When the torque developed by the motor is equal to the resistance moment of the actuator, the drive speed is constant.

However, in many cases the drive speeds up or slows down, i.e. operates in transient mode.

Transitional The electric drive mode is the operating mode during the transition from one steady state to another, when the speed, torque and current change.

The reasons for the occurrence of transient modes in electric drives are changes in the load associated with the production process, or the impact on the electric drive when controlling it, i.e. starting, braking, changing the direction of rotation, etc., as well as disruption of the power supply system.

The equation of motion of the electric drive must take into account all moments acting in transient modes.

IN general view the equation of motion of the electric drive can be written as follows:

At positive speed, the equation of motion of the electric drive has the form

Equation (2.10) shows that the torque developed by the engine is balanced by the resistance torque and dynamic torque. In equations (2.9) and (2.10), it is assumed that the moment of inertia of the drive is constant, which is true for a significant number of actuators.

From the analysis of equation (2.10) it is clear:

1) for > , , i.e. drive acceleration takes place;

2) when< , , т.е. имеет место замедление привода (очевидно, замедление привода может быть и при отрицательном значении момента двигателя);

3) when = , ; in this case the drive operates in steady state.

Dynamic moment(the right side of the torque equation) appears only during transient modes when the drive speed changes. When the drive accelerates, this torque is directed against the movement, and when braking, it supports the movement.

3. The concept of static stability of the drive.

Static stability, generally speaking, is understood as the ability of a system to independently restore its original operating mode with a small disturbance. Static stability is a necessary condition the existence of a steady-state operating mode of the system, but does not at all predetermine the ability of the system to continue operating in the event of sudden disturbances, for example, during short circuits.

Fig3.1 – Change in power with angle increments.

So, period A and, any other point on the increasing part of the sinusoidal power characteristic corresponds to statically stable modes and, conversely, all points of the falling part of the characteristic correspond to statically unstable modes. This implies the following formal sign of static stability of the simplest system considered: increments of the angle and power of the generator R must have the same sign, i.e. or, passing to the limit:

It is positive when< 90° (рис. 3.3). В этой области и возможны устойчивые установившиеся режимы работы системы. Критическим с точки зрения устойчивости в рассматриваемых условиях (при чисто индуктивной связи генератора с шинами приемной системы) является значение угла = 90°, когда достигается максимум характеристики мощности.

Above, we considered the operating conditions of an electric drive in steady state, when the torque developed by the motor is equal to the moment of resistance of the mechanism and the drive speed is constant. However, in many cases, the drive accelerates or decelerates, and then an inertial force or inertial torque is created that the motor must overcome while in transient mode. Thus, transitional regime An electric drive is called an operating mode during the transition from one steady state to another, when speed, torque and current change.

The reasons for the occurrence of transient modes in electric drives are either a change in load associated with the production process, or the impact on the electric drive when controlling it, i.e. starting, braking, changing the direction of rotation, etc. Transient modes in electric drives can also arise as a result of accidents or violations normal conditions power supply (for example, changes in voltage or frequency of the network, voltage asymmetry, etc.).

The equation of motion of the electric drive must take into account all forces and moments acting in transient modes.

During translational motion, the driving force is always balanced by the resistance force of the machine and the inertial force that occurs when speed changes. If the mass of a body is expressed in kilograms and the speed in meters per second, then the inertial force, like other forces acting in a working machine, is measured in newtons (kg m s -2).

In accordance with the above, the equilibrium equation of forces during translational motion is written as follows:

. (2.14)

Similarly, the moment equilibrium equation, Nm, for rotational motion (drive equation of motion) has the following form:

. (2.15)

Equation (2.15) shows that the torque developed by the engine is balanced by the resistance moment on its shaft and the inertial or dynamic torque. In (2.14) and (2.15), it is assumed that the body mass and, accordingly, the moment of inertia of the drive are constant, which is true for a significant number of production mechanisms. From analysis (2.15) it is clear:

1) at , i.e. the drive accelerates;

2) when , i.e. the drive slows down (obviously, the drive slows down even when the motor torque is negative);

3) when , in this case the drive operates in steady state.

