Coursework on design. Calculation of propellers Lifting force of a propeller in kg

PHYSICS OF THE ROTOR

A magnificent machine - a helicopter! Its remarkable qualities make it indispensable in thousands of cases. Only a helicopter can take off and land vertically, hang motionless in the air, move sideways and even tail first.

Where do such wonderful opportunities come from? What is the physics of its flight7 Let's try to briefly answer these questions.

A helicopter rotor creates lift. The propeller blades are the same propellers. Installed at a certain angle to the horizon, they behave like a wing in the flow of incoming air: pressure arises under the lower plane of the blades, and vacuum occurs above it. The greater this difference, the greater the lift. When the lifting force exceeds the weight of the helicopter, it takes off, but if the opposite happens, the helicopter descends.

If on an airplane wing the lift force appears only when the airplane is moving, then on the “wing” of a helicopter it appears even when the helicopter is standing still: the “wing” is moving. This is the main thing.

But the helicopter gained altitude. Now he needs to fly forward. How to do it? The screw only creates upward thrust! Let's look into the cockpit at this moment. He turned the control stick away from him. The helicopter tilted slightly on its nose and flew forward. Why?

The control knob is connected to an ingenious device - a transfer machine. This mechanism, extremely convenient for controlling a helicopter, was invented during his student years by academician B. N. Yuryev. Its design is quite complex, but its purpose is to enable the pilot to change the angle of the blades to the horizon at will.

It is not difficult to understand that during a horizontal flight of a helicopter, the pressure from its blades moves relative to the surrounding air at different speeds. The blade that goes forward moves towards the air flow, and the blade that turns back moves along the flow. Therefore, the speed of the blade, and with it the lifting force, will be higher when the blade moves forward. The propeller will tend to turn the helicopter on its side.

To prevent this from happening, the nonstrunters connected the blades to the axis movably, on hinges. Then the forward blade began to soar and flap with greater lifting force. But this movement was no longer transmitted to the helicopter; it flew calmly. Thanks to the flapping motion of the blade, its lifting force remained constant throughout the revolution.

However, this did not solve the problem of moving forward. After all, you need to change the direction of the propeller thrust and force the helicopter to move horizontally. This was made possible by the swashplate. It continuously changes the angle of each propeller blade so that the greatest lift occurs approximately in the rear sector of its rotation. The resulting thrust force of the main rotor tilts, and the helicopter, also tilting, begins to move forward.

It took a long time for such a reliable and convenient helicopter control device to be created. A device for controlling the direction of flight did not appear immediately.

You, of course, know that a helicopter does not have a rudder. Yes, it is not needed by a rotorcraft. It is replaced by a small propeller mounted on the tail. If the pilot tried to turn it off, the helicopter would turn itself. Yes, it turned so that it would begin to rotate faster and faster in the direction opposite to the rotation of the main rotor. This is a consequence of the reactive torque that occurs when the main rotor rotates. The tail rotor prevents the tail of the helicopter from turning under the influence of the reaction torque and balances it. And if necessary, the pilot will increase or decrease the tail rotor thrust. Then the helicopter will turn in the right direction.

Sometimes they do without a tail rotor altogether, installing two main rotors on helicopters, rotating towards each other. Reactive moments in this case, of course, are destroyed.

This is how the “aerial all-terrain vehicle” flies and the tireless worker - the helicopter.

General provisions.

The main rotor of a helicopter (HV) is designed to create lift, driving (propulsive) force and control moments.

The main rotor consists of a hub and blades, which are attached to the hub using hinges or elastic elements.

The main rotor blades, due to the presence of three hinges on the hub (horizontal, vertical and axial), perform a complex movement in flight: - rotate around the HB axis, move with the helicopter in space, change their angular position, turning in the indicated hinges, therefore the aerodynamics of the blade a rotor is more complex than the aerodynamics of an airplane wing.

The nature of the flow around the NV depends on the flight modes.

Basic geometric parameters of the main rotor (RO).

The main parameters of the NV are diameter, swept area, number of blades, fill factor, spacing of horizontal and vertical hinges, specific load on the swept area.

Diameter D is the diameter of the circle along which the ends of the blades move when the NV operates in place. Modern helicopters have a diameter of 14-35 m.

Sweeping area Fom is the area of the circle that the ends of the NV blades describe when it operates in place.

Fill factorσ is equal to:

σ = (Z l F l) / F ohm (12.1);

where Z l is the number of blades;

F l – blade area;

F ohm – swept area of the NV.

Characterizes the degree of filling of the swept area by the blades, varies within the range s=0.04¸0.12.

As the fill factor increases, the NV thrust increases to a certain value, due to an increase in the actual area of the load-bearing surfaces, then falls. The drop in thrust occurs due to the influence of the flow bevel and the wake vortex from the blade in front. As s increases, it is necessary to increase the power supplied to the NV due to an increase in the drag of the blades. As s increases, the step required to obtain a given thrust decreases, which moves the NV away from stall modes. The characteristics of stall modes and the reasons for their occurrence will be discussed further.

The spacing of the horizontal l g and vertical l v hinges is the distance from the hinge axis to the HB rotation axis. Can be considered in relative terms (12.2.)

Located within . The presence of joint spacing improves the efficiency of longitudinal-transverse control.

is defined as the ratio of the weight of the helicopter to the area of the swept explosives.

(12.3.)

Basic kinematic parameters of NV.

