KShM during engine operation is exposed to the following forces: from the pressure of gases on the piston, the inertia of the moving masses of the mechanism, the gravity of individual parts, friction in the links of the mechanism and the resistance of the energy receiver.
The calculated determination of the friction forces is very difficult and is usually not taken into account when calculating the forces of the loading CRS.
In FOD and SOD, gravity forces of parts are usually neglected due to their insignificant value in comparison with other forces.
Thus, the main forces acting in the KShM are the forces from the pressure of gases and the forces of inertia of the moving masses. The forces from the pressure of gases depend on the nature of the flow 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 speed of rotation.
Finding these forces is necessary for calculating engine parts for strength, identifying bearing loads, determining the degree of unevenness of the crankshaft rotation, calculating the crankshaft for torsional vibrations.
Bringing the masses of parts and links of the KShM
To simplify calculations, the actual masses of the moving links of the CRM are replaced by the reduced masses concentrated at the characteristic points of the CRM and dynamically or, in extreme cases, statically equivalent to the real distributed masses.
The centers of the piston pin, the connecting rod journal, and the point on the crankshaft axis are taken as the characteristic points of the KShM. In crosshead diesel engines, instead of the center of the piston pin, the center of the crosshead is taken as the characteristic point.
The translational-moving masses (LDM) M s in trunk diesel engines include the mass of the piston with rings, the 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, the rod, the crosshead and part of the mass of the connecting rod.
The reduced LHD M S is considered to be centered either in the center of the piston pin (trunk ICEs) or in the center of the crosshead crosshead (crosshead engines).
The unbalanced rotating mass (NVM) M R is the sum of the remaining part of the connecting rod mass and part of the mass of the crank reduced to the connecting rod journal axis.
The distributed mass of the crank is conventionally replaced by two masses. One mass located in the center of the connecting rod journal, the other - located on the crankshaft axis.
The balanced rotating mass of the crank does not cause inertial forces, since its center of mass is located on the axis of rotation of the crankshaft. However, the moment of inertia of this mass is included as a constituent part of the given 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 crankshaft rotation axis.
Replacing the distributed masses of the connecting rod, knee (crank) and counterweight with lumped masses is called mass reduction.
By reducing the masses of the connecting rod
The dynamic model of the connecting rod is a straight line segment (weightless rigid rod) with a length equal to the connecting rod length 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 ШS, on the axis of the connecting rod journal - the mass of the rotating part of the connecting rod M ШR.
Rice. 8.1
M w - the actual mass of the connecting rod; Ts.m. - the center of mass of the connecting rod; L is the length of the connecting rod; L S and L R - the distance from the ends of the connecting rod to its center of mass; M шS - the mass of the progressively moving part of the connecting rod; M wR - mass of the rotating part of the connecting rod
For full dynamic equivalence of a real connecting rod and its dynamic model, three conditions must be met
To satisfy all three conditions, it would be necessary to create a dynamic model of the connecting rod with three masses.
To simplify the calculations, the two-mass model is retained, limiting ourselves to the conditions of only static equivalence
In this case
As can be seen from the obtained formulas (8.3) for calculating M шS and M шR it is necessary to know L S and L R, i.e. the location of the center of mass of the connecting rod. These values can be determined by calculation (graphical-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 take roughly
M wS? 0.4 M w; M wR? 0.6 M 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 k and M k0.
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 tread; c is the 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 counterweight masses
The dynamic counterweight model is similar to the crank model.
Figure 8.3
Reduced unbalanced counterweight
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 crankshaft axis.
Dynamic model of KShM
The dynamic model of the CSM as a whole is made on the basis of the models of its links, while the masses concentrated at the points of the same name are summed up.
1. Reduced translational-moving mass concentrated in the center of the piston pin or crosshead
M S = M P + M SHT + M KR + M SHS, (8.9)
where M P is the mass of the piston set;
M SHT - the mass of the rod;
М КР - crosshead mass;
М ШS - PDM of the connecting rod part.
2. Reduced unbalanced rotating mass concentrated in the center of the connecting rod journal
M R = M K + M SHR, (8.10)
where M K - unbalanced rotating part of the knee mass;
М ШR - НВМ of the connecting rod part;
Usually, for the convenience of calculations, the absolute masses are replaced by relative
where F p is the area of the piston.
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 diesel engines of the same type, the values of m S and m R vary within narrow limits and their values are given in the 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 acceleration due to gravity, g = 9.81 m / s 2.
