- •Foreword
- •Предисловие
- •Chapter 1. Introduction
- •From the history of aeroengines development. Classification of air gas turbine engines
- •Table 1.1
- •Table 1.2
- •1.2. Design features of manifold types of gas turbine engines
- •Main specifications for some serial turboprop and turboshaft
- •Fig. 1.3. Principal scheme of a two-shaft afterburning
- •Fig. 1.4. Principal scheme of a two-shaft tfe
- •Fig. 1.5. Principal scheme of a three-shaft tfe
- •Fig. 1.8. Principal scheme of a tpfe with a coaxial propfan
- •Main stages of gas turbine engines creation
- •1.4. Absolute and specific parameters of gas turbine engines
- •1.4.1. Absolute and specific parameters of turbojet engines
- •1.4.2. Absolute and specific parameters of turboprop engines
- •I.5. Air gas turbine engine’s lives
- •1.5.1. Nomenclature of lives
- •1.5.2. Sequence of assigning, setting and increase of lives
- •1.5.3. General requirements to life testing of engines and their main elements
- •1.5.4. Forming of test cycles
- •1.5.5. Forming of programs of life tests
- •Questions for self-check
- •2.1. Types of loads acting upon gas turbine engine structural elements
- •2.1.1. Classification of loads
- •2.1.2. Gas loads
- •2.1.3. Mass (inertial) forces and momenta
- •2.1.4. Temperature stresses
- •Fig. 2.4. For determination of the centrifugal forces
- •Fig. 2.5. For determination of the disc temperature stresses
- •2.1.5. Concept of dynamic loads
- •Fig. 2.9. Gas flow velocity behind nozzle vanes
- •2.2. Axial gas forces coming into action in gas turbine engines. Formation of thrust in gas turbine engines of manifold types
- •2.2.1. Axial gas forces acting on the basic gas turbine engine units
- •Fig. 2.10. Scheme of axial forces acting on basic gte units
- •2.3. Determination of axial gas force acting on impeller of gas turbine engine centrifugal compressor
- •2.4. Torques coming into action in gas turbine engines. Balance of torques
- •In gas turbine engines
- •2.4.1. Torques in turbine and compressor
- •Fig. 2.14. For determination of turbine rotor wheel torque
- •2.4.2. Torque balance in gas turbine engines of manifold types
- •Questions for self-check
- •Engine blades
- •Loads acting on blades. The blade stressed state characteristic
- •Fig. 3.1. Loads acting on the blade (a) and the scheme of blade loading
- •Determination of rotor blade tensile stress caused by centrifugal forces
- •The design scheme
- •3.2.2. Equation of a rotor blade stressed state
- •Integrating equation (3.3) in view of the ratio (3.1), we will get
- •3.2.3. Calculation of tensile stress at manifold laws of change of blade section area along its length
- •If the blade section area decreases from the root to periphery under the linear law:
- •In this case an integration by formula (3.7) yields
- •Determination of rotor blade bending stress caused by gas forces
- •3.3.1. Design scheme of a blade
- •3.3.2. Determination of gas load intensities
- •Determination of the bending momenta in axial and circumferential planes
- •3.3.4. Determination of the blade section geometrical characteristics
- •Determination of bending stress caused by gas force
- •Determination of rotor blade bending stress caused by centrifugal forces
- •The design scheme
- •3.4.2. Equation of the bending momenta
- •3.5. Guide and nozzle diaphragm vanes strength calculation features
- •3.5.1. Console type vanes
- •3.5.2. Double-support vanes
- •3.5.3. Frame type vanes
- •3.6. Evaluation of gte rotor blades strength
- •3.6.1. Grounding of blade stressed state criterion
- •3.6.2. Estimation of the blade temperature
- •3.6.3. Determination of blade strength safety factor coefficients
- •Questions for self-check
- •4.1. Loads affecting discs
- •The design scheme and assumptions made at disc strength calculations
- •Fig.4.1. Design scheme of the disc
- •4.3. Design ratings
- •4.4. Disc thermal condition
- •4.5. The disc stressed state equation. Boundary conditions
- •4.5.1. An equilibrium equation
- •4.5.2. Equation of deformations generality
- •4.5.3. Determination of stresses in rotating, unevenly heated elastic disc with an arbitrary profile
- •Fig. 4.2. Elementary disc forms
- •Fig. 4.3. Discs of arbitrary profiles
- •4.5.4. The procedure of the arbitrary profile disc stresses calculation
- •4.6. Disc durability criteria and safety factor coefficients
- •4.6.1. Selection of the stressed state criteria
- •4.6.2. Disc safety factor coefficients
- •Integrating an equilibrium equation, we find
- •4.7. Features of strength calculation of centrifugal compressor and radial-inflow turbine discs
- •The weight of the carrier disc for a chosen ring makes
- •Fig. 4.5. Design scheme and character of the radial and circumferential stresses change along radius of two-sided impeller of centrifugal compressor
- •4.8. Peculiarities of stresses calculation in drum-and-disc designs
- •Fig. 4.6. Design scheme of a drum-and-disc rotor
- •From here
- •Questions for self-check
- •Chapter 5. Static strength of gas turbine engine shafts
- •Loads acting on shafts