The main kinematic parameters of the NV include the frequency or angular velocity of rotation, the angle of attack of the NV, and the angles of the general or cyclic pitch.

Rotation frequency n s - number of NV revolutions per second; angular speed of rotation of the NV - determines its peripheral speed w R.

The value of w R on modern helicopters is 180¸220 m/sec.

Angle of attack NV (A) is measured between the free-stream velocity vector and c
Rice. 12.1 Angles of attack of the rotor and its operating modes.

plane of rotation of the NV (Fig. 12.1). Angle A is considered positive if the air flow approaches the air flow from below. In horizontal flight and climb modes, A is negative, in descent, A is positive. There are two operating modes of the NV – axial flow mode, when A = ±90 0 (hovering, vertical climb or descent) and oblique blowing mode, when A¹± 90 0 .

The collective pitch angle is the installation angle of all NV blades in the section at a radius of 0.7R.

The angle of the cyclic step of the NV depends on the operating mode of the NV; this issue is discussed in detail when analyzing the oblique blowing of the NV.

Main parameters of the NV blade.

The main geometric parameters of the blade include radius, chord, installation angle, cross-sectional profile shape, geometric twist and blade planform.

The current cross-sectional radius of the blade r determines its distance from the axis of rotation of the NV. The relative radius is determined

(12.4);

Profile chord– a straight line connecting the most distant points of the section profile, denoted by b (Fig. 12.2).

Rice. 12.2. Blade profile parameters. Blade angle j is the angle between the chord of the blade section and the plane of rotation of the HB.

Installation angle j by `r=0.7 with the neutral position of the controls and the absence of flapping motion is considered to be the installation angle of the entire blade and the overall pitch of the NV.

The cross-sectional profile of the blade is a cross-sectional shape with a plane perpendicular to the longitudinal axis of the blade, characterized by a maximum thickness with max, the relative thickness concavity f and curvature . As a rule, biconvex, asymmetrical profiles with slight curvature are used on rotors.

Geometric twist is produced by reducing the angles of the sections from the butt to the end of the blade and serves to improve the aerodynamic characteristics of the blade. Helicopter blades have a rectangular shape in plan, which is not optimal in an aerodynamic sense, but is simpler from a technology point of view.

The kinematic parameters of the blade are determined by the angles of azimuthal position, swing, swing and angle of attack.

Azimuth angle y is determined by the direction of rotation of the NV between the longitudinal axis of the blade at a given time and the longitudinal axis of the zero position of the blade. The zero position line in horizontal flight practically coincides with the longitudinal axis of the helicopter tail boom.

Swing angle b determines the angular movement of the blade in the horizontal hinge relative to the plane of rotation. It is considered positive when the blade deflects upward.

Swing angle x characterizes the angular movement of the blade in the vertical hinge in the plane of rotation (Fig. 12.). It is considered positive when the blade deflects against the direction of rotation.

The angle of attack of the blade element a is determined by the angle between the chord of the element and the oncoming flow.

Blade drag.

The frontal drag of the blade is the aerodynamic force acting in the plane of rotation of the hub and directed against the rotation of the propeller.

The frontal resistance of the blade consists of profile, inductive and wave resistance.

Profile drag is caused by two reasons: the difference in pressure in front of and behind the blade (pressure drag) and the friction of particles in the boundary layer (friction drag).

The pressure resistance depends on the shape of the blade profile i.e. on the relative thickness () and relative curvature () of the profile. The more and the greater the resistance. Pressure resistance does not depend on the angle of attack at operating conditions, but increases at critical a.

Friction resistance depends on the speed of rotation of the propeller and the condition of the surface of the blades. Inductive drag is the drag caused by the slope of the true lift due to flow shear. The induced drag of the blade depends on the angle of attack α and increases with its increase. Wave drag occurs on the advancing blade when the flight speed exceeds the design speed and shock waves appear on the blade.

Drag, like traction, depends on air density.

Impulse theory of rotor thrust generation.

The physical essence of the impulse theory is as follows. A working ideal propeller rejects air, imparting a certain speed to its particles. A suction zone is formed in front of the screw, an ejection zone is formed behind the screw, and air flow through the screw is established. The main parameters of this air flow: induced speed and air pressure increase in the plane of rotation of the propeller.

In the axial flow mode, the air approaches the NV from all sides, and a narrowing air stream is formed behind the propeller. In Fig. 12.4. a fairly large sphere is depicted with the center on the NV bushing with three characteristic sections: section 0, located far in front of the screw, in the plane of rotation of the screw, section 1 with flow speed V 1 (suction speed) and section 2 with flow speed V 2 (throwing speed).

The air flow is thrown back by the HB with a force T, but the air also presses on the propeller with the same force. This force will be the thrust force of the main rotor. Force is equal to the product of body mass times
Rice. 12.3. Towards an explanation of the impulse theory of thrust creation.

acceleration that the body received under the influence of this force. Therefore, the NV thrust will be equal to

(12.5.)

where m s is the second mass of air passing through the area of air equal to

(12.6.)

where is the air density;

F - area swept by the screw;

V 1 - inductive flow velocity (suction speed);

a is the acceleration in the flow.

Formula (12.5.) can be presented in another form

(12.7.)

since, according to the theory of an ideal propeller, the speed of air ejection V by the propeller is twice as high as the speed of suction V 1 in the plane of rotation of the NV.

(12.8.)

Almost doubling of the inductive speed occurs at a distance equal to the radius of the NV. The suction speed V 1 for Mi-8 helicopters is 12 m/s, for Mi-2 – 10 m/s.