The torque developed by the engine during operation is assumed to be positive if it is directed in the direction of movement of the drive. If it is directed in the direction opposite to the movement, then it is considered negative. The minus sign in front of , indicates the braking effect of the moment of resistance, which corresponds to the cutting force, friction losses, lifting the load, spring compression, etc. with a positive sign of the speed.

When lowering a load, unwinding or decompressing a spring, etc., a plus sign is placed in front of it, since in these cases the moment of resistance helps the rotation of the drive.

Inertial (dynamic) moment(the right side of the torque equation) appears only during transient modes when the drive speed changes. When the drive accelerates, this torque is directed against the movement, and when braking, it supports the movement. The inertial moment, both in value and sign, is determined by the algebraic sum of the engine moments and the moment of resistance.

Taking into account what has been said about the signs of the moments, formula (2.15) corresponds to the operation of the engine in the motor mode with a reactive torque of resistance (or with a potential braking torque of resistance). In general, the equation of motion of the drive can be written as follows:

. (2.16)

The choice of signs in front of the moment values ​​in (2.16) depends on the engine operating mode and the nature of the resistance moments.

Design diagram of the mechanical part of the electric drive

Electric drive mechanics

An electric drive is an electromechanical system consisting of an electrical and mechanical part. In this chapter we will look at the mechanical part of the electric drive.

In general mechanical part The electric drive includes the mechanical part of an electromechanical converter (rotor or armature of an electric motor), a mechanical energy converter (reducer or mechanical transmission) and the executive body of the working machine (IO RM). Since our task is to set the IO RM in motion, the characteristics of the working machine and the features of the mechanical part of the ED are fundamental for the selection and calculation of the electric drive.

In the general case, the mechanical part of an electric drive is a complex mechanical system consisting of several rotating and translationally moving links at different speeds, having different masses and moments of inertia, connected by elastic connections (of low or finite rigidity). At the same time, gaps often occur in kinematic transmissions.

This complex mechanical system is affected by external moments and forces of different directions and magnitudes, which, in turn, often depend on time, the angle of rotation of the mechanism, the speed of movement and other factors. Since this mechanical system is an integral part of the electric drive, it is necessary to know its characteristics and have a mathematical description sufficiently accurate for engineering calculations. The mechanical part of the electric drive is described in the general case by a system of nonlinear partial differential equations with variable coefficients. To describe the mechanical part of the electric drive, the most convenient way is to use Lagrange equations of the second kind.

Considering that the movement of a mechanical system is determined by the largest masses, the smallest rigidities and the largest gaps; very often a complex mechanical system can be reduced to a two- or three-mass model, which can be used when calculating EP systems. (These are systems with flexible shafts, systems subject to sudden dynamic loads, precision tracking systems).

In most cases, the mechanical part consists of highly rigid links with rigid connections, and we strive to reduce the gaps to zero, and then it becomes possible to present the design diagram of the mechanical part as a single-mass system mounted on the ED shaft, while we neglect the elasticity of the mechanical connections and the gaps in transfer. This model is widely used for engineering calculations.

To analyze the movement of the mechanical part of the electric drive, a transition is made from a real kinematic diagram to a calculated one, in which the masses and moments of inertia of the moving elements of their rigidity, as well as the forces and moments acting on these elements, are replaced by equivalent values ​​reduced to the same speed (usually total to the speed of movement of the ED). The condition for the obtained design scheme to correspond to the real mechanical part of the electric drive is the fulfillment of the law of conservation of energy.

Rice. 2.1. Kinematic diagram of the lifting device

The transition from the real scheme (Fig. 2.1) to the calculated one (Fig. 2.2) is called reduction. All parameters of the mechanical part lead to the ED shaft (in some cases to the gearbox shaft).

Rice. 2.2. Design diagram of the lifting device

Reduction of moments of inertia and masses carried out using the following formulas known from mechanics:

For rotational motion, (2.1)

For forward motion, (2.2)

Total moment of inertia of the system, (2.3)

where is the moment of inertia of the engine, kg∙m 2 ;

– moment of inertia of the k-th rotating element, kg∙m 2 ;

– mass of the i-th progressively moving element, kg;

, – reduced moments of inertia of k and i elements, kg∙m 2 .

