The strength of the helicopter structure. General requirements for the design of the elements of the main rotor An example of the calculation of the main rotor of a helicopter in tension
Introduction
Helicopter design is a complex process that develops over time, divided into interrelated design stages and stages. The created aircraft must meet technical requirements and comply with the technical and economic characteristics specified in the terms of reference for the design. The terms of reference contain the initial description of the helicopter and its performance characteristics, which ensure high economic efficiency and competitiveness of the designed machine, namely: carrying capacity, flight speed, range, static and dynamic ceiling, resource, durability and cost.
The terms of reference are specified at the stage of pre-project research, during which a patent search is performed, an analysis of existing technical solutions, research and development work. The main task of pre-design research is the search and experimental verification of new principles of functioning of the designed object and its elements.
At the stage of preliminary design, an aerodynamic scheme is selected, the appearance of the helicopter is formed, and the calculation of the main parameters is performed to ensure the achievement of the specified flight performance. These parameters include: the mass of the helicopter, the power of the propulsion system, the dimensions of the main and tail rotors, the mass of fuel, the mass of instrumentation and special equipment. The results of the calculations are used in the development of the layout scheme of the helicopter and the preparation of the balance sheet to determine the position of the center of mass.
The design of individual units and components of the helicopter, taking into account the selected technical solutions, is carried out at the stage of developing a technical project. At the same time, the parameters of the designed units must satisfy the values corresponding to the draft design. Some of the parameters can be refined in order to optimize the design. During technical design, aerodynamic strength and kinematic calculations of units are performed, as well as the choice of structural materials and structural schemes.
At the detailed design stage, working and assembly drawings of the helicopter, specifications, packing lists and other technical documentation are prepared in accordance with accepted standards
This paper presents a methodology for calculating the parameters of a helicopter at the stage of preliminary design, which is used to complete a course project in the discipline "Helicopter Design".
1. Calculation of the takeoff weight of a helicopter of the first approximation
- payload mass, kg; - mass of the crew, kg. -range of flight kg.2. Calculation of the parameters of the main rotor of a helicopter
2.1Radius R, m, the main rotor of a single-rotor helicopter is calculated by the formula:
, - helicopter takeoff weight, 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 for the area swept by the screw is selected according to the recommendations presented in the work /1/: where p = 280
m.We accept the radius of the main rotor equal to R = 7.9
Angular velocity w, s -1 , rotation of the main rotor is limited by the circumferential speed w R the ends of the blades, which depends on the takeoff weight
helicopter and made w R = 232 m/s. with -1 . rpm2.2 Relative air densities on static and dynamic ceilings
2.3 Calculation of the economic speed near the ground and on the dynamic ceiling
The relative area is determined
equivalent harmful plate: , where S uh = 2.5The value of the economic speed near the ground is calculated V h, km/h:
,where I
km/h.The value of the economic speed on the dynamic ceiling is calculated V din, km/h:
,where I\u003d 1.09 ... 1.10 - induction coefficient.
km/h.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 din\u003d 182.298 km / h - flight speed;
w R=232 m/s - peripheral speed of the blades.
2.5 Calculation of permissible ratios of the thrust coefficient to the filling of the main rotor for top speed near the ground and for economic speed on a dynamic ceiling:
pripri2.6 Main rotor thrust coefficients near the ground and at the dynamic ceiling:
, , , .2.7 Calculation of the filling of the main rotor:
Rotor filling s calculated for cases of flight at maximum and economic speeds:
; .As an estimated filling value s rotor, the largest value is taken from s Vmax and s V din .
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1. Initial data
To design an HB blade made of polymer composite materials of a rectangular shape in plan for an average multi-purpose helicopter with a takeoff weight of 2.5 tons, Table 1.
Table 1.
Helicopter takeoff weight |
mvzl |
2500 kg |
|
Peripheral speed HB |
wr |
200 m/s |
|
Radius HB |
rHB |
||
Maximum flight speed |
Vmax |
270 km/h |
|
Chordaloplasty |
0,318 m |
||
Blade extension |
|||
X ct section |
0,0765m |
||
Spar width |
0,143438m |
||
Profile thickness |
|||
Thickness c, m (12%) at r=0.5 - 1 |
0,03825 m |
||
Thickness c, m (15%) at r=0.4 |
0,0478 m |
||
Thickness c, m (17%) at r=0.3 |
0,0542 m |
||
Thickness c, m (19%) at r=0.2 |
0,0606 m |
The calculation of the spar and the butt joint of the blade is carried out for the action of the centrifugal force created during the rotation of the propeller on the values of wr. In order to equalize the field of inductive velocities along the main rotor disk and, accordingly, reduce the inductive losses of the HB, the blade is performed with a twist within 7 ... 10 °. Aerodynamic profile of the NACA 230 blade. Calculation of the tail section with honeycomb filler is carried out for the value of the distributed aerodynamic load on the characteristic section of the blade r = 0.7 with normal flow around the blade and the maximum flight speed of the helicopter. The calculation of the adhesive connection of the tail compartment with the blade spar is carried out for the value of the aerodynamic load acting at the junction of the compartment with the spar and acting on the tail compartment of the Coriolis force for the blade cross section r = 0.7.
The safety factors adopted in the design of the HB blade according to NLGV-2:
Main: f main \u003d 2.0;
Optional for connections: f aux. = 1.15;
Additional for RMB: f additional ..RMB = 1.25.
2. Technical description of the design
Structurally, the blade includes a large number of elements, which are subject to different requirements for strength, density, rigidity. These elements include the spar, the tail section of the blade (tail compartment), anti-abrasive protection, anti-icing system, docking unit with the propeller hub.
Spar blade- this is the main power element of the blade, perceiving a significant part of all mass and inertial loads acting on the blade. The spar is the connecting link for all elements of the blade. It is subject to a variety of static and variable (cyclic) force factors: tensile and compressive forces, bending and torque. These loads act in different planes and with different frequencies and amplitudes. The spar is made of fiberglass SK-2561 on a binder 5-211B. In order to ensure the desired centering in the front of the spar, a metal-composite counterweight is installed.
tail compartment The blades form the rear part of the airfoil. It is made in the form of a profiled honeycomb three-layer panel and perceives part of the power load (partially M izg and the shear force from the aerodynamic load), transferring them to the spar. bending of the tail panel of the stabilizer. Polymer calendered paper PSP-1 (3-OST1 00851-77) with a hexagonal cell shape (cell size 2.5 mm) was used as a honeycomb filler.
Anti-abrasion protection(Groove) blades include anti-abrasion stainless steel fittings and an abrasion resistant rubber coating. Rubber has a high resistance to sand erosion, but its resistance to water erosion is insufficient. Metals are inferior to rubber in resistance to sand erosion, but are superior to rubber in resistance to water erosion.
Anti-icing system electrothermalto protect the blade from icing installed on the blade . The main element of such a system is a heater that provides the required temperature on the surface of the blade. The supply of electric current for the operation of the heater is carried out through wires located in the toe of the blade. From the outside and inside the heater is closed with electrical insulating layers.
docking station is designed to fasten the blade and transfer loads from the blade to the hub. This joint is collapsible, i.e. operational. A two-bolt docking unit with a vertical arrangement of bolts is used on the blade. It is formed directly from the material of the spar with additional reinforcement by layers of cordon fabric and titanium foil. Docking washers and bushings are installed in the butt part.
The entire surface of the blade, except for parts made of stainless steel and rubber, is covered with a paint and varnish coating.
Anti-flutter weight serves to detuning from the bending-torsional flutter of the blade in the range of helicopter operating speeds.
3. Requirements for the unit
The blade must provide:
High aerodynamic perfection,
High static and fatigue strength over the entire service life range,
high resource,
High reliability.