Conclusion: The thrust force of the main rotor is proportional to the air density, the swept area of the air blower and the inductive speed (the speed of rotation of the air blower).

The pressure drop in section 1-2 relative to atmospheric pressure in an undisturbed air environment is equal to three speed pressures of the inductive speed

(12.9.)

which causes an increase in the resistance of the helicopter structural elements located behind the NV.

Blade element theory.

The essence of the blade element theory is as follows. The flow around each small section of the blade element is considered, and the elementary aerodynamic forces dу e and dх e acting on the blade are determined. The lifting force of the blade U l and the resistance of the blade X l are determined as a result of the addition of the following elementary forces acting along the entire length of the blade from its butt section (r k) to the tip section (R):

Aerodynamic forces acting on the rotor are defined as the sum of the forces acting on all blades.

To determine the main rotor thrust, a formula similar to the formula for wing lift is used.

(12.10.)

According to the blade element theory, the thrust force developed by the main rotor is proportional to the thrust coefficient, the swept area of the blade, the air density and the square of the tip speed of the blades.

The conclusions drawn from the impulse theory and the theory of the blade element complement each other.

Based on these conclusions, it follows that the thrust force of the NV in the axial flow mode depends on the air density (temperature), the installation angle of the blades (the pitch of the NV) and the rotational speed of the main rotor.

NV operating modes.

The operating mode of the main rotor is determined by the position of the NV in the air flow. (Fig. 12.1) Depending on this, two main operating modes are determined: the mode of axial and oblique flow. The axial flow mode is characterized by the fact that the oncoming undisturbed flow moves parallel to the axis of the NV bushing (perpendicular to the plane of rotation of the NV bushing). In this mode, the main rotor operates in vertical flight modes: hovering, vertical climb and descent of the helicopter. The main feature of this mode is that the position of the blade relative to the flow incident on the propeller does not change, therefore, the aerodynamic forces do not change when the blade moves in azimuth. The oblique flow mode is characterized by the fact that the air flow approaches the NV at an angle to its axis (Fig. 12.4.). The air approaches the propeller at a speed V and is deflected downward due to the inductive suction speed Vi. The resulting flow velocity through the NV will be equal to the vector sum of the velocities of the undisturbed flow and the inductive velocity

V1 = V + Vi (12.11.)

As a result of this, the second air flow rate flowing through the air intake increases, and, consequently, the rotor thrust, which increases with increasing flight speed. In practice, an increase in NV thrust is observed at speeds above 40 km/h.

Rice. 12.4. Main rotor operation in oblique blowing mode.

Oblique blowing. Effective speed of flow around a blade element in the plane of rotation of the airborne element and its change along the swept surface of the airborne element.

In the axial flow mode, each element of the blade is in a flow whose speed is equal to the circumferential speed of the element , where is the radius of a given blade element (Fig. 12.6).

In the oblique flow mode with an angle of attack HB not equal to zero (A=0), the resulting speed W with which the flow flows around the blade element depends on the peripheral speed of the element u, the flight speed V1 and the azimuth angle.

W = u +V1 sinψ (12.12.)

those. at a constant flight speed and a constant rotation speed of the propeller (ωr = const.), the effective flow velocity around the blade will vary depending on the azimuth angle.

Fig. 12.5. Change in the speed of flow around the blade in the plane of rotation of the explosive.

Change in the effective flow velocity over the swept surface of the air force.

In Fig. 12.6. shows the velocity vectors of the flow that impinges on the blade element as a result of the addition of the peripheral speed and flight speed. The diagram shows that the effective flow velocity varies both along the blade and in azimuth. The peripheral speed increases from zero at the axis of the propeller hub to maximum at the tips of the blades. In an azimuth of 90 o the speed of the blade elements is equal to , at azimuth 270 o the resulting speed is , at the butt of the blade in the area with diameter d, the flow comes from the side of the flow fin, i.e. a reverse flow zone is formed, a zone that does not participate in the creation of thrust.

The larger the NV radius and the higher the flight speed at a constant NV rotation speed, the larger the diameter of the reverse flow zone.

At azimuths y=0 and y=180 0 the resulting speed of the blade elements is equal to .

Fig. 12.6. Change in the effective flow velocity over the swept surface of the explosive.

Oblique blowing. Aerodynamic forces of the blade element.

When the blade element is in the flow, the total aerodynamic force of the blade element arises, which can be decomposed in the velocity coordinate system into lift force and drag force.

The magnitude of the elementary aerodynamic force is determined by the formula:

Rr = CR(ρW²r/2)Sr (12.13.)

By summing up the elementary thrust forces and rotational resistance forces, one can determine the magnitude of the thrust force and rotational resistance of the entire blade.

The point of application of the aerodynamic forces of the blade is the center of pressure, which is located at the intersection of the total aerodynamic force with the chord of the blade.

The magnitude of the aerodynamic force is determined by the angle of attack of the blade element, which is the angle between the chord of the blade element and the oncoming flow (Fig. 12.7).

The installation angle of the blade element φ is the angle between the structural plane of the rotor (KPV) and the chord of the blade element.

The inflow angle is the angle between the velocities and .(Fig. 12.7.)

Fig. 12.7. Aerodynamic forces of the blade element during oblique blowing.

