Presentation on the topic "Dynamic analysis of mechanisms". Dynamic analysis of Tert's mechanisms in bag and roller bearings

The head of the dynamics: Directly the head of the dynamics - the force analysis of the mechanism - according to this law, the movement is determined by the development of forces on yoga lanka, as well as the reactions in the kinematic pairs of the mechanism. Different forces were applied to the mechanism of the machine unit for an hour. The whole strength of the strength of the support is sometimes called the forces of the core support of the strength of the strength of the strength of the rubbing and more strength. Their work is applied by forces to support the mechanism of that other law.

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Lecture N6

Dynamics of mechanisms.

Dynamic manager:

1. Directly zavdannya dynamics (power analysis of the mechanism) - according to this law, the movement is determined by the force acting on the yoga lanka, as well as the reactions in the kinematic pairs of the mechanism.
2. Zavdannya dynamics - for given forces, adding to the mechanism, signify the right law to the movement of the mechanism.

The dynamic analysis of mechanisms can include the task of investigating and vibroprotection.

Let's take a quick look at the solutions of the pivotal task of dynamics, taking into account all aspects of the mechanisms.

Different forces were applied to the mechanism of the machine unit for an hour. All the forces, the forces of the support (sometimes they are called the forces of the core support), the forces of gravity, the forces of rubbing that other forces. The nature of their children can be different:

A) deyakі lie down in the position of the legs of the mechanism;

B) deyakі zmіni їх shvidkosti;

C) deyakі fastіynі.

Their work is applied by forces to support the mechanism of that other law.

Forces that are found in machines, those characteristics

Forces that parity of forces (moments), which are added to the mechanism of the machine, can be divided on the steps of the group.

1. Rukhovi forces and moments, sho robyat positivelyto the robot for an hour of its work or for one cycle, as the stench periodically changes. These forces and moments are applied to the legs of the mechanism, as they are called conductors.

2. Strength and moment support, which has a negative effectto the robot for an hour of his work in one cycle. The strength of that moment is divided, first, by the strength of that moment of the core support, as it is necessary for the machine to work and is applied to the legs, the ranks of knowledge, and, in a different way, by the strength of that moment, the support of the middle (gas, radiator), which the arms of the mechanism are collapsing. If the strengths of the support of the center ring out a little against other forces, the distant stench will not be able to clear anything up, and the forces of that moment of the core support will be called simply the forces and moments of the support.

3. Forces of gravity rukhomih lanok and the strength of the springs. On okremih dilyankah, the movement of the mechanism of qi forces can win both positive and negative work. Prote for the latest kinematic cycle of the robot and its forces are equal to zero., shards of the point їх zastosuvannya collapse cyclically.

4. Forces are those moments that reach the body of the machine(Tobto to the post) call. Before them, the cream of the gravitational force of the hull can be seen the reaction of the base (foundation) of the machine on the її hull and many other forces. All these forces of that moment, shards of stink are applied to an indestructible body (strings), robots do not beat.

5. Forces of mutual modality between the sides of the mechanism, That is, the forces that develop in yoga kinematic pairs. The number of forces is based on Newton's 3rd law of always reciprocity. Your normal warehouse work roar, and dotichnі warehouses, so rubbing the forces, the robot is forced, moreover, the robot is rubbing the forces on the external movement of the kinematic steam negative.

The strengths and moments of the first three groups are brought up to the category of active ones. Ring out the stench in the house that can be appreciated. All these forces are applied to the call mechanism, and to that zvishnіmi. Until the ovnіshnіh vіdnosjatsya also all the forces and moments of the 4th group. Prote chi all stinks are active.

Forces of the 5th group, as if to see the mechanism in a haze, not seeing a few other parts, є internal. Qi forces є reactions to the action of active forces. The reaction will also be the force (or the moment), which is the basis (foundation) of the machine and the body (that is, on the mechanism's stand). Reactions are unknown in advance. The stench is to lie down in the form of active forces and moments, and in the form of a quick turn to the mechanism.

The greatest impact on the law of the movement of the mechanism is to give the destructive forces of that moment, as well as the forces of that moment and support. Their physical nature, the magnitude and nature of the dii are determined by the working process of the machine or the attachment, in some sort of twisting mechanism. In the case of greater fluctuations, the forces of that moment do not become constant, but change their value for changing the position of the mechanism or their flexibility. Qi functional deposits, presented graphically, or as an array of numbers, or analytically, soundmechanical characteristicsand at the hour of the cherishing of the day, they are respected by the authorities.

With the depiction of mechanical characteristics, we will apply the advancing rule of signs: the force and moment are taken as positive, as if on a distance (linear or cut) stench, a positive work is carried out.

Characteristics of forces, yakі vіd shvidkostі.On fig. 6.1 shows the mechanical characteristic of an asynchronous electric motor - the stagnation of the breaking moment in the apex of the rotor of the machine. Working part of the characteristic є dіlyanka ab at what moment the moment changes sharply for a slight increase in the wrapping.

Vіd shvidkostі lie down the forces and moments that are also found in such rotary machines, like electric generators, fans, blowers, water centers pumps (small. 6.2) and many others.

Figure 6.3

Improved speed, the moment of the engines will change, and the moment of the machines-saving mechanical energy will sound more. Such power is dear, to that which automatically brings stability to the regime, the movement of the machine, and the stronger it is expressed, the greater the stability. We call this power of machines self-regulation.

Characteristics of forces, yakі vіd peremіshchennya. In Fig.6.3 the kinematic diagram of the mechanism of the two-stroke engine of the internal combustion (DVZ) and its mechanical characteristic is shown. Strength, applied to the piston 3, move to the left. Therefore, when the piston is turned to the left (the process of expansion of gases), it won’t work positively and is shown with a plus sign (hilka czd). When the piston is pushed to the right (the process of squeezing gases), the forcetake away the minus sign (g_lka dac). Since the supply of paliva to the DVZ does not change, then for the offensive turnover of the cob lanka (lanka 1 ) a mechanical characteristic to repeat its shape. Tse means that powerchange periodically.

robot force be graphically depicted as a plane, circumscribed by a curve(s c). In Fig.6.3, there are two parts of the area: positive and negative, moreover, the first one is larger for the other. To that robot, the forces for the next period will be positive. Otzhe, the power is rushy, although it is sign-changing. Significantly, it is worth noting that the force, being familiar, influences the negative work during the period, it is a support by force.

Forces, which lie only in moving, are found in luggage machines and accessories (in piston compressors, sledge machines, planers and slotting machines, various accessories, both with a pneumatic drive, and with spring motors, etc.), moreover, the power of forces is 6 can be both periodic and non-periodic.

At the same time, about those traces, it is important that the moment of machines of the rotary type is displaced, i.e., the moment of rotation of the rotor is deposited; characteristics of such machines when depicted in Fig. 6.4, a, b . At the same time, the machines-dvigunіv, and the machines-spozhivachіv mechanical energy (tobto working machines).

If you change the supply of fire in the DVZ, then this mechanical characteristic will look like a family of curves (Fig. 6.5, a ): which is more fuel supply (parameter h families), more importantly, a characteristic. The family of curves depicts the mechanical characteristic of the shunt electric motor (Fig. 6.5, b ): what is the larger opir of the winding of the winding of the motor excitation (parameter h ), then the curve is more right. The characteristic of a hydrodynamic muff also looks like a family of curves (Fig. 6.5, c): h ), Tim is more right and more є characteristics.

In this rank, spitting on the parameter h , it is possible to use the robotic drive mode - thermal, electric or hydraulic, with greater power or speed. Water hour control parameter h ties with the magnitude of the flow of energy that flows through the machine, so that it signifies the vanity and productivity.

The mechanism of the machine unit sounds like a Bagatolan system, navantage by the forces of that moment, applied to different її lanok. In order to see more quickly, let's look at the power pumping unit with a drive from an asynchronous electric motor.

Up to the piston 3, the force of the support is applied, up to the rotor 4 of the electric motor - the driving moment. As a rich-cylinder pump, then the force of support is on the skin of the piston, so that the picture of the adventure becomes more foldable.

For the purpose of the law of movement, the mechanism under the influx of tasks of the ovnishnіh (active) forces, it is necessary to virate the same movement. The basis for the folding of the equal movement is the theorem about the change of the kinetic energy of the mechanism W \u003d 1, as it is formulated as follows:

The change of kinetic energy of the mechanism is charged for the work of all forces and moments applied to the mechanism

=
(6.1)

In a flat mechanism, the straps have wraparound, translational and plane-parallel movements, the same kinematic energy of the mechanism

(6.2)

for all ruhomih lanok mechanism

=
(6.3)

Sumarna work of all the forces of the moment

(6.4)

After the substitution is taken

(
+
) - =(
)

Transition to the bagatioh nevіdomih to one zdіysnyuєtsya for help methods of bringing forces that wt. To that real mechanism we pass to a model, tobto. we replace the entire folding mechanism with one mental lantern.

The butt mechanism has one step of freedom ( W =1). Tse means that it is necessary to enact the law of circulation of only one of your legs, as you yourself will be the cob.

Dynamic model

The position of the mechanism W \u003d 1 as a whole is assigned to one coordinate, as it is called an overridden coordinate. As a zagalnenu coordinate, it is most common to take the hull coordinate of lanka, which creates a wraparound ruh. In this view, the dynamic model will be presented in the view:

The apex coordinate of the model has been specified

Kutova swidk_st model_

Total pointing moment (intensified force is the equivalent of the entire given drive, which is given to the mechanism)

The total guidance moment of inertia is equivalent to the inertia of the mechanism.

