This disclosure relates generally to a blade and a disk within a turbomachine. More particularly, this disclosure relates to redistributing loads on the disk and a base of the blade by adjusting the interface between the disk and the base of the blade.
Turbomachines are well known. Turbomachines typically include multiple rotor assemblies within a fan assembly, a compressor section, and a turbine section. The rotor assemblies each include an array of blades circumferentially distributed about a rotational axis of the turbomachine. The blades each include a base section, a platform section, and an airfoil section that extends radially outwardly from the platform section.
During assembly, the base section is received within a recess established within an outer rim of the disk. The base has multiple lobes that contact areas of the disk to limit radial movement of the blade relative to the disk. Such a base is sometimes referred to as a fir-tree base. As the turbomachine reaches an operating speed, centrifugal forces cause the base to move within the recess from an unloaded position and a loaded position relative to the disk. The blades are locked into place axially with bolts, locking pins, etc.
Referring to the prior art arrangement of
In the unloaded position, there are gaps 5a-5f between the lobes 3a-3f and the disk 2 at the contact area 4a-4-f. In the prior art, the size of the gaps 5a-5f does not vary from side to side. In the prior art, some of the lobes 3a-3f experience high loads that can fracture or otherwise damage the base 1 or the disk 2 when the blade is in the loaded position.
An example method of designing blade lobes of a turbomachine blade and corresponding disk lobes includes determining contact areas between the blade lobes on a blade model and the disk loads on a disk model when the turbomachine blade is in a loaded position. The method adjusts the blade lobes, the disk lobes, or both, so that gaps are established between the blade lobes and the disk lobes at the contact areas when the turbomachine blade is in an unloaded position. The size of the gaps varies.
An example method of designing blade lobes of a turbomachine blade and corresponding disk lobes includes spacing a radially outer lobe of a blade base away from a first corresponding contact area of a disk a first distance and spacing a radially middle lobe of a blade base away from a second corresponding contact area of the disk a second distance. The method spaces a radially inner lobe of a blade base away from a third corresponding contact area of the disk a third distance. The first distance is greater than the second distance. The second distance is greater than the third distance. The blade is in an unloaded position during the spacing.
An example blade assembly includes a base of a blade that is configured to be installed within a recess and moved radially within the recess between a loaded position and an unloaded position. Lobes on the base each have a blade contact area that contacts a corresponding disk contact area on the disk when the base is in the loaded position. Gaps are established between the blade contact areas and the disk contact areas when the base is in the unloaded position. The size of the gaps varies.
The various features and advantages of the disclosed examples will become apparent to those skilled in the art from the detailed description. The figures that accompany the detailed description can be briefly described as follows:
Referring to
During operation, air is compressed in the low pressure compressor section 16 and the high pressure compressor section 18. The compressed air is then mixed with fuel and burned in the combustion section 20. The products of combustion are expanded across the high pressure turbine section 22 and the low pressure turbine section 24.
The high pressure compressor section 18 and the low pressure compressor section 16 include rotor disks 32 and 33, respectively, that rotate about the axis 12. The high pressure compressor section 18 and the low pressure compressor section 16 also include alternating rows of rotating blades 34 and static vanes 36.
The high pressure turbine section 22 and the low pressure turbine section 24 each include rotor disks 26 and 27, respectively, which rotate in response to expansion to drive the high pressure compressor section 18 and the low pressure compressor section 16. The example rotors 26 and 27 also include rotating blades and static vanes.
The examples described in this disclosure are not limited to rotors of the two spool gas turbine architecture described. That is, these examples may be used in other architectures, such as a single spool axial design, a three spool axial design, and still other architectures. Further, there are various types of gas turbine engines, and other turbomachines, that would benefit from the examples disclosed herein.
Referring now to
Referring now to
In this example, a designer using the modeling computer 56 manipulates the surfaces and sizes of the base model 50m and the disk model 32m. When the interface 70m between the base model 50m and the disk model 32m is in a desired position, data is outputted from the modeling computer 56 as component model data 72 to a component manufacturer 76. The component manufacturer 76 then generates the base 50 and the disk 32. The interface 70 between the base 50 and the disk 32 is the same as the interface 70m between the base model 50m and the disk model 32m.
