 tabulated.
2.2.2 Gas pressure forces
The gas pressure forces acting on the piston area, to simplify the dynamic calculation, are replaced by a single force directed along the cylinder axis and close to the piston pin axis. This force is determined for each moment of time (angle q) according to a real indicator diagram built on the basis of a thermal calculation (usually for normal power and the corresponding number of revolutions).
Reconstruction of the indicator diagram into an expanded diagram by the angle of rotation of the crankshaft is usually carried out according to the method of prof. F. Brix. For this, an auxiliary semicircle of radius R = S / 2 is built under the indicator diagram (see the figure on sheet 1 of A1 format under the title "Indicator diagram in P-S coordinates"). Further from the center of the semicircle (point O) in the direction of N.M.T. the Brix correction equal to Rl / 2 is postponed. The semicircle is divided by rays from the center O into several parts, and from the center of Brix (point O), lines are drawn parallel to these rays. The points obtained on the semicircle correspond to certain rays q (in the A1 format figure, the interval between the points is 30 0). From these points, vertical lines before crossing the lines of the indicator diagram, and the obtained pressure values are drifted along the vertical
corresponding angles c. The unfolding of the indicator chart usually starts from V.M.T. during the intake stroke:
a) the indicator diagram (see the figure on sheet 1 of the A1 format), obtained in the thermal calculation, is deployed along the angle of rotation of the crank by the Brix method;
Brix Correction
where Ms is the scale of the piston stroke on the indicator diagram;
b) the scale of the expanded diagram: pressures Мр = 0.033 MPa / mm; angle of rotation of the crank Mf = 2 gr p.c. / mm;
c) according to the expanded diagram, every 10 0 of the angle of rotation of the crank, the values of Ap g are determined and entered into the dynamic calculation table (in the table, the values are given after 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 counted from absolute zero, and the expanded diagram shows the overpressure over the piston
MN / m 2 (2.7)
Consequently, the pressures in the engine cylinder, less than atmospheric, will be negative in the expanded diagram. The gas pressure forces directed to the crankshaft axis are considered positive, and from the crankshaft - negative.
2.2.2.1 Force of gas pressure on the piston Рг, Н
P g = (p g - p 0) F P * 10 6 H, (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 pressure forces of the gases P g along the angle of rotation of the crankshaft will have the same character of change as the curve of the gas pressure Ap g.
2.2.3 Reduction of masses of parts of the crank mechanism
By the nature of the movement, the masses of the parts of the crank mechanism can be divided into masses moving reciprocally (piston group and upper connecting rod head), masses performing rotational motion (crankshaft and lower connecting rod head): masses performing complex plane-parallel movement ( connecting rod).
To simplify the dynamic calculation, the actual crank mechanism is replaced by a dynamically equivalent lumped mass system.
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 crank axis at point B.The values of these masses are determined from the expressions:
where L ШК 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 - the distance from the center of the piston head to the center of gravity of the connecting rod
Taking into account the cylinder diameter - the S / D ratio of an in-line engine and a sufficiently high value of p g, the mass of the piston group (piston made of aluminum alloy) is set t P = m j
2.2.4 Forces of inertia
The forces of inertia acting in the crank mechanism, in accordance with the nature of the motion of the reduced masses P g, and the centrifugal forces of inertia of the rotating masses K R (Figure 32, a;).
Inertial force from reciprocating masses
2.2.4.1 From the calculations obtained on a computer, the value of the inertia force of reciprocating 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 inertial force is directed in the direction opposite to the acceleration. The forces of inertia of the reciprocating masses act along the axis of the cylinder and, like the forces of pressure of gases, are considered positive if they are directed to the axis of the crankshaft, and negative if they are directed from the crankshaft.
The construction of the curve of the inertia force 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 of P J should be made for the same positions of the crank (angles q) for which Dr r and Dr were determined
2.2.4.2 Centrifugal force of inertia of rotating masses
The force K R is constant in magnitude (at u = 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 rotating connecting rod masses
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 the algebraic addition of the gas pressure forces and the inertia forces of the reciprocating masses. The total force concentrated on the axis of the piston pin
P = P Г + P J, Н (2.17)
Graphically, the curve of the total forces is plotted using diagrams
Pg = f (q) and P J = f (q) (see Figure 30,) When summing these two diagrams built on the same scale MR, the resulting P diagram will be on the same scale MR.