At the time of the given, in fact, the force of the moment is replaced by the total pointing moment, which is added to the dynamic model.

It follows that the replacement is not guilty of violating the law of the movement of the mechanism, which is due to actually adding forces and moments.

The basis for bringing the forces of that moment may be put to the intelligence of the zealousness of elementary robots, tobto. elementary work of skin force on a possible moving point її supplement or a moment on a possible apex moving tієї lanka, it’s necessary to do moreelementary work of the induced moment on the apex of the displacement of the dynamic model.

Let's look at it as an example of the reduction of forces and moments applied to the legs of the machine unit (Fig. 6.6), recognizing the kutov coordinate as a fixed coordinate.

Significantly, what will replace the applied force
. For mental zeal of elementary robots

virishivshi shkodo shukanoї values ​​and dividing the possibility of moving for an hour, take

=

cos(
,
), de cos(

)= 1

=

=

= , de

for the cherry on the EOM,

To vikoristannyam shvidkost.

Similarly, we reduce to a dynamic model (lank 1) forces
,
, і
.

=
cos(
,
) = 0.0 t. to. cos(
,
) = 0.

=
=

Projection of speed to the center of mass
on the whole

So we know.

How to algebraically add up all the induced moments, applied to the cob lanka, then we takecrazy hovering moment, which replaces all the forces of that moment that blow on the mechanism.

(6.5)

Given wt.

Bringing the mass to roble іz tієyu w method, like and bringing forces:

revise and simplify the dynamic scheme of the mechanism, tobto. to develop a new dynamical model, and also, to simplify the solution of a similar movement.

As a dynamic model, a postal lanka was adopted with a specified coordinate, then the kinetic energy of the model can be added to the sum of the kinetic energies of all the parameters of the mechanism, that is. the basis mas to the cob lanka put the mind's equanimity of kinetic energies.

Inducing the moment of inertia is the parameter of the dynamic model, the kinetic energy of which is the most expensive sum of kinetic energies that are really collapsing.

Let's write down the mindfulness of the kinetic energy of Okremo Lanka, the whole mechanism and model for Okremo Lanka:

(6.6)

de for model, for real lanok mechanism

(6.7)

The transmitting functions of the arms should not lie in the vіd, so it may have been assigned to that vapadku, as the law of the model (cob lanka) is nevidomy. At
=

de,

Let's meaningfully induce moments of inertia

All the moments of inertia should not lie in the apex position of the cob lanka. This group of lanks, which in the dynamic model are called lanks of the first group, like moments of inertia - moments of inertia of the first group.

Significant moments of inertia of the 2nd and 3rd legs

The moment of inertia of the first and the other group of planes and the total guidance moment of inertia of the analyzed installation is shown in fig. 6.7

Control food before the lecture No. 6

1. Formulate the purpose of direct and pivotal tasks of dynamics.
2. What to think about the dynamic model of the mechanism?
3. What method is used to bring forces and moments to the mechanism? What mind is put in the basis of bringing the forces of that moment?
4. Yaka umova put as the basis for replacing the mass of moments of inertia when hovering?
5. Write the formula of kinetic energy for the crank mechanism.

It's easy to send your harn to the robot to the basics. Vikoristovy form, raztastovanu below

Students, graduate students, young adults, like victorious base of knowledge in their trained robots, will be your best friend.

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Dynamic analysis of mechanisms

1. Task of kinetostatics

The design of new mechanisms is accompanied by the development of their elements on the mind, and the expansion of the legs is restored to the quiet forces, as if they were breathed on.

Yakshcho in Kinematitsky Mechanism, in the Yaki -gaze of the deprivation of the geometer of the ruhu, the contour Lanok was uneasy, fіksuychi of the deprivation of the characteristic rosemiri, the yak, the deposit, the centers of the chain roshyri, the vale of the utensils of the upper trivial. space. The forces that are exerted on the elements of kinematic pairs, which appear as a result of technological and mechanical supports, determine the stresses at the lanks, thus expanding the rest of the arms, or they indicate the expansion of the lanks, as well as setting the stresses for the material of the lanks.

In this way, the development of mechanisms on the mind can be changed by the designation of forces, that one of the main tasks of kinetostatics is the designation of quiet forces, as it works on the elements of kinematic pairs and calls out deformations of the legs in the robotic process.

Methods for the development of forces, which can be applied to the legs of a mechanism without balancing the forces of inertia, are combined under the name of the statics of mechanisms, and methods for the development of forces with the balancing of the forces of inertia of the legs, which are close, are the kinetostatics of mechanisms. Practically, the methods of static and kinetostatic rozrahunkіv mehanіzmіv are not disturbed in any way, so that the forces of inertia are taken into account by the tasks of zvnіshnіmi forces.

Kinetostatics is a progressive method of raising the forces that blow on the sides of the mechanism, with the improvement of the forces of inertia.

2. Forces that work on the mechanism

2.1 Classification of forces

In the process of a robotic machine, up to the legs, the tasks of the rank forces are applied, to which one can be seen: the breaking force, the power of the technological support, the forces of the tension of the legs, the mechanical or additional support and the forces of inertia, which blame the result on the movement of the Lanka. Invisible forces will be the reactions of links, like the elements of kinematic pairs.

Forces, yakі dіyut lanka, mentally divide into 2 groups: rushіnі forces P dv і forces support R Z.

Destroying forces are called forces, as if they vibrate a positive work, tobto. Directions of the rushing force and the sharpness of the point of її zastosuvannya either escape, or they make the hostile kut.

However, in some cases, the force applied to the provіdnoї lanka, you can turn back to the support i, then, you will carry out a negative work. As a butt, you can show a thermal engine, in which force, which is applied to the piston, when the gas mixture is squeezed, it negatively affects the robot.

In the engine of internal combustion, for example, the driving force will be equal to the forces of the vice when the combustible sum is ignited.

Forces call the support forces that override the movement of the legs of the mechanism. The work of these forces is always negative, tobto. Directly, the strength of that swidkosti point її zastosuvannya or protilezhnі, or make a stupid kut. Distinguish the forces of the koris support and the shkidly support. In working machines, by the force of the core support є, for example, opіr cutting metal, opіr when gas is squeezed. By the forces of the shkidly support, the forces of rubbing, the forces of the support of the middle.

Krіm tsikh forces nebhіdno to vrakhovuvat the force of heaviness (strength vagi) lanok G, as applied in the centers of їhnої heaviness, the force of inertia of the lanok and the force of reaction zv'yazku.

The forces of inertia P u blame for the uneven Russian of Lanka. Forces of inertia like і, like і vagi forces, can win both positive and negative work.

The forces of the reaction linkage R, which occur in kinematic pairs, are introduced when looking at whether it is isolated from the mechanism. When looking at the entire mechanism of the whole reaction, the links should be taken into account by internal forces, tobto. in pairs v_vnovazhuyusya.

Mechanical or supplementary supports F in machines are worn with the head rank at the sight of the forces of the support, which are in the presence of the elements of the kinematic pairs, otherwise, they lose forces, at the sight of the support of the middle, for example, aerodynamic supports, the strength of the support, the zoom , for example, ropes, lanceugs, belts toshcho. bud. Forces of rubbing blame under the influx of normal reactions, like in kinematic pairs, and also under the influence of forces. Forces rubbing, as a rule, vibrate negatively to the robot, so that the stench is always straightened out at the bik, wrapped up to the fluidity of the perceptible movement of the elements of the kinematic pairs. This kind of supplementary support, which accompanies the robot of machines, is the most important, to that in rich vipadkas all the energy can be, which is stained on the movement of the machine, stained on the underside of the forces of rubbing. Looking at the strength of the rubbish, they will be looked at especially.

2.2 External forces and mechanical characteristics of machines

Windy forces can be constant, like for example, the forces of gravity, the support of cutting metal with a constant overcutting of chips and other, or lie down only in the position of the Lanka, on the way the stink is blown by a press punch when flashing the openings of those others.), at the moment of the Lanka electric motor, rubbing the smeared bodies and others.), at the hour. In addition, there can be children of forces in the car, which lie in the resurrected more than the independent ones. The appointment of a specific value of the outer power is only possible at times, as long as this characteristic is given.

So for the main mechanism of a chotiritic engine of internal combustion, the law of change in pressure P for gas in a cylinder is indicated by an indicator diagram - fallow P=ѓ(H) (Fig. 1)

The next cycle of the robotic engine ends with the pull of two wraps around the crank. For the first half of the turn, the burning sum FO is smoky, for the other half the turn is the squeezing of the sum OD, according to the DA curves - the burning sum, along the AB curve - the expansion of the burnt sum (working run) along the BF curves - exhaust.

Considering the displacement x along the H axis, taken from the plan of the mechanism, it is easy to know the exact ordinate on the indicator diagram.

The excess pressure P on the piston is the difference between the pressure of gas in the cylinder and the atmospheric pressure, in proportion to the ordinate, which is blown in the line of the atmospheric pressure.

The force acting on the piston is determined from the formula:

de d – piston diameter.

For a compressor of idle time, the law of changing the pressure of gas in the cylinder is also hoped for by an indicator diagram (Fig. 2).

kinetostatics of gear forging machine

FCD curve - throttle grip

DA - whip,

AB - expansion of the gas, which is stuck in a dead obsіzі,

BF - smoking a new portion of gas

Force scale factor

de - ordinate, which shows the changing x.

The diagram of the change in tension on the shaft of the dvigun or the average moment, depending on the number of wraps, is called the mechanical characteristic of the dvigun (Fig. 3).