Its design should ensure the absence of stress concentrators, sharp changes in stiffness. The blades must have stability of properties over time, be protected from damage during operation, but if they nevertheless appear, allow them to be repaired, i.e. be repairable. They must have a "soft" nature of the development of the defect that has appeared, excluding the avalanche-like development of the defect. External atmospheric influences (rain, hail, solar radiation, sea air, etc.) should not affect the performance of the blade. It should provide convenience in carrying out operational activities.
The unit must be designed so that in all permitted flight modes there is a certain margin before any kind of unstable operation (flutter, increased oscillations and vibrations due to stall from the blade, etc.). Blade deformations must not increase so much as to impair propeller aerodynamics, balance and controllability.
4. Determination of external loads on the unit
1) Scheme of loading of the spar of the HB blade
In flight, the spar of the blade experiences tension, bending in 2 planes and torsion. The largest load on the blade is the centrifugal force DR cb (Fig. 6.3). The centrifugal force causes tensile deformations in the spar and, as a result, normal stresses along the longitudinal axis of the blade. Since the speed of rotation of the main rotor changes little with time, the centrifugal force is considered a constant in time and is referred to as a static load. In addition to the centrifugal force, the HB spar is affected by time-varying cyclic loads with an oscillation period that is a multiple of one HB revolution. In the thrust plane, the aerodynamic thrust force DT acts and, due to the angular oscillations of the blade, the inertial force ДJ B . In the plane of rotation, the resistance force of the blade DQ and the inertial Coriolis force DJ k act. All these forces are variable along the length of the blade and over time.
In addition to forces, variable moments act on the spar relative to its longitudinal axis (Fig. 2). One of these points is the articulated M w. The second - the moment of inertia Min is a consequence of the angular oscillations of the blade relative to the axial hinge of the main rotor hub. The action of these moments causes the rotor blades of the helicopter to rotate.
Fig.2 The occurrence of a hinge moment on the blade.
spar helicopter blade
2) Scheme of loading the tail section of the blade.
The skin of the tail section of the blade perceives the aerodynamic load acting on the airfoil. This load causes normal stresses to appear in the skin. In addition, depending on the design of the fastening of the skin to the spar, additional normal and shear stresses may arise in it, which must also be taken into account when choosing the thickness of the skin. Since the aerodynamic load is variable along the length of the blade and over time, the shear force Q and moment M created by it tend to bend the tail compartment, up or down (Fig. 6.5).
In this case, normal stresses arise in the skin from the moment, and shear stresses arise from the shearing force in the skin and rib. The spar of the blade, bending in the plane of rotation, tends to lead the compartment.
In this case, additional stresses appear in the skin. When the spar is bent with the outer end along the radius forward (in rotation) in the middle along the radius part of the compartment in the areas perpendicular to the chord and parallel to it, compressive normal stresses arise, and tensile stresses occur at the ends of the compartment. When the blade is bent in the plane of stroke, stresses also arise in the skin.
5. Choice of structural-power scheme of the HB blade
The spar and the tail compartment are attached to each other with an adhesive joint. Concentrated forces perceive: the attachment point of the blade (reactions from centrifugal and aerodynamic forces). They are then transferred to the HB sleeve of the helicopter.
The blade spar is made in the form of a profiled layered shell of rotation with a cross-section variable along the span. When the spar is bent, the layers experience alternate tension-compression, therefore, local buckling of the thin wall of the spar in a dangerous section is possible, and critical buckling stresses are taken as destructive ones.
The tail section of the blade is designed as a profiled three-layer panel with a honeycomb core. When the compartment is bent, the upper and lower layers experience tension-compression, therefore, local buckling of the thin skin of the compartment in a dangerous section is possible, and critical buckling stresses are taken as destructive stresses.
The cross-sections of the elements of the attachment of the blade are selected according to the destructive stresses, and the margin of safety must be at least one.
6. Choice of design parameters
The design parameters should be:
a) Geometric parameters of the blade section (Fig. 3), (Table 2)
Table 2.
b) Mass parameters of composite blade elements (Table 3)
Table 3
7. Cases of loading
1. hover mode.
In this case, we perform a static calculation of the blade and determine the stresses,
acting on centrifugal force.
We calculate the butt part with docking nodes for strength.
2. Parking.
In this case, we determine the stresses acting in the blade in the parking lot from the forces of its own weight.
3. Level flight mode with maximum speed.
In this case, we rely on the strength of adhesive joints: spar - honeycomb filler, spar - skins of the tail panel.
Choice of parameters and strength calculation of HB blade.
The process of designing HB blades from PCM includes:
Choice of design scheme and blade material;
Determination of the required sections of the blade elements according to the requirements of static and fatigue strength;
Adjustment of the mass characteristics of the blade;
Blade detuning from resonance at operating speeds;
Ensuring reserves of aeroelastic stability of the blade;
Design of the butt joints of the blade and calculation of adhesive joints of the blade.
1. Static blade overhang [y] in the parking lot (the end of the blade should not touch the tail boom) should be: [y]< 0,1 r, r -радиуслопастиНВ;
a) the stresses acting in the spar from centrifugal forces must not exceed the allowable stresses:
at R< [у R] = 60 MPa;
b) the stresses acting in the spar in the parking lot from the forces of the own mass of the blade must not exceed the add. voltage:
at at< [ at y]= 70 MPa;
3. Necessary margin for flutter-type buckling: Hef=0.24b;
4. Ensuring restrictions on natural vibration frequencies.
For a helicopter blade, such a limitation is rather complicated due to the fact that the speed of the oncoming flow along the length of the blade is variable and there will be quite a lot of such resonant frequencies in the range of helicopter operation.
Choicematerial
Based on the operating conditions of the main rotor, as the main ones when choosing
the material of the blade parts made of PCM, the following requirements are put forward:
Fatigue strength, which manifests itself in crack resistance and low sensitivity to stress concentrators;
The invariability of the mechanical properties of the material of parts and their connections from
time and external operating conditions;
Technological and economic requirements.
For spar choose high strength fiberglassSK-2561based on cord fiberglass T25-(VM) on the binder 5-211B With
Tensile strength[ s-- +--]=--1500MPa,
Limiting shear stresses: [fWed] =48 MPa and
wrinkle: [ scm] =100MPa,
modulus of elasticity of the material E=55GPa,
Poisson's ratio m 12=--0,26,
density r-- =--2500kg/m 3,
can be operated at temperatures up to 1000 FROM.
For plating tail sectionchoose fiberglassT-10 on the binder 5-211B With
Compressive strength [ s-- ---]=--230MPa
Has a modulus of elasticity E=27GPa,
Poisson's ratio m 12=--0,11.
For cellularplaceholder applied polymer calendered paper PSP-1(3-OST1 00851-77) with a hexagonal cell size of 2.5 mm.
Elastic modulus E= 170MPa,
Density r-- =--42,1kg/m 3.
For adhesive joint honeycomb filler of the tail section with a spar choose gluecold curing PU-2, the adhesive has the ability to foam, increasing in volume, while filling the gaps in the range of 0.1 - 3 mm.
With the thickness of the glue line dto=--0,35mm
Has shear strength[ t-- ]shear=--18MPa,
Shear modulus G=--42MPa.
For gluing tail section plating to spar let's take hot curing glue VK-9. It is used for bonding steels, aluminum and titanium alloys to each other and to non-metallic materials. For radio engineering products, glue-and-thread connections. It is a viscous-fluid gray mass. Operating temperature range from minus 196° to 125°С.
Shear strength
Shear modulus
For bolts choose steel45G.The main advantage of this steel is its hardenability to large thicknesses.