The occurrence of an overturning moment when the blades are rigidly fastened. Thrust forces are created by all elements of the blade, but the greatest elementary forces Tl will be for elements located at ¾ of the radius of the blade; the magnitude of the resultant Tl in the mode of oblique flow around the blade thrust depends on the azimuth. At ψ = 90 it is maximum, at ψ = 270 it is minimum. This distribution of elementary thrust forces and the location of the resultant force leads to the formation of a large variable bending moment at the root of the blade M bend.

This moment creates a large load at the point where the blade is attached, which can lead to its destruction. As a result of the inequality of thrusts T l1 and T l2, a helicopter overturning moment occurs,

M x =T l1 r 1 -T l2 r 2, (12.14.)

which increases with increasing helicopter flight speed.

A propeller with rigidly mounted blades has the following disadvantages (Fig. 12.8):

The presence of an overturning moment in the oblique flow mode;

The presence of a large bending moment at the point where the blade is attached;

Changing the thrust moment of the blade in azimuth.

These disadvantages are eliminated by attaching the blade to the hub using horizontal hinges.

Fig. 12.8 Occurrence of an overturning moment when the blades are rigidly fastened.

Alignment of the thrust moment in different azimuthal positions of the blade.

In the presence of a horizontal hinge, the thrust of the blade forms a moment relative to this hinge, which turns the blade (Fig. 12. 9). The thrust moment T l1 (T l2) causes the blade to rotate relative to this hinge

or (12.15.)

therefore, the moment is not transmitted to the bushing, i.e. The helicopter's overturning moment is eliminated. Bending moment Muzg. at the root of the blade becomes equal to zero, its root part is unloaded, the bending of the blade decreases, due to this the fatigue stresses are reduced. Vibrations caused by changes in azimuth thrust are reduced. Thus, the horizontal hinge (HS) performs the following functions:

Eliminates overturning moment in oblique blowing mode;

Unloads the root part of the blade from M bend;

Simplify rotor control;

Improves the static stability of the helicopter;

Reduce the amount of change in blade thrust in azimuth.

Reduces fatigue stress in the blade and reduces its vibration due to changes in azimuth thrust;

Changing the attack angles of a blade element due to flapping.

When the blade moves in oblique blowing mode in azimuth ψ from 0 to 90 o, the flow speed around the blade constantly increases due to the component of the horizontal flight speed (at low angles of attack NV ) (Fig. 12. 10.)

those. . (12.16.)

Accordingly, the thrust force of the blade increases, which is proportional to the square of the oncoming flow velocity, and the thrust moment of this blade relative to the horizontal hinge. The blade flaps upward
Fig.12.9 Alignment of the thrust moment in various azimuthal positions of the blade.

The cross section of the blade is additionally blown from above (Fig. 12.10), and this causes a decrease in the true angles of attack and a decrease in the lifting force of the blade, which leads to aerodynamic compensation of the flapping. When moving from ψ 90 to ψ 180, the flow velocity around the blades decreases and the angles of attack increase. At azimuth ψ = 180 o and at ψ = 0 o the flow velocities around the blade are the same and equal to ωr.

Towards azimuth ψ = 270 o the blade begins to descend due to a decrease in flow velocity and a decrease in Tl, while the blades are additionally blown from below, which causes an increase in the angles of attack of the blade element, and therefore a certain increase in lift.

At ψ = 270, the flow velocity around the blade is minimal, the downward swing Vy of the blade is maximum, and the angles of attack at the tips of the blades are close to critical. Due to the difference in the speed of flow around the blade at different azimuths, the angles of attack at ψ = 270 o increase several times more than they decrease at ψ = 90 o. Therefore, with an increase in helicopter flight speed, in the region of azimuth ψ = 270 o, the angles of attack can exceed critical values, which causes flow separation from the blade elements.

Oblique flow leads to the fact that the flapping angles of the blades in the front part of the NV disk in the region of azimuth 180 0 are significantly greater than in the rear part of the disk in the region of azimuth 0 0 . This tilt of the disk is called the obstruction of the HB cone. Changing the azimuth swing angles of the blade on a free airflow, when there is no swing regulator, changes as follows:

azimuth from 0 to 90 0:

The resulting flow velocity around the blade increases, the lift force and its moment increase;

The swing angle b and the vertical speed V y increase;

azimuth 90 0:

The upward swing speed V y is maximum;

azimuth 90 0 – 180 0:

The lifting force of the blade decreases due to a decrease in the resulting flow velocity;

The upward swing speed V y decreases, but the blade swing angle continues to increase.

azimuth 200 0 – 210 0:

The vertical flapping speed is zero V y = 0, the flapping angle of the blade b is maximum, the blade, as a result of a decrease in lift, goes down;

azimuth 270 0:

The flow speed around the blade is minimal, the lift force and its moment are reduced;

Downward swing speed V y – maximum;

The swing angle b decreases.

azimuth 20 0 – 30 0:

The speed of flow around the blade begins to increase;

V у = 0, downward swing angle is maximum.

Thus, in a free air blower of right rotation with oblique blowing, the cone falls back to the left. As the flight speed increases, the cone collapse increases.

Fig. 12.10.Changing the angles of attack of a blade element due to flapping.