The total force P, as well as the forces P g and P 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 created by it relative to the axis of the crankshaft of the journals has a direction opposite to the direction of rotation of the engine cotton wool.
The values of the normal force Ntgw 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 transmitted * to the crank. It is considered positive if it compresses the connecting rod, and negative if it is stretched.
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 connecting rod journal, two components of the force arise:
d) force directed along the radius of the crank K, N
e) tangential force directed tangentially to the circle of the radius of the crank, T, N
The T-force is considered positive if it compresses the cheeks of the knee.
2.2.6 Average tangential force per cycle
where Р Т - average indicator pressure, MPa;
F p is the area of the piston, m;
f - stroke of the prototype engine
2.2.7 Torques:
a) by value d) the torque of one cylinder is determined
M kr.ts = T * R, m (2.22)
The curve of the change in the force T depending on q is also the curve of the change in M cr.ts, but on a scale
M m = M p * R, N * m in mm
To plot the curve of the total torque M cr of a multi-cylinder engine, the curves of the torques of each cylinder are graphically summed up, shifting one curve relative to the other by the angle of rotation of the crank between flashes. Since the values and nature of the change in the torque in the angle of rotation of the crankshaft are the same from all cylinders of the engine, 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 sufficient to have a torque curve of one cylinder
b) for an engine with equal intervals between flashes, the total torque will periodically change (i is the number of engine cylinders):
For a four-stroke engine through O -720 / L deg. When graphically plotting the M cr curve (see sheet of Whatman paper 1, A1 format), the M cr.ts curve of one cylinder is divided into a number of sections equal to 720 - 0 (for four-stroke engines), all sections of the curve are brought together and summed up.
The resulting curve shows the change in total engine torque as a function of the angle of rotation of the crankshaft.
c) the average value of the total torque M cr.sr is determined by the area enclosed under the curve M cr.
where F 1 and F 2 are, respectively, the positive area and negative area in mm 2, enclosed between the M cr curve and the AO line and are equivalent to the work performed by the total torque (for i? 6, the negative area is usually absent);
ОА — length of the interval between flashes on the diagram, mm;
M m is the scale of moments. N * m in mm.
The moment M kr.sr is the average indicator moment
engine. The actual effective torque taken from the motor shaft.
where s m is the mechanical efficiency of the engine
The main calculated data on the forces acting in the crank mechanism by the angle of rotation of the crankshaft are given in Appendix B.
Kinematics and dynamics of the crank mechanism. The crank mechanism is the main mechanism piston engine, which perceives and transmits significant loads. Therefore, the calculation of the strength of the KShM is of great importance. In turn, the calculations of many engine parts depend on the kinematics and dynamics of the KShM. The kinematic analysis of the KShM establishes the laws of motion of its links, primarily the piston and connecting rod. To simplify the study of KShM, we assume that the crankshaft cranks rotate uniformly, i.e. with constant angular velocity.
There are several types and varieties. crank mechanisms(Fig. 2.35). Of greatest interest from the point of view of kinematics is the central (axial), offset (disaxial) and with a trailed connecting rod.
The central crank mechanism (Fig. 2.35.a) is a mechanism in which the cylinder axis intersects with the engine crankshaft axis.
Defining geometric dimensions the 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 car engines 
.
In the kinematic study of the crank mechanism, the piston stroke, the angle of rotation of the crank, the angle of deviation of the connecting rod axis in the plane of its swing from the cylinder axis are usually introduced into consideration (deviation in the direction of rotation of the shaft is considered positive, and in the opposite direction - negative), angular velocity. The piston stroke and length of the connecting rod are the main design parameters of the central crank mechanism.
Kinematics of the central KShM. 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 data of the kinematic calculation, a dynamic calculation is performed and the forces and moments acting on the engine parts are determined.