2.3 Designation of the forces of inertia

Under the hour of the robotic mechanism, the forces of inertia are blamed. The stench calls out the additional vice in kinematic pairs. Particularly great values ​​\u200b\u200bof the force reach in shvidkohіdnih machines.

The forces of inertia are assigned to a given band of legs and yoga to the quick. The method of deposition is to lie in the sight of the ruhu of Lanka.

First swing: lanka with a plane-parallel movement (rod). Vіdomo, scho elementary forces of inertia in tsomu vpadka produce up to equal force P u і moment of inertia M u .

The force of inertia P u is applied in the center of gravity of the Lanka and the road:

de m - Masa Lanka

a s - linearly accelerated to the center of Vaga Lanka.

Moment of forces of inertia:

de J s - moment of inertia of the lanka according to the center of gravity,

Kutove priskorennya Lanka.

The minus sign indicates those that the force of inertia P u is directed at the turning point a s , and the moment M u is directed at the turning point of the turning point.

The value of that is directly attributed to the kinematic expansion. And the value of m, J s can be given.

The force P u and the moment M u can be replaced by one resultant force P u added at the point of hitting (Fig. 4).

For whom the force of inertia P u needs to be transferred to the other side

The value of this shoulder is changed in the following way: from the plan of acceleration (Fig. 3.3), a tricot is transferred to the lanka AB

Vіdrіzok znayshovshi point "K" (point of hitting) is applied to the vector of force of inertia, directing at the opposite side to the vector of acceleration to the center of gravity.

Another vipadok: lanka zdіysnyuє obertalny ruh (Fig. 5)

a) In case of an uneven wrapping, with a difference in the center of gravity from the weight of the wrapping, the force of inertia Pu and the moment of forces of inertia may be affected. When the force is induced, the moment shoulder SK is assigned to the formula (3.4):

de SK - rise from the center of gravity to the point of hitting.

b) In case of equal Russian P and put at the center of gravity.

M i \u003d 0 because =0.

c) The center of gravity rises from the weight of the wrapping = 0, then Р i = 0; M i = 0.

Third swing: lanka zdijsnyuє forward movement (povzun) (Fig. 6).

Here, M i \u003d 0. As a result, the movement of the Lanka is uneven, because of the force of inertia

Even though the tasks for the course design are not tasks, the moment of inertia of Lanka can be approximated by the formula:

de m - masa of lanka,

l - dovzhina lanka,

K - coefficient 810

One of the leaders of the dynamics of mechanisms is the designation of forces that operate on the elements of kinematic pairs, and so are the names of forces that are different. The knowledge of these forces is necessary for the development of mechanisms for mechanical failure, the indication of the tightness of the engine, the wear of the third surfaces, the installation of the type of bearings and the yogo sealing is thin. bud., tobto. forceful development of the mechanism is one of the essential stages of the design of machines.

Under the leveling forces, the mind of the force is adopted, which is equal to the tasks of the equal force and the force of the inertia of the legs of the mechanism, assigned from the mind of the equal wrapping of the crank. The number of chewing forces that need to be applied to the mechanism, the greater number of cobs, otherwise, the number of steps of freedom to the mechanism. So, for example, if a mechanism has two levels of freedom, then in the mechanism, two equally important forces are applied.

3. Force analysis of mechanisms. Significance of reactions in kinematic couples

The power analysis of mechanisms is based on the development of straight lines, or first, the head of dynamics - for the task of determining the dynamic forces. To this end, the revolution of cob lanoks for force analysis is vvazhayutsya tasks. Sound forces, applied to the sides of the mechanism, sound the same as given by the tasks and, therefore, induce a specific reaction in kinematic pairs. Ale, other ovnіshnі forces, applied to the cobs, vvazhayut invincibly. Todi forceful analysis to enter the designation of forces, from which they are entrusted with the law of cob lanoks. При вирішенні обох завдань використовується принцип Д"Аламбера, згідно з яким ланка механізму може розглядатися як така, що знаходиться в рівновазі, якщо до всіх зовнішніх сил, що діють на нього, додати сили інерції. Рівняння рівноваги в цьому випадку називають рівняннями кінетостатики, щоб induce the plane of the plane mechanisms to create the plane of symmetry, parallel to the plane of the ruhu.

de m-masa of lanka;

The vector is accelerated to the center of the mass.

In the case of a kinetostatic expansion of the mechanism, it is necessary to indicate the reactions in kinematic pairs and either the equally important force or the equally important moment of the bet of forces.

We will allow the forceful expansion of mechanisms, which is rubbed in kinematic pairs during the day, and all the forces that blow on the mechanism, are spread in one plane.

One of the main methods of power lifting is the method of looking at the skin lank to the mechanism of equalization. In this method, the mechanism is divided into deuces of Lanka.

On the back, one looks at the jealousy of the extreme Lanka, staring at the head (wire), then the jealousy of the Lanka, behind the extreme, and so on. The equal head of the Lanka is seen in the rest of the black.

Looking at the taken lanka in equal measure, it is necessary to report to it all the relevant forces (P DV, R PS, P І, G), including the reactions of sounds, with some kind of lanka taken, to attack the taken lanka.

We demonstrate the technique of rozrahunka with the butt of the chotirilank mechanism. The back of the head is looked at in the rіvnovazi lanka 3 (yoke), having brought to the new all the chinnі forces, including the reactions of the bells and whistles. (Mal. 7)

The reaction of the obertal couple "C" is neither in magnitude nor directly.

For the purpose of the reaction, we replace two warehouses (Fig. 7b), one of them is directed along the connecting rod (2), and the other warehouse - along the rocker (3).

The value can be found from the mind of the jealous Lanka, which is being looked at.

Lanka (3) is rebuying at Rivnovazi under the influx of offensive forces R P.S.; P iz; G3; R03; ; .

We add the equal moment of the forces around the point D

If the intended value of the value won't appear negative, then it will be directly opposite to the opposite. Skladova can be known by looking at the rіvnovazi okrem lanka (2) (Fig. 8a).

From the mind of the jealous lanka (2) you can write

The invisible reaction R12 can be known by the graphical method, inducing the plan of the forces of the lanka (Fig. 3.8b).

Rivnyannia Rivnovagi Lanka (2) may look like this:

From a sufficiently reversed pole, we add the force of the vector to the scale, to a new geometrically add a vector that depicts the force G in the same scale, etc.

The vector gives the magnitude of the reaction R 12 in scale.

For which one is considered in equal position, the crank AB. (Fig. 9).

The crank is controlled by the force of the shaft G 1 of the reaction of the connecting rod (2) to the crank R 21 by the force of inertia P u 1 .

Under the influx of these crank forces, at the end of the day, there is nothing to change from the rіvnovazi. For equal time, it is necessary to apply an equally important force P y or an equally important moment M y .

Tsimi vr_vnovazhuyuchimi force and moment є reactive forces or moment vіd dvigun.

Let the equalizing force be straightened out for the normal to the crank and the appendage at point B. If you understand the equal angles AB, you can add the equal sum of the moments of the combined forces to point A.

The vrіvnovavazhuyuchu force can be known in the same way, with some kind of jealousy, the whole mechanism is looked at.

Umov's jealous mechanism can be countered by the approaching jealousies:

The sum of the strains of all the forces applied to the mechanism, with the adjustment of the forces of inertia and the forces that are equal, equal to zero.

The tension of the force applied at the i-th point is proportional to the moment of the force along the end of the vector of the rotated swidity of the given point (Fig. 10).

From the jealousy of the jealousy one can know the equal strength. It is often easy to know Ry for the help of Zhukovsky's additional importance, if the mechanism of inducement is the polar plan of shifts, turns by 90 °. In the rest of the year before the last days of knowing the vectors of swiddos, we should report on the great forces that are blowing.

If so, looking at the rotational plan of the speed, as a zhorst important, which wraps around the pole P, you can write the equal equivalence of the importance of looking at the sum of the momentum of the forces of the pole:

It is equal to the plan of tightness, which is seen as a zhorst important, the same equal to tightness.

As far as the mechanism of the cream of the forces of giving the moment M (Fig. 11), you can see it as a couple of forces that make it stronger:

The known forces P are applied at the visible points, which represent the plane of the pliability.

4. Rubbing at kinematic couples

4.1 Tertya forging

Under the cost of the third at the mechanism, the third may be at the expense of the third at the kinematic pairs. There are two main types of grating: forging grating and stiffening grating. In the lower kinematic pairs, the rubbing of forging is blamed, in the higher ones - it is less than rubbing the stiffness, or rubbing the stiffness at once from the forging.

If the surfaces of the body, which collapse, A and B (Fig. 12) stick, then rubbing, which is blamed for it, is called dry. Even though the surfaces do not stick (Fig. 13) and between them there is a ball of butter, so rubbing is called native. There are also fluctuations, if they are drunk dry (overwhelming dry), or if they are drunk, rubbing.

4.2 Dry rubbing

Main laws:

1. In the singing range of tightness and navantage, the coefficient of forging wear can be taken constant, and the rubbing force - F proportional to the normal grip:

de f - coefficient of forging,

N - normal vice.

2. Coefficient of rubbish forging to fall into the material and I will become on top to rub.

3. The forces of rubbing are straightened at the bik, protilezhny vіdnosnym shvidko.

4. The coefficient of rubbing calmness is greater than the coefficient of rubbing for an hour.

5. With the increase in speed, the strength of the loss of the big one changes, approaching a certain constant value; with small dryness, the coefficient of loss may lie in the dryness.

6. With the growth of the pet vice, the coefficient of the loss of the big one is increased. With small pet vices, the coefficient of loss may lie down depending on the size of the pet vice and the area of ​​\u200b\u200bthe zone.