Swing regulator (RF). The flapping movement leads to an increase in dynamic loads on the blade structure and an unfavorable change in the angles of attack of the blades on the rotor disk. Reducing the amplitude of the swing and changing the natural inclination of the NV cone from left to right is carried out by the swing regulator. The swing regulator (Fig. 12.11.) is a kinematic connection between the axial hinge and the rotating swashplate ring, which ensures a decrease in the blade installation angles j with a decrease in the stroke angle b and vice versa, an increase in the blade installation angle with an increase in the stroke angle. This connection consists in shifting the point of attachment of the rod from the swashplate to the axial hinge arm (point A) (Fig. 12.12) from the axis of the horizontal hinge. On Mi-type helicopters, the flapping regulator tilts the HB cone back and to the right. In this case, the lateral component along the Z axis from the resulting NV force is directed to the right against the direction of tail rotor thrust, which improves the conditions for lateral balancing of the helicopter.

Fig. 12.11 Swing regulator, Kinematic diagram. . . Equilibrium of the blade relative to the horizontal hinge.

During the flapping movement of the blade (Fig. 12.12.) in the plane of the traction force, the following forces and moments act on it:

The thrust T l, applied to ¾ of the length of the blade, forms a moment M t = T·a, turning the blade to increase the stroke;

Centrifugal force F cb acting perpendicular to the design axis of rotation of the NV in the outer direction. The inertial force from the flapping of the blade, directed perpendicular to the axis of the blade and opposite to the acceleration of the flapping;

The force of gravity G l is applied to the center of gravity of the blade and forms a moment M G = G · in turning the blade to reduce the stroke.

The blade occupies a position in space along the resulting force Rl. The equilibrium conditions of the blade relative to the horizontal hinge are determined by the expression

(12.17.)

Fig. 12.12. Forces and moments acting on the blade in the swing plane.

The NV blades move along the generatrix of a cone, the apex of which is located in the center of the hub, and the axis is perpendicular to the plane of the ends of the blades.

Each blade occupies, at a certain azimuth Ψ, the same angular positions β l relative to the plane of rotation of the HB.

The flapping motion of the blades is cyclic, strictly repeating with a period equal to the time of one revolution of the NV.

Moment of horizontal bushing joints NV (M gsh).

In the mode of axial flow around the NV, the resultant force of the blades Rn is directed along the axis of the NV and is applied at the center of the hub. In the oblique blowing mode, the force Rn is deflected towards the obstruction of the cone. Due to the separation of the horizontal hinges, the aerodynamic force Rn does not pass through the center of the bushing and a shoulder is formed between the force vector Rn and the center of the bushing. A moment M gsh arises, called the inertial moment of the horizontal hinges of the HB bushing. It depends on the spacing l r of the horizontal hinges. The moment of the horizontal hinges of the NV M gsh bushing increases with increasing distance l r and is directed towards the obstruction of the NV cone.

The presence of spacing of horizontal hinges improves the damping property of the NV, i.e. improves the dynamic stability of the helicopter.

Equilibrium of the blade relative to the vertical hinge (VH).

During rotation of the NV blade is deflected by an angle x. The swing angle x is measured between the radial line and the longitudinal axis of the blade in the plane of rotation of the HB and will be positive if the blade rotates backward relative to the radial line (lags behind) (Fig. 12.13.).

On average, the swing angle is 5-10 o, and in the self-rotation mode it is negative and equal to 8-12 o in the plane of rotation of the HB. The following forces act on the blade:

The drag force X l is applied at the center of pressure;

Centrifugal force directed along a straight line connecting the center of mass of the blade and the axis of rotation of the propeller;

The inertial force F in, directed perpendicular to the axis of the blade and opposite to the acceleration, is applied at the center of mass of the blade;

Alternating Coriolis forces F k applied at the center of mass of the blade.

The emergence of the Coriolis force is explained by the law of conservation of energy.

The energy of rotation depends on the radius; if the radius has decreased, then part of the energy is used to increase the angular velocity of rotation.

Therefore, when the blade flaps upward, the radius r c2 of the center of mass of the blade and the peripheral speed decrease, Coriolis acceleration appears, tending to accelerate the rotation, and hence the force - the Coriolis force, which turns the blade forward relative to the vertical hinge. As the swing angle decreases, the Coriolis acceleration, and therefore the force, will be directed against the rotation. The Coriolis force is directly proportional to the weight of the blade, the speed of rotation of the blade, the angular speed of the flapping and the flapping angle

The above forces form moments that must be balanced at each azimuth of the blade movement

. (12.15.)

Fig. 12.13.. Equilibrium of the blade relative to the vertical hinge (VH).

Occurrence of moments on NV.

When operating the NV, the following points arise:

The torque Mk, created by the aerodynamic drag forces of the blades, is determined by the parameters of the air force;

The reaction torque M p is applied to the main gearbox and through the gearbox frame on the fuselage.;

The torque of the engines, transmitted through the main gearbox to the NV shaft, is determined by the torque of the engines.

The torque of the motors is directed along the rotation of the NV, and the reactive and torque of the NV is directed against the rotation. Engine torque is determined by fuel consumption, automatic control program, and external atmospheric conditions.

At steady flight modes M k = M p = - M dv.

The NV torque is sometimes identified with the NV reactive torque or the torque of the engines, but as can be seen from the above, the physical essence of these moments is different.

Critical zones of flow around the NV.

With oblique blowing on the air blower, the following critical zones are formed (Fig. 12.14.):

Reverse flow zone;

Flow stall zone;

Wave crisis zone;

Reverse flow zone. In the area of azimuth 270 0 in horizontal flight, a zone is formed in which the butt sections of the blades flow around not from the leading edge, but from the trailing edge of the blade. The section of the blade located in this zone does not participate in creating the lifting force of the blade. This zone depends on the flight speed; the higher the flight speed, the larger the reverse flow zone.