Lecture 13. 8.2. Inertia forces of one cylinder
When the CRM moves, inertial forces arise from the translationally moving and rotating masses of the CRM.
Forces of inertia LDM (referred to F P)
thermodynamic piston marine engine
q S = -m S J. (8.12)
The sign "-" because the direction of inertial forces is usually in the opposite direction to the acceleration vector.
Knowing that, we get
At TDC (b = 0).
At BNM (b = 180).
Let us denote the amplitudes of the inertial forces of the first and second orders
P I = - m S Rsh 2 and P II = - m S l Rsh 2
q S = P I cosb + P II cos2b, (8.14)
where P I cosb is the first-order inertia force of the LDM;
P II cos2b - second-order inertia force of the LDM.
The force of inertia 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 inertial force of the PDM P I cosb can be represented as a projection onto the cylinder axis of a certain vector directed along the crank from the center of the crankshaft and acting as if it were the centrifugal force of inertia of the mass m S located in the center of the connecting rod journal.
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 force of inertia of the first order.
The introduction of fictitious inertial forces with only one real vertical projection into consideration is a conditional technique that makes it possible to simplify the LDM calculations.
The vector of a fictitious force of inertia of the first order can be represented as the sum of two components: the real force P I cosb, directed along the axis of the cylinder and the fictitious force P I sinb, directed perpendicular to it.
The force of inertia of the second order P II cos2b can be similarly represented as the projection onto the axis of the cylinder of the vector P II of the fictitious force of inertia of the second order PDM, which makes an angle of 2b with the axis of the cylinder and rotates with an angular velocity of 2sh.
Rice. 8.5
The fictitious force of inertia of the second order of the LDM 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 is fictitious P II sin2b, directed perpendicular to the first.
Forces of inertia NVM (referred to F P)
Force q R is applied to the crankpin axis and is directed along the crank away from the crankshaft axis. The inertial force vector rotates with the crankshaft in the same direction and with the same rotational speed.
If you move 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 forces of inertia
The total force of inertia of the LDM and NVM in the vertical plane
If we consider separately the inertial forces of the first and second orders, then in the vertical plane the total inertial force of the first order
Second-order inertial force in the vertical plane
The vertical component of the first-order inertia forces tends to raise or press the engine to the foundation once per revolution, and the second-order inertial force - twice per revolution.
The first-order inertia force in the horizontal plane tends to displace the motor from right to left and back once during one revolution.
Joint action of the force from the pressure of gases on the piston and the forces of inertia of the KShM
The gas pressure generated during engine operation acts on both the piston and the cylinder cover. 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 г = P - P 0, (8.19)
where Р is the current absolute pressure of gases in the cylinder, taken from indicator chart;
Р 0 - ambient pressure.
Figure 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 defined as the driving force
Pd = Pr + 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 = P d tgv; (8.21)
The normal force P n presses the piston against the cylinder bushing 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 connecting rod journal and decompose into two components - the tangential force t directed tangentially to the circle described by the radius R
and the radial force z directed along the radius of the crank
In addition to the force P w, the inertial 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 balancing forces and, parallel and equal to the tangential force t. The pair of forces t and rotates 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 frame bearings of the crankshaft. Let's split the force into two components - vertical and horizontal. The vertical force, together with the force of gas pressure on the cylinder cover, stretches the parts of the skeleton and is not transmitted to the foundation. It is the oppositely directed forces that form a pair of forces with the shoulder H. This pair of forces tends to rotate the skeleton 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 frame to the foundation frame supports, to the ship foundation hull. Consequently, M def 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
The calculation of these forces is carried out 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.
|
P n = P d tgv |
||||
The driving force referred to the area of the piston
P d = P g + q s + g s + P tr. (8.20)
We neglect the friction force P tr.
If g s? 1.5% P z, then we also neglect.
The P g values are determined using the pressure of the indicator diagram P.
P g = P - P 0. (8.21)
The force of inertia is determined analytically
Rice. 8.8
The driving force curve Pd is the initial one for plotting the force diagrams Pn = f (b), Psh = f (b), t = f (b), z = f (b).
To check the correctness of the construction of the tangential diagram, it is necessary to determine the average tangential force t cf.
From the diagram of the tangential force, it can be seen that t cf is defined as the ratio of the area between the line t = f (b) and the abscissa to the length of the diagram.
The area is determined by a planimeter or by integration using the trapezoidal method
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 sections;
Having determined t cp in cm, using the scale along the ordinate, 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 indicated pressure Pi and the average value of the tangential force tcp as follows
P i F п 2Rz = t cp F п 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 internal combustion engines
For four-stroke internal combustion engines
The permissible discrepancy should not exceed 5%.