7. With an increase in the forward contact, the rubbing force increases.

4.3 Red carpet

When rubbed dry, there is a large vitreous work, which transforms into warmth, and wears on the surface, which rubs. For usunennya tsikh yavisch mizh surfaces, scho to rub, a ball of butter is introduced. In this case, in case of pre-Trimannian singing minds, the ball of oil can be divided into thirds on the surface (Fig. 3.13).

4.4 Rubbing when forged by a horizontal plane

A progressive kinematic pair, which develops from a horizontal straight line 2 and a bend 1, is shown in the little 14. Let the advancing forces come on the bend 1: P D - rushina, G - vaga vantage or tension, scho dіє on the bend, N - normal reaction, F 0 - rubbing force (dotic reaction) at rest. When it rises, it is collapsing, the replacement of the force is losing F 0 the force is losing F in Russia, moreover, the same reaction.

Kut vіdhilennya povnoї rektsії vіd normalі ubіk, protilezhny ruhu podzuna, called kutom tertya.

Vrakhovuyuchi sho

Otzhe, coefficient tertya dorivnyu tangent kuta tertya.

4.5 Rubbing in a kinematic pair of thorn-bearing

With the presence of a gap, the trunnion pіd dієyu M D zі its lower position will move to a new position, as it is characterized by equal inter-destructive forces and support forces. On fig. 15 accepted offensive designations: - stud radius, Q - plunging ring, R - bearing reaction to the stud, - rubbing, - rubbing stake radius.

The forces Q and R make a pair of forces, the moment of which is the moment of support; skin moment vіn vrіvnovazhuє moment of rushing forces, tobto. .

moment force support

Losing a moment of strength

de; - spike radius;

Vnaslidok trohi kuta size. Also, the radius of the stake is losing the old usunennia of the new reaction R in the face of the surreal pressure Q.

Father, losing the moment of strength

5. Coefficient of the core function of the mechanism

Mechanical efficiency The machines are called the absolute value of the robotic bearings A P.S. to the work of the driving forces A D for the period of tired rush:

Z equal to the movement of the machine with the installed Russia is known.

After substitution in viraz (1), it is necessary to take the step of viraz for efficiency:

de – cost factor.

the more, the less the robot of the wheelbarrows. For example, having determined the mittev of the efficiency of the twelve positions of an important mechanism in one turn, you can induce a graph of the function. In practice, chime in with the arithmetic mean values ​​of the efficiency for the period of growth, which has risen:

The machine may have an even lower efficiency in the other positions of the mechanism. Mitteviy K. p.

de N P.S. - mitteva the tension of the forces of the core support to the skin for the camp mechanism;

N D - mitteva the intensity of the disruptive forces for the correct position of the mechanism.

groups of sequentially connected mechanisms or machines. A number of machines or mechanisms that enter the unit can be sequentially connected (Fig. 16 a), in parallel (Fig. 16 b)

Zagalny k.p.d.

Have a sizzling glare

K. p. d. groups of parallel to the z'єdnanih mehanіzmіv chi machines. Tsya spoluka is characterized by the expansion of the wild energy flow.

Zagalny k.p.d.

Malyunok 16

6. Significance of reactions in kinematic pairs with improved rub

Vikonaniya in the first part of the rosary without urahuvanny rubbing gives the value of reactions in the kinematic pairs of the mechanism in the first close. Determination of forces with urahuvannyam tertya є further clarifications і be carried out (in our opinion) by the method of sequential observation. For the other approach, the values ​​of the coefficients of forging wear are set for all pairs and the diameter of the trunnions of the wrap pairs. The technique of rozrahunka mekhanіzmu z urahuvannyam і without urahuvannya rubs itself. The only difference is that the forces of reactions in progressive pairs are driven by their many normals on the edge of the line against the vector of speed of the progressive bet. In the overt - lines їx dії passed through the rub, the reaction can be replaced by the reaction applied in the center of the hinge, with which it is necessary to apply to this hinge the moment of the rub is due to the formula:

de r - the radius of the rub, which is determined by the formula:

de D y - diameter of pins,

Kut rubbing.

R in the formula (3.13) - the reaction at the given hinge, otrimana in the first part, without balancing the forces of rubbing. Directly to the moment, the protilezhny kutovy shvidkostі lanki schodo this hinge.

6.1 Force analysis of gear mechanisms

For the most important gears, the main one is the robot mode. Therefore, in transmissions of this type, the moments in the form of inertia forces are equal to zero (without improving the colivan, which is called out by a change of hardness and pardons to Croc).

The pressure between the involute profiles is transmitted by a hooking line, as if it were running with its own wild normal.

If a moment of support M C is applied to the driven wheel, then the support force is:

The force P C is applied to the wire wheel 1; driving wheel 2 is subjected to a driving force. Z formulas are clear, scho, yakscho force P C vise between teeth is constant both for magnitude and for direct; won't get bigger from the bigger kuta chained.

At the center of the driving wheel 1, there are two equal and oppositely straightened forces P C . Forces R * - vice in the wheel bearings; two other forces R establish a pair of forces, the moment of which is equal to the moment M D. Substituting the value of P C of the formula,

The pair applied up to wheel 2 makes applications up to wheel 2 the moment of support M C .

Equal and backward directing forces R * і Q * satisfy a couple with a moment

Tsya couple pragne to turn the rack (frame) of the transmission (at our vapadka for the year's arrow). In order for something not to happen, the stance can be fixed. The moment created by the analyzed couple, having removed the name of the reactive moment.

It is obvious that even with a change in M ​​C, the pressure forces between the teeth and the shaft supports will be constant. This is one of the advantages of the involute chaining, the shards ensure a calm transmission robot.

Since the profiles of the teeth in the process of their engagement can be easily forged, then between them the forces of rubbing are blamed, equal F of which is straightened against the hardness of the forging.

The magnitude of the force

de f - coefficient of the forging of profiles.

The exhaustion of forces is loosing at the old chained

Also, the tension of forces losing in the meshing is changing and increasing in the world of that, like the point M of the profiles turning away from the poles of the meshing.

In the supports of the shafts, the forces of rubbing are also blamed, proportional to the vice R and Q of their supports. The magnitude of these forces, losing to lie down due to low factors (in terms of the minds of the ground on the surface, which are sticking, in the form of spring powers, which determine the law of distribution under the petty pressure, due to the lack of forging of the supporting surfaces, etc.). Rivnochinna force, de f n 1 - the coefficient of friction, which is safe to wash the robotic shaft in the bearings. The force is applied to one of the points of the supporting surface of the shaft on the r B in the axis.

The exhaustion of forces rubbing in the supports

It can be seen from the formulas that the hardness of forces rubbing in the supports is constant.

Using this formula, it is possible to calculate the moment M D and tension N D of the engine, which is responsible for the operation of the transmission shaft, as well as the tasks M C i i 12

The values ​​of the coefficients f і f n occur due to the large number of various factors and can ripple at even wide boundaries. For example, the coefficients of loss of profiles lie not only in terms of materials and the accuracy of their processing, but also in terms of oil; krim tertya forging, between profiles may be tertya kochennya; as the transfer works in an oil bath, then the robot is stained for mixing the oil too thinly.

6.2 Assignment of moments to the planetary mechanism without compensation

Let's look at the nourishment of the appointed moments of the planetary mechanism, the legs of which are wrapped step by step. At the planetary mechanism depicted in (Fig. 18) the sleepy wheel 1, the carrier 2 and the crown wheel 4 are wrapped around the central axis C. The tangential warehouse P 31 reaction to the satellite 3 from the side of the sleepy wheel 1 without balancing the force of friction is applied to the pole of the chain A. turning bik the force R 13 is straightened. At the point there are warehouse reactions R 34 and R 43, and in the center of the satellite - R 23 and R 32.

Let's take a look at such planetary mechanisms, in some satellites having ceased to be a vihіdnim Lanka, tobto. M3=0. To the same:

de k - number of satellites to the mechanism.

From Rivnovagi Lanka 2 May:

Vrakhovuchi (3.15) and (3.16), we rewrite (3.17):

Let's write down the mind's jealousy of Lanka 4:

To that, vrakhovuyuchi mind: P 43 \u003d -P 13 (3.19) maybe:

Also, as one of the moments that the planetary mechanism has, knowing the radii of the corn cobs, formulas (3.18) and (3.19) can be used to calculate certain moments.

The task of the appointment of moments can be broken for the help of the wild plan of the top shvidkos. Let's take a look at the methodology for determining moments.

Let's go for a planetary gearbox with twisted gear wheels, a deep plan of the hull gears was suggested (Fig. 19)

The tension that comes up to Lanka 1.

The tension that znimaetsya drove.

Don’t waste your money, then:

Shards under the influx of moments, the planetary mechanism is in an equally important mode, when you get up, you are in jealousy, then you can have a place of jealousy

de M 4, next to understand as a moment, which must be applied to Lanka 4, in order to reduce this kind of wrapping.

З (3.21) we take:

6.3 Designation of the coefficient of the core function of the planetary mechanism

efficiency Mechanical transmission to lie down due to various factors, for which the most significant may be the loss of tightness in the meshed pairs of gear wheels. Significant efficiency. planetary gearbox when transmitting torque from lane 1 to lane 2 according to the formula:

de nazivaetsya to the power of transmission. Here i are the moments that strike the lanks 2 and 1 with the improvement of the fastening at the hooked - kinematic transmission of the movement.

6.4 Power opening of cam mechanisms

Oskіlki vedene lanka (rod-pusher) - collapses with changing speed, then the schemes of di forces applied to the cam mechanism in different cases of the interval of yogo movement, raznі.