In the 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 values 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 movement of the piston, depending on the angle of rotation of the crank of the engine with a central control gear, is calculated by the formula. (1)
Lecture 7.Piston movement for each of the angles of rotation can be determined graphically, which is called the Brix method. To do this, from the center of the circle with a radius, the Brix correction is deposited in the direction of BDC. there is a new center. From the center, through certain values (for example, every 30 °), draw the radius vector until it intersects with the circle. The projections of the intersection points on the cylinder axis (TDC-BDC line) give the desired piston positions for the given angle values.
Figure 2.36 shows the dependence of the piston movement on the crankshaft angle.
Piston speed. Derivative of piston displacement - equation (1) with respect to time
rotation gives the speed of piston movement: (2)
Similar to the movement of the piston, the speed of the piston can also be represented in the form of two components: where is the first order component of the piston speed, which is determined; is the second-order piston velocity component, which is determined 
The component represents the speed of the piston 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 the speed of the piston on the angle of rotation of the crankshaft is shown in Fig. 2.37. The speed reaches its maximum values at crankshaft angles of rotation less than 90 and more than 270 °. Meaning maximum speed piston with sufficient accuracy can be determined as 
Piston acceleration is defined as the first derivative of the velocity over time or as the second derivative of the piston displacement over time: (3)
where and - harmonic components of the first and second order of 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 final 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 at the position of the piston at TDC, and minimum values at BDC or near BDC. These changes in the curve in the range from 180 to ± 45 ° depend on the value .
The ratio of piston stroke to cylinder bore is one of the main parameters that determines the size and weight of the engine. In automobile engines, the values are between 0.8 and 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 engine height decreases; due to a decrease in the average piston speed, the mechanical losses and wear of parts is reduced; the conditions for the placement of valves are improved and the 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 aspects: 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 deteriorates, 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 increasing engine speed.
Values for different engines: carburetor engines-; medium speed diesels -; high-speed diesels -.
When choosing values, it should be borne in mind that the forces acting in the KShM 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 KShM, which not only affect the parts of the KShM and other units, but also cause the engine to run unevenly. These forces include: the force of gas pressure is balanced in the engine itself and is not transmitted to its supports; the inertial force is applied to the center of the reciprocating masses and is directed along the cylinder axis, through the crankshaft bearings they act on the engine housing, causing it to vibrate on the bearings in the direction of the cylinder axis; 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 vibrate on the bearings in the direction of the crank. In addition, forces such as pressure on the piston from the side of the crankcase and gravity forces of the crankcase arise, which are not taken into account due to their relatively small value. All forces acting in the engine interact with the resistance on the crankshaft, friction forces and are perceived by the engine mounts. During each operating cycle (720 ° - for four-stroke and 360 ° for two-stroke engines) the forces acting in the KShM 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 cylinder axis and applied to the piston pin axis.
This force is determined for each moment in 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 a special installation. Figure 2.39 shows the expanded indicator charts forces acting in the KShM, in particular, the change in the force of gas pressure () from the value of the angle of rotation of the crankshaft. Forces of inertia. To determine the inertial forces acting in the KShM, it is necessary to know the masses of the moving parts. To simplify the calculation of the mass of moving parts, we will replace the system of conditional masses, equivalent to the actually existing masses. This change is called mass reduction. Bringing the masses of the KShM parts. By the nature of the movement of the mass of the KShM parts, it can be divided into three groups: parts moving back and forth (piston group and upper connecting rod head); parts that perform rotary motion (crankshaft and lower connecting rod head); parts that perform a complex plane-parallel movement (connecting rod rod).
The mass of the piston group () is considered concentrated on the axis of the piston pin and 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 crank axis at the point . The values of these masses are found by the formulas:
;
where is the length of the connecting rod; - the 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 in terms of the structural mass obtained from 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). Point-centered masses 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 inertial forces. The forces of inertia acting in the CRM, in accordance with the nature of the motion of the reduced masses, are divided into the forces of inertia of the translationally moving masses and the centrifugal forces of inertia of the rotating masses. The force of inertia from the reciprocating moving masses can be determined by the formula (4). The minus sign indicates that the inertial force is directed in the direction opposite to the acceleration. The centrifugal force of inertia of the rotating masses is constant in magnitude and is 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 CRM can be obtained only as a result of the combination of the action of various forces arising from the operation of the engine.