The shear strength is [fWed] =370MPa.
8. Static calculation of the blade
The designed blade must meet the following requirements:
1. Ensuring a static overhang in the parking lot (the end of the blade should not touch the tail boom): .
2. Ensuring the requirements of static strength:
a) the stresses acting in the spar from centrifugal forces must not exceed the allowable stresses: .
b) the stresses acting in the spar in the parking lot from the forces of the own mass of the blade must not exceed the allowable stresses: .
3. Required margin for flutter-type buckling: .
hover mode.
Determination of stresses,operating in the section of the blade from centrifugal force
To calculate the blade, we use the model proposed by A.V. Nekrasov - finite element method. An undeformed blade is divided into 9 equal sections with sections perpendicular to its axis. The radius of each section, the length of all sections is the same and equal. The mass of the blade is concentrated at 8 points, which are interconnected by elastic elements that have constant rigidity within each section of the partition.
In each section of the blade, internal force factors act: bending moment M i, normal N i and cutting Q i strength.
For a given type of spar, according to the coordinates of the blade profile, characteristic theoretical sections are built in the program, which are simplified as consisting of the following structural elements: spar, honeycomb block, CW skin, anti-flutter load. For each theoretical section according to the drawing, the following parameters are determined:
P lounge, m - the perimeter of the longer on the middle line;
F lounge, m 2 - sectional area of the spar;
d lounge, m-thickness of the spar;
X c.t. lounge, Y c.t. lounge. , m - coordinates of the center of gravity of the spar;
F obsh., m 2 - area of \u200b\u200bplating CW;
X c.t. General. , m - coordinate of the center of gravity of the skin;
F honeycomb, m 2 - the area of the honeycomb block;
X c.t. honeycomb, m - coordinate of the center of gravity of the cell block;
X c.t. cargo, m - coordinate of the center of gravity of the anti-flutter load.
The mass of each element is calculated for i-of that theoretical section:
where With, kg / m 3 - the density of the material of the corresponding element, is given in the reference data;
----------------DR=R i+1-R i, m-distance between i-m and i+1 -m sections.
The calculation of the stresses acting in the section of the blade from the centrifugal force, we summarize in table No. 4.
Conclusion: The maximum stress on the spar at N \u003d 59.7 MPa, therefore N \u003d 59.7 MPa<[у N ]=60МПа. Требование по статической прочности выполняется.
9. Strength calculationnode of docking of the blade and sleeve
The joint between the blade and the bushing is an element of the "ear - fork" type connection, and the calculation of the unit for strength is reduced to the calculation for the strength of the docking holes in the butt part of the blade spar. The external force factor in the calculation is the centrifugal force of the blade.
For this type of connection "ear - fork" the blade is represented by the connection "ear" and the types of destruction are considered characteristic, in which the critical parameters are:
diameter of connecting bolts;
sectional area of the spar in the plane of the axes of the docking holes;
physical and mechanical characteristics of the materials of the connection.
Initial data for calculation:
"safety factor" for all design cases f = 2;
tensile strength: fiberglass foil: [ c] = 2.810 8 Pa;
ultimate stresses of bolt shear (steel 45G): [ c] b = 3.7 10 8 Pa;
ultimate shear stresses of fiberglass (T-25(VM)-78):
[ c] fiberglass = 1.4 10 8 Pa;
ultimate crushing stresses of fiberglass (T-25(VM)-78):
[ see] fiberglass = 4.4 10 8 Pa;
external force factor: centrifugal force of the blade N cb 56806.31N;
allowable pack collapse stress: pak = 0.8 10 7 Pa;
number of bolt shear planes: n cf =4
number of holes in the panel: n holes = 4
The parameters of the joint of the butt part of the blade are selected based on the centrifugal force acting on the blade.
Shear strength of connecting bolts.
Determine the diameter of the bolt for attaching the blade to the hub:
Condition shear strength of connecting bolts(Fig. 4, a) their sufficient diameter and, consequently, the diameter of the docking holes are determined. This condition is defined as
calc f [ in ],
where calc - calculated value of stresses "on a cut"; f- “safety factor”; [ c] - the limiting value of stresses "notched" for the material of the bolt.
Since the bolt is inserted into the sleeve, we add another sleeve size:
d=12.22+6=18.22 mm
bolt d =20 mm
margin of safety:
n=[ in ]/ calc f 1
[ calc ]= MPa;
2. Determine the thickness of the foil joint package
first approximation in the spar panel from the collapse conditions
Panel package thickness.
3. Determine the thickness of the foil.
A coefficient of 0.2 is 20% of the foil in the package, with this percentage, optimal joint parameters are obtained.
4. Determine the thickness of the cord.
Where is the number of foil layers.
The index "m" indicates that the value refers to the monolayer. For foil made of titanium alloy OT-4 a - for fabric T-25(VM)-78.
5. Determine the thickness of the spar.
6. Determine the thickness of the adhesive.
7. Determine the thickness of the foil joint package
second approximation in the spar panel.
13,809 mm
8. We define. We analyze:
a) If =0 - go to the definition of the geometry of the blade.
b) If >0 - add the number of layers of cord fabric.
c) If<0 - переходят к определению геометрии лопасти, используя в качестве толщины пакета значение.
<0 - переходим к определению геометрии лопасти, используя в качестве толщины пакета значение
We proceed to the determination of safety margins, using the value as the thickness of the package.
Breakaway strength of the butt of the blade(Fig. 4, b):
It depends mainly on the cross-sectional area of the spar in the plane of the axes of the docking holes. Strength condition in this case: calc f [ in ], where calc - calculated value of stresses in the operational case; f- safety factor; [ in ] rast is the limiting value of stresses for the material. And the magnitude of the acting stresses is calculated by the formula:
calc = Ncb / F.
Sectional area of the spar F sec required to use these formulas is determined by the formula:
where F ext.ct, F plst, F resp - respectively, the area of the outer contour of the spar, the cavity and the total area of the cross-sections of the holes in the spar.
Representing the areas as functions of the geometric parameters of the spar section, we obtain the formula in expanded form:
where b l, c l - respectively, the width and height of the spar in the considered section; c , n - thickness of the "wall" and "shelf" of the spar; n resp. d-number and diameter of holes for docking elements in the side member, respectively.
F sec \u003d 0.02541 m 2
calc = 34.165 MPa;
margin of safety
n= [ in] rast/ calc = 4.1
Strength onjumper breakout
When determining strength onjumper breakout(Fig. 4, c) use the condition expressed by the formula
where f- “safety factor”; n ps is the total number of cut planes; n - thickness of the "wall" of the spar in the section; b- jumper width, [ c] - limiting shear stresses for the material of the spar.
margin of safety
n=[ in ]/ calc f= 1,41
The strength of the assembly according to the condition of crushing the surfaces of the contacting parts(Fig. 2, d) is determined by the condition:
cm calc = f N CB/ n p cm P d [ cm ], |
where f- “safety factor”; n p cm is the total number of crushing surfaces; n is the height of the crushing surface; d-diameter of contacting surfaces; [ cm] - limiting crushing stresses for the material of the contacting parts.
see calc. = 155.025 MPa
margin of safety
n= [ cm ]/ calc = 1.42
Conclusion: the strength conditions of the joint between the blade and bushing are met.
Parking
Determination of the stresses acting in the blade for stoyanke from the forces of its own weight
The stresses acting in the blade in the parking lot from the forces of its own weight are calculated by the formula:
where M i, N. m - bending moment acting in i-m section of the lo-paw from the forces of its own weight. In the accepted model:
where is the length i-th section,
W x- moment of resistance to bending:
,
where I x-moment of inertia i- section relative to the axis of the main central axis X.