It should be noted that various computing devices can be used to implement various functions of the modeling computer 56. In terms of hardware architecture, the computing devices can include the processor 58, memory 62, and one or more input and/or output (I/O) device interface(s) that are communicatively coupled via a local interface. The local interface can include, for example but not limited to, one or more buses and/or other wired or wireless connections. The local interface may have additional elements, such as controllers, buffers (caches), drivers, repeaters, and receivers to enable communications. Further, the local interface may include address, control, and/or data connections to enable appropriate communications among the aforementioned components.
The example processor 58 may be a hardware device for executing software, particularly software stored in memory. The processor can be a custom made or commercially available processor, a central processing unit (CPU), an auxiliary processor among several processors associated with the computing device, a semiconductor based microprocessor (in the form of a microchip or chip set) or generally any device for executing software instructions.
The example memory 62 can include any one or combination of volatile memory elements (e.g., random access memory (RAM, such as DRAM, SRAM, SDRAM, VRAM, etc.)) and/or nonvolatile memory elements (e.g., ROM, hard drive, tape, CD-ROM, etc.). Moreover, the memory 62 may incorporate electronic, magnetic, optical, and/or other types of storage media. Note that the memory 62 can also have a distributed architecture, where various components are situated remotely from one another, but can be accessed by the processor.
The software in the memory 62 may include one or more separate programs, each of which includes an ordered listing of executable instructions for implementing logical functions. A system component embodied as software may also be construed as a source program, executable program (object code), script, or any other entity comprising a set of instructions to be performed. When constructed as a source program, the program is translated via a compiler, assembler, interpreter, or the like, which may or may not be included within the memory.
The Input/Output devices that may be coupled to system I/O Interface(s) may include input devices, for example but not limited to, a keyboard, mouse, scanner, microphone, camera, proximity device, etc. Further, the Input/Output devices may also include output devices, for example but not limited to, a printer, display, etc. Finally, the Input/Output devices may further include devices that communicate both as inputs and outputs, for instance but not limited to, a modulator/demodulator (modem; for accessing another device, system, or network), a radio frequency (RF) or other transceiver, a telephonic interface, a bridge, a router, etc.
When the modeling computer 56 is in operation, the processor 58 can be configured to execute software stored within the memory 62, to communicate data to and from the memory 62, and to generally control operations of the modeling computer 56 pursuant to the software. Software in the memory 62, in whole or in part, is read by the processor 58, perhaps buffered within the processor 58, and then executed.
Referring now to
In the unloaded position (
In the loaded position of
The designer utilizing the modeling computer 56 manipulates the surfaces of the base model 50m, the disk model 32m, or both, to adjust when the lobes 80a-80d of the base 50 (that is created from the base model 50m) will contact the disk 32 (that is created from the disk model 38m) at the contact areas 84a-84f.
In this example, the designer generally determines how to adjust the surfaces of the base model 50m, the disk model 32m, or both, by first moving the base model 50m to the unloaded position of
In this example, to establish the size of the gaps 88a-88f, the designer first establishes a local coordinate system associated with the suction side (X′s, Z′s), and a local coordinate system associated with the pressure side (X′p, Y′p, Z′p). The local coordinate systems are transformations of a global coordinate system (X, Y, Z) utilized by the modeling computer 56.
A transformation matrix [R] is used to provide the local coordinate system (X′s, Y′s, Z′s) based on the global coordinate system (X, Y, Z). In this example:
Another, similar, transformation matrix (not shown) relates the local coordinate system (X′p, Y′p, Z′p) to the global coordinate system (X, Y, Z).
A person having skill in this art would understand the global coordinate system (X, Y, Z) associated with the base model 50m positioned within the disk model 32m, and how to establish local coordinate systems based on the global coordinate system using the transformation matrix [R].
After establishing local coordinate systems (X′s, Y′s, Z′s) and (X′p, Y′p, Z′p), the operator adjusts surfaces of the base model 50m, the disk model 32m, or both. The scale of the adjustments is made based on the local coordinate systems (X′s, Y′s, Z′s) and (X′p, Y′p, Z′p) In this example, the surfaces are adjusted so that the gaps 88a-88f are asymmetric when the base model 50m is in the unloaded position. More specifically, the surfaces are adjusted so that the gaps 88e and 88f for the radially outer lobes 80f and 80e are larger than the gaps 88c and 88d for the radially middle lobes 80c and 80d, which are larger than the gaps 88a and 88b for the radially inner lobes 80a and 80b.