The total forces acting in the KShM. The forces acting in a single-cylinder engine are shown in Figure 2.41. The force of gas pressure acts in the KShM ,
force of inertia of reciprocating masses and centrifugal force .
Forces are both applied to the piston and act along its axis. Adding these two forces, we get 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 connecting rod axis: - force perpendicular to the cylinder wall. Force P N is perceived by the lateral surface of the cylinder wall and causes wear on the piston and cylinder. Force ,
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 magnitude of the indicated torque of one cylinder is determined: (9) Normal and tangential forces transferred to the center of the crankshaft form a resultant force, which is parallel and equal in magnitude to the force .
The force loads the crankshaft main bearings. In turn, strength can be decomposed into two components: strength P "N, perpendicular to the cylinder axis, 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 indicated torque and is directed in the opposite direction:. Torque is transmitted through the transmission to the drive wheels, and the overturning torque is taken up by the engine mounts. Force 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 crank journal and is directed away from the crankshaft axis. She, like the force, is unbalanced and is transmitted through the main bearings to the engine mounts.
Forces acting on the crankshaft journals. Radial force Z acts on the crankpin, tangential force T and centrifugal force from the rotating mass of the connecting rod. Forces Z and 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) The action of the force causes the crankpin to wear. The resulting force applied to the main journal of the crankshaft is found graphically as the forces transmitted from two adjacent knees.
Analytical and graphical presentation of forces and moments. An analytical representation of the forces and moments acting in the KShM is presented by formulas (4) - (12).
A clearer change in the forces acting in the control gear, depending on the angle of rotation of the crankshaft, can be represented as detailed diagrams that are used to calculate the strength of the control gear parts, assess the wear of the friction 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 journal 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 acting 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 abscissa 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 by 8). For each obtained point of the abscissa, I determine the algebraic sum of the ordinates of the two curves (above the abscissa, values with a "+" sign, below the abscissa, values with a "-" sign). The resulting values are plotted accordingly in coordinates , and the resulting points are connected by a curve (Figure 2.43). This curve is the curve of the resulting torque per engine cycle.
To determine the average value of the torque, the area limited by the torque curve and the ordinate axis is calculated (above the axis is positive, below it is negative: 
where is the length of the diagram along the abscissa; -scale.
Since when determining the torque, losses inside the engine were not taken into account, then, expressing the effective torque through the indicator torque, we obtain 
where is the mechanical efficiency of the motor
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 arrangement of the crankshaft cranks should, firstly, ensure the uniformity of the engine stroke, and, secondly, ensure the mutual balance of the inertial forces of the rotating masses and reciprocating moving masses. In order to ensure the uniformity of the stroke, it is necessary to create conditions for the alternation of 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 are even, and the cranks must be located symmetrically relative to the center of the crankshaft. The arrangement of the cranks that is symmetrical about 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 work of cylinders of single-row (a) and V-shaped (b) four-stroke engines
The optimal order of operation of the cylinders, when the next working stroke occurs in the cylinder farthest from the previous one, reduces the load on the crankshaft main bearings and improves engine cooling.
Balancing motorsForces and moments causing engine imbalance. 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 car, as a result of which fasteners are weakened, the adjustments of units and mechanisms are disrupted, the use of control and measuring instruments is difficult, and the noise level rises. This negative impact reduces different ways, v including the selection of the number and arrangement 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 vibration, i.e., engine imbalance, are called engine balancing.
Balancing the engine is reduced to creating a system in which the resultant forces and their moments are constant in magnitude or equal to zero. The engine is considered to be completely balanced if, during steady-state operation, the forces and moments acting on its bearings are constant in magnitude and direction. All piston internal combustion engines have a reactive moment opposite to the torque, which is called overturning. Therefore, it is impossible to achieve the absolute balance of the piston internal combustion engine. However, depending on the extent to which the causes of engine imbalance are eliminated, a distinction is made between fully balanced, partially balanced and unbalanced engines. Balanced engines are considered to be those in which all forces and moments are balanced.
Equilibrium conditions for 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 inertial forces 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 decision to balance the engine is reduced to balancing only the most significant forces and their moments.