Flow stall zone. In flight at an azimuth of 270 0 - 300 0 at the ends of the blades, due to the downward swing of the blade, the angles of attack of the blade section increase. This effect increases with increasing helicopter flight speed, because at the same time, the speed and amplitude of the flapping movement of the blades increase. With a significant increase in the pitch of the propeller or an increase in flight speed, a flow stall occurs in this zone (Fig. 12.14.) due to the blades reaching supercritical angles of attack, which leads to a decrease in lift and an increase in the drag of the blades located in this zone. The thrust of the main rotor in this sector decreases and when the flight speed is greatly exceeded, a significant heeling moment appears on the NV.

Wave crisis zone. Wave drag on the blade occurs in the region of azimuth 90 0 at high flight speed, when the flow speed around the blade reaches the local speed of sound, and local shock waves are formed, which causes a sharp increase in the coefficient C xo due to the occurrence of wave drag

C xo = C xtr + C xv. (12.18.)

The wave resistance can be several times greater than the friction resistance, and since shock waves on each blade appear cyclically and for a short period of time, this causes vibration of the blade, which increases with increasing flight speed. Critical flow zones around the main rotor reduce the effective area of the main rotor, and hence the thrust of the main rotor, and worsen the aerodynamic and operational characteristics of the helicopter as a whole, therefore, speed restrictions on helicopter flights are associated with the phenomena considered.

.“Vortex ring”.

The vortex ring mode occurs at low horizontal speed and high vertical speed of descent of the helicopter when the helicopter engines are running.

When the helicopter descends in this mode, at some distance under the NV a surface a-a, where the inductive rejection rate becomes equal to the rate of decrease V y (Fig. 12.15). Having reached this surface, the inductive flow turns towards the NV, is partially captured by it and is thrown down again. As V y increases, the surface a-a approaches the HB, and at a certain critical rate of descent, almost all of the ejected air is again sucked in by the main rotor, forming a vortex torus around the rotor. The vortex ring regime sets in.

Fig12.14. Critical zones of flow around the NV.

In this case, the total thrust of the NV decreases, and the vertical rate of decline V y increases. Surface section a-a periodically breaks, the torus vortices sharply change the distribution of the aerodynamic load and the nature of the flapping motion of the blades. As a result, the NV thrust becomes pulsating, shaking and pitching of the helicopter occurs, control efficiency deteriorates, the speed indicator and variometer give unstable readings.

The smaller the installation angle of the blades and the horizontal flight speed, the greater the vertical speed of descent, the more intense the vortex ring mode is manifested. reduction at flight speeds of 40 km/h or less.

To prevent the helicopter from entering the “vortex ring” mode, it is necessary to comply with the flight manual requirements for limiting the vertical speed

Introduction

Helicopter design is a complex process that evolves over time, divided into interrelated design stages and phases. Created aircraft must satisfy technical requirements and comply with the technical and economic characteristics specified in the design specifications. Technical task contains the initial description of the helicopter and its flight performance characteristics, ensuring high economic efficiency and competitiveness of the designed vehicle, namely: load capacity, flight speed, range, static and dynamic ceiling, service life, durability and cost.

The terms of reference are clarified at the stage of pre-design research, during which a patent search, analysis of existing technical solutions, research and development work are carried out. The main task of pre-design research is the search and experimental verification of new principles for the functioning of the designed object and its elements.

At the preliminary design stage, an aerodynamic design is selected, the appearance of the helicopter is formed, and the main parameters are calculated to ensure the achievement of the specified flight performance. These parameters include: the weight of the helicopter, the power of the propulsion system, the dimensions of the main and tail rotors, the weight of fuel, the weight of instrumentation and special equipment. The calculation results are used in developing the helicopter layout and drawing up a centering sheet to determine the position of the center of mass.

The design of individual helicopter units and components, taking into account the selected technical solutions, is carried out at the development stage technical project. In this case, the parameters of the designed units must satisfy the values corresponding preliminary design. Some parameters can be refined in order to optimize the design. During technical design, aerodynamic strength and kinematic calculations of components, selection of structural materials and design schemes are performed.

At the detailed design stage, working and assembly drawings of the helicopter, specifications, picking lists and other materials are prepared. technical documentation in accordance with accepted standards

This paper presents a methodology for calculating helicopter parameters at the preliminary design stage, which is used to complete a course project in the discipline "Helicopter Design".

Calculation take-off weight first approach helicopter

where is the mass of the payload, kg;

Crew weight, kg.

Range of flight

Calculation of helicopter rotor parameters

2.1 The radius R, m, of the main rotor of a single-rotor helicopter is calculated by the formula:

where is the take-off weight of the helicopter, kg;

g - free fall acceleration equal to 9.81 m/s2;

p - specific load on the area swept by the main rotor,

The value of the specific load p on the area swept by the propeller is selected according to the recommendations presented in work /1/: where p=280

We take the radius of the main rotor equal to R=7.9

The angular speed, s-1, of rotation of the main rotor is limited by the value of the peripheral speed R of the ends of the blades, which depends on the take-off mass of the helicopter and amounted to R=232 m/s.

2.2 Relative air densities on static and dynamic ceilings

2.3 Calculation of economic speed at the ground and on a dynamic ceiling

The relative area of the equivalent harmful plate is determined:

Where Se=2.5

The value of the economic speed at the ground Vз, km/h is calculated:

The value of the economic speed on the dynamic ceiling Vdin, km/h is calculated:

where I = 1.09…1.10 is the induction coefficient.