The deflection of the blade from its own weight in the parking lot is calculated by integrating the differential equation of the elastic line of the beam:
EI-blade stiffness.
In the adopted model, the deflection in i-th section is calculated by the formula:
where c i, rad - rotation angles of the current section, determined from the expression:
The calculation of the stresses acting in the blade in the parking lot from the forces of its own weight, we will summarize in table No. 5.
Conclusion: The stresses acting in the spar in the parking lot from the forces of the own mass of the blade do not exceed add. voltage:
at at = 39.9 MPa< [ at y]= 70 MPa
The maximum deflection of the blade from its own overhang is 0.292 m, which is much less than 0.1 r= 0,51m. The static strength conditions are met.
10. Horizontal Modeflying at maximum speed
Initial datafor calculation |
||||||
Definitionestimateddistributed load
The load is determined for the characteristic section of the blade (Fig. 5).
Where f=2 - safety factor,
S ots . =b L ots. - compartment area
S ots . \u003d b L ots \u003d 1143210 mm 2
c=1.226kg/m 3 - air density,
V-flow velocity on the characteristic section of the blade.
V floor \u003d 70m / s - Helicopter flight speed,
R 07 \u003d 0.7L-radius of the characteristic section of the blade
L = 5.1m - blade length,
w is the speed of rotation of the screw.
The load distribution along the chord is calculated for normal flow:
From the similarity of triangles we find:
With this load distribution, we get:
17134.169H
Moment due to aerodynamic load:
The maximum moment from the forces of the own weight of the blade according to the table:
M the weight = 347,852 Hm
M the weight
The calculated distributed load is determined by the aerodynamic load and the following is taken:
Tail compartment calculation
Strength under normal stresses in skins
1. As a first approximation, the skin thickness is selected.
2. The stresses in the skins arising under the action of the design load N are determined:
3. Critical stresses of the total buckling of the structure are determined:
= 110.815 MPa
L-The length of the tail section of the blade. D- Bending rigidity of the honeycomb structure. m t - coefficient of support of the structure.
= 0,314N m
5589743.59 N/m
h is the height of the placeholder. µ - Poisson's ratio of the skin material.
k- Shift parameter.
G xz - Shear modulus in the direction of greatest rigidity.
r is the size of the face of the hexagonal cell, d c is the thickness of the face of the filler, G m is the shear modulus of the filler material.
4459MPa
µ is here Poisson's ratio for the core material.
4. The values of normal stresses in the structure arising from the design load N are compared, and critical stresses total buckling. The condition must be met:
If the condition is not met, then the sheathing loses stability. It is necessary to increase the thickness of the skin, reduce the size of the cell face, increase the thickness of the cell face.
Aggregate shear stress strength
5. The shear forces in the aggregate are determined.
0,0151N/m
6. Shear stresses in the aggregate are determined.
MPa
7. Stresses of local buckling of the filler are determined.
8. The values of shear stresses and critical shear stresses in the aggregate are compared. The condition must be met:
If the condition is not met, then it is necessary to increase the thickness of the cell face and reduce the size of the cell face.
According to shear stresses in the skins
9. Shear stresses in the skins are determined.
123,99MPa
123299N/m
m c - coefficient depending on the shift parameter k (Fig. 6.)
10. Critical stresses of local buckling of the skin due to tangential load are determined.
871.82 MPa
11. The following condition is checked:
If the condition is not met, then the thickness of the skin should be increased.
Conclusion: The strength of the tail compartment is respected.
Adhesive calculationconnectionstail section with spar
initial datafor calculations |
|||
With honeycomb |
|||
With obsh. |
|||
E cell |
|||
Calculation of the adhesive connection of the tail panel skin with the spar
From the values of stresses from aerodynamic loads and stresses from deformations of the spar in the plane of rotation, one can find the shear stresses that occur in the adhesive layer used to glue the compartment to the spar. The calculation of the adhesive joint begins with the calculation of the loads coming to the tail section in the calculated section 1-1, see Fig. fig.7.
When connecting the spar with the tail section, we have 2 types of adhesive joints: 1) In an overlap - when the tail section skin is connected to the spar (zone A); 2) Butt - when connecting honeycomb block with a spar (zone B).
Calculation of the adhesive connection of the tail section plating with the spar
Calculation of the adhesive connection of the tail section plating with the spar is carried out in the following sequence:
1. Determine the bending moment in the design section 1-1:
Coriolis force:
Adhesive type selection
Choosing hot glue VK-9, used for bonding steels, aluminum and titanium alloys to each other and to non-metallic materials. For radio engineering products, glue-and-thread connections. It is a viscous-fluid gray mass. Operating temperature range from minus 196° to 125°С.
Determining the area of the adhesive joint
From the shift condition:
F- gluing area, m 2
Permissible stresses in the adhesive line, [MPa]
The stress concentration factor in the adhesive line.
Medium stresses in the adhesive line.
Calculation scheme of the lap adhesive joint (Fig. 8.):
Determination of average stresses in the adhesive line:
(spar fiberglassSK-2561);
(T-10 tail panel trim);
(thickness of the skin of the tail panel);
(thickness of the adhesive layer VK-9);
(adhesive layer shift module VK-9)
Required gluing area:
Required overlap length:
Accepted for technological reasons, taking into account the margin for fatigue failure
B= 14 mm
Checking the strength of the adhesive bond:
Calculation of adhesive connection of a honeycomb block with a spar wall
Average force in the adhesive joint:
Adhesive type selection
Choose gluecold curing PU-2. The adhesive has the ability to foam, increasing in volume, while filling gaps within 0.1 - 3 mm. We choose cold curing adhesive PU-2 due to the impossibility of heating in the joint zone, the adhesive has the ability to foam, increasing in volume, while filling the gaps within 0.1 -3 mm.
[f] shift = 18 MPa
Determining the area of the adhesive joint:
m 2
Determination of the stress concentration factor in the adhesive line:
0,358 MPa
(spar fiberglass SK-2561);
(paper BFSK);
(spar wall thickness in zone A);
(paper thickness);
(thickness of the adhesive layer PU-2);
(adhesive layer shift module PU-2)
MPa
Checking the strength of the adhesive bond
Conclusion: The strength condition for adhesive joints is fulfilled.
Analysis of calculations. General conclusions
From the calculations, the following safety margins were obtained? for the designed blade presented in Table 4.
Table 4
Safety margins for the tail section |
||
According to normal stresses in skins |
||
According to shear stresses in the aggregate |
||
According to shear stresses in the skins |
||
Safety margins for adhesive bonding |
||
For connecting the skin to the spar |
||
To connect the spar with the filler |
||
Safety margin for blade spar |
||
From the effect of centrifugal force |
||
Margins of safety for the butt attachment of the blade |
||
By bolt shear |
||
By separation of the butt of the blade |
||
Jumper breakout |
||
According to the condition of the crushing of the surfaces of the contacting parts |
General conclusion: the strength of the elements of the blade made of PCM, its connections and attachment point is observed. According to Table 4, the mass of the blade is 19.3 kg, which is significantly lower than the mass of similar metal rotor blades.
FROMlist of used literature
Basharov E.A., Dudchenko A.A. - Calculation of structures from PCM. Tutorial. M.MAI - 2014
Basharov E.A. -Design of Helicopter Units-Methodological Manual-M.MAI - 2016
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INTRODUCTION
The helicopter industry has traditionally been a leader in the use of composites. Recently, the share of their use in the design of the helicopter has increased significantly. The use of composites imposes additional requirements on the content of the designer's knowledge. The complexity of designing parts made of composites is due to the fact that the part and material are manufactured simultaneously. Therefore, along with the choice of an external shape that is optimal from the point of view of manufacturing a part, the designer must determine the structure of the composite that would be optimal for the selected shape of the part and best correspond to the action of external loads. To successfully solve this problem, the designer must know the properties of composites, methods for their calculation and methods for manufacturing structures from them.