- •Design schemes and stressed state of shafts. Safety factor coefficient estimation
- •In an axial direction the shaft tensile (compressive) stresses are equal to
- •The shaft static strength is estimated by a safety factor coefficient value
- •Questions for self-check
- •Chapter 6. Dynamic strength of gas turbine engine blades
- •6.1. Vibrations of blades and forces causing vibrations
- •6.2. Kinds and forms of blade normal modes
- •Fig. 6.3. Flexural vibration modes of rotor blades
- •Fig. 6.4. For rotor blade normal mode frequency definition
- •6.3. Normal modes of blades with a stationary cross-section area
- •6.4. Normal modes of blades with a variable cross-section area
- •6.5. Influence of blade attachment effort to the disc
- •6.6. Influence of centrifugal forces on blade vibration frequency
- •F ig. 6.7. Determination of blade dynamic normal mode frequency
- •Influence of variable temperature
- •6.8. Forces damping blade vibrations
- •6.9. Resonant modes of the blade vibrations. The frequency diagram
- •F ig. 6.8. Example of turbine rotor wheel frequency diagram
- •6.10. Torsional and composite blade vibrations
- •6.11. Elimination of blade vibrational breakages
- •6.12. Concept of blades self-oscillations
- •Versus vibration amplitude
- •Questions for self-check
- •Chapter 7. Dynamic strength of gas turbine engine discs
- •General information
- •Forms of disc normal modes
- •Wave linear speed equals
- •Disc normal mode frequency
- •The compressor and turbine rotor wheel vibration calculation
- •Factors influencing the disc normal mode frequency
- •Disc forced undulations
- •The ways to eliminate dangerous resonance oscillations of rotor wheels
- •Questions for self-check
- •Chapter 8. Critical rotational speeds of gas turbine engine rotor
- •8.8. Measures taken to reduce intensity of rotor oscillation connected with critical rotational speeds.
- •Concept of critical rotational speeds of gas turbine engine rotor
- •Critical rotational speed of the two-support weightless shaft with disc
- •Fig. 8.8. Value of shaft static sag for different rotor schemes
- •Fig. 8.9. To the problem of a rotated rotor stability in a subcritical area
- •Connection of rotor critical rotational speed with its
- •Concept of two-support rotor critical rotational speeds of higher order
- •Critical rotational speed of the two-support ponderable shaft without disc
- •8.6. Critical rotational speeds of the ponderable shaft with several discs
- •8.6.1. Method of decomposition into elementary systems
- •8.7. Operational factors affecting critical rotational speeds of gas turbine engine rotor
- •Fig. 8.11. Taking into account supports elasticity influence on rotor critical speeds
- •Fig. 8.12. Static elastic anisotropy of a casing
- •Determination of critical rotational speeds taking into account
- •Influence of gyroscopic moment
- •Table 8.1
- •Values of the influence coefficients
- •8.7.2. Reduction of a real flexural system to equivalent computational
- •Example of rotor critical speed calculation
- •The rotor operational rotational speed margin is equal to:
- •The rotational speed margin at an idle is equal to:
- •8.8. Measures taken to reduce intensity of rotor oscillation connected with critical rotational speeds
- •Questions for self-check
- •8.7. What is dependence of rotor critical rotational speed on its cross-sectional oscillation frequency?
- •Of gas turbine engine shell designs
- •9.1. Shell strength calculation
- •Fig .9.1. Design scheme of a shell
- •9.2. Stability of cylindrical and conical shells
- •9.3. Vibrations of cylindrical shells
- •Questions for self-check
- •Chapter 10. Control of gas turbine engine
- •Vibration state
- •10.2. Control of gas turbine engine vibrations
- •10.3. The ways to lower the vibration level of gas turbine engines
- •10.3.1. The procedures of vibration level lowering at stage of designing
- •10.3.2. The procedures of the vibration level lowering at production stage
- •Fig. 10.3. Scheme of the rotor static balancing
- •Fig. 10.4. Scheme of the rotor dynamic balancing
- •Will be compensated by centrifugal force of balanced elements weights
- •10.3.3. The procedures of the vibration level lowering at maintenance stage
- •Questions for self-check
- •Сhapter 11. Gas turbine engine rotor supports
- •11.1. Brief data about gas turbine engine rotor supports
- •Fig. 11.3. Scheme of gte rotor support
- •11.2. Calculation of support bearings
- •Fig. 11.9. Ball bearing:
- •For roller bearings we use the formula
- •11.2.2. Estimation of the bearing safe life
- •11.2.3. Check of the bearing high-speed
- •11.2.4. Check of the bearing static load-bearing capacity
- •11.2.5. Definition of the necessary oil circulation through the bearing
- •Questions for self-check
1.5.3. General requirements to life testing of engines and their main elements
For lives approving (demonstration) the following types of bench tests are used:
- equivalently-cyclical tests (ECT) of main elements;
- ECT of engine;
- engine’s tests according to operational program.