In the interval of working movement to the lanka, which is being carried out, the force of the core support R is applied, it is straightened against the firmness of the lanka. Force R, ring out, always given; you can be fast and changeable.

If the mechanism is triggered by the power of the zamikannya of the greater bet, then the lanka has a direct force on the spring force R P of the spring, which is squeezing at the hour.

Through the nervous movement of the rod, the force of inertia is vindicated:

de - masa of the bar, - її quickening; the power of Ra is straightened in the opposite direction to the fastening of the bar. If the weight of the barbell has become, then the law (schedule) changes the forces, and the law (schedule) changes the accelerated barbell.

Equivalent Q of all forces applied to the bar, more:

In order to resist the friction at the pair of the cam - the rod, then directly the force P of the cam vice on the rod zbіgaєtsya from the normal to the profile of the cam. If you don’t mind rubbing in direct C, then, so that the bar collapsed according to the given law, it was required that the skin position of the mechanism force P to press the cam on the bar

de - kut mizh by force that straight to the ruhu of the bar - kut transfers to the ruhu.

If you don’t rub it in the cam shaft bearings, then the breaking moment on the cam shaft

de is the radius vector of the cam profile.

Self-galvanizing. While rubbing the forces with a forceful expansion of the mechanism, one can show such spontaneity between the parameters of the mechanism, with some successes rubbing the lanks in the necessary direct direction, one can’t grow independently of the magnitude of the rushing force.

In most of the mechanisms of self-galvanization, it is unacceptable, but in certain situations it will be victorious to intimidate a fleeting rush into a turning point (a jack, deacisi types of pidyomnyh mehanizmіv and іn.).

Kut vise. A tight grip on the lanka from the side of the lanka is called a kut between a straight line of force (normal reaction) to the lanka from the side of the lanka and a quick point of congestion of the force. Cut the vice on the lanka from the side of the lanka is indicated through. Often, however, less than one corner of the vise is visible. Same indexes are omitted from the signs.

4. Analysis of the movement of the mechanism under the influence of forces

Dynamic vise - tse dodatkovі zusillya, which is blamed on the kinematic couples for the hour of the movement of the mechanism. This vise is the cause of the vibrations of the working legs of the mechanism, the stench is changed for the magnitude of that directly. The bed of this mechanism is also a dynamic vise, like a shkidly vplyvayvayut on yogo fastening and destroying the links of the bed with the foundation. Also, the dynamic vices increase the forces rubbing at the bearing points of the shafts, which wrap around, increase the wear of the bearings. Therefore, when designing mechanisms, it is possible to achieve full partial repayment of dynamic pressures (zavdannya about the equalization of the forces of inertia of mechanisms).

Lanka the mechanism should be vr_vnovazhenoyu, so that the head vector and the head moment of the forces of inertia of the material points are equal to zero. Nevrіvnovazhennoyu can be the skin lanka of the mechanism is OK, but the mechanism in case of this in general can be vrіvnovazhenija povnіstyu or chastkovo. The problem of the inertia forces in the mechanisms can be divided into two tasks: 1) about the pressures in the kinematic pairs of the mechanism; 2) about the pressure on the mechanism as a whole on the foundation.

Greater significance may be the vrіvnovazhennia of the legs that wrap around. A slight imbalance of the rotors and electric motors, which wrap around tightly, calls out a great dynamic vice on the bearings.

Zavdannya about the vrіvnovazhennja bodies that wrap around, lie in such a choice of їх masses, with which there will be more or less frequent redemption of additional inertial pressures on the support.

The resulting water center force of inertia:

The resultant moment of the forces of inertia of the body is wide enough for the area to pass through the center of the shaft.

de m - mass of the whole body,

V_dstan center S mas tila v_d os_ wrapping;

Vіdtsentrovy moment of inertia schodo axis wrapping that plane, perpendicular to the axis wrapping ta pass through the center S of the oil.

When wrapping tila cut between vectors and take the whole hour those same values. If the resultant force of inertia and the resultant moment of the forces of inertia are equal to zero, then the body will be more powerful, and it means that the body that wraps around does not rely on the usual dynamic pressure on the support.

Tsі think will be vikonuvatsya only once, if the center of the oil lies on the axis of wrapping, as if it will be one of the head axes of inertia. If equalities (4.1) and (4.2) are converging at once, then the central moment of inertia is equal to zero. If it wins (4.1) of the mind, then the body is considered statically, if it wins (4.2) of the mind, the body is considered dynamically.

Static imbalance is overcome by a static moment.

G - vaga body, what wraps around, n.

Dynamic imbalance of the body, which wraps around

Really neurotic body vrіvnovazhuyut with additional countermeasures. Tі, scho wrap around, in some kind of deep dozhina significantly less than their diameter, there may be insignificant water center moments of inertia; to that tіla dosit vrіvnovazhity less statically.

Let's assume that body A is statically neurotic. At the simplest point, the counterweight is placed on the line that passes through the center of gravity S, from the other side in the axis of the wrap on the front of the line. (Fig. 21)

The mass of the opponent is known to be equal (4.1):

Zam_st installation against can be seen part of the masi. The value of the mass that can be seen depends on the formula (4.5). In some cases, the area of ​​strengthening the counterweight can be constructed constructively in that area of ​​the wrap, in a kind of stitching of the neuron-weight. At this angle, you can install two counterarms at two planes perpendicular to the axis of the wrapping, call the names of the planes of the correction, or, if necessary, turn off the possibility of a vice appearing on the support, not only in the resultant force of inertia, but also in the moments of forces of inertia. Masses and opposites are vis-a-vis and viable up to formulas (4.1) and (4.2) equal

Clay masi tsikh counterag, otrimayemo

Externally, the body that wraps around can also be reached for the help of two counters, spread at quite selected areas 1 and 2 and on sufficient windows in the axis of the wrap.

The body that wraps around, ring out so that the stench will be vrіvnovazhenі themselves. Most of all, those that wrap around, wrap around the shape of one or a few cylinders, which can hold the whole thing, which run out of the body wrapping. However, in rich vipadkah, such a form cannot be vikonan and body without counters, which wraps around, it is neuro-impressive. In order to determine the size and position of the opposite, it is necessary to see by the armchair the part of the body that has been added, and to determine for the parts that are missing - kolіn, cams, etc. centers of gravity їх, respecting that they have the heart of the masses of these elements.

Let's assume that for any body, all neuron-involved masses amounted to three neuron-inflected masses (Fig. 22). Using the method of reduction of the vector to the given center, it is possible to have a large number of masses that are wrapped in different planes, to match two counters. Let the center of the wag mas raztashovanі in three planes perpendicular to the axis of the wrap. Wash the pressure on the bearings in the direction of the head vector and the head moment according to the center of the reduction.

There will be rich vectors of forces and vectors of moments (Fig. 22 d, e). The vector that matters in the first direction is the vector, the image in the area 2 is the vector (Fig. 22 c) and in the other - the vector (Fig. 22 e), which depicts the turning moment of the pair of vectors, embossed in the area 1, and embossed in the area 2. Leather їх dorivnyuє for size. In this order, the tasks of the masks will be mostly equal to two masses, ruffled at the area 1 and equal in the area 2.

1.) whether there are a lot of masses that are wrapped around, wrapped in the same plane, wrapping, vrіvnovazhuєєє one opposing, scho to be found in the same plane, with dotrimannі nіvnіvаgi

2.) whether there is a large number of masses, which lie at the different flats of the wrap, vrіvnovazhuєtsya two counters, installed at two flat flats, perpendicular to the axis of the wrap, for the dominance of two minds of equal:

For the installation of a flat mechanism on the foundation, it is necessary and sufficient to substantiate the mass of the legs of this mechanism, so that the central center of the mass of the lanks of the yogo becomes unruly:

and center moments of inertia of the oil flares for the axes x and z, y and z were constant:

When dotrimani tsikh minds will be vr_vnovazhen head vector of forces of inertia and head moment of forces of inertia along the axes x and y. The head moment of forces of inertia along the axis z, perpendicular to the plane of the movement of the mechanism, is equal to the moment of the driving forces and the forces of support on the head shaft of the machine. In practice, when the mechanisms for designating the mind (4.9) and (4.10) are reversed, they are often beaten.

Come on, for example, given the mechanism of the hinged chotirilanka ABCD (small 23) it is necessary to add more than the head vector of inertia forces. Significantly masi lanok AB, BC and CD can be seen through і; dodzhini lanok - through and v_dstan tsentr_v tyazhnostі і tsikh lanok vіd point A, B і C - through і. To be satisfied, think (4.9.) It is necessary that the main center of the mass mechanism be located on the line AD, or between points A and D, or behind them. In this way, the center of the S mas mechanism in the course of yogo Russia will become unruly and, therefore, the head vector of the forces of inertia to the mechanism will be invested.

Masi lanok and the position of the center of gravity of their responsibilities, but choose so that

If the mechanism is composed of n rukhomih lanok, then when solving problems about the sub-mechanism, it will satisfy the minds of the head vector of the forces of inertia of the mechanism, maybe 2n unknown quantities; Rіvnyan, scho pov'yazuyut qі values, you can add up (n-1). After sufficient selection (n+1) of values, the other values ​​gain the same values. At the end of the mechanism, the number of ruhomy lanoks is n=3, the number of selected values ​​is 2n=6, the number of independent rows is n-1=2. In this way, by setting, for example, the values ​​of m 3 і s 3 are equal (4.12), the value of m 2 s 2 can be taken as one of the unknowns and taken otherwise. By substituting the value of equal (4.11), we determine the value of m 1 s 2, in which it is also possible to set one value. From equal (4.11) and (4.12) at different weekends, it is possible to choose three variants of schemes of the rіvnovazhenny chotirilank mechanism. 23 (a, c, e). Also, in order to consider that the expansion of the center of gravity of the lanka behind the yogo hinges in the installation of counterarms, it can be said that the task of adjusting the head vector of forces of inertia to the mechanism of the hinged chotirilanka can be done with the help of the installation of counterarms on two yogo lankas.