At first glance, to obtain the best design, it is enough to make a mathematical model of the designed object and find its optimal parameters according to one or several pre-selected efficiency criteria. However, there are fundamental difficulties that do not allow us to solve this problem correctly enough. Firstly, the determination of the optimal design parameters is possible only for a given structural-power scheme, while the question of the optimality of the scheme itself remains unresolved. Secondly, it is not always possible to formalize all the restrictions and requirements for the design when building a mathematical model. The choice and definition of a complex optimization criterion is also a rather complex and ambiguous task in its solution. Therefore, the above design issues are usually resolved sequentially, in the order of a certain subordination.
Significant progress in improving the design process is achieved with the transition to CAD/CAM/CAE technologies. The wide range of design automation tools available in them allows not only to reduce the time for designing and producing a product, but also to improve the quality of the design in many respects.
The aim of this thesis project is:
– optimization of the design of the spar of the main rotor blade of the helicopter. The selection of the optimal design will be carried out using a personal computer and the Solid Works application;
- evaluation of the possibility of using the Solid Works application as a tool for computer-aided design (CAD) of CM structures.
HELICOPTER ROTOR
General requirements for the design of rotor elements
The general requirements for the design of the elements of the NV are contradictory and the design of the helicopter carrier system is a difficult task of finding a compromise between them. Requirements can be divided into the following groups.
aerodynamic requirements. The relative position of the NV parts, its shape and parameters must ensure high flight performance. The design of the blades must provide the specified characteristics of the aerodynamic contour and balancing within the limits that allow the helicopter to be operated, taking into account the established limitations, resources and service life.
strength requirements. All elements of the helicopter structure must withstand all types of loads in accordance with the helicopter airworthiness standards, which provide for various cases of loading of helicopter parts.
According to the types of loads, the elements of the main rotor should be designed taking into account the static, fatigue strengths and their combination. Also, in view of the fact that the HB blade is a long-length structure, it is necessary to take into account the strength of the stability of the structure.
The static strength of the structure is tested under large, infrequently acting loads. In this case, the calculation and selection of design parameters is carried out according to the breaking load Рrazr. which should exceed the operational Re by a certain number of times. This number is called the safety factor f. For aircraft structures, it is customary to choose f equal to 1.5. An excessive increase in the value of this coefficient leads to an increase in dimensions and weight, which is unacceptable for the design of the aircraft. For each helicopter unit and a specific case of its loading, the recommended values of the safety factors are given in the "Aviation Rules". The initial stage in determining the dimensions of a part is a design calculation for allowable stresses. The dimensions of the sections of the part are calculated in such a way that the stresses acting in them from the design load ur are equal to the allowable stresses [y], [f]. As allowable stresses, the strength limits y v, f v or yield strength y t are taken, depending on the nature and conditions of loading the structure. Certain difficulties arise when choosing the allowable stresses in parts made of composite materials, due to the nature of their destruction. Figure 1.1 shows a diagram of stress changes depending on the elongation of a sample of unidirectional fiberglass when a load is applied along the reinforcing fibers.
At the beginning of loading, up to a certain moment, the material retains its integrity and behaves as elastic, obeying Hooke's law: y = E·e. After reaching the stresses corresponding to point 1 (Figure 1.1), small cracks appear in the binder at the media interface. The reinforcing elements here are not destroyed, and the structure does not lose its load-bearing properties. Moreover, for some materials, an increase in stiffness is observed. At the second stage (Figure 1.1, point 2), significant cracks appear along the reinforcing elements, but the fibers are not damaged. The design still retains load-bearing properties. In the third stage (Figure 1.1, point B), the reinforcing threads are torn, and the material is completely destroyed. If the allowable stresses under the action of maximum operational loads are chosen corresponding to the last stage of destruction (cf), then it may turn out that under the action of nominal loads the material will be in the first or second stages of destruction. This is unacceptable, since under repeated loads, cracks in the structure will grow, accelerating its destruction. Therefore, the strength of parts made of composite materials should be evaluated both at maximum and at nominal operating loads. In some cases, this contradiction is overcome by choosing a large value of the safety factor f = 2.0-2.5 and underestimating the allowable stresses in the composite to the level of 2/3uv when calculating the structure for the ultimate bearing capacity.
Figure 1.1 - Diagram of changes in stresses y depending on the elongation of the sample e of unidirectional fiberglass, where y1 and e1 are stress and strain according to Hooke's law; y2 - stress of the appearance of significant cracks without damaging the fibers; uv - sample fracture stress; 1 - proportional limit point; 2 - point; characterizing the beginning of the accumulation of cracks; B - destruction of the composite
When calculating the spar according to the conditions of static strength (for the case of a blade falling on the overhang limiter), the condition is set that the calculated stresses in the layer do not exceed y1. This is done in order to prevent microcracks even under static, short-term loading. In the future, they can lead to a decrease in fatigue strength under the action of cyclic loads. With this approach, the main rotor blade acquires a long resource, limited not so much by the fatigue characteristics of the original material as by other factors, for example, its natural aging time.
The calculation of a structure working for stability is carried out according to breaking loads and is reduced to determining the critical buckling force Рcr, which should not be less than the calculated Рр.
Fatigue failures are the main type of destruction of the mechanical units of the helicopter and often lead to severe consequences. The fatigue characteristics of composite materials are influenced by many factors. Among the main ones: the composition and structure of the material, temperature, ambient humidity, type of loading. Therefore, for each sample of material that is supposed to be used in the structure, it is necessary to carry out a full cycle of fatigue tests. The fatigue strength of composites, like that of metals, is assessed by fatigue curves. There is a direct relationship between the fatigue and static characteristics of the composite. The higher the static strength of a material, the better it resists fatigue.
The practice of using composites in structures has shown that their service life under conditions of variable high-cycle loads significantly exceeds the service life of similar structures made of metals. In particular, the resource of a blade made of polymer composites is limited not so much by the possibility of fatigue failure, but by a change in the physical and mechanical properties of blade parts and their adhesive joints during long-term operation and storage due to aging and brittleness.
rigidity requirements. Due to the susceptibility of the HB blade to alternating loads, as well as cases of significant static loading, the blade design must have the necessary rigidity to prevent residual deformations and maintain the specified aerodynamic profile of the blade surface. The result of low bending and torsional rigidity can be a loss of helicopter control efficiency, when due to bending and twisting of the aerodynamic surface under the influence of external forces, uncontrolled changes in installation angles and, accordingly, angles of attack along the length of the blade appear. Insufficient flexural and torsional stiffness can cause unacceptable aeroelastic phenomena such as flutter and divergence.
Reliability requirement. The main requirement for a helicopter and its structures is reliability - the ability to perform its functions while maintaining flight and operational performance within the specified limits for a specified period of time. The design of the elements of the helicopter NV, the values of their strength, stiffness, mass, resource must ensure the reliability of operation under specified operating conditions and cases of abnormal loads.
Design manufacturability. The design of the elements of the helicopter NV should provide the possibility of using progressive and economical technological processes.
Mass perfection. For aircraft structures, the requirement of a minimum mass is mandatory, of course, subject to strength and rigidity. Since the HB blade and its constituent elements (spar, fasteners) are power elements, the main way to reduce the mass is the choice of a rational structural power scheme, the use of structural materials with high characteristics of relative strength and relative rigidity. However, the mass of the blade must provide the necessary inertial characteristics for safe flight in the rotor autorotation mode, and also correspond to the values necessary to eliminate aeroelastic phenomena (flutter, divergence).