Kinematics and dynamics of the crank connecting rod 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 of crank mechanisms (Fig. 2.35). The most interesting 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 (the deviation in the direction of rotation of the shaft is considered positive, and in the opposite direction - negative), and the 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. For this, the Brix correction is plotted from the center of the circle with a radius in the direction of Brix. 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 °. The value of the maximum piston speed can be determined with sufficient accuracy 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 points: the length of the engine and the length of the crankshaft increase; the loads on the parts from the forces of gas pressure and from the forces of inertia increase; the height of the combustion chamber decreases and its shape worsens, which in carburetor engines leads to an increase in the tendency to detonation, and in diesel engines - to a deterioration in the conditions of mixture formation.
It is considered advisable to decrease the value with increasing engine speed.
Values for different engines: carburetor engines-; medium speed diesels -; high-speed diesels -.
When choosing the 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, there are forces such as pressure on the piston from the crankcase, and the gravity force of the crankcase, 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 expanded indicator diagrams of 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).
Mass 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 in the form of 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 reciprocating 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 axis of the cylinder, and the force R", acting along the axis of the cylinder. Forces P "N and P N form a pair of forces, the moment of which is called overturning. Its value is determined by the formula (10) This moment is equal to the indicator torque and is directed in the opposite direction:. 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 out. 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 crankcase, depending on the angle of rotation of the crankshaft, can be represented as detailed diagrams that are used to calculate the strength of the crankcase parts, assess the wear of the rubbing surfaces of 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 must, 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. 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 meet the balance requirement, it is necessary that the number of cylinders in one row and, accordingly, the number of crankshaft crankshaft is even, and the crankshaft 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 increases. 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, at 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 forces of inertia of the second order of translationally moving masses and their moments are equal to zero; c) the resulting centrifugal forces of inertia of the rotating masses and their moments are equal to zero.
Thus, the 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 with 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 advance angles, 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 the centrifugal forces of the rotating masses relative to any point of the shaft axis must be equal to zero. When these two conditions are met, the axis of rotation coincides with one of the 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 crank of the crankshaft, 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 of the crankshafts are also accompanied by a loss of engine power and negatively affect the operation of related mechanisms. Therefore, when designing engines, as a rule, the calculation of crankshafts for torsional vibrations is performed 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 up 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.
Kinematics of KShM
In autotractor internal combustion engines, the following three types of crank mechanism (KShM) are mainly used: central(axial), displaced(deaxial) and trailed connecting rod mechanism(fig. 10). Combining these schemes, it is possible to form KShM of both linear and multi-row multi-cylinder internal combustion engines.
Fig. 10. Kinematic diagrams:
a- central KShM; b- displaced KShM; v- a mechanism with a trailed connecting rod
The kinematics of the KShM is fully described if the laws of change in time of movement, speed and acceleration of its links are known: crank, piston and connecting rod.
At ICE operation the main elements of KShM perform different kinds displacement. The piston moves reciprocally. The connecting rod performs a complex plane-parallel movement in the plane of its swing. The crankshaft crank makes a rotational movement about its axis.
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In the course project, the calculation of the kinematic parameters is carried out for the central KShM, the design scheme of which is shown in Fig. 11.
Rice. 11. Design scheme of the central KShM:
The diagram uses the following notation:
φ - the angle of rotation of the crank, measured from the direction of the axis of the cylinder in the direction of rotation of the crankshaft clockwise, at φ = 0 the piston is at top dead center (TDC - point A);
β - the angle of deviation of the axis of the connecting rod in the plane of its rolling away from the direction of the axis of the cylinder;
ω - angular speed of rotation of the crankshaft;
S = 2r- piston stroke; r- radius of the crank;
l w- the length of the connecting rod; - the ratio of the radius of the crank to the length of the connecting rod;
x φ- movement of the piston when turning the crank at an angle φ
The main geometric parameters, determining the laws of motion of the elements of the central crankshaft, are the radius of the crankshaft crank r and connecting rod length l NS.
Parameter λ = r / l w is a criterion for the kinematic similarity of the central mechanism. Moreover, for KShM different sizes but with the same λ the laws of motion of analogous elements are similar. In automotive internal combustion engines, mechanisms are used with λ = 0,24...0,31.
The kinematic parameters of the KShM in the course project are calculated only for the nominal power mode of the internal combustion engine with a discrete setting of the crank angle from 0 to 360º with a step of 30º.
Crank kinematics. The rotational motion of the crankshaft crank is determined if the dependences of the angle of rotation φ are known , angular velocity ω and acceleration ε from time t.
In the kinematic analysis of KShM, it is customary to make an assumption about the constancy of the angular velocity (rotational speed) of the crankshaft ω, rad / s. Then φ = ωt, ω= const and ε = 0. The angular speed and crank speed of the crankshaft n (rpm) related by the ratio ω = πn/thirty. This assumption allows us to study the laws of motion of the KShM elements in a more convenient parametric form - as a function of the angle of rotation of the crank and, if necessary, go to the temporal form using the linear relationship φ and t.
Piston kinematics. The kinematics of a reciprocating piston is described by the dependences of its movement NS, speed V and acceleration j from the angle of rotation of the crank φ .
Piston displacement x φ(m) when turning the crank through an angle φ is defined as the sum of its displacements from turning the crank through an angle φ (x I ) and from the deflection of the connecting rod at an angle β (NS II ):
The values x φ are determined up to small second order inclusive.
Piston speed V φ(m / s) is defined as the first derivative of the piston movement over time
, (7.2)
The speed reaches its maximum value at φ + β = 90 °, while the connecting rod axis is perpendicular to the radius of the crank and
(7.4)
Widely used to assess the design of internal combustion engines average piston speed, which is defined as V p.w. = Sn / 30, connected with maximum speed piston ratio 
which for the used λ is equal to 1.62 ... 1.64.
· Piston acceleration j(m / s 2) is determined by the derivative of the piston speed with respect to time, which corresponds exactly
(7.5)
and approximately
In modern internal combustion engines j= 5000 ... 20000m / s 2.
Maximum value 
holds for φ =
0 and 360 °. Angle φ = 180 ° for mechanisms with λ<
0.25 corresponds to the minimum acceleration value 
.
If λ>
0.25, then there are two more extrema 
at . A graphic interpretation of the equations of displacement, velocity and acceleration of the piston is shown in Fig. 12.
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Rice. 12. Kinematic parameters of the piston:
a- moving; b- speed, v- acceleration
Kinematics of the connecting rod. The complex plane-parallel movement of the connecting rod consists of the movement of its upper head with the kinematic parameters of the piston and its lower crank head with the parameters of the end of the crank. In addition, the connecting rod makes a rotational (rocking) movement relative to the point of articulation of the connecting rod with the piston.
· Angular movement of the connecting rod 
... Extreme values
take place at φ = 90 ° and 270 °. In automotive engines 
· Angular speed of rocking of the connecting rod(rad / s)
or . (7.7)
Extreme value observed at φ = 0 and 180 °.
· Angular acceleration of the connecting rod(rad / s 2)
Extreme values 
are achieved at φ = 90 ° and 270 °.
The change in the kinematic parameters of the connecting rod by the angle of rotation of the crankshaft is shown in Fig. 13.
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Rice. 13. Kinematic parameters of the connecting rod:
a- angular movement; b- angular velocity, v- angular acceleration
KShM dynamics
Analysis of all the forces acting in the crank mechanism is necessary for calculating the strength of engine parts, determining the torque and bearing loads. In the course project, it is carried out for the nominal power mode.
The forces acting in the crank mechanism of the engine are divided into the force of the gas pressure in the cylinder (index r), the force of inertia of the moving masses of the mechanism and the force of friction.
The forces of inertia of the moving masses of the crank mechanism, in turn, are divided into the forces of inertia of the masses moving reciprocally (index j) and the forces of inertia of the rotationally moving masses (index R).
During each working cycle (720º for a four-stroke engine), the forces acting in the control gear 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 individual sequential positions of the shaft with a step equal to 30º.
Gas pressure force. The force of gas pressure arises as a result of a working cycle in the engine cylinder. This force acts on the piston, and its value is defined as the product of the pressure drop across the piston by its area: P G = (p G - R o ) F n, (H) . Here R g - pressure in the engine cylinder above the piston, Pa; R o - pressure in the crankcase, Pa; F n is the area of the piston, m 2.
To assess the dynamic loading of the CRM elements, the dependence of the force P r from time (angle of rotation of the crank). It is obtained by rebuilding the indicator chart from the coordinates p - V in coordinates R -φ. When graphically rearranging on the abscissa axis of the diagram p - V postpone moving x φ piston from TDC or change in cylinder volume V φ = x φ F n (Fig. 14) corresponding to a certain angle of rotation of the crankshaft (practically after 30 °) and the perpendicular is restored to the intersection with the curve of the considered cycle of the indicator diagram. The resulting ordinate value is transferred to the diagram R- φ for the considered angle of rotation of the crank.
The force of gas pressure acting on the piston loads the moving elements of the crankshaft, is transmitted to the main bearings of the crankshaft and is balanced inside the engine due to the elastic deformation of the elements that form the intracylinder space, by forces R r and R d "acting on the cylinder head and on the piston, as shown in Fig. 15. These forces are not transmitted to the engine mounts and do not cause imbalance.
Rice. 15. The impact of gas forces on the structural elements of the KShM
Forces of inertia. A real KShM is a system with distributed parameters, the elements of which move unevenly, which causes the appearance of inertial forces.
A detailed analysis of the dynamics of such a system is in principle possible, but it involves a large amount of computation.
In this regard, in engineering practice, dynamically equivalent systems with lumped parameters, synthesized on the basis of the method of replacing masses, are widely used to analyze the dynamics of CWM. The criterion of equivalence is the equality in any phase of the working cycle of the total kinetic energies of the equivalent model and the mechanism it replaces. The synthesis methodology for a model equivalent to a CSM is based on replacing its elements with a system of masses interconnected by weightless absolutely rigid bonds (Fig. 16).
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Parts of the crank mechanism have different character movement, which causes the appearance of inertial forces of various types.
Rice. 16. Formation of an equivalent dynamic KShM model:
a- KShM; b- equivalent KShM model; c - forces in KShM; G- mass of KShM;
d- the mass of the connecting rod; e- the mass of the crank
Parts of the piston group perform a rectilinear reciprocating motion along the axis of the cylinder and in the analysis of its inertial properties can be replaced by an equal mass T NS , concentrated in the center of mass, the position of which practically coincides with the axis of the piston pin. The kinematics of this point is described by the laws of motion of the piston, as a result of which the force of inertia of the piston P j n = –M NS j, where j- acceleration of the center of mass equal to the acceleration of the piston.
The crank of the crankshaft performs a uniform rotary motion. Structurally, it consists of a set of two halves of the main necks, two cheeks and a connecting rod neck. The inertial properties of the crank are described by the sum of the centrifugal forces of the elements, the centers of mass of which do not lie on the axis of its rotation (cheeks and crankpin):
where K r sh.sh, K r u and r, ρ u - centrifugal forces and distances from the axis of rotation to the centers of mass, respectively, of the connecting rod journal and cheek, T sh and m u - masses, respectively, of the crankpin and cheeks. When synthesizing an equivalent model, the crank is replaced with a mass m to, located at a distance r from the axis of rotation of the crank. The quantity m k is determined from the condition that the centrifugal force created by it is equal to the sum of the centrifugal forces of the masses of the crank elements, from which, after the transformations, we obtain m To = t sh.sh + m SCH ρ SCH / r.
The elements of the connecting rod group perform a complex plane-parallel movement, which can be represented as a set of translational motion with the kinematic parameters of the center of mass and rotational motion around an axis passing through the center of mass perpendicular to the rocking plane of the connecting rod. In this regard, its inertial properties are described by two parameters - inertial force and moment. Any system of masses in its inertial parameters will be equivalent to the connecting rod group in the case of equality of their inertial forces and inertial moments. The simplest of them (Fig. 16, G) consists of two masses, one of which m wp = m NS l sh.k / l w is focused on the axis of the piston pin, and the other m sh.k = m NS l wp / l w - in the center of the crankshaft connecting rod journal. Here l wp and l sh.k - the distance from the points of mass placement to the center of mass.
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 of the 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. To do this, an auxiliary semicircle with a 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) towards 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 lines parallel to these rays are drawn from the center of Brix (point O). The points obtained on a semicircle correspond to certain rays q (in the A1 format figure, the interval between 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; the 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.
The mass of the piston group is not considered concentrated on the axle.
piston pin at point A [2, Figure 31, b].
The mass of the connecting rod group m Ш is replaced by two masses, one of which m ШП is concentrated on the axis of the piston pin at point A - and the other m ШК - on the crank axis at point B.The values of these masses are determined from the expressions:
where L ШК - 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 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 M P, the resulting P diagram will be on the same scale Mp.
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 - piston area, 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 from all engine cylinders the values and nature of the torque change in the angle of rotation of the crankshaft are the same, 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 - 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.
The main link of the power plant designed for transport equipment is the crank mechanism. Its main task is to convert the rectilinear movement of the piston into the rotational movement of the crankshaft. The operating conditions of the elements of the crank mechanism are characterized by a wide range and high repetition rate of alternating loads, depending on the position of the piston, the nature of the processes occurring inside the cylinder and the engine crankshaft speed.
The calculation of the kinematics and the determination of the dynamic forces arising in the crank mechanism are performed for a given nominal mode, taking into account the results of the thermal calculation and the previously adopted design parameters of the prototype. The results of the kinematic and dynamic calculations will be used to calculate the strength and determine the specific design parameters or dimensions of the main units and engine parts.
The main task of the kinematic calculation is to determine the movement, speed and acceleration of the elements of the crank mechanism.
The task of the dynamic calculation is to determine and analyze the forces acting in the crank mechanism.
The angular speed of rotation of the crankshaft is assumed to be constant, in accordance with the given rotation frequency.
The calculation considers loads from the forces of pressure of gases and from the forces of inertia of moving masses.
The current values of the gas pressure force are determined on the basis of the results of calculating the pressures at the characteristic points of the working cycle after the construction and development of the indicator diagram in coordinates along the angle of rotation of the crankshaft.
The inertia forces of the moving masses of the crank mechanism are divided into the inertia forces of the reciprocating masses Pj and the inertia forces of the rotating masses KR.
The forces of inertia of the moving masses of the crank mechanism are determined taking into account the dimensions of the cylinder, design features KShM and masses of its parts.
To simplify the dynamic calculation, we replace the actual crank mechanism with an equivalent system of lumped masses.
According to the nature of their movement, all parts of the KShM are divided into three groups:
- 1) Reciprocating parts. These include the mass of the piston, the mass of the piston rings, the mass of the piston pin, and we consider it concentrated on the axis of the piston pin - mn .;
- 2) Parts that perform rotary motion. We replace the mass of such parts with the total mass reduced to the radius of the crank Rkp, and denote it as mk. It includes the mass of the connecting rod journal mshsh and the reduced mass of the crank cheeks msh, concentrated on the axis of the connecting rod journal;
- 3) Parts performing a complex plane-parallel movement (connecting rod group). To simplify calculations, we replace it with a system of 2 statically replacing spaced masses: the mass of the connecting rod group, concentrated on the axis of the piston pin - mshp and the mass of the connecting rod group, related and concentrated on the axis of the connecting rod journal of the crankshaft - mshk.
Wherein:
mшn + mшк = mш,
For most existing designs of automotive engines, the following are accepted:
mшn = (0.2 ... 0.3) · mш;
mshk = (0.8 ... 0.7) · msh.
Thus, we replace the system of mass KShM with a system of 2 concentrated masses:
Mass at point A - reciprocating
and the mass at point B performing rotational motion
The values of mn, mw and mk are determined on the basis of existing designs and structural specific weights of the piston, connecting rod and crank elbow, referred to the unit of surface area of the cylinder diameter.
Table 4 Specific structural masses of KShM elements
The area of the piston is
To start performing the kinematic and dynamic calculation, it is necessary to take the values of the structural specific weights of the elements of the crank mechanism from the table
We accept:
Taking into account the accepted values, we determine the real values of the mass of individual elements of the crank mechanism
Piston weight kg,
Connecting rod weight kg,
Crank knee weight kg
The total mass of the KShM elements performing reciprocating - translational motion will be equal to
The total mass of the elements performing rotary motion, taking into account the reduction and distribution of the mass of the connecting rod, is equal to
Table 5 Initial data for the calculation of KShM
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Parameter Name |
Designations |
Units |
Numerical values |
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1. The frequency of rotation of the crankshaft |
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2. Number of cylinders |
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3. Crank radius |
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4. Cylinder diameter |
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5. Rcr / Lsh ratio |
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6. Pressure at the end of the inlet |
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7. Ambient pressure |
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8. Exhaust pressure |
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9. Maximum cycle pressure |
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10. Pressure at the end of expansion |
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11. Starting angle of calculation |
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12. End angle of calculation |
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13. Calculation step |
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14. Structural weight of the piston group |
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15. Structural weight of the connecting rod group |
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16. Structural weight of the crank |
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17. Piston weight |
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18. Mass of the connecting rod |
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19. Mass of the knee of the crank |
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20. The total mass of reciprocating - translational moving elements |
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21. The total mass of the rotating elements of the KShM |