By a similar rank, you can solve the problem of picking up the masses of the okremikh lanes for the installation of the articulated six-lane and whatever mechanism, established by the way, nasharuvannya dvovovodkovyh groups. Given a rank (9.) can be replaced with one vector rank

De r s - Vector that determines the position of the center of the mass.

Umov (4.13) is satisfied, zokrema, if r s =0; tsya umova to bring to the method of selection of mechanisms from symmetrically riveted lanks of equal weight.

Small 24 shows diagrams of symmetrical crank-sliding and hinged chotyri-lank mechanisms. In quiet situations, if the placement of the straps in symmetrical mechanisms is too cumbersome or the weight is structurally inadequate, the method of installing an antidote is established.

Come on, for example, it is necessary to bring only the head vector of the forces of inertia of the crank-linked mechanism, the scheme of which is shown in the little 25. Significantly, the mass of the crank 1, the connecting rod 2 and the link 3 through m 1, m 2, m 3 і will be taken into account їх in the center of gravity S 1, S 2 i lanok. It is installed on the line AB at the point D to the opposite and it is significant її masu m pr іz mind, so the center of gravity mass m pr, m 2 and m 3 zbіgavsya with point A. Z equaling the static moments shdo point A is possible

Mass, counterweight, installed at the point 3 of the crank, it is important to understand that the center of gravity of the mass, and zbigavsya with the point O. The alignment of static moments at the point O is known

The radii s and z of the opposites are chosen fairly. After the installation of the opposite center of the mass mechanism at all positions, it will be with the point O i, then, the whole hour of work will be unruly. In this manner, the two opponents and invariably vindicate all the forces of inertia to the mechanism that is being looked at. However, it is rare that in practice it is rare to have a similarly equal inertia forces of inertia of crank-mounted mechanisms, which, with a small value of the radius from the mass, is even greater, which led to the appearance of additional forces in the kinematic pairs of the cranks of the mechanism. With a large value of the radius, the overall dimensions of the entire mechanism are greatly increased. That is why they are often separated by less close approximations of the forces of inertia. So, in crank-sliding mechanisms, the method of installing a counterweight on the cranks is the most expanded by the method of approximate alignment of inertia forces. In these mechanisms, it is practical to zastosovuyt vrіvnovazhuvannya less crank weight and part of the connecting rod weight.

When the existing power of the dynamics of the mechanism is violated with one step of freedom, it is possible to impose the law of change of kinetic energy, which is formulated as follows:

de - kinetic energy of the mechanism in a sufficient position

Kinetic energy of the mechanism in cob position

Algebraic sum works all forces and moments applied to the mechanism

For a plane-parallel ruhu:

de - the moment of inertia of the lanka shodo axis, scho to pass through the center of mass S

Behind the nature of the change in kinetic energy, the last cycle of the robotic machine unit in a wild swing is composed of three parts: acceleration (start-up), that having risen that vibration (zupinki) (Fig. 4.6). The hour t p is characterized by an increase in the speed of the wire, and it is possible if >, and in an hour<, т.е. кривая зависимости кинетической энергии в первом случае монотонно возрастает, во втором случае - монотонно убывает.

Establishments ruh є more trivalim. By stretching this stage, the core of the robot is drawn, for which a mechanism is recognized. Therefore, the last hour of a weary rush can be formed from any number of cycles of rush, which is equivalent to one or a dekil wrapper of the crank.

There are two options for movement.

The first option: the kinetic energy of the mechanism T is constant in the current mode. Butt: a system of toothed wheels, which are wrapped with permanent kutovnyh shvidkost, maє permanent kinetic energy.

Another option: characterized by the periodicity of the movement of the wire shaft to the mechanism with small knocks in the middle of the period. Periodicity can include one or two turns of the crank, for example, for the engine, the frequency of change T-two turns of the crank.

The entire flow of energy that is brought to the machine, as well as the kinetic energy of the machine itself in the process of work, can be balanced as follows:

de-robot forces ruin

Robot Forces

The robot forces rubbing

Gravity work

Work of forces of inertia

For the hour of the installed rush, like the end of the cycle and the ear of the onset cycle, the value of the speed is the same, tobto. work and cost zero, then.

Nehtuyuchi force rubbing, maєmo

Tse equal to the main energy equals of the periodic movement of the mechanism that has risen.

Kutova shvidkіst provіdnoї lanka in between the cycle of the rush, which standing up, in a scatterful fall є the size of the zminnoy.

Change the apical fastness of the reduced lanka to call out to the kinematic pairs of the additional (dynamic) vice, as if lowering the hard KKD of the machine, the reliability of the work and the durability. In addition, kolyvannya shvidkosti pogrіrshuyut working process of the machine.

Kolivannya svidkostі є naslіd dvh faktorіv - periodic change induced by the moment of inertia of the mechanism and the periodic nature of the forces and moments.

The cream of periodic cracking of dryness in the mechanism can be cracked and non-periodic, that is. non-repetition, viklikanі for various reasons, for example, rapt change of ambition.

The first type of coliving is regulated no more than the permissible unevenness of the movement, mounted on the shaft of the additional mass (flywheel).

In another way, the regulation manager is violating, installing a special mechanism, which is called a regulator.

Between the allowable changes in the top of the windshield, they are installed by an additional path. Roughness of machine movement is characterized by the settings of absolute unevenness up to її medium smoothness

Call to ask and de

Mayuchi so spіvvіdnoshennia:

We see two equals (4.14) and we know:

But with an unimaginable size, through її deshchitsu it is possible:

p align="justify"> Periodic uneven running of the machine, as a rule, represents a sloppy inflow and can be allowed for more cars only in the song ranges. Numerous shkidlivy things in cars are manifested, for example, in the offensive: rivki in Russian transport machines, shaving threads in textile machines, overheating of the windings of electric motors, flashing light through the uneven wrapping of the armature of the electric jet generator, lack of cleanliness and accuracy of inconsistency of processing the surfaces of parts on methane, unequal tovshchina zvarnyh shvyv when zvaryuvanni for the help of zavaryuvalnyh automatic machines, having opened the sheet for an hour of drawing the sacks on the presses thinly.

Permissible unevenness in the course of the machine is determined by the coefficient d and deposited in the recognition of the machine. The number of values ​​is established by the bugatory certificate of operation of the machine.

In this order, and vіd_znyayutsya vіd vіd ї vіd ї srednії ї kutoї ї ї ї ї ї ї scho d = 1/25 become vsogo 2%, and d \u003d 1/50 the most vіdhilennya vіdhilennya vіdhilennya vіd 1% vіd. You can see what to build with equal numbers of great d, ruh wired lanes of the machine to finish even.

Rukh providnoї lanki tim closer to equal, chim more guidance moment of inertia or induced mass mechanism. The improvement of the scale of the moment of inertia is carried out practically by landing on the shaft of the flywheel machine with a singing mass and moment of inertia.

In the analysis of the robotic machine and the mechanism assigned to the law of the turn of the cob, with one step of freedom, it is necessary to manually operate not with the action masses that collapse with the change of clothes, but with masses, or equivalent, mentally transferred to the be-yak Lanka mechanism.

So the force itself, or the moment, applied to the knees, can be mentally replaced by the force, or the moment, applied to the mechanism to the point.

Such a force is called an induced force, the tension of which is more expensive than the sum of the tensions of all forces applied to the legs.

A lanka, to which a force is applied, is called a lanka brought.

The tension, whether as a force, applied in the "point", moving out of the front section, may be designated as a moment of force strength along the end of the swidkost vector

Intensity can be recorded through pointing the moment of forces

The mass is induced - such a fictitious mass, zoseredzhena at the point of the lanka reduced, the kinetic energy is like a healthy kinetic energy of the entire mechanism

de-guiding moment of inertia of Lanka,

Kutova shvidkost lanka brought,

Shvidk_st point U lanka is given.

Guidance moment of inertia

We bring to the main shaft (reduced lanka) the moment of inertia is called such a smart moment of inertia, which allows the head shaft to move kinetic energy in the given position of the machine, which improves the kinetic energy of the whole mechanism.

Most of the machines operate, as a rule, in a mode that is characterized by the fact that the machine takes away the engine for 1 cycle of energy, the amount of energy is spent in the same hour for the production of work, for which it is recognized.

The cycle is called the interval of an hour, after which all the parameters that characterize the robot of the machine are repeated (periodic repetition of speed, quickness, effortlessness). Rukh lanok machines, in such a rank, may be a periodic character. Understanding about the Rukh zovsіm does not mean that the wired lanka of the machine is collapsing step by step.

Let's take a look at the Rukh of Lanka brought:

Why is it so equal that for equal movement (if e = 0) at some point in the cycle, one should think:

tobto. change the moment you can follow the law, change the creation, which in practice can be accessible by simple means.

In this manner, navit with

So, for example, the crank of a planing verst, to the warehouse of which the crank mechanism enters, or the crank press, to the warehouse of which the crank-sliding mechanism enters, wind without tension will not collapse evenly.