Equivalently-cyclical tests are the main type of resource tests.
Forming of life test programs of engine and its main elements before operation starts is carried out on the base of generalized flight cycle (GFC), given in TR for engine, correspondent to prospective operational conditions. This GFC and programs may be specified by the results of flight tests on airplane’s prototype or flying laboratory.
At increase of lives of engines and main elements the GFC and life test programs may be specified by the data of actual operation conditions. At this the equivalent non-failure operating time of engine in whole and its main elements during tests, which were carried out before, are recalculated for conditions of specified GFC.
To the main elements belong engine’s elements, failures of which may lead to catastrophic situation for an aircraft (according to airworthiness requirements classification). As a rule, elements of rotors, casings, which are under pressure, uncontrolled fan blades, and engine’s mounting elements belong to them.
Specific list of main elements for each engine’s type is determined by Engine’s Manufacturer in agreement with State Air Service and Customer representative on the base of analysis of functional failures and taking into account the engine development experience and its prototypes operation.
Bench life tests of main engine’s elements are carried out in structure of full-size engine. It is allowed to carry out the life tests of 2-nd (3-rd) specimen of main engine’s elements on specialized installations at reproduction of their principal loading conditions.
Bench engine’s life tests (at confirmation of all types of lives, such as first overhaul period, overhaul period and specified life) till the value of life equals 2500 hours are carried out with reserve (load factor) KN=1,2 and at lives more than 2500 h – with the excess on number of flight cycles over 500 h.
While testing of engine it is recommended to use test cycles with conformity factors for the most loaded elements within limits =0,75…1,25 (at commensurable conditions on temperature and pressure in the engine’s inlet).
At bench engine’s life tests the damageability of engine’s elements in expected operational conditions should be reproduced in maximum possible degree.
Engine’s life tests are carried out by the way of multiple realizations of testing cycles on benches with atmospheric conditions in the inlet, which imitate the altitude-velocity conditions.
During tests on operational program all steady-state ratings and transient processes (ratings) are repeated in sequence, corresponding to engine’s use in prospective operational conditions.
While carrying out of equivalently-cyclical tests the reduction of bench engine’s tests duration is achieved by decrease of working time at long low-loading ratings and reducing of number of weakly damaging variable processes at their equivalent reduction to “heavy” ratings and more loading variable processes in engine’s elements, limiting its life.
In case of carrying out of life tests of main engine’s elements on separate benches the equivalently-cyclical tests are used, which provide the reproduction of damageability of these elements in prospective working conditions consisting of engine.
Test cycle is the change in time of parameters, which characterize engine’s operation and conditions in engine’s inlet at bench tests.
Steady-state rating is engine’s working rating at which its parameters don’t change in time more than in allowable limits, given in TR for engine.
Transient process is the process of engine’s parameters change in time between two steady-state ratings (start, full and partial acceleration, chop deceleration, shutdown, etc).
During testing on increase of engine’s specified life the replacement of engine’s elements, the specified life of which (in cycles or hours) is less than engine’s specified life, is foreseen.
While engine’s testing for confirmation of first repair overhaul period and overhaul period, partial dismantling and revisions of engine’s elements (according to the program, adjusted with Customer representative), foreseen by in-line documentation are allowed.
It is allowed the replacement of engine’s elements, on which the defects occurred during testing that are not connected with lifetime duration.
It is allowed the combination of ECT of main elements with ECT of engine for definition and increase of first overhaul period, overhaul period and specified life.
Engine’s life testing is ended by characterization, engine’s dismantling and flaw detection of its elements by means of industry and repair plants. At that the report about technical state of engine, its main elements and components is made.
Tests for definition and increase of all types of engine’s lives are evaluated as successful, if during their carrying out there were no destructions of main engine’s elements, their damages (set by methods, approved in series technology), and also failures and defects of other elements, which in operation conditions may lead to failures with dangerous consequences (according to airworthiness requirements).
Engine’s characteristics and its systems parameters during testing process should correspond to technical specifications (TS).