2.4 The relative values of the maximum and economic speeds of horizontal flight at the dynamic ceiling are calculated:

where Vmax = 250 km/h and Vdin = 182.298 km/h - flight speed;

R=232 m/s - peripheral speed of the blades.

Lifting force and thrust for forward movement of a helicopter are created using a main rotor. In this way, it differs from an airplane and a glider, in which the lift force when moving in the air is created by a load-bearing surface - a wing, rigidly connected to the fuselage, and thrust - by a propeller or jet engine (Fig. 6).

In principle, an analogy can be drawn between the flight of an airplane and a helicopter. In both cases, the lifting force is created due to the interaction of two bodies: air and an aircraft (airplane or helicopter).

According to the law of equality of action and reaction, it follows that with whatever force the aircraft acts on the air (weight or gravity), with the same force the air acts on the aircraft (lift).

When an airplane flies, the following phenomenon occurs: the oncoming oncoming air flow flows around the wing and is beveled down behind the wing. But air is an inextricable, rather viscous medium, and this bevelling involves not only the layer of air located in close proximity to the surface of the wing, but also its neighboring layers. Thus, when flowing around the wing, each second a fairly significant volume of air is beveled downwards, approximately equal to the volume of a cylinder, the cross-section of which is a circle with a diameter equal to the wing span, and the length is the flight speed per second. This is nothing more than the second flow of air involved in creating the lifting force of the wing (Fig. 7).

Rice. 7. The volume of air involved in creating the lift of the aircraft

From theoretical mechanics it is known that the change in momentum per unit time is equal to the acting force:

Where R - active force;

as a result of interaction with the aircraft wing. Consequently, the lifting force of the wing will be equal to the second increase in the amount of vertical motion in the outgoing jet.

And -velocity of flow slant behind the wing vertically in m/sec. In the same way, it is possible to express the total aerodynamic force of a helicopter's main rotor in terms of the second air flow rate and the flow shear velocity (the inductive speed of the outgoing air stream).

The rotating rotor sweeps away a surface that can be thought of as a load-bearing surface, similar to an airplane wing (Fig. 8). Air flowing through the surface swept by the rotor is, as a result of interaction with the rotating blades, thrown down at an inductive speed And. In the case of horizontal or inclined flight, air flows to the surface, swept by the main rotor at a certain angle (oblique blowing). Like an airplane, the volume of air involved in creating the total aerodynamic force of the main rotor can be represented as a cylinder, the base area of which is equal to the surface area swept by the main rotor, and the length equals the flight speed, expressed in m/sec.

When the main rotor operates at a standstill or in vertical flight (direct blowing), the direction of the air flow coincides with the axis of the main rotor. In this case, the air cylinder will be located vertically (Fig. 8, b). The total aerodynamic force of the main rotor will be expressed as the product of the mass of air flowing through the surface swept by the main rotor in one second and the inductive speed of the outgoing jet:

inductive speed of the outgoing jet in m/sec. It is necessary to make a reservation that in the considered cases, both for the aircraft wing and for the helicopter rotor, the induced speed And the inductive velocity of the outgoing jet at some distance from the bearing surface is assumed. The inductive speed of the air stream that occurs on the load-bearing surface itself is half as large.

This interpretation of the origin of wing lift or the total aerodynamic force of the rotor is not entirely accurate and is only valid in an ideal case. It only fundamentally correct and clearly explains the physical meaning of the phenomenon. Here it is appropriate to note one very important circumstance arising from the analyzed example.

If the total aerodynamic force of the rotor is expressed as the product of the mass of air flowing through the surface swept by the rotor and the induced velocity, and the volume of this mass is a cylinder whose base is the surface area swept by the rotor and whose length is the flight speed, then absolutely it is clear that to create a thrust of a constant value (for example, equal to the weight of the helicopter) at a higher flight speed, and therefore with a larger volume of ejected air, a lower induced speed and, consequently, less engine power is required.

On the contrary, to maintain a helicopter in the air while “hovering” in place, more power is required than during flight at a certain forward speed, at which there is a counter flow of air due to the movement of the helicopter.

In other words, with the expenditure of the same power (for example, the rated power of the engine) in the case of inclined flight with sufficient high speed a higher ceiling can be reached than with a vertical lift when the overall travel speed

there is less helicopter than in the first case. Therefore, the helicopter has two ceilings: static, when altitude is gained in vertical flight, and dynamic when the altitude is gained in inclined flight, and the dynamic ceiling is always higher than the static one.

The operation of a helicopter's main rotor and an airplane's propeller have much in common, but there are also fundamental differences, which will be discussed later.

Comparing their work, one can notice that the total aerodynamic force, and therefore the thrust of the helicopter rotor, which is a component of the force

Rin the direction of the hub axis, is always greater (5-8 times) with the same engine power and the same weight of the aircraft due to the fact that the diameter of the helicopter rotor is several times larger than the diameter of the aircraft propeller. In this case, the air ejection speed of the main rotor is less than the ejection speed of the propeller.

The amount of thrust of the main rotor depends to a very large extent on its diameter

Dand number of revolutions. When the screw diameter is doubled, its thrust will increase approximately 16 times; when the number of revolutions is doubled, the thrust will increase approximately 4 times. In addition, the thrust of the main rotor also depends on the air density ρ, the angle of installation of the blades φ (rotor pitch),geometric and aerodynamic characteristics of a given propeller, as well as the flight mode. The influence of the last four factors is usually expressed in the propeller thrust formulas through the thrust coefficient a t . .