The equanimity of the moment is practically achieved extremely rarely. As a result of these reasons for the collapse of machines, which, having risen, are due to a periodic change in speed, as in the middle of the cycle, they change between:

Most machines operate, as a rule, in a mode that is characterized by the fact that the machine performs such a work in one cycle, as it will take away for a cycle the type of the engine, which is obov'yazykovoy umovoyu installed ruhu є.

The physical role of the flywheel in the machine can be shown in this way. Just as in the midst of a deaky kuta, the turn of the cob lanka to the mechanism of the robot of the driving forces is greater for the work of the forces of support, then the cob lanka turns around quickly and the kinetic energy of the mechanism increases.

For the life of the flywheel, the entire increase in kinetic energy is distributed between the masses of the mechanism. The flywheel will increase the driving force of the mechanism and, at the same time, the increase in kinetic energy will be greater without the flywheel, lower due to the presence of the flywheel.

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Entry

1. The task of dynamic follow-up of mechanisms

2. Forces at mechanisms

3. Forces of inertia

4. Kinetostatic development of mechanisms

5. Theorem N.Є. Zhukovsky

Literature

opir inertia kinetostatic mechanism

Entry

The theme of the control work "Dynamic analysis of mechanisms" from the discipline "Theory of mechanisms and machines".

Purpose: forming knowledge of dynamic analysis of mechanisms.

Task: learn about the methods of dynamic analysis of mechanisms.

Robots have been reviewed by the following topics:

Head of dynamic maintenance of mechanisms;

Forces at mechanisms;

Forces of inertia;

Kinetostatic development of mechanisms;

The theorem of N.E. Zhukovsky about the hard value.

1. The task of dynamic follow-up of mechanisms

The main tasks of the dynamics of mechanisms are:

1) the designation of the forces that exist in the kinematic pairs of the mechanism;

2) vyznachennya forces rubbing that їх having poured into the robot mechanism;

3) according to the law, the movement of the mechanism, which follows the action of the singing forces;

4) manifestation of minds, yakі zabezpechuyut tasks law to the movement of the mechanism;

5) vrіvnovazhennya mehanіzmіv.

To complete the first task, a power follow-up mechanism is carried out.

2. Forces at mechanisms

The main forces, the primary nature of the movement of the mechanism, are the destructive forces that create a positive robot, and the forces of the core (virobnic) support, which blame the process on the mechanism of the core robot and the negative of the robot. One can see the driving forces: the force of the pressure of the working sum on the piston of the engine cylinder, the moment that the electric motor develops on the wire shaft of the pump or the compressor, etc.

The forces of the core support are the strengths, the support of some kind of mechanism. With such forces є: they strengthened the support of the rіzanny in the verst and so on. Krіm tsikh forces nebhіdno brahovuvati also the forces of the support of the middle, in which the mechanism collapses, and the forces of tension of the legs, which vibrate positively or negatively the work in the fallow in a straight line to the center of gravity of the lanoks - down or uphill.

When the mechanism is opened, all the forces of the coris support are responsible for the task - so are the names of the forces that are set. The qi forces are set to sound like mechanical characteristics.

The mechanical characteristic of the engine or a robotic machine is called the fallback to the moment applied to the driven shaft of the engine or the wired shaft of the robotic machine, depending on one or more kinematic parameters. The mechanical characteristics are determined by the experimental path, or by the help of various mathematical deposits.

Practicing the mechanism in the wake of all the applied forces in kinematic pairs, they blame reactions, without intermediary injecting the nature of the movement into the mechanism, and yet from the surfaces of the elements of the kinematic pairs, vibrate the forces of friction. Qi force є shkіdly support.

Reactions in kinematic pairs are blamed not only for the influx of external forces, which are given to the mechanism, but also for the collapse of the whole mass of the mechanism with quickening, which can generate additional dynamic forces in kinematic pairs.

Therefore, the task of the kinematic rozrahunka is due to the designated reactions in the kinematic pairs of mechanisms, otherwise, apparently, pressing, which is blamed on the places of the zіtknennia of the elements of the kinematic pairs, as well as in the designated moment of force, which is important, again.

Under the forces, which are vrіvnovazhuyut, but by the moments they razumіyut tі nіvіdіmі and pіdlyagayut vyznachennyu forces or moments, prikladnі to provіdnih lanok, yakі vrіvnovuzhuyut system of all zvn_shnіh forces and pairs of forces and all forces of inertia and pairs of forces of inertia.

As in the machine, in the process of robots, the quickening of the legs reaches an insignificant value, then the reactions in the kinematic pairs are determined from the mind of the equal movement of all the legs of the mechanism for the mind of the equal statics:

∑Fi=0; ∑ M (Fi) = 0.

As soon as the speed in the car reaches a significant value, then on the coast there is a dynamic ambition, which is no longer possible. For a power rozrahunka in the same moment, it would be necessary to lay down a dynamically equal ruin, which is even more important.

If the task can be set, victorious d'Alembert's principle, zgіdno z zgіdno, yakshcho to the lanks of the mechanism at once with the forces of reporting and inertial force, then the mechanism can be seen as such that it changes into a static rіamivnovazi,

∑ M (Fi) + ∑ M (Fu) + Mu=0

3. Forces of inertia

At the slope of the flat-parallel ruh of the lanka, there is an increase in the number of different material points of difference (for the value of i directly). Therefore, the difference is the elementary forces of inertia

de: m - Masa Lanka;

WS - accelerated center of gravity of Lanka;

ε - kutove prikorennya lanka;

IS - the moment of inertia of the lanka of any axis that passes through the center of gravity.

The moment of Lanka's inertia and the world of Lanka's inertia in Obertal Russia. Yogo value to lay down only from the very body: from yogo masi and rozpodіlu masi. The moment of inertia at the drop is determined by the formula:

de: ρ - the appearance of the skin elementary mass in the axis, which passes through the center of gravity.

The force of inertia Fu is applied in the center of gravity of the lanka S and is straightened up to the acceleration vector of the center of gravity WS.

The moment of the parity of the forces of inertia of the straightening is proportional to the apex of the lanka ε.

Let's see what the forces of inertia create for the various fluctuations of the rush of Lanka.

1. Progressive movement of Lanka (Fig. 1).

Accelerating all points are the same, to that:

The force of inertia was applied at the center of gravity. Lanka's hour of inertia Mu=0, because with progressive Russian Lanka, there is no apical acceleration (ε=0).

2. Lanka unevenly (ε≠0) wraps around the axis to pass through the center of gravity (Fig. 2).

Fig.2

The force of inertia at times is more expensive Fu=0, because accelerated to the center of the vaga WS=0.

The moment of inertia force is more: Mu=-IS·ε і straightening up to the apex acceleration ε.

3. Lanka evenly (ε=0) wraps around the axis, so as not to pass through the center of gravity (Fig. 3).

In what direction:

Moment of forces of inertia Mu=0, oskolki kutove accelerated =0.

4. Lanka evenly (ε=0) wraps around the axis to pass through the center of gravity (Fig. 4).

And here the force of inertia is Fu=0, because аS=0 і moment of inertia µu=0 (bo ε=0).

Such a Lanka is called vrіvnovazhenoyu.

5. The lanka wraps unevenly around the axis, so as not to pass through the center of gravity.

In this way, the force of inertia is blamed and the moment of forces of inertia:

The force of inertia is applied at the center of gravity and parallel to the accelerated center of gravity WS. The moment of the parity of the forces of inertia Mu of the straightening is proportionally up to the apex of the acceleration.

It is often necessary to bring the force of inertia Fu and the moment of inertia Mu to one equal force Fu (Fig. 6). To this, we replace the moment Mu with a pair of Fu і -Fu, the moment is more expensive: Fu·h=Mu.

The force -Fu tsієї bet is applied in the center of gravity S. Todі іnsha force is applied in the deyakіy point "K" of Lanka. Forces Fu and -Fu, applied at the center of gravity, are mutually respected, therefore, only one force is left, applied at the point "K" of Lanka. This point is called the point of hitanya.

The position of the hit point is significant.

Dynamic analysis of mechanisms

Dynamic analysis The mechanism is called the direction of the movement of the mechanism under the action of the applied forces, or the assignment of forces for the task of the movement of the legs. Fallen in the form of a sign of elementary work, all the forces that blow on the legs of the mechanism, support on the ruined forces and forces. Rush power force is called, elementary work is positive, and support by force- Force, elementary robot yakoї negative. Elementary robot power appears as a scalar gain of strength on the elementary displacement of the point of stagnation. Rushing forces, that forces, sound the support with the functions of displacement and the speed of the points of congestion of forces, and sometimes with the functions of the hour.

The forces of gravity can be either by the forces of destruction, or by the forces of support in the fallow land in the direct movement of the elementary. Forces rubbing at the kinematic pairs are functions of the forces of normal pressure on the surface, the permeable smoothness of the movement of the legs, the parameters of the oil are thin.

Global methods of dynamic analysis of mechanisms to fully stop up to mechanisms from one step of freedom. With dynamic analysis, a task is assigned to the rotation of the corn lanka for the given forces. The purpose of this task is to swear by the law of the pochatkovo lanka, the fallow land of the zagalnennoy coordinate at the hour.

The law of the revolution of the pochatkovo lanka is equal to the decisions of the revolution of the mechanism. The most simple form of roaring to come out on the basis of a theorem about changing the kinetic energy of a mechanical system. The mass of the lanka of the given lank is determined by the mind, that this kinetic energy is more valuable to the sum of the kinetic energies of all the lanoks of the mechanism, and the tension of the induced force is more than the sum of the tension of all the forces that are induced. I have induced the force manually by the method of N. Ye. Zhukovsky.