Balancing methods. The inertial forces of the first and second orders and their moments are balanced by the selection of the optimal number of cylinders, their location and the selection of the appropriate crankshaft scheme. If this is not enough, then the forces of inertia are balanced by counterweights located on additional shafts that are mechanically connected to the crankshaft. This leads to a significant complication in the design of the engine 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 units 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.
When operating an engine, it is necessary that identical work processes in all its cylinders proceed in the same way. And this depends on the composition of the mixture, ignition or fuel injection timing, cylinder filling, thermal conditions, uniformity of mixture distribution over the cylinders, etc.
Crankshaft balancing. The crankshaft, like the flywheel, being a massive movable part of the crank mechanism, must rotate evenly, without beating. For this, its balancing is performed, which consists in identifying the imbalance of the shaft relative to the axis of rotation and the selection and fastening of balancing weights. Balancing of rotating parts is subdivided into static and dynamic balancing. Bodies are considered to be statically balanced if the body's center of mass lies on the axis of rotation. Rotating disc-shaped parts with a diameter greater than the thickness are subjected to static balancing.
Dynamic balancing is ensured subject to the condition of static balancing and the fulfillment of the second condition - the sum of the moments of 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 main axes of inertia of the body. Dynamic balancing is carried out by rotating the shaft on special balancing machines. Dynamic balancing provides greater accuracy than static balancing. Therefore, crankshafts, which are subject to increased balance requirements, are dynamically balanced.
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. The relative angular vibrations of the 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 crankshafts are also accompanied by a loss of engine power and negatively affect the operation of the mechanisms associated with it. Therefore, when designing engines, as a rule, 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 - dampers - can be used. Their work is based on two principles: the energy of vibrations is not absorbed, but is extinguished due to dynamic action in antiphase; vibration energy is absorbed.
Pendulum dampers of torsional vibrations are based on the first principle, which are also made in the form of counterweights and are connected to the bandages installed on the cheeks of the first knee by means of pins. The pendulum damper does not absorb the vibration energy, but only accumulates it during the twisting of the shaft and gives off the stored energy when it is unwound 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; fluid friction absorbers; absorbers of molecular (internal) friction.
These dampers usually represent a free mass connected to the shaft system in the zone of the greatest torsional vibrations by a non-rigid connection.
When studying the KShM kinematics, 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 fact, due to the unevenness of the engine 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 the kinematic analysis, the laws of motion of the KShM links, and first of all the piston and connecting rod, are established.
The initial position of the piston at the 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 V), which, together with the piston, reciprocates along the axis of the cylinder, and the axis of the crank pin of the crank (point A) rotating around the crankshaft axis O.
To determine the dependences of the KShM kinematics, we introduce the following designations:
l- the length of the connecting rod;
r- radius of the crank;
λ - the ratio of the radius of the crank to the length of the connecting rod.
For modern automobile and tractor engines the value is λ = 0.25–0.31. For high-speed engines, in order to reduce the inertial forces of reciprocating moving masses, more long connecting rods 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 β angles 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 NS(see fig. 1.20), which is equal to:
Rice. 1.20. Central KShM scheme
Of triangles A 1 AB and OA 1 A follows that
Considering that , we get:
Of right-angled triangles A 1 AB and A 1 OA we establish that
Where
then, substituting the obtained expressions into the formula for the piston movement, we get:
Since then
The resulting equation characterizes the movement of the KShM parts depending on the angle of rotation of the crankshaft and shows that the piston path can be conventionally represented as consisting of two harmonic displacements:
where is the first order piston path, which would take place in the presence of a connecting rod of infinite length;
- the path of the second order piston, that is, an additional movement depending on the final length of the connecting rod.
In fig. 1.21 shows the curves of the piston path along the angle of rotation of the crankshaft. It can be seen from the figure that when the crankshaft is turned through an angle of 90 °, the piston travels more than half its stroke.
Rice. 1.21. Change in the piston path depending on the angle of rotation of the crankshaft
Speed
where is the angular speed 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 first-order piston, i.e., the speed with which the piston would move in the presence of a connecting rod of infinitely long length;
- harmonically changing speed of the second order piston, i.e. the speed of additional displacement arising from the presence of a connecting rod of a finite length.
In fig. 1.22 shows the curves of the speed of the piston on the angle of rotation of the crankshaft. The angles of rotation of the crankshaft, where the piston reaches the maximum speed, depend on? and its increase are shifted towards the dead points.