The optimal weight of the structure can be achieved by competent design.
Structural durability. Durability is the total time (usually calculated in years) of the structure's operation in the nominal mode under normal operation conditions without a significant reduction in the design parameters at an economically acceptable total cost of repairs. The durability of helicopter units, especially those with power parts and assemblies, is largely determined by the value of their resource.
The resource is the operating time of the unit (calculated in hours) from the start of operation until the onset of the limit state, after which there is a possibility of its destruction. For most of the main units of the helicopter (blades and bushings of the main and tail rotors, propeller control systems, transmission, gearboxes, under-gear frame, etc.), a resource is established according to the fatigue strength conditions.
There are two ways to design aircraft structures for endurance under variable loads: design according to the principles of "safe resource" and "safe damage".
When assigning a safe resource, it is assumed that during the development of the specified service life, no fatigue cracks will occur in any of the parts of the series under consideration.
In a structure with safe damage, cracks in individual structural structural elements are allowed, however, cracks should not lead to destruction or excessive deformation of the entire structure. This is achieved by choosing a type of structure where possible failure or fatigue cracks will only reduce to some extent the static strength and stiffness of the structure sufficient to complete the helicopter's accident-free flight. The increase in allowable stresses in structural elements with safe damage can be 15-20% compared to the corresponding stresses accepted for a safe service life structure. The benefit of using failsafe designs is to reduce the weight of the product, increase the service life and reduce its cost.
An effective way to ensure safe damage is to use "redundant" structures with several load transfer channels. An example of such a solution is a main rotor blade with a multi-spar shown in Figure 1.2.
Figure 1.2 - Blade compartment with a multi-circuit spar
When using composite materials in the design of NV, design is often used according to the principle of safe damage.
List of symbols
Introduction
1. Chapter 1. Overview of the current state of the problem
1.1 Blade deformation equations. Basic assumptions. Coordinate systems
1.2 Distribution of inductive speeds on the main rotor
1.3 Calculation of the butt section of the blade
1.4 Methods for solving the equations of blade deformations
Conclusions to chapter 1
2. Chapter 2. Development of the calculation method
2.1 Description of the calculation method
2.2 Transformation of the original system of equations
2.3 Solving the system of equations
2.4 Specifying boundary conditions
2.5 Transformation of the terms of the equations of aerodynamic load on the blade
2.6 Modeling the butt section of the blade
2.7 Modeling dampers
2.8 Calculation algorithm
Conclusions to chapter 2
3. Chapter 3. Study of elastic oscillations of the helicopter main rotor blade
3.1 Initial data
3.2 Natural vibrations of an undamped system
3.2.1 Vibrations of a non-rotating cantilever beam
3.2.2 Studies of free oscillations of a non-rotating blade
3.2.3 Studies of free oscillations of a rotating blade
3.2.4 Research of joint free flexural-torsional vibrations of a rotating blade
3.3 Study of forced oscillations
3.3.1 Study of the steady state. Level flight mode
3.3.2 Study of the stationary regime. hover mode
Conclusions to chapter 3
4. Chapter 4. Application of the calculation method for solving practical problems of designing the helicopter carrier system
4.1 Investigation of the inherent characteristics of the Mi-8 helicopter blade, pivotally suspended in a horizontal hinge, when it falls on the overhang limiter
4.2 Study of the inherent characteristics of the Mi-8 helicopter blades operating in the SLE8 system
4.3 Study of the maneuvering mode "hill"
4.3.1 Problem statement
4.3.2 Results of maneuver calculation by direct integration method
4.3.3 Comparison of the results of the calculation of the maneuvering mode with the results obtained by the quasi-stationary method
Conclusions to chapter 4
Conclusion
Literature
List of symbols
x0, y0, r0 - fixed coordinate system associated with the hub center x1, y1, r1 - rotating coordinate system associated with the hub center x, y, z - coordinate system associated with the hub sleeve of the corresponding blade
x2,y2,r2 - coordinate system associated with the blade section
x3, y3, z3 - coordinate system associated with the main axes of the blade section
y/ - blade azimuth, rad
w - angular speed of rotation of the sleeve, rad/s
e0 is the distance between the y and y axes<пм
хр, yr - coordinates of the tension center in the x3, y3 axes, m
xm, ym - coordinates of the center of gravity of the section in the axes x3, y3, m
xzh - distance of the stiffness axis from the tip of the blade, m
b - blade chord, m
y(ghLo) - free stream velocity and its components, m/s
ab - propeller angle of attack, rad
(p - installation angle of the blade section, rad
c - angle of twist of the blade due to its torsion deformation and distance, rad
prime - derivative with respect to z or with respect to z
the dot above the letter is the time derivative
ax, ay, ar - linear acceleration of the blade point, m/s2
px, ru, rg - components of the linear load in the sections of the blade, kg
Components of linear moments in blade sections, kg-m
p is the density of the material from which the blade is made, kg-m
^ - blade cross-sectional area, m
linear weight of the blade, kg - s / m
1w, 1m - linear mass moments of inertia of the blade relative to the axes x, and
Uz > kg-s
/=/+/- linear mass moment of inertia of the blade relative to the axis
hardness, kg-s
r - coordinate 2 of the center of rigidity of the section of the undeformed blade, m u = r-r - displacement of the center of rigidity of the section of the undeformed blade along the axis z, M R - radius of the screw, m
Е1х, Е12 - bending stiffness of the blade, kg-m2
01 k - torsional stiffness of the blade, kg-m2
E, C - tension and shear moduli for the blade spar
y - Poisson's ratio
N - tensile force in the blade section, kg
/ - polar moment of inertia of the section working in tension,
relative to the axis of rigidity, m
^ - cross-sectional area, working in tension, m
c - angle of twist of the blade section due to its stretching, rad
0izg - angle of rotation of the blade section due to bending, rad
yy, gy, state offsets of the horizontal, vertical and axial hinges, m
Квм - coefficient of the blade stroke compensator around the horizontal
P - circular frequency of natural oscillations of the blade, number / min a-rg
L ^ ^ > ^ y -components of linear gyroscopic forces and moments
x (r, y (r, (), v (r,?) - blade deformation, m
Md - moment of the damper of the vertical hinge, kg - m
Mpred - the maximum moment developed by a vertical hinge damper with a non-linear characteristic, kg-m
% 7 - azimuth-average value of the installation angle of the undeformed blade at the relative radius of the blade r = 0.7, rad
BUT<р - закрутка сечения недеформированной лопасти относительно сечения г = 0,7, рад
ae - longitudinal deviation of the swash plate (positive - for pitching), rad
d] - transverse deflection of the swash plate (positive - towards the incoming blade), rad
Vap - vertical displacement of the swash plate, m Ay/ap - azimuthal position of the blade control rod at y/ = 0 relative to the xap axis passing through the longitudinal control rod of the swashplate, rad
Yaa, 1, - arms of the blade control rod relative to the axis of the propeller shaft and the axis of the axial hinge of the blade, m
y/ap = (// + D|//pn - blade azimuth relative to the xap axis, rad 2h - number of blades b - blade chord, m p - air density, kg - m3
Wp - normal to the blade axis component of the flow velocity, m/s q - linear aerodynamic damping moment on the blade, kg - mxx =xx/b - relative distance of the stiffness axis from the blade toe Msh - hinge moment of the blade, kg-m
^m "Mhap" M-ap" force and moments acting on the swashplate from the side of the blades
M, M, M - components of the moment acting on the screw, relative to
fixed axes of the bush x0,y0,z0, kg-m
Tu, Tx - lifting and propulsion forces of the main rotor in high-speed axes, kg MVM2 - bending moments in the blades relative to the main axes,
passing through the center of tension, kg - m
G \u003d l 117 - filling factor of the screw l
b0 7 - blade chord per g - 0.7, m
G, =-, Gn =^2- - bending stresses in the blade, kg/m2
WY, W2 - blade resistance moments when bending in the planes of the lowest and highest stiffness, m3
X - sweep angle of the leading edge of the blade, deg a - angle of attack of the blade section, deg
vy - axial component of the velocity inductance in the plane of the screw (o0 > 0-up), m/s
o0 - the average value of the speed inductance over the propeller disk (u0 > 0 - down), m / s Kl - coefficient taking into account the variability of the speed inductance along the rotor disk
I = Vsmai>-. percolation coefficient coR
c \u003d - b - - mode characteristic
Crr = -t - thrust coefficient
G p7iR2(a>R)2
B - end loss coefficient
сх,с,тп_ - aerodynamic coefficients of resistance, thrust and longitudinal
profile moments
M \u003d --- number M for the blade section
a - speed of sound, m/s2
W - full speed of the flow on the blade, m/s
Рх2а, Ру2а, Р:2а - components of linear aerodynamic force along the axes x2, y2, r2, kg
Rsh, Rua, P:a - component of linear aerodynamic force along the axes x, y, z, kg tska - linear torque from aerodynamic forces, kg-m hf - distance of the reference point of the aerodynamic moments of the blade from the stiffness axis (Хf > 0, if moment reference point is ahead of the stiffness axis), m
screech - rotation of the blade section, caused by its bending in two planes, rad
Introduction to the thesis (part of the abstract) on the topic "Study of the load and strength of the rotor blade of a helicopter in maneuvering and unsteady modes"
Introduction
The carrier system of helicopters is the main unit that ensures the existence of a helicopter as an aircraft with vertical takeoff and landing and does not require specially prepared runways. It is its trouble-free operation that ensures the safety of the helicopter flight in all expected operating conditions, including unsteady modes, such as takeoff, acceleration, landing and maneuvers. The design process and the provision of specified resources require the availability of calculation methods and applied mathematical software to determine the loads on the units of the carrier system and calculate its dynamics, both at the design stage and during flight and certification tests.