Thus, the thrust of the helicopter rotor will be proportional to:

- thrust coefficient............. α r
It should be noted that the amount of thrust when flying near the ground is influenced by the so-called “air cushion”, due to which the helicopter can take off from the ground and rise several meters while expending less power than that required to “hover” at an altitude of 10- 15 m. The presence of an “air cushion” is explained by the fact that the air thrown by the propeller hits the ground and is somewhat compressed, i.e., it increases its density. The influence of the “air cushion” is especially pronounced when the propeller operates near the ground. Due to air compression, the thrust of the main rotor in this case, with the same power consumption, increases by 30-
40%. However, with distance from the ground this influence quickly decreases, and at a flight altitude equal to half the diameter of the propeller, the “air cushion” increases thrust by only 15- 20%. The height of the “air cushion” is approximately equal to the diameter of the main rotor. Further, the increase in traction disappears.
To roughly calculate the thrust value of the main rotor in hover mode, use the following formula:
coefficient characterizing the aerodynamic quality of the main rotor and the influence of the “air cushion”. Depending on the characteristics of the main rotor, the value of the coefficient A when hanging near the ground it can have values of 15 - 25.

The main rotor of a helicopter has an extremely important property - the ability to create lift in the self-rotation (autorotation) mode in the event of an engine stop, which allows the helicopter to make a safe gliding or parachute descent and landing.

The rotating main rotor maintains the required number of revolutions during gliding or parachuting if its blades are set to a small installation angle

(l--5 0) 1 . At the same time, the lifting force is maintained, ensuring descent at a constant vertical speed (6-10 m/sec), s subsequent reduction of it when leveling before planting to l--1.5 m/sec.

There is a significant difference in the operation of the main rotor in the case of motor flight, when power from the engine is transmitted to the propeller, and in the case of self-rotating flight, when it receives the energy to rotate the propeller from the oncoming air stream.

In motorized flight, oncoming air flows into the rotor from above or from above at an angle. When the propeller operates in self-rotation mode, air flows onto the plane of rotation from below or at an angle from below (Fig. 9). The slant of the flow behind the main rotor in both cases will be directed downwards, since the induced speed, according to the momentum theorem, will be directed directly opposite to the thrust, i.e. approximately downward along the axis of the main rotor.

Here we are talking about the effective installation angle as opposed to the constructive angle.

Introduction

Helicopter design is a complex process that evolves over time, divided into interrelated design stages and phases. The aircraft being created must meet the technical requirements and meet the technical and economic characteristics specified in the design specifications. The terms of reference contain the initial description of the helicopter and its flight performance characteristics, ensuring high economic efficiency and competitiveness of the designed machine, namely: load capacity, flight speed, range, static and dynamic ceiling, service life, durability and cost.

At the preliminary design stage, an aerodynamic design is selected, the appearance of the helicopter is formed, and the main parameters are calculated to ensure the achievement of the specified flight performance characteristics. These parameters include: the weight of the helicopter, the power of the propulsion system, the dimensions of the main and tail rotors, the weight of fuel, the weight of instrumentation and special equipment. The calculation results are used in developing the helicopter layout and drawing up a centering sheet to determine the position of the center of mass.

The design of individual helicopter units and components, taking into account the selected technical solutions, is carried out at the technical design development stage. In this case, the parameters of the designed units must satisfy the values corresponding to the preliminary design. Some parameters can be refined in order to optimize the design. During technical design, aerodynamic strength and kinematic calculations of components, selection of structural materials and design schemes are performed.

At the detailed design stage, working and assembly drawings of the helicopter, specifications, picking lists and other technical documentation are prepared in accordance with accepted standards

This paper presents a methodology for calculating helicopter parameters at the preliminary design stage, which is used to complete a course project in the discipline "Helicopter Design".

1. First approximation calculation of helicopter take-off weight

- payload mass, kg; -crew weight, kg. -range of flight

kg.

2. Calculation of helicopter rotor parameters

2.1Radius R, m, of the main rotor of a single-rotor helicopter is calculated by the formula:

, - take-off weight of the helicopter, kg;

g- free fall acceleration equal to 9.81 m/s 2 ;

p- specific load on the area swept by the main rotor,

p =3,14.

Specific load value p the area swept by the screw is selected according to the recommendations presented in work /1/: where p = 280

We take the radius of the rotor equal to R = 7.9

Angular velocity w, s -1, rotation of the main rotor is limited by the value of the peripheral speed w R ends of the blades, which depends on the take-off mass

helicopter and made up w R = 232 m/s.

s -1 .

rpm

2.2 Relative air densities on static and dynamic ceilings

2.3 Calculation of economic speed at the ground and on a dynamic ceiling

The relative area is determined

equivalent harmful plate: , where S uh = 2.5

The value of economic speed near the ground is calculated V h, km/h:

Where I

km/hour

The value of the economic speed on the dynamic ceiling is calculated V ding, km/h:

Where I= 1.09...1.10 - induction coefficient.

km/hour

2.4 The relative values of the maximum and economic speeds of horizontal flight on the dynamic ceiling are calculated:

Where Vmax=250 km/h and V ding=182.298 km/h - flight speed;

w R=232 m/s - peripheral speed of the blades.

2.5 Calculation of the permissible ratios of the thrust coefficient to the rotor filling for the maximum speed at the ground and for the economic speed at the dynamic ceiling:

Pripri