The moment of inertia of a body relative to an axis passing through the center of gravity is the sum of the products of the mass of each elementary particle of the body by the square of the distance from the corresponding particle to the axis of rotation

Where Rj– radius of inertia

i k– gear ratio of the kinematic chain between the engine shaft and the k-th element,

– angular velocities motor shaft and k-th element, s -1.

where is the radius of bringing the progressively moving i element to the motor shaft, m,

– speed of movement of the progressively moving i element, m/s.

The radius of inertia is the distance from the axis of rotation (passing through the center of gravity) at which the mass of the body in question must be placed, concentrated at one point, in order to satisfy the equality

Bringing moments and forces, acting on the elements to the motor shaft, are carried out as follows:

First option: transfer of energy from the engine to the working machine

For rotationally moving elements, (2.6)

For progressively moving elements. (2.7)

Second option: energy is transferred from the working machine to the engine

For rotationally moving elements, (2.8)

For progressively moving elements. (2.9)

In these expressions:

– moment acting on element k, N∙m;

– force acting on the i element, N;

– reduced moment (equivalent), N∙m;

– efficiency of the kinematic chain between the k and i elements and the motor shaft.

Using the above calculation schemes, the parameters, stability and nature of transient processes in a mechanical system are determined.

The dynamics of the electric drive, as a rule, is determined by the mechanical part of the drive as it is more inertial. To describe transient regimes, it is necessary to compile an equation of motion for the electric drive that takes into account all the forces and moments acting in transient regimes.

The most convenient method for composing the equations of motion of mechanisms is the method of Lagrange equations of the second kind. The complexity of the equation of motion will depend on which design scheme of the mechanical part of the drive we have chosen. In most practical cases, a single-mass design scheme is chosen, reducing the entire electric motor-working machine (EM-RM) system to a rigid reduced mechanical link.

A single-mass system (rigid reduced link) is an integrating link. In the case when the kinematic chain of the electric drive contains nonlinear connections, the parameters of which depend on the position of individual links of the mechanism (pairs of crank - connecting rod, rocker mechanism, and so on), the movement of a single-mass system is described by a nonlinear differential equation with variable coefficients. The moments included in this equation in the general case can be functions of several variables (time, speed, angle of rotation).

As follows from the block diagram, the motor torque is a control action, and the resistance moment is a disturbing action.

When designing and studying an electric drive, the task arises of rounding various mechanical quantities (speed, acceleration, path, angle of rotation, moments of effort), in order to make the mathematical description of the electric drive definite, take one of the 2 possible directions of rotation of the drive as the positive direction, and the second as negative. Taken as a positive reference direction, it remains the same for all values ​​of the drive motion characteristics (speed, torque, acceleration, angle of rotation). This is understood in that if the direction of the torque and velocity in the considered time interval coincide, i.e. speed and torque have the same signs, then the work is done by the engine that creates the given torque. In the case when the signs of torque and speed are different, then the engines that create this torque consume energy.

The concept of reactive and active moments of resistance.

The movement of electric drives is determined by the action of 2 moments - the moment developed by the movement and the moment of resistance. There are two types of moment of resistance - reactive and active. The reactive torque appears only due to the movement of the drive. This contradicts the reaction of a mechanical link to movement.

Reactive moments include: friction moment, moment on the working element, on metal-cutting machines, fans, etc.

The reactive moment of resistance is always directed against the movement, i.e. has the opposite sign of the direction of speed. When the direction of rotation changes, the sign of the reactive torque also changes. An element that creates a reactive torque is always a consumer of energy.

reactive characteristic; active mechanical characteristic.

The active moment of resistance appears regardless of the movement of the electric drive and is created by an external source of mechanical energy.

For example: the plumb moment of a falling load. The moment is created by the flow of water, etc.

The direction of the active torque does not depend on the direction of movement of the drive, i.e. When the direction of rotation of the drive changes, the sign of the active torque of the drive does not change. An element that creates an active torque can be both a source and a consumer of mechanical energy.

Equation of motion and its analysis.

To analyze the movement of the rotor or the movement of the armature, the basic law of dynamics is used, which states that for the rotation of a body, the vector sum of moments acting relative to the axis of rotation is equal to the derivative of the angular momentum.