When looking at the movement of the mechanism, three modes are distinguished: expansion, movement and vibration. Kinematic characteristics of a tired roo:

the coefficient of unevenness of the movement of the mechanism, which evaluates the visual impact of the smoothness of the lanka of the reduction,

coeficient of the brown movement of the mechanism, the equal development of the work, stained for the period of the movement on the underlay of the brown supports, to the work of the breaking forces.

One of the goals of a dynamic analysis of the mechanism is a kinetostatic rozrahunka, with which reactions are indicated in kinematic pairs and a timely important moment, applications to the cob lanka, in the presence of dif ferent forces and forces of inertia.

The forceful expansion of the flat and space mechanism is carried out behind the largest structural groups of Assur, which are statically dependent kinematic lances. The presence of superfluous connections led to the overextension of a number of unknown reactions over a number of minds of kinetostatics, to the point of static insignificance of the task. That is why mechanisms without superfluous links are called so very statically primary mechanisms.

Analytical assignment of reactions in kinematic pairs of statically assigned mechanisms is brought up to the last review of the minds of equal limbs that establish structural groups. The instruction from the analytical decisions of the head of the forceful rozrahunka zastosovuetsya graphic design of the reactions of the way and encourage the plans of forces.

In order to improve the strength by rubbing with a forceful expansion of the mechanism, it is possible to show such spontaneity between the parameters of the mechanism, in which, through the rubbing of the lanka in the necessary direction, one can independently develop the magnitude of the rupture force. Such a phenomenon is called a self-tampering mechanism, as it is unacceptable for most people to fall, but sometimes it is victorious to intimidate the turnaround mechanism in a straight line.

When designing a mechanism, a task is set for a rational selection of oil mechanisms for a mechanism that ensures the repayment of dynamic pressures - a task for the restoration of a mass mechanism, a task for the restoration of forces of inertia that a mechanism has.

Won share:

On the task of introducing dynamic investments into the foundation,

On a task about the vrіvnovazhennja dynamіchіchnyh navantagenі kіnematicheskih couples.

When you look at the vrіvnovazhuvannya of the lanka, what wraps, what folds from the obertovy shaft with zhorstko po'yazanimi tasks masses, it is possible to reach the full vrіvnovazhuvannya of all masses, fixed on the shaft, by installing two counters in fairly open flats, budovikat bugatically Forces and moments of pairs of forces can be reduced to one lanka, as it is called lankou brought.

Balansuvannyam called rіvnovazhuvannya obertovy or step by step ruhomy masses of mechanisms in order to reduce the influx of forces of inertia. Neuro-importance rotor (wrapped in the supports of the body) is called the yogo mill, which is characterized by such a distribution of mass, which is the hour of the wrapping, which calls for changes in the tension on the supports. Tsі navantazhennya є the reason for the stresses and vibrations, before the wear and tear, reduce the efficiency. the productivity of machines. Static neurodevelopment of the body - the camp, if the center of gravity of yoga lies on the axis of the wrap. For the recovery of the body that wraps, it is necessary that the center of gravity of yoga lies on the axis of the wrap. For vrіvnovazhennia of the head vector of the forces of inertia of the flat mechanism is sufficient, so that the central center of the mass of all the legs will change the mind's strength of the coordinates.

The neurodevelopment of the rotor is characterized by the magnitude of the imbalance. Tvіr nevrіvnovazhenoy masi її eccentricity is called the value of the imbalance and is shown by g-mm.

If that momentary neurodevelopment is static and is discovered overnight, then such neurodevelopment is called dynamic. In case of significant neurodevelopment, put counterpoints.

Zalezhno, I will stand on top of the rubble bodies, I see rubbed forging: grating cleaner(on surfaces without adsorbing slabs or chemical slabs), rubbing dry(Rubbing unsmeared surfaces), borderline rubbing (with an insignificant ball of mastila) that rubbing homeland(Rubbing the smeared surface). The deformations of the protrusions can be springy and not springy. The strength of the support while moving on top creates the force by rubbing. As if protruding unevenness on the surface stick together, rubbing dryly, as if between the surfaces there is a ball of mastic - rubbing normally. When rubbed forging one and the same maidan chimneys on top of one body enter at the contact with different maidan chimneys of another body. When rubbed stiffness different maidan chimneys on top of the same body successively run up from the maidan maidan chimneys of another tile.

Dependence of the moment applied to the driven shaft of the engine-machine, or to the wired shaft of the robotic machine, is called mechanical characteristics of the machine. For motor vehicles, a change in the torque with an increase in the top speed is characteristic, for working machines, with an increase in the top speed, the torque is increased.

The mode of releasing the mechanism may be at the start of the machine, or the mechanism in the run when the mechanism is shifted from a smaller speed to a large one. The period of change of forces with the Russian mechanism, which, having risen, sounds like one, two, or dekilkom turns of the lanka, and can be repeated without limiting the number of times, so that the robots and the mechanism do not change. The mode vibіgu mehanіzm vіdpovіdaє hour, by stretching such a mechanism zupinyaєtsya or with more swidkіstyu be translated into less. For most machines, the main ruh is ruh, and rozbіg і vibіg may be spaced only at start-up and teeth of the machine.

Dynamic analysis - has developed the theory of mechanisms and machines, in which the rukh lanok of the mechanism is being developed under the influx of a given system of forces. The main meta-dynamic analysis is based on the established deep fallows between the forces (moments of forces) that strike the mechanism, and the kinematic parameters of the mechanism to improve the weight (moments of inertia) of the yoga lanes. The number of fallows is recognized as equal to the movement of the mechanism.

With all the diversity of tasks of dynamic analysis, they are divided into two main types: in tasks of the first type, they are distinguished, under the influence of such forces, tasks are assigned to the movement mechanism (before the task of dynamics); in another type of task for a given system of forces, which are on the sides of the mechanism, they know their kinematic parameters (another task of dynamics).

The law of the movement of the mechanism in an analytical form is determined by looking at the fallows of the specified coordinates at the hour. Most simply, the task of dynamics is viable for mechanisms with hard lines and one step of freedom for the help of classical methods in the theory of mechanisms and machines. Prote current technical practice is to create a variety of folding factories, in which the dynamics of hand-held machines and mechanisms are achieved with the improvement of the spring authorities of the materials of the legs, the obvious gaps in those kinematic lances and other chinniks. In similar modes, the control of the dynamics of mechanical systems with dekilkom steps of freedom (or with an innumerable number of steps of freedom) and of the folding mathematical apparatus of rich differential systems of sizable differential rіvnіn, rіvnyan of the latter private and іntegro-differential ones.

The forces that strike the mechanism, that is their classification

The developmental lanka of the mechanism of force can be divided on the foot group.

Russian forcesF d (otherwise, the bet of forces with the moment M d ) – all the forces, the elementary work of which on possible displacements is positive Rushing forces are applied to the guide rails on the side of the engines. The stench is recognized for bringing the machines to the mines, the support of the forces for the support of the given technological process. How the drive motors stop the motors of internal combustion, electric, hydraulic, pneumatic and other.

Sealy propF c (or bet forces support with moment M h ) – tse forces, the elementary work of yay on possible moving points is negative. Forces support the movement of the mechanism. The stench is subdued by the strength of brown supports (F ps, Mps), for the support of some appointments of the given mechanisms, that power of the shkidlivih supports (F BC, MVS) that calls out unproductive waste of the energy of the disruptive forces.

The forces of brown supports are equipped with technological processes, that is why they are called technological or forging supports. Ring out the stench applied to the weekends of vikonavchih machines. The forces of the shkidlivy support are more important than the forces of rubbing in the kinematic pairs and the strength of the support of the middle. Let's understand the concept of "shkidlivi forces", that in a row of vipadkiv stench they will ensure the safety of the mechanism (for example, the operation of a skating rink will be ensured by the forces of its connection with the roadway).

Seeley waghi lanokF g, fallow in direct їхної вії shkodo directly rushing forces, can be brown or sloppy, if the stench is likely to stick or overshoot the mechanism.

Forces of inertiaF or moment of inertia M And, what is blamed for changing the speed of the wind of the lanok, can be like a destroying force, so it is the strength of the support, fallow in a straight line to the wind of the lanok.

In the fall of the power of the rush and the power of the support є by the functions of the kinematic parameters (hour, coordinates, speed, acceleration of the point of the report of the power). Functions for specific engines and working machines are called їх mechanical characteristics, which are set graphically in analytical form.

On fig. 1.20 mechanical characteristics M d = \u003d Md (ω) of electric motors of various types.

fast strumu with parallel awakenings(the motor start winding is switched on in parallel with the armature winding) may look like a linear monotonically falling fall to the moment Md in the apex winding of the shaft wrap (Fig. 1.20, a). The engine with such a mechanical characteristic works steadily on the entire range of windshield speeds.

Mechanical characteristics of the electric motor fast strumu with the last awakening(the wake-up winding is connected sequentially with the armature winding) M d = Md(ω), depicted in fig. 1.20 b.

Mechanical characteristic asynchronous electric motor(Fig. 1.20, in) is described by a folded fallow. Characteristics of the highest and lowest parts. Areas of steel robot and electric

Rice. 1.20

engine is the lowest part of the characteristic. Just a moment of support M s more than the maximum moment of the driving forces M e, the engine hums. Such a moment M called overturning moment M def. Kutova shvidkost ω = = ωnom, for which dvigun develops maximum tightness, is called the nominal kutovoy shvidkost, and the main moment M d = M nom - rated torque. Kutova dryness ω = ωс. when yakіy M d = 0, called synchronous windshield.

The mechanical characteristics of working machines are most often є vish_dnimi curves (Fig. 1.21). Such a look may be the characteristics of compressors, air-center pumps and others.