For practical assessments of engine parameters, the concept is used average piston speed:
For modern car engines Vav= 8-15 m / s, for tractor - Vav= 5-9 m / s.
Acceleration The piston is defined as the first time derivative of the piston path:
Rice. 1.22. Change 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 varying acceleration of the first order piston;
- harmonically varying second-order piston acceleration.
In fig. 1.23 shows the curves of the piston acceleration in the angle of rotation of the crankshaft. Analysis shows that the maximum acceleration occurs when the piston is at TDC. When the piston is positioned at 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
When the engine is operating in the KShM, the following main force factors act: the forces of gas pressure, the forces of inertia of the moving masses of the mechanism, the forces of friction and the moment of useful resistance. Friction forces are usually neglected in the dynamic analysis of CWM.
Rice. 8.3. Impact on the elements of KShM:
a - gas forces; b - forces of inertia P j; в - centrifugal force of inertia К 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 defined as the product of the pressure drop by its area: P g = (p 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 elements of the CRM, the dependence of the force P g on time is of great importance.
The force of gas pressure acting on the piston loads the moving elements of the crankcase, is transmitted 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 transferred to the engine mountings and do not cause imbalance.
Forces of inertia of moving masses. KShM is a system with distributed parameters, the elements of which move unevenly, which leads to the occurrence of inertial loads.
A detailed analysis of the dynamics of such a system is in principle possible, but it involves a large amount of computation. Therefore, in engineering practice, models with lumped parameters, created on the basis of the method of replacement masses, are used to analyze the dynamics of the engine. In this case, for any moment in time, the dynamic equivalence of the model and the considered real system must be fulfilled, which is ensured by the equality of their kinetic energies.
Usually, a model of two masses is used, 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 point where the piston meets the connecting rod and reciprocates with the kinematic parameters of the piston, the second m r is located at the point where the connecting rod meets the crank and rotates uniformly with an angular velocity ω.
Parts of the piston group perform a rectilinear reciprocating motion along the cylinder axis. Since the center of mass of the piston group practically coincides with the axis of the piston pin, then to determine the inertial force 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 п j.
The crank of the crankshaft performs a uniform rotary motion. Structurally, it consists of a set of two halves of the root collar, two cheeks and a crankpin. With uniform rotation, a centrifugal force acts on each of the indicated elements of the crank, proportional to its mass and centripetal acceleration.
In the equivalent model, the crank is replaced with 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 = K r w.sh + 2K r u or m to rω 2 = m w.sh rω 2 + 2m u ρ u ω 2 , whence we obtain m k = 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 crankshaft connecting rod journal. In this case, the following conditions must be met:
1) the sum of the masses concentrated at the replacement points of the connecting rod model should be equal to the mass of the replaced link of the KShM: m w. n + 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 should be unchanged. Then m w. n = m w l w.k / l w and m w.k = 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 is usually not met for two-mass models of connecting rods of existing engines; it is neglected in the calculations due to its small numerical values.
Having finally combined the masses of all links of the KShM in the replacement points of the dynamic model of the KShM, we get:
the mass concentrated on the axis of the finger and reciprocating along the axis of the cylinder, m j = m p + m w. NS;
the mass located on the axis of the connecting rod journal and performing a rotational movement around the axis of the crankshaft, m r = m to + m sh.k. For V-shaped internal combustion engines with two connecting rods located on one connecting rod journal of the crankshaft, m r = m to + 2m crank.
In accordance with the accepted KShM model, the first replacement mass mj, moving unevenly with the kinematic parameters of the piston, causes the inertial 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 + К к = - 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, it, if no special measures are provided, can be the cause of the external imbalance 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 the acceleration y on the angle of rotation of the crank φ, the force P j is represented as the sum of inertia forces of the first (P jI) and second (P jII) orders:
where С = - m j rω 2.
The centrifugal force of inertia К r = - m r rω 2 from the rotating masses of the KShM is a constant in magnitude vector directed along the radius of the crank and rotating with a constant angular velocity ω. The force K r is transmitted to the engine mounts, causing a variable in magnitude of the reaction (see Fig. 8.3, c). Thus, the force K r, like the force P j, can be the cause of the external imbalance of the internal combustion engine.