In an electric drive, the components of the effective torque are the motor torque and the resistance torque. Both moments can be directed both in the direction of movement of the engine rotor and against it. Most often, an electric drive uses a motor mode of operation. Electric machines at this moment of resistance have a braking character in relation to the rotor and are aimed at meeting the motor torque. Therefore, the positive direction of the moment of resistance is taken to be the direction opposite to the direction of the positive moment of the engine. As a result, the equation of motion is written as follows:

In this expression, both moments are algebraic quantities since they act about the same axis.

MM With– dynamic moment.

The direction of the dynamic torque always coincides with the direction of acceleration dw/ dt. The last expression is valid for a constant radius of gyration of the mass.

Depending on the sign of the dynamic torque, the following drive operations are distinguished:

M ding  0 ,dw/ dt 0 ,w 0 – take-off or braking when w 0 .

M ding  0 ,dw/ dt 0 ,w 0 – braking, at w 0 - take-off run.

M ding =0 ,dw/ dt=0 – steady state w= const.

Or a special case w=0 - peace.

Thousands of people around the world do repairs every day. When performing it, everyone begins to think about the subtleties that accompany the repair: in what color scheme choose wallpaper, how to choose curtains to match the color of wallpaper, arrange furniture correctly to obtain uniform style premises. But rarely does anyone think about the most important thing, and this main thing is replacing the electrical wiring in the apartment. After all, if something happens to the old wiring, the apartment will lose all its attractiveness and become completely unsuitable for living.

Any electrician knows how to replace the wiring in an apartment, but anyone can do it to an ordinary citizen, however, when performing this type of work, he should choose high-quality materials in order to obtain a safe electrical network in the room.

The first action to be performed is plan future wiring. At this stage, you need to determine exactly where the wires will be laid. Also at this stage, you can make any adjustments to the existing network, which will allow you to arrange lamps and lamps as comfortably as possible in accordance with the needs of the owners.

12.12.2019

Narrow-industry devices of the knitting sub-industry and their maintenance

To determine the stretchability of hosiery, a device is used, the diagram of which is shown in Fig. 1.

The design of the device is based on the principle of automatic balancing of the rocker arm by the elastic forces of the product being tested, acting at a constant speed.

The weight beam is an equal-armed round steel rod 6, having an axis of rotation 7. At its right end, the legs or the sliding form of the trace 9 are attached using a bayonet lock, on which the product is put on. A suspension for loads 4 is hinged on the left shoulder, and its end ends with an arrow 5, showing the equilibrium state of the rocker arm. Before testing the product, the rocker arm is brought into balance using a movable weight 8.

Rice. 1. Diagram of a device for measuring the tensile strength of hosiery: 1 - guide, 2 - left ruler, 3 - slider, 4 - hanger for loads; 5, 10 - arrows, 6 - rod, 7 - axis of rotation, 8 - weight, 9 - trace shape, 11 - stretch lever,

12— carriage, 13—lead screw, 14—right ruler; 15, 16 — helical gears, 17 — worm gear, 18 — coupling, 19 — electric motor

To move the carriage 12 with the stretching lever 11, a lead screw 13 is used, at the lower end of which a helical gear 15 is fixed; through it the rotational motion is transmitted to the lead screw. Changing the direction of rotation of the screw depends on the change in rotation of 19, which is connected to the worm gear 17 by means of a coupling 18. A helical gear 16 is mounted on the gear shaft, which directly imparts movement to gear 15.

11.12.2019

In pneumatic actuators, the adjustment force is created by the action of compressed air on a membrane, or piston. Accordingly, there are membrane, piston and bellows mechanisms. They are designed to install and move the control valve according to a pneumatic command signal. The full working stroke of the output element of the mechanisms is carried out when the command signal changes from 0.02 MPa (0.2 kg/cm 2) to 0.1 MPa (1 kg/cm 2). The maximum pressure of compressed air in the working cavity is 0.25 MPa (2.5 kg/cm2).

In linear diaphragm mechanisms, the rod performs a reciprocating movement. Depending on the direction of movement of the output element, they are divided into mechanisms of direct action (with increasing membrane pressure) and reverse action.