The main rotor of a helicopter determines its flight characteristics, stability and controllability. The presence of a main rotor can lead to phenomena such as earth resonance and flutter. It is a source of vibrations and variable loads in the power elements of the helicopter structure. Therefore, the calculation of the main rotor is the most important task in the design of a helicopter.
The rotor blade works under the combined action of aerodynamic and centrifugal forces, bending and torque. In the general case of forward flight, the distribution of the external load on the blades depends on its azimuthal position, as well as on the movement of the helicopter in space. Therefore, the calculation of the main rotor blade is a complex task, for the solution of which it is necessary to consider the entire range of flight modes that arise during the operation of a helicopter.
Calculation of loads on the blades of helicopter propellers in maneuvering modes is one of the most important tasks in the design of helicopter bearing systems,
since high stresses in the design of the blade in these modes significantly affect their resource. Currently, to calculate the loads in these modes, a quasi-static method is used, when at each moment of time the main rotor operating mode is considered to be steady. This approach does not provide high accuracy of calculations, because does not take into account the real dynamics of the main rotor blade. Thus, the creation of a method for calculating the rotor blades for maneuvering and transient modes will improve the reliability of calculating the loads of the helicopter carrier system, and clarify the resources of the carrier system units.
The maneuvering and transient modes of operation of the main rotor are non-stationary. Finding a solution to the equations of blade deformations for such a problem by approximate methods, such as the method of B.G. Galerkin ,, is not possible, due to the impossibility of setting the external load function as periodic. It is most expedient to solve this problem using the method of direct integration.
In this regard, the task of developing a generalized method for calculating the rotor blades of a helicopter, which makes it possible to calculate both steady and unsteady flight modes (maneuverable, transitional) and obtain more accurate results compared to existing methods, is very relevant.
Thus, the general problem of oscillations of the main rotor blades with an arbitrarily given distribution of loads along their length at each moment of time is solved.
A feature of the developed technique is also that all rotor blades are analyzed simultaneously, which makes it possible to obtain instantaneous values on the rotor at each moment of time, while, for example, in the work, the thrust value was taken as an average per revolution of the propeller. This circumstance improves the accuracy of calculations.
The validity of the scientific provisions and the reliability of the results obtained are confirmed by the use of certified software environments (Excel, Visual basic) in the development of the solution algorithm, the use of the apparatus of higher mathematics, theoretical mechanics and the theory of elasticity. The obtained results were compared with the solutions obtained in the certified software environment MSC Patran/Nsactran, with existing exact solutions and solutions obtained by other authors.
The RNV program is designed to obtain the values of stresses in the sections of the main rotor blades in any flight modes, including maneuvering ones;
The MF program allows you to obtain blade deformations during its own oscillations.
The eigenfrequencies and blade shapes were obtained from the deformations found in the MF program, transformed by the spectral analysis method. For this, a program developed by V.A. Ivchin, which implements the fast Fourier transform algorithm.
Chapter 1 of this work contains an overview of the existing methods for calculating the blades used in the practice of designing helicopters, some theoretical aspects of the calculation are given, the equations of blade deformations taken as initial assumptions are given, boundary conditions are formulated. Based on the analysis of the state of the problem, the purpose and objectives of the study are formed.
Chapter 2 is devoted to the description of the method for solving the equations of blade deformations. It formulates the accepted assumptions due to the chosen method, describes the transformation of the original system
of the blade deformation equations, according to the proposed method, the boundary conditions are written.
Chapter 3 is devoted to substantiating the reliability of the developed methodology. It deals with the problems of own and forced vibrations of the blade. For example, the blade of the Mi-8 helicopter was considered. To study the natural oscillations of the blade, a number of problems are considered, the solution of which is compared with known exact solutions, with the results obtained by other authors, with the results obtained in a modern finite element package. The problem of forced oscillations of the blade is considered for the modes "horizontal flight" and "hovering". Due to the lack of data, a general analysis of the obtained solution is made for the "hovering" mode. The steady state problem is a special case for the problem studied in this paper. Therefore, the solution obtained in the work for the steady state "horizontal flight" mode is used to confirm the correctness of the developed methodology. Studies have been carried out on the influence on the calculation results of methods for calculating the inductive speed along the main rotor disk. Two methods for calculating inductive velocities are considered: the Glauert-Locke method based on the impulse theory used in the work and the Mangler-Squire method based on the disk theory used in the work.
Chapter 4 is devoted to the study of a number of problems using the developed methodology. Using the developed MF program, the author of this work, together with V.A. Ivchin, studies were carried out developed at JSC "MVZ them. M.L. Mile" of the ZIEB system. This system was proposed by V.M. Pchelkin and N.S. Pavlenko to reduce the load on the control system of a single-rotor helicopter and involves pinching the blade in the horizontal hinge, depending on its azimuth position. As an example, the blade of the Mi-8 helicopter was considered. Also, with the help of the SC program, the problem
calculation of own characteristics of the blade of the Mi-8 helicopter hinged in the horizontal hinge, when it falls on the overhang limiter. With the help of the developed RNV program, the problem of calculating the blade in the “hill” maneuvering mode was studied. The calculation results are compared with the results obtained on the basis of the quasi-static method.
The results of the research have shown that the developed technique is applicable both to the analysis of the rotor blades of helicopters operating in steady-state conditions, and to the calculations of blades operating in transient and maneuvering conditions.
The work contains a list of used literature, including 53 titles. The volume of the main text is 137 pages. The results of the work are presented in the articles , , .