Total forces and moments acting in the mechanism. Forces P g and P j, which have a common point of application to the system and a single line of action, in the dynamic analysis of KShM are replaced by the total force, which is an algebraic sum: P Σ = P g + P j (Fig. 8.5, a).
Rice. 8.5. Forces in KShM: a - design scheme; b - the dependence of the forces in the KShM on the angle of rotation of the crankshaft
To analyze the action of the force P Σ on the elements of the CRM, it is decomposed into two components: S and N. The force S acts along the axis of the connecting rod and causes repeated-alternating compression-tension of its elements. Force N is perpendicular to the cylinder axis and presses the piston against its mirror. The effect 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 crankshaft main bearings. To analyze their action, the forces are transferred to the center of the root 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 transmitted 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.
Obviously, N "= - N and = P Σ. Forces N and N" on the shoulder h create a overturning moment M def = Nh, which is then transmitted to the engine mounts and balanced by their reactions. M def and the reactions of the supports caused by it change in time and can be the cause of the external imbalance of the engine.
The main relations for the considered forces and moments are as follows:
On the connecting rod journal crank 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 sh.sh (Fig. 8.5, b), loading the connecting rod journal, is determined as the vector sum of these two forces.
Root necks single-cylinder engine cranks are loaded with force 
and the centrifugal force of inertia of the masses of the crank. Their net 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 main journal.
Total engine torque. 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's imagine a multi-cylinder engine as a set of single-cylinder engines, in which the working processes proceed identically, but are shifted relative to each other by angular intervals in accordance with the accepted order of engine operation. The torsional moment of the main journals can be defined as the geometric sum of the torques acting on all cranks preceding a given connecting rod journal.
Let us consider, as an example, the formation of torques in a four-stroke (τ = 4) four-cylinder (i = 4) linear engine with the order of operation of cylinders 1 - 3 - 4 - 2 (Fig. 8.6).
With a uniform alternation of flares, the angular shift between successive working strokes will be θ = 720 ° / 4 = 180 °. then, taking into account the order of operation, the angular shift of the moment 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 up the curves of the forces T (Fig. 8.6, b) acting on all the i-1 cranks preceding it.
The torque that twists the last main journal is the total torque of the engine M Σ, which is then transmitted to the transmission. It changes according to the angle of rotation of the crankshaft.
The average total torque of the engine pa at the angular interval of the working cycle M c. 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
The initial value when choosing the size of the KShM links is the value of the full stroke of the slider, set by the standard or for technical reasons for those types of machines for which the maximum value of the stroke of the slider is not specified (scissors, etc.).
The following designations have been introduced in the figure: dО, dА, dВ - the diameters of the fingers in the hinges; e - the magnitude of the eccentricity; R is the radius of the crank; L is the length of the connecting rod; ω - angular speed of rotation of the main shaft; α is the angle of under-reach of the crank to KNP; β is the angle of deflection of the connecting rod from the vertical axis; S - the value of the full stroke of the slide.
For a given value of the stroke of the slider S (m), the radius of the crank is determined:
For the axial crank mechanism, the functions of the slider movement S, the speed V and the acceleration j from the angle of rotation of the crank shaft α are determined by the following expressions:
S = R, (m)
V = ω R, (m / s)
j = ω 2 R, (m / s 2)
For the deaxial crank mechanism, the functions of the slider movement S, the speed V and the acceleration j from the angle of rotation of the crank shaft α, respectively:
S = R, (m)
V = ω R, (m / s)
j = ω 2 R, (m / s 2)
where λ is the coefficient of the connecting rod, the value of which for universal presses is determined in the range of 0.08 ... 0.014;
ω is the angular speed of rotation of the crank, which is estimated based on the number of strokes of the slider per minute (s -1):
ω = (π n) / 30
The nominal force does not represent the actual force developed by the drive, but represents the ultimate strength of the press parts that can be applied to the slider. The nominal force corresponds to a strictly defined angle of rotation of the crank shaft. For single-acting crank presses with one-sided drive, the nominal force is taken as the force corresponding to the angle of rotation α = 15 ... 20 о, counting from the bottom dead center.