Rice. 1. Design of a direct-acting membrane actuator: 1, 3 - covers, 2 - membrane, 4 - support disk, 5 - bracket, 6 - spring, 7 - rod, 8 - support ring, 9 - adjusting nut, 10 - connecting nut

The main structural elements of the membrane actuator are a membrane pneumatic chamber with a bracket and a moving part.

The membrane pneumatic chamber of the direct action mechanism (Fig. 1) consists of covers 3 and 1 and membrane 2. Cover 3 and membrane 2 form a sealed working cavity, cover 1 is attached to bracket 5. The moving part includes support disk 4, to which the membrane is attached 2, a rod 7 with a connecting nut 10 and a spring 6. One end of the spring rests against the support disk 4, and the other through the support ring 8 into the adjusting nut 9, which serves to change the initial tension of the spring and the direction of movement of the rod.

08.12.2019

Today there are several types of lamps for. Each of them has its own pros and cons. Let's consider the types of lamps that are most often used for lighting in a residential building or apartment.

The first type of lamps is incandescent lamp. This is the cheapest type of lamp. The advantages of such lamps include their cost and simplicity of the device. The light from such lamps is the best for the eyes. The disadvantages of such lamps include a short service life and a large amount of electricity consumed.

The next type of lamps is energy-saving lamps. Such lamps can be found for absolutely any type of base. They are an elongated tube containing a special gas. It is the gas that creates the visible glow. For modern energy-saving lamps, the tube can have a wide variety of shapes. The advantages of such lamps: low energy consumption compared to incandescent lamps, daylight glow, large selection plinths. The disadvantages of such lamps include the complexity of the design and flickering. Flicker is usually not noticeable, but your eyes will get tired from the light.

28.11.2019

Cable assembly- a type of mounting unit. The cable assembly consists of several local ones, terminated on both sides in the electrical installation shop and tied into a bundle. Installation of the cable route is carried out by placing the cable assembly in the cable route fastening devices (Fig. 1).

Ship cable route- an electrical line mounted on a ship from cables (cable bundles), cable route fastening devices, sealing devices, etc. (Fig. 2).

On a ship, the cable route is located in hard-to-reach places (along the sides, ceiling and bulkheads); they have up to six turns in three planes (Fig. 3). On large ships, the longest cable length reaches 300 m, and the maximum cross-sectional area of ​​the cable route is 780 cm2. On individual ships with a total cable length of over 400 km, cable corridors are provided to accommodate the cable route.

Cable routes and cables passing through them are divided into local and main, depending on the absence (presence) of compaction devices.

Trunk cable routes are divided into routes with end and feed-through boxes, depending on the type of application of the cable box. This makes sense for the selection of technological equipment and cable installation technology.

21.11.2019

In the field of development and production of instrumentation and automation devices American company Fluke Corporation occupies one of the leading positions in the world. It was founded in 1948 and since that time has been constantly developing and improving technologies in the field of diagnostics, testing, and analysis.

Innovations from an American developer

Professional measuring equipment from a multinational corporation is used in the maintenance of heating, air conditioning and ventilation systems, refrigeration units, air quality testing, calibration electrical parameters. The Fluke brand store offers the purchase of certified equipment from an American developer. Full the lineup includes:

• thermal imagers, insulation resistance testers;
• digital multimeters;
• electrical energy quality analyzers;
• rangefinders, vibration meters, oscilloscopes;
• temperature, pressure calibrators and multifunctional devices;
• visual pyrometers and thermometers.

07.11.2019

Use a level gauge to determine the level different types liquids in open and closed storages and vessels. It is used to measure the level of a substance or the distance to it.
To measure liquid levels, sensors are used that differ in type: radar level gauge, microwave (or waveguide), radiation, electrical (or capacitive), mechanical, hydrostatic, acoustic.

Principles and features of operation of radar level meters

Standard instruments cannot determine the level of chemically aggressive liquids. Only a radar level gauge is capable of measuring it, since it does not come into contact with the liquid during operation. In addition, radar level gauges are more accurate compared to, for example, ultrasonic or capacitive ones.