In one example, the operator establishes appropriate sizes for the gaps 88a-88f utilizing an equation associated with each of the gaps 88a-88f. In these equations, the following nomenclature is used:
As can be appreciated, the lobes 80a-80f are displaced relative to other portions of the base 50 as the base 50 moves to the loaded position. In this example, δ10 represents the displacement of the lobes 80a and 80b when the lobes 80b-80f are not in contact with the disk 32.
When the lobes 80a-80d contact the disk 32 and the lobes 80e-80f are spaced from the disk 32 (
When the lobes 80a-80f each contact the disk 32, δ13 represents the displacement of the lobes 80a-80b, δ23 represents the displacement of the lobes 80c-80d, and δ33 represents the displacement of the lobes 80e-80f.
Variables δ1A, δ2A, and δ3A are compared to the displacements δ10, δ12, δ13, δ22, δ23, and δ33. The variables δ1A, δ2A, and δ3A represent the total displacement at the each of the radial positions for the lobes 80a-80f and correspond to a limit stress of each of these lobes.
As shown in the following equations, the individual displacements of the lobes 80a-80f at the contact points are less than or equal to the limit stress:
For lobes 80a-80b: δ10+δ12+δ13≦δ1A (1)
For lobes 80c-80d: δ22+δ23≦δ2A (2)
For lobes 80e-80f: δ33≦δ3A (3)
In this example, δ1A represents the total potential displacement at the lobes 80a and 80b. That is, δ1A corresponds to the displacement of the lobes 80a and 80b when the lobes 80a and 80b are at their allowable limit stress.
In this example, δ10 represents the displacement of the bottom lobes 80a and 80b as the rotational speed of the blade 34 increases from zero to ω1. At this speed, the lobes 80c and 80d contact the disk 32 and start to carry load.
Accelerating the blade 34 further moves the rotational speed toward ω2, which is a higher rotational speed than ω1. In this example, ω2 is the rotational speed where the lobes 80e and 80f also contact the disk 32. From ω1 to ω2, the radial displacements of the lobes 80a and 80b at the contact points 84a and 84b is δ12, and the radial displacements of the lobes 80c and 80d at the contact points 84c and 84d is δ22.
Accelerating the blade 34 further moves the rotational speed toward ωn, which is a higher rotational speed than ω2 and corresponds to a full operating speed. At the full operating speed ωn, the radial displacement of the lobes 80a and 80b at the contact points 84a and 84b is δ13, the radial displacement of the lobes 80c and 80d at the contact points 84c and 84d is δ23, and the radial displacement of the lobes 80e and 80f at the contact points 84e and 84f is δ33.
Load sharing factors (LSi) are also calculated for the lobes 80a-80f. The net forces carried by the lobes 80a-80f are evaluated at the full speed of the engine 10. In this calculation, F1 is the net force carried by the lobes 80a-80b, F2 is the net force carried by the lobes 80c-80d, and F3 is the net force carried by the lobes 80e-80f. The computing device is configured to calculate these net forces. Then the total load and the load sharing factors are:
In some examples, the load distribution is not the same on the pressure and suction sides of the blade 34. Thus:
F
L
−F
R
=ΔF
As can be appreciated, a designer using the above techniques is left with seven unknown variables: ω1, ω2, δ10, δ12, δ13, δ22, and δ23. In one example, these unknowns are determined using the following techniques.
For example, from equations (1), (2) and (3), and the load sharing factors, the corresponding forces may be established using the following equations:
F
1
=k
1δ1A (4)
F
2
=k
2δ2A (5)
F
3
=k
3δ3A (6)
F=F
1
+F
2
+F
3 (7)
Also, the speeds may be established using the following equations.
Mrω
1
2
=k
1δ10 (8)
Mr[ω
2
2
−w
1
2
]=k
1δ12+k2δ22 (9)
From rotational speed ω2 to full speed ω1:
Mr[ω
n
2−ω22]=k1δ13+k2δ23+k3δ33 (10)
From Finite Element Analysis, the equivalent lobe stiffness is then calculated. From material properties and load sharing ratio, the displacement limits can then be established. The Finite Element Analysis provides the k1, k2, and k3 variables, and δ1A, δ2A, and δ3A are known from equations (1)-(3). Also, from equation (3), δ33 is also known. In this example, the designer assumes that:
δ22=δ23−½(δ2A) (11)
Referring now to a method 100 of
In one example, Finite Element Analysis is then used to evaluate the asymmetric loading at a step 114, and the gaps may be readjusted as a result at a step 116.
Alternatively, in another example, the ω2 is obtained graphically. From manufacturing tolