Home Wheels Changing the tangent forces on a native neck. Forces acting in the crank-connecting rod mechanism. Dynamic calculation of CSM.

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Changing the tangent forces on a native neck. Forces acting in the crank-connecting rod mechanism. Dynamic calculation of CSM.

Forces acting on crankshaft necks. These forces include: the power of gases is balanced in the engine itself and it is not transmitted to its support; The inertia force is applied to the center of returnable moving masses and is directed along the axis of the cylinder through the crankshaft bearings affect the engine body causing it vibration on the supports in the axis direction of the cylinder axis; Centrifugal force from rotating masses is directed by crank in the middle plane affecting the crankshaft supports on the engine housing ...

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Lecture 12.

Dynamics of KSM.

12.1. Pressure power gases

12.2. Forces inertia

12 .2.1. Mass cshmatic mass

12.3. Total Forces acting in KSHM

12.3.1. Forces acting on crankshaft necks

12.4. The order of the engine cylinders depending on the location of the crank and the number of cylinders

When the engine is running in KShM, the forces and moments act, which not only affect the Details of the CSM and other nodes, but also cause the engine to be unevenness. These forces include:

the power of gas pressure is balanced in the engine itself and it is not transmitted to its support;
the inertia force is applied to the center of reciprocating moving masses and is directed along the axis of the cylinder, through the crankshaft bearings affect the engine body, causing it vibration on the supports in the axis direction of the cylinder axis;
the centrifugal force from the rotating masses is directed by crank in the middle plane, acting through the crankshaft supports on the engine body, causes the engine fluctuations on the supports in the direction of the crank.

In addition, such forces arise as the pressure on the piston from the crankcase, and the gravity of CSM, which are not taken into account in view of them relatively small magnitude.

All intensifying power in the engine interact with the knee resistance, friction forces and Perceived engine supports. During each working cycle (720 ° - for four-stroke and 360 ° for two-stroke engines) The forces acting in CSM are continuously varying in magnitude and the direction of I. To establish the nature of the change in these forces from the corner of the rotation of the crankshaft, they are determined every 10-30 ° for certain positions of the crankshaft.

12.1. Pressure power gases

Gas pressure forces act on the piston, walls and cylinder head. To simplify the dynamic calculation of pressure Gas replaced by one force directed along the axis of the cylinder and affairs flanged to the axis of the piston finger.

This force is determined for each point of time (the angle of rotationthe crankshaft φ) on the indicator diagram obtained on the basis of the thermal calculation or removed directly from the engine using a special installation. In fig. 12.1 shows the detailed indicator diagrams of forces acting in in particular a change in gas pressure force(R ) From the magnitude of the angle of rotation of the crankshaft.

Fig. 12.1. Expanded indicator charts forces,
operating in KSM.

12.2. Forces inertia

To determine the inertia forces operating in the CSM, it is necessary to know the masses of moving parts. To simplify the calculation of the mass of moving parts by replacing the conditional mass system equivalent to the actual existing masses. Such a replacement is called the masses.

12.2.1. Mass cshmatic mass

According to the nature of the mass movement of parts, KSM can be divided into three groups:

details moving reciprocating (piston group and outer head rod);
details performing rotational motion (crankshaft and lower head rod);
details performing complex flat-parallel movement (rod rod).

Mass of a piston group (T P) consider focused on the piston finger axis at the point A (Fig. 12.2).

Fig. 12.2. Mass chatting

Mass of the connecting rod group Replaced with two masses: T SP - focused on the axis of the piston finger at the point A, T SK - on the axis of the crank at the point of the V. The values \u200b\u200bof these masses are found according to the formulas:

where L w - the length of the connecting rod;

L Shk. - distance from the center of the crank head to the center of gravity of the rod.

For most existing enginest SP. Located in the limit of 0.2t Ø to 0.3 t, A T SK from 0.7 tx to 0.8 tons. The value t sh It can be determined through a constructive mass (Table 12.1) obtained on the basis of statistical data.

Mass crank Replaced with two masses focused on the axis of the crank at the point In (t to) and on the axis of the indigenous neck at the pointO (T O) (Fig. 12.3).

Fig. 12.3. Mass crank resorts:a - real; B. - Equivalent

The mass of the native neck with a part of the cheeks located symmetrically relative to the axis of rotation is balanced. Unbalanced masses of crank are replaced by one resolved mass in compliance with the condition of equality of the centrifugal force of the inertia of the real mass of the centrifugal strength of the resulting mass. Equivalent mass lead to a radius of crankR and denote T to.

Mass rod cervicalt SHSH With the adjacent parts of the cheeks take the cervical axis concentrated in the middle, and since the center of gravity is removed from the shaft axis to the distance equalR. , bringing this mass is not required. Mass cheekt sh With the center of gravity at a distance p from the axis of the crankshaft, replaced with a given mass located at a distance R. From the crankshaft axis. The above mass of the whole crank is determined by the sum of the masses of the cranium cervical and cheeks:

When designing engines, the valuet K. can be obtained through the structural masses of the crankt "K. (See Table. 12.1). Contemporary short-terrestrial enginest sh Mala compared tot SHSH And it can be neglected.

Table 12.1. Values \u200b\u200bof the structural masses of KSHM, kg / m2

Element KSM.	Carburetor engines S.D from 60 to 100 mm	Diesels with D from 80 to 120 mm
Piston group(t "n \u003d t sh / f n)
Aluminum alloy piston	80-50	150-300
Cast iron piston	150-250	250-400
Schitun (T "K \u003d T W / F n)
Shatun.	100-200	250-400
Unbalanced parts of one knee of the crankshaft without counterweight(T "K \u003d T to / F n)
Steel wrought crankshaft with solid necks	150-200	200-400
Cast-iron cast crankshaft with hollow cakes	100-200	150-300

Notes.

1. When using Table. 12.1 It should be borne in mind that big valuest. "Correspond to engines with a large diameter of the cylinder.

2. Reducing S / D reduces T "W and T" to.

3. V-shaped engines with two rods on the neck correspond to the big values t "k.

Thus, the system of focused masses, dynamically equivalent to KSM, consists of masst A. focused on the point BUT and receiving reciprocating movement:

and mass t in focused on the point IN and having a rotational movement:

In V. -s-like engines with dual kshm T \u003d T to + 2t set.

When dynamically calculated the engine valuet p and t sh Determine according to prototypes or calculated. Valuest shsh and t sh Determine based on the size of the crank and density of the crankshaft material. For approximate determination of the valuet p, t and t to You can use structural masses:

where.

12.2.2. Definition of inertia forces

Inertia forces acting in KSM, in accordance with the nature of the movement of the masses, are divided intothe strength of the inertia of progressively moving massesP J. and centrifugal inertia forces of rotating masses R c.

The power of inertia from reciprocating masses can be determined by the formula

(12.1)

The minus sign indicates that the power of inertia is directed to the opposite acceleration. It can be viewed as consisting of two forces (similar to acceleration).

First component

(12.2)

first order inertia.

Second component

(12.3)

second order inertia.

In this way,

Centrifugal inertia power of rotating masses permanent largest and directed from the axis of the crankshaft. Its value is determined by the formula

(12.4)

A complete idea of \u200b\u200bthe loads acting in the details of the CSM can be obtained only as a result of a combination of the action of various forces arising from the engine operation.

12.3. Total Forces acting in KSHM

Consider Work single-cylinder engine.Forces acting in single-cylinder engine, shown in Fig. 12.4. In KSM. gas pressure force act R G The power of inertia reciprocaltelno moving massesP J. and centrifugal force R c. Forces R G and P J applied to the piston and act on its axis. Folding these twoforces We obtain the total force acting on the axis of the cylinder:

(12.5)

The displaced force p into the center of the piston finger is folded into two components:

(12. 6 )

force directed along the rod axis;

(12. 7 )

power perpendicular to the wall of the cylinder.

Fig. 12.4. Forces acting in the KSM single-cylinder engine

Power P n. It is perceived by the side surface of the cylinder wall and determines the wear of the piston and cylinder. It is considered positive if the moment created by it relative to the axis of the crankshaft is directed opposite to the direction of rotation of the engine shaft.

Power r sh It is considered positive if the connecting rod is compressed, and negative, if it stretches.

Strength p sh attached to the rod cervical (P "Sh ), folded into two components:

(12.8)

tangential force tangent to the circle of radius of crank;

(12.9)

normal force (radial), directed along the radius of crank.

Power Z. It is considered positive if it squeezes the cheeks of the crank. ForceT. It is considered positive if the direction of the moment created by it coincides with the direction of rotation of the crankshaft.

By magnitude T. determine the indicator torque of one cylinder:

(12.10)

Normal and tangential forces transferred to the center of the crankshaft (Z "and t "), form an automatic strengthP "" W, which is parallel and equal in magnitude P sh. Power p "" sh Loads the native crankshaft bearings. In turn, strength P "" W You can decompose into two components: forceP "N, perpendicular to the axis of the cylinder, and strength p "acting through the axis of the cylinder. ForcesP "N and P N Form a couple of forces, the moment of which is called tipping. Its value is determined by the formula

(12.11)

This moment is equal to the indicator torque and sent to the opposite side to him:

Since, then

(12.12)

The torque is transmitted through the transmission of the drive wheels, and the tipping point is perceived by the engine supports. ForceP "equal to force p and similarly to the last one can imagine how

Component P "G It is equilibrated by the power of gases applied to the cylinder head,a P "J It is a free unbalanced force transmitting to the engine support.

The centrifugal power of the inertia is applied to the rod cervice and is aimed away from the crankshaft axis. She just like powerP "J. it is unbalanced and transmitted through the indigenous bearings on the engine support.

12.3.1. Forces acting on crankshaft necks

Radial force act on the connecting rodZ. , Tangential Strength T. and centrifugal force R C. from the rotating mass of the rod. ForcesZ and r c directed on one straight line, so their relative

(12.13)

Here rt It is not defined as , but as , because we are talking about centrifugal strength only the connecting rod, and not the whole crank.

The equally all forces acting on the connecting rod cervix is \u200b\u200bcalculated by the formula

(12.14)

Action force R w Calling the hunted neck. The resulting force applied to the root crankshaft is found graphically as forces transmitted from two adjacent knees.

12.3.2. Analytical and graphical representation of forces and moments

Analytical representation of forces and points operating in KSM is represented by formulas (12.1) - (12.14).

Changing the forces acting in CSM depending on the corner of the rotation of the crankshaft, can be represented as unfolded diagrams, which are used to calculate the parts of the CSM for strength, assess the wear of the driving surfaces of parts, analysis of the uniformity of the stroke and determining the total torque of multi-cylinder engines, as well as Construction of polar chart loads on the neck shaft and its bearings.

Typically, two deployed charts are built during the calculations: one is depicted depending on, I. (see Fig. 12.1), on the other - dependence and (Fig. 12.5).

Fig. 12.5. Deployed charts of the tangential and real forces operating in CSM

The detailed charts operating in the CSM forces make it possible to make a relatively simple way to determine the torque of multi-cylinder engines.

From equation (12.10) it follows that the torque of the single-cylinder engine can be expressed as a function T \u003d F. (φ). Value of powerT. Depending on the change in the angle of rotation, it changes significantly, as can be seen in Fig. 12.5. Obviously, the torque will change similarly.

In the multi-cylinder engines, the variable torque of individual cylinders are summed up along the length of the crankshaft, as a result of which the total torque acts at the end of the shaft. The values \u200b\u200bof this moment can be defined graphically. For this projection of the curve T \u003d F. (φ) 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 on 8). For each obtained point of the abscissa, the algebraic amount of the ordents of two curves determine (above the abscissa value with the "+" sign, the values \u200b\u200bof the value with the sign "-") below the abscissa. The obtained values \u200b\u200bare delayed accordingly in the coordinates X, U. And the points obtained are connected to the curve (Fig. 12.6). This curve is a curve of the resultant torque in one working engine cycle.

Fig. 12.6. Deployed Diagram of Result Torque
for one working engine cycle

To determine the average torque value, the area is calculatedF, Limited torque curve and ordinate axis (above the axis value is positive, below - negative):

where L. - the length of the diagram along the abscissa axis; M.M - scale.

With a known scale of tangential force MT. Find the scale of torque MM \u003d m T R, R - radius crank.

Since when determining torque, losses inside the engine were not taken into account, then, expressing an effective torque through the indicator, we obtain

where mk - effective torque;η M. - Mechanical engine efficiency.

12.4. Order Engine cylinder works depending on the location of the crank and the number of cylinders

In the multi-cylinder engine, the location of the crankshaft crankshaft must, first, ensure the uniformity of the engine, and, secondly, to ensure the mutual balance of the inertia for the rotating masses and the reciprocating moving masses.

To ensure uniformity of the stroke, it is necessary to create conditions for alternation in flash cylinders at equal intervals of the corner of the crankshaft. Therefore, for a single-row engine, the angle f corresponding to the angular interval between flashes at a four-stroke cycle is calculated by the formula φ \u003d 720 ° /i, where I - the number of cylinders, and with a two-stroke according to the formula φ \u003d 360 ° /i.

On the uniformity of the alternation of outbreaks in the cylinders of the multi-row motor, except the angle between the crankshaft crankshafts, the angle Γ between the rows of cylinders is also affected. To obtain optimal uniformityn. -One engine this angle should be inn. Once less than the angle between the crankshaft cranks, i.e.

Then the angular interval between flashes for the four-stroke engine

For two-stroke

To meet the requirements of the equilibration, it is necessary that the number of cylinders in one row and, accordingly, the number of crankshaft crankshafts was even, and the crank must be located symmetrically relative to the middle of the crankshaft.Symmetrical relative to the middle of the crankshaft location of the crank is called "mirror". When choosing a shape of the crankshaft, except for the engine equilibrium and the uniformity of its turn, also takes into account the procedure for the operation of cylinders.

The optimal operating order of cylinders, when the next workforce occurs in the cylinder most remote from the previous one, reduces the load on the root bearing of the crankshaft and improve the cooling of the engine.

In fig. 12.7 shows the sequences of the cylinders of the single-row (a) and v-shaped (b ) Four-stroke engines.

Fig. 12.7. Sequence of cylinders of four-stroke engines:

a - single-row; b - v -

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Lecture 11.

Kinematics of the crank-connecting mechanism

11.1. Types of KSM.

11.2.1. Move piston

11.2.2. Piston speed

11.2.3. Piston acceleration

Crank mechanism (K sh M. ) It is the main mechanism of piston internal combustion engine, which perceives and transmits significant loads by magnitude. Therefore, the calculation of the strengthK sh M. it's important. In turn Calculations of many details the engine depends on the kinematics and the dynamics of KSM. Kinematic kSHM analysis establishes the laws of movement units, First of all, the piston and connecting rod.

To simplify the study of CSM, we assume that the crankshaft cranks are uniformly, that is, with a constant angular speed.

11.1. Types of KSM.

Three types of KSHM are used in the piston engine:

central (axial);
mixed (dexal);
with trailed connecting rod.

In central KSM. The axis of the cylinder intersects with the axis of the crankshaft (Fig. 11.1).

Fig. 11.1. Scheme of Central CSM:φ - current angle of rotation of the crankshaft; β is the angle of deviation of the rod axis from the axis of the cylinder (with the deviation of the connecting rod in the direction of rotation of the crank angle β is considered to be positive, in the opposite direction - negative);S - piston stroke;
R. - radius of crank;L - the length of the connecting rod; H. - movement of the piston;

Ω - Crankshaft Angle Speed

Corner speed is calculated by the formula

An important constructive parameter of KSM is the ratio of the radius of the crank to the length of the connecting rod:

It has been established that with a decrease in λ (by increasingL) There is a decrease in inertia and normal forces. This increases the height of the engine and its mass, so in automotive engines are taken λ from 0.23 to 0.3.

The values \u200b\u200bλ for some automotive and tractor engines are shown in Table. 11.1.

Table 11. 1. The values \u200b\u200bof the parameter λ for pazloe engines

Engine
VAZ-2106.	0,295
ZIL-130.	0,257
D-20	0,280
SMD-14.	0,28
YAMZ-240.	0,264
KAMAZ -740.	0,2167

IN deaxal CSM. (Fig. 11.2) The axis of the cylinder does not cross the axis of the crankshaft and is shifted relative to its distancebut .

Fig. 11.2. Diagram of dexali KSHM

Divexial CSM have relatively central KSM some advantages:

the increased distance between the crankshaft and the camshafts, as a result of which the space increases to move the lower head of the connecting rod;
more uniform wear of the engine cylinders;
with the same valuesR. and λ is more piston stroke, which helps to reduce the content of toxic substances in the exhaust engine gases;
increased engine volume.

In fig. 11.3 showsCSM with a trailer connecting rod. The connecting rod, which is cranked directly with the neck of the crankshaft, is called the main thing, and the connecting rod, which is connected to the main thing through the finger located on its head, is called trailers.Such a CSM scheme is applied on engines with a large number of cylinders when they want to reduce the engine length.Pistons connected to the main and trailed connecting rod have not the same move, since the axis of the crank head is trailedgO The connecting rod during operation describes an ellipse, a large semi-axis is greater than the radius of the crank. INV. -Food D-12 twelve-cycle engine difference during the pistons is 6.7 mm.

Fig. 11.3. CSM with trailed connecting rod:1 - piston; 2. - compression ring;3 - piston finger; 4 - Piston plug Palc; five - Top head bushingrod; 6 - main connecting rod; 7 - trailed connecting rod; 8 - lower head bushing rod; 9 - finger fixture trailed connecting rod; 10 - installation pin; 11 - liners; 12- Konich sky pin

11.2. Kinematics of the Central CSM.

With kinematic analysis, KSHM believes that the angular velocity of the crankshaft is constant.The kinematic calculation task includes the definition of the movement of the piston, the speed of its movement and acceleration.

11.2.1. Move piston

Moving the piston depending on the corner of the rotation of the crank for the engine with the central KSHM is calculated by the formula

(11.1)

Analysis of equation (11.1) indicates that the movement of the piston can be represented as the sum of two movements:

x 1 - moving first order, corresponds to the movement of the piston with an infinitely long connecting rod (L \u003d ∞ at λ \u003d 0):

x 2 - Movement of the second order, is a correction to the end length of the connecting rod:

The value X 2 depends on λ. At a given λ. Extreme values x 2 will take place if

i.e. within one turn of extreme values x 2 will correspond to the angles of rotation (φ) 0; 90; 180 and 270 °.

Maximum values \u200b\u200bmovement reaches at φ \u003d 90 ° and φ \u003d 270 °, i.e. when withs. φ \u003d -1. In these cases, the actual movement of the piston will be

Λr / 2 value It is called the Brics Amendment and is amendment to the final side of the connecting rod.

In fig. 11.4 shows the dependence of the movement of the piston from the angle of rotation of the crankshaft. When you turn a crank at 90 °, the piston passes more than half of his stroke. This is explained by the fact that when turning the crank from VTC to NMT, the piston moves under the action of moving the rod along the axis of the cylinder and deviate it from this axis. In the first quarter of the circle (from 0 to 90 °), the connecting rod simultaneously with the movement to the crankshaft, deviates from the axis of the cylinder, and both movements of the connecting rod correspond to the movement of the piston in one direction, and the piston passes more than half of its path. When the crank movement in the second quarter of the circle (from 90 to 180 °), the direction of movements of the connecting rod and the piston does not coincide, the piston passes the smallest path.

Fig. 11.4. The dependence of the movement of the piston and its components from the corner of the rotation of the crankshaft

Move the piston for each of the angles of rotation can be determined by graphically, which is called the Brix method. To do this, from the center of the circumference with a radiusR \u003d S / 2 deposited towards NMT Amendment Brix, there is a new centerO 1. From the center of 1 Through certain values \u200b\u200bφ (for example, every 30 °), a radius-vector is carried out to the intersection with a circle. The projection of the intersection points to the axis of the cylinder (Line VTT-NMT) give the desired position of the piston in these angles of the angle φ. The use of modern automated computing means allows you to quickly get a dependencyx \u003d f (φ).

11.2.2. Piston speed

The displacement derivative of the piston - equation (11.1) by the time of rotation gives the speed of movement of the piston:

(11.2)

Similarly Moving piston Piston speed can also be represented as two components:

where V 1. - component of the first-order piston velocity:

V 2. - the component of the second-order piston velocity:

Component V 2. It is the speed of the piston with an infinitely long connecting rod. ComponentV 2. It is amendment to the piston velocity to the final side of the connecting rod. The dependence of the change in the piston rate from the corner of the rotation of the crankshaft is shown in Fig. 11.5.

Fig. 11.5. Piston speed dependence on crankshaft rotation angle

The maximum values \u200b\u200bof the speed reaches the corner of the crankshaft less than 90 and more than 270 °. The exact value of these angles depends on the values \u200b\u200bλ. For λ from 0.2 to 0.3, the maximum piston velocities correspond to the corners of the rotation of the crankshaft from 70 to 80 ° and from 280 to 287 °.

The average rate of piston is calculated as follows:

The average piston rate in car engines is usually in the limit of 8 and to 15 m / s. The value of the maximum piston velocity with sufficient accuracy can be defined as

11.2.3. Piston acceleration

The acceleration of the piston is defined as the first derivative of the speed of time or as the second derivative of the movement of the piston by time:

(11.3)

where I. - harmonic components of the first and second order acceleration of the piston, respectivelyj 1 and J 2. At the same time, the first component expresses the acceleration of the piston at an infinitely long connecting rod, and the second component is a correction of acceleration to the end length of the connecting rod.

The dependence of the change in the acceleration of the piston and its components from the angle of rotation of the crankshaft is shown in Fig. 11.6.

Fig. 11.6. The dependence of changes in the acceleration of the piston and its components
from the angle of rotation of the crankshaft

Acceleration reaches maximum values \u200b\u200bwhen the piston is positioned in the VTT, and the minimum in NMT or about NMT. These changes are curvej. on the site from 180 to ± 45 ° depend on the valueλ. At λ\u003e 0.25 curve j It has a concave shape towards the axis φ (saddle), and the acceleration reaches the minimum values \u200b\u200btwice. For λ \u003d 0.25 acceleration curve convex, and acceleration reaches the greatest negative value only once. Maximum piston accelerations in car engine 10,000 m / s2. Kinematics of Dezaxia Lion KSHM and KSHM with a trailer several connecting rod distinguishes xia from kinematics Central CSM and in the present Edition Not considered.

11.3. The ratio of the stroke of the piston to the diameter of the cylinder

The ratio of the stroke of the pistonS. To the diameter of the cylinderD. It is one of the main parameters that determines the size and mass of the engine. In car motors valuesS / D from 0.8 to 1.2. Engines with S / D\u003e 1 are called long-weight, and withS / D.< 1 - short-terrestrial. This attitude directly affects the piston rate, which means the engine power.With a decrease in valueS / D. The following advantages are obvious:

the engine height is reduced;
due to the decrease in the average piston velocity, mechanical losses are reduced and the wear of parts decreases;
the conditions for placing the valves are improved and prerequisites are created to increase their size;
the possibility of increasing the diameter of the indigenous and connecting skeins, which increases the rigidity of the crankshaft.

However, there are negative points:

the engine length and the length of the crankshaft increases;
increased loads on the parts from the gas pressure forces and from the inertial forces;
the height of the combustion chamber decreases and its shape deteriorates that in carburetor engines leads to an increase in the tendency to detonation, and in diesels - to deterioration of the mixing conditions.

It is advisable to reducing the valueS / D. With increasing engine speed. This is especially profitable forV. --like engines, where the increase in short spectability allows you to get optimal mass and overall indicators.

S / D values For different engines:

carburetor engines - 0.7-1;
medium speed diesel engines - 1.0-1.4;
high-speaking diesel engines - 0.75-1.05.

When choosing valuesS / D. It should be borne in mind that the forces acting in CSM are largely dependent on the diameter of the cylinder and in a smaller - from the stroke of the piston.

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The crank-connecting rod mechanism (KSM) is the main mechanism of piston engine, which perceives and transmits significant loads by magnitude. Therefore, the calculation of the strength of KSM is essential. In turn The calculations of many parts of the engine depend on the kinematics and the dynamics of KSM. KSHM kinematic analysis establishes the laws of movement of his links, first of all the piston and connecting rod.

11.1. Types of KSM.

Three types of KSHM are used in the piston engine:

central (axial);

mixed (dexal);

with trailed connecting rod.

IN central KSM. The axis of the cylinder intersects with the axis of the crankshaft (Fig. 11.1).

Fig. 11.1. The diagram of the central KSHM: φ is the current angle of rotation of the crankshaft; β is the angle of deviation of the rod axis from the axis of the cylinder (with the deviation of the connecting rod in the direction of rotation of the crank angle β is considered to be positive, in the opposite direction - negative); S - piston stroke;
R. - radius of crank; L - the length of the connecting rod; x - movement of the piston;

Ω - Crankshaft Angle Speed

Corner speed is calculated by the formula

An important constructive parameter of KSM is the ratio of the radius of the crank to the length of the connecting rod:

It has been established that with a decrease in λ (by increasing L) There is a decrease in inertia and normal forces. This increases the height of the engine and its mass, so in automotive engines are taken λ from 0.23 to 0.3.

The values \u200b\u200bλ for some automotive and tractor engines are shown in Table. 11.1.

Table 11. 1. The values \u200b\u200bof the parameter λ for different engines

IN deaxal CSM. (Fig. 11.2) The axis of the cylinder does not cross the axis of the crankshaft and is shifted relative to its distance but.

Fig. 11.2. Diagram of dexali KSHM

Divexial CSM have relatively central KSM some advantages:

the increased distance between the crankshaft and the camshafts, as a result of which the space increases to move the lower head of the connecting rod;

more uniform wear of the engine cylinders;

with the same values R. and λ is more piston stroke, which helps to reduce the content of toxic substances in the exhaust engine gases;

increased engine volume.

In fig. 11.3 shows CSM with a trailer connecting rod. The connecting rod, which is cranked directly with the neck of the crankshaft, is called the main thing, and the connecting rod, which is connected to the main thing through the finger located on its head, is called trailers. Such a CSM scheme is applied on engines with a large number of cylinders when they want to reduce the engine length.The pistons connected to the main and trailed connecting rod have not the same move, since the axis of the crank head of the trailed connecting roddle when working describes the ellipse, a large semi-axis is greater than the radius of the crank. In the V-shaped twelve-cylinder engine D-12, the difference during the piston is 6.7 mm.

Fig. 11.3. CSM with trailed connecting rod: 1 - piston; 2 - compression ring; 3 - piston finger; 4 - plug piston finger; 5 - sleeve of the top head of the rod; 6 - main rod; 7 - trailed connecting rod; 8 - bushing of the bottom head of the trailed connecting rod; 9 - finger fastening the trailed connecting rod; 10 - installation pin; 11 - liners; 12- conical pin

11.2. Kinematics of the Central CSM.

With kinematic analysis, KSHM believes that the angular velocity of the crankshaft is constant. The kinematic calculation task includes the definition of the movement of the piston, the speed of its movement and acceleration.

11.2.1. Move piston

Moving the piston depending on the corner of the rotation of the crank for the engine with the central KSHM is calculated by the formula

Analysis of equation (11.1) indicates that the movement of the piston can be represented as the sum of two movements:

x. 1 - the movement of the first order corresponds to the movement of the piston at an infinitely long connecting rod (L \u003d ∞ at λ \u003d 0):

x 2 - the movement of the second order, is a correction to the final length of the connecting rod:

The value X 2 depends on λ. At a given λ extremal values \u200b\u200bof X 2 will take place if

i.e. within one turn, extreme values \u200b\u200bX 2 will correspond to the angles of rotation (φ) 0; 90; 180 and 270 °.

Maximum values \u200b\u200bThe movement will reach at φ \u003d 90 ° and φ \u003d 270 °, i.e. when compass φ \u003d -1. In these cases, the actual movement of the piston will be

Value λr / 2, It is called the Brics Amendment and is amendment to the final side of the connecting rod.

Fig. 11.4. The dependence of the movement of the piston and its components from the corner of the rotation of the crankshaft

Move the piston for each of the angles of rotation can be determined by graphically, which is called the Brix method. To do this, from the center of the circumference with R \u003d S / 2 radius, the BRICS Amendment is deposited towards NMT, a new center is located. ABOUT one . From the center ABOUT 1 Through certain values \u200b\u200bφ (for example, every 30 °), a radius-vector is carried out to the intersection with a circle. The projection of the intersection points to the axis of the cylinder (Line VTT-NMT) give the desired position of the piston in these angles of the angle φ. The use of modern automated computing means allows you to quickly get a dependency x.=f.(φ).

11.2.2. Piston speed

The displacement derivative of the piston - equation (11.1) by the time of rotation gives the speed of movement of the piston:

Similar to the movement of the piston, the piston rate can also be represented as two components:

where V. 1 - the component of the first-order piston velocity:

V. 2 - the component of the second-order piston velocity:

Component V. 2 is a piston speed with an infinitely long connecting rod. Component V. 2 is amendment to the velocity of the piston to the end length of the connecting rod. The dependence of the change in the piston rate from the corner of the rotation of the crankshaft is shown in Fig. 11.5.

Fig. 11.5. Piston speed dependence on crankshaft rotation angle

The maximum values \u200b\u200bof the speed reaches the corner of the crankshaft less than 90 and more than 270 °. The exact value of these angles depends on the values \u200b\u200bλ. For λ from 0.2 to 0.3, the maximum piston velocities correspond to the corners of the rotation of the crankshaft from 70 to 80 ° and from 280 to 287 °.

The average rate of piston is calculated as follows:

The average piston rate in car engines is usually in the limit of 8 and to 15 m / s. The value of the maximum piston velocity with sufficient accuracy can be defined as

11.2.3. Piston acceleration

The acceleration of the piston is defined as the first derivative of the speed of time or as the second derivative of the movement of the piston by time:

where I. - harmonic components of the first and second order acceleration of the piston, respectively j. 1 and J 2. At the same time, the first component expresses the acceleration of the piston at an infinitely long connecting rod, and the second component is a correction of acceleration to the end length of the connecting rod.

The dependence of the change in the acceleration of the piston and its components from the angle of rotation of the crankshaft is shown in Fig. 11.6.

Fig. 11.6. The dependence of changes in the acceleration of the piston and its components
From the angle of rotation of the crankshaft

Acceleration reaches maximum values \u200b\u200bwhen the piston is positioned in the VTT, and the minimum in NMT or about NMT. These changes in curve j on the section from 180 to ± 45 ° are dependent on the value of λ. At λ\u003e 0.25, the curve j has a concave shape towards the φ axis (saddle), and the acceleration reaches the minimum values \u200b\u200btwice. At λ \u003d 0.25, the acceleration curve is convex, and acceleration reaches the greatest negative value only once. Maximum piston accelerations in automotive engineers 10 000 m / s 2. The kinematics of the dexali KSHM and KSHM with a trailer rhat is somewhat different from the kinematics of the Central CSM and in this edition is not considered.

11.3. The ratio of the stroke of the piston to the diameter of the cylinder

The ratio of the stroke of the piston S. To the diameter of the cylinder D. It is one of the main parameters that determines the size and mass of the engine. In car motors values S / D. from 0.8 to 1.2. Engines with S / D\u003e 1 are called long-weight, and with S / D< 1 - короткоходными. This attitude directly affects the piston rate, which means the engine power. The following benefits are obvious with a decrease in the S / D value:

the engine height is reduced;

due to the decrease in the average piston velocity, mechanical losses are reduced and the wear of parts decreases;

the conditions for placing the valves are improved and prerequisites are created to increase their size;

the possibility of increasing the diameter of the indigenous and connecting skeins, which increases the rigidity of the crankshaft.

However, there are negative points:

the engine length and the length of the crankshaft increases;

increased loads on the parts from the gas pressure forces and from the inertial forces;

the height of the combustion chamber decreases and its shape deteriorates that in carburetor engines leads to an increase in the tendency to detonation, and in diesels - to deterioration of the mixing conditions.

It is advisable to reducing the value S / D. With increasing engine speed. This is especially beneficial for V-shaped engines, where the increase in short-spectability allows you to obtain optimal mass and overall indicators.

S / D values \u200b\u200bfor different engines:

Carburetor engines - 0.7-1;

Medium speed diesel engines - 1.0-1.4;

High-speaking diesel engines - 0.75-1.05.

When choosing S / D values, it should be borne in mind that the forces acting in KSM are more dependent on the diameter of the cylinder and in less - from the stroke of the piston.

The main link of the energy installation intended for transport equipment is a crank-connecting mechanism. Its main task is to transform the rectilinear movement of the piston in the rotational motion of the crankshaft. The conditions for the elements of the crank-connecting mechanism are characterized by a wide range and high frequency of repetition of the alternate loads, depending on the position of the piston, the nature of the processes occurred inside the cylinder and the rotation frequency of the engine.

Calculation of the kinematics and determination of the dynamic forces arising in the crank-connecting mechanism for a given nominal regime, 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 calculation will be used to calculate the strength and definition of specific structural parameters or sizes of the main nodes and parts of the engine.

The main task of kinematic calculation is to determine the movement, speed and acceleration of the elements of the crank-connecting mechanism.

The task of dynamic calculation is to determine and analyze the forces acting in the crank-connecting mechanism.

The angular speed of rotation of the crankshaft is made by constant, in accordance with the specified rotation frequency.

In the calculation, the loads from the pressure forces of gases and on the inertial forces of moving masses are considered.

The current values \u200b\u200bof the gas pressure force are determined based on the results of the pressure calculation at the characteristic points of the working cycle after constructing and sweep the indicator chart in the coordinates at the corner of the crankshaft rotation.

The inertia forces of the moving masses of the crank-connecting mechanism are divided into the strength of the inertia of reciprocating moving masses PJ and the inertia forces of rotating masses of Kr.

The inertia forces of the moving masses of the crank-connecting mechanism are determined taking into account the size of the cylinder, the design features of the KSM and the masses of its parts.

To simplify the dynamic calculation, the valid crank-connecting mechanism is replaced by an equivalent system of focused masses.

All Details of the CSM in the nature of their movement are divided into three groups:

1) Details that make reciprocating movements. These include a mass of piston, a mass of piston rings, a mass of piston finger and we consider focusing on the piston finger axis - Mn.;
2) Details performing rotational motion. We replace the mass of such parts with a common mass given to the radius of the RKP crank, and indicate Mc. It includes the mass of the rocker cervix MSH and the mass of the cheeks of the crank mesh, focused on the axis of the rod cervix;
3) Details performing complex plane-parallel movement (connecting rod). To simplify the calculations, it is replaced by a system of 2 statically substituting separated masses: the mass of the connecting rod group focused on the axis of the piston finger - the MSP and the mass of the connecting rod, attributed and focused on the axis of the crankshaft crankshaft - MSK.

Wherein:

mSHN + MSH \u003d MSh,

For most existing car engine designs, adopt:

mSHN \u003d (0.2 ... 0.3) · MS;

mSK \u003d (0.8 ... 0,7) · MSh.

Thus, the system of mass CSMs replace the system of 2 concentrated masses:

Mass at point A - Performing reciprocating movement

and weight at point in rotational motion

The values \u200b\u200bof Mn, MS and MK are determined, based on the existing structures and the structural specific masses of the piston, the connecting rod and the knee of the crank, referred to the unit of the surface of the diameter of the cylinder.

Table 4 Specific structural masses of KSM elements

Piston area is equal

To begin with kinematic and dynamic calculation, it is necessary to make the values \u200b\u200bof the structural specific masses of the crank-connecting mechanism from the table

We accept:

Taking into account the received values, determine the real values \u200b\u200bof the mass of individual elements of the crank mechanism

Mass piston kg,

Mass rod kg,

Mass knee crank kg

The total mass of the elements of the KSHM performing returns - the translational movement will be equal to

The total mass of the elements of the rotational movement, taking into account the solid and distribution of the mass of the connecting rod

Table 5 Original data to the calculation of KSM

Name of parameters	Designations	Units	Numerical values
1. Crankshaft rotation frequency
2. Number of cylinders
3. Radius crank
4. Cylinder diameter
5. RCR / LS ratio
6. Pressure at the end of the intake
7. Environmental Pressure
8. The pressure of the exhaust gases
9. Maximum cycle pressure
10. Pressure at the end of the expansion
11. The initial settlement angle
12. Finite Calculation Angle
13. Accounting step
14. Constructive mass of the piston group
15. Constructive mass of the connecting rod
16. Constructive mass of crank
17. Mass of piston
18. Mass rod
19. Mass knee crank
20. Total mass of reciprocating - progressively moving elements
21. Total mass of rotating elements KSHM

When studying kinematics, KSHM suggest that the crankshaft of the engine rotates with a constant angular velocity Ω , There are no gaps in conjugate details, and the mechanism is considered with one degree of freedom.

In fact, due to the irregularity of the engine torque, the angular speed of the variable. Therefore, when considering the special questions of the dynamics, in particular the twist oscillations of the crankshaft system, it is necessary to consider the change in the angular velocity.

An an angle of rotation of the crankshaft crankshaft φ is taken by an independent variable. In the kinematic analysis, the laws of movement of the KSHM links are established, and first of all the piston and connecting rod.

For the original take the position of the piston at the top dead point (point IN 1) (Fig. 1.20), and the direction of rotation of the crankshaft clockwise. At the same time, the most characteristic points are set to identify the laws of movement and analytical dependencies. For the central mechanism, these points are the axis of the piston finger (point IN), Returnable movement along with the piston returning along the axis of the cylinder, and the axis of the cranium cervice (point BUT), rotating around the crankshaft axis ABOUT.

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

l. - the length of the rod;

r.- radius of crank;

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

For modern automotive and tractor engines, the value λ \u003d 0.25-0.31. For high-speed engines in order to reduce the inertial forces of reciprocating moving masses, longer connecting rods are used than for low-speed.

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

The largest angles β for modern automotive and tractor engines are 12-18 °.

Move (path) The piston will depend on the corner of the rotation of the crankshaft and determine the segment H. (See Fig. 1.20), which is equal to:

Fig. 1.20. Scheme of Central KSM.

From triangles A 1 ABand OA 1 A.follows that

Considering that , we get:

From rectangular triangles A 1 AB and A 1 OA Install that

From

that, substituting the received expressions in the formula for moving the piston, we get:

As that

The resulting equation characterizes the movement of parts of KSM, depending on the angle of rotation of the crankshaft and shows that the path of the piston can be consecrated consisting of two harmonious movements:

where - the path of the first-order piston, which would have a place in the presence of a connecting rod of an endless length;

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

In fig. 1.21 Dana Piston Way curves at the corner of the crankshaft rotation. It can be seen from the figure that when the crankshaft is rotated at an angle equal to 90 °, the piston passes more than half of its stroke.

Fig. 1.21. Changing the piston path depending on the corner of the rotation of the crankshaft

Speed

where -augal speed of rotation of the shaft.

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

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

- Harmonically changing second-order piston rate, i.e., the speed of additional movement arising from the presence of a roller end of the final length.

In fig. 1.22 There are piston velocity curves at the corner of the rotation of the crankshaft. The values \u200b\u200bof the angles of rotation of the crankshaft, where the piston reaches the maximum speed values \u200b\u200bdepend on? And its magnification is shifted to the sides of the dead points.

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

For modern automotive engines VSR\u003d 8-15 m / s, for tractor - VSR\u003d 5-9 m / s.

Acceleration The piston is defined as the first derivative of the piston path in time:

Fig. 1.22. Changing the piston speed depending on the corner of the rotation of the crankshaft

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

where - the harmoniously changing acceleration of the first order piston;

- Harmonically changing acceleration of the second order piston.

In fig. 1.23 Dana Piston acceleration curves at the corner of the crankshaft rotation. The analysis shows that the maximum speed of acceleration takes place when the piston is in the NMT. When the piston is positioned in the NMT, the amount of acceleration reaches the minimum (the greatest negative) opposite to the value of the value and the absolute value of it depends on?.

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