Similar theses in the specialty "Strength and thermal conditions of aircraft", 05.07.03 VAK code
Calculation of the stress-strain, limit state and damping characteristics of elements of composite structures of the helicopter carrier system 2014, candidate of technical sciences Gorelov, Alexey Vyacheslavovich
Dynamic models of a gyroplane and standardization of structural loading conditions 2005, candidate of technical sciences Kalmykov, Alexey Aleksandrovich
Dynamics and strength of an autorotating rotor 2003, candidate of technical sciences Polyntsev, Oleg Evgenievich
Improvement of the Aeroelastic Characteristics of an Aircraft with a Large Aspect Wing 2008, Candidate of Technical Sciences Mazutsky, Andrey Yurievich
Methods for expanding the scope of ultralight and very light helicopters 2013, Doctor of Technical Sciences Dudnik, Vitaly Vladimirovich
Dissertation conclusion on the topic "Strength and thermal conditions of aircraft", Averyanov, Igor Olegovich
In accordance with the goals and objectives set within the framework of the dissertation work, the following was done:
1. Based on the equations of blade deformations, a mathematical model of the helicopter carrier system was developed, taking into account the simultaneous operation of all rotor blades, taking into account the blade deformations in the thrust, rotation and torsion planes, and reflecting the actual behavior of the blades in steady and unsteady flight modes.
2. An algorithm has been developed for calculating the parameters of the proper motion of the blade, which allows solving problems with various boundary conditions, including those that change during the revolution of the main rotor.
3. Studies of the specific tasks of designing a helicopter main rotor to determine the parameters of the proper movement of the blade were carried out, using the example of the structures of the SLE8 carrier system and the case of a blade falling on the overhang limiter (described in P-2 NGLV), which showed that a reliable solution to such problems can be obtained only with the use of the method of direct integration of the equations of deformations of the blade. Based on the results of the research, it can be concluded that the developed algorithm for calculating the parameters of the proper motion of the blade makes it possible to obtain reliable results.
4. An algorithm has been developed for calculating the stress-strain state of a blade operating under conditions of both steady and unsteady flight modes, which makes it possible to calculate the loading and stress values in the blade at each moment of time.
5. Studies of the tasks of the operation of the main rotor of a helicopter in steady state conditions were carried out using the example of the "level flight" and "hover" modes, which showed the correspondence of the results obtained by the developed method to the existing solutions of other authors, as well as to existing theories and experimental results. Based on the results of the research, it can be concluded that the developed algorithm for calculating the stress-strain state of the blade makes it possible to obtain reliable results and improve the accuracy of calculations. 6. A study of the problem of the operation of the main rotor of a helicopter under conditions of an unsteady regime was carried out using the example of the maneuvering mode "hill", which showed the correspondence of the obtained results to experimental data. The comparison with the quasi-static method for solving this problem showed that the quasi-static method underestimates the results with rapidly changing characteristics of the flight mode. This allows us to conclude that the developed method for calculating the load and strength of rotor blades can significantly improve the accuracy of calculations.
Conclusion
On the basis of the conducted studies, it can be concluded that it is necessary to use the developed methodology and calculation algorithm in the design of helicopter load-bearing systems, especially in the analysis of maneuvering flight modes.
List of references for dissertation research Candidate of Technical Sciences Averyanov, Igor Olegovich, 2012
Literature
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On the fatigue strength of a helicopter main rotor blade under the action of wind loads
A.I. Bratukhin
The article is devoted to the issue of stresses in a non-rotating blade and rotor hub of a helicopter under the action of wind loads. The assumption is made that the helicopter is parked and its propeller does not rotate. The calculation was carried out for a main rotor with hinged blades. The problem of natural and forced oscillations of a helicopter blade is solved. Deformations and internal forces (bending moments and stresses in the blade spar) are determined. The analysis of the results was carried out and the influence of the mooring of the blade in ground operating conditions was assessed.
In this paper, the cases of loading of the structural elements of the blade and hub in ground conditions are considered. The need for such calculations always exists, due to the constant damage to the propellers during operation of the helicopter on the ground.
The need to consider ground loading cases for a helicopter is confirmed in the "Airworthiness Standards for Civil Helicopters", as well as certification requirements imposed abroad.
The problem of determining deformations and internal forces (bending moments and stresses) in the spar of a helicopter main rotor blade under the action of wind loads is considered. It is assumed that the helicopter is parked and its propeller is not rotating. At some point in time, a gust of wind acts on the blade. Under the action of a gust of wind on the blades, an aerodynamic lifting force arises, which, depending on the direction of its action, lifts the blade up or presses it down. As a result, the blade performs forced vibrations in the vertical plane, and the spar is loaded with a bending moment, acting mainly in the plane of least rigidity.
The calculation was carried out for a main rotor with hinged blades.
The movement of the blade relative to the horizontal hinge occurs freely up to a certain position, characterized by the angle of the overhang limiter (Fig. 1a). After that, the movement of the blade can occur only due to its elastic deformations. Thus, if the blade oscillating under the action of an external load is above the OR line, then its movement is described by the design scheme shown in Fig. 1b. After point A of the butt of the blade has reached the stop of the overhang limiter, its further movement should be described by the diagram shown in Fig. 1c. For a moored blade, the design scheme corresponds to Fig. 1g
Small vibrations of a non-rotating rotor blade of a helicopter are described by a partial differential equation:
. (1)
In the equation: - displacement of the blade section in the plane of least rigidity; - bending stiffness of the blade section relative to the main axis, which lies in the plane of the chords; - external distributed load:
, (2)
Linear weight of the blade;
Gravity acceleration.
After substituting (2) into (1), we obtain
(3)
We represent the solution of equation (3) as an expansion into a series in terms of eigenmodes :
, (4)
where is the number of proper forms taken in the calculation;
Shape - th tone of natural vibrations of the blade in the void, which is a function of its radius;
Some functions of time (strain coefficients).
Eigenforms are determined from differential equation (3) when its right side is equal to zero:
(5)
After determining the frequencies and modes of natural oscillations in solution (4), only the strain coefficients remain unknown. Applying the method of B.G. Galerkin to the system of differential equations of blade bending oscillations, written in partial derivatives (3), after twofold differentiation, we obtain:
, (6)
. (7)
We substitute (4), (6) and (7) into equation (3), and then multiply it in turn by and integrate over the blade radius. Due to the orthogonality of the eigenmodes, we obtain a system of ordinary differential equations, interconnected only through the aerodynamic load:
(8)
;
The frequency of natural oscillations of the blade on the j-th tone,
.
The calculation of the aerodynamic forces included in the right-hand side of equation (8) is performed depending on the aerodynamic coefficients of lift and drag on the angle of attack of the blade profile and the Mach number, obtained from the results of blowing in wind tunnels. The calculation of the coefficients of deformation of the blades is carried out by the method of numerical integration of equation (8).
Under the action of the wind load, the blade of the helicopter, which is in the parking lot, begins to move in a vertical plane. Depending on whether the blade is on or away from the overhang stop, solution (4) uses hinged or cantilever modes. The deformation coefficients determined from the system of differential equations (8) will also correspond to hinged or cantilever forms. During the oscillatory movement of the blade at the moment of changing the cantilever forms to hinged and vice versa, the condition of conjugation of solutions must be observed. This can be obtained by ensuring the equality of the displacements and speeds of the blade at the time of changing forms. Let us denote the displacements and velocities for the hinged blade as
(9)
(10)
and for console fixing
, (11)
. (12)
Equating expressions (9), (11) for displacements and (10), (12) for movement speeds and taking into account the angle , we obtain, after some transformations, the initial conditions for the deformation coefficients and their derivatives at the moment when the blade rises from the overhang limiter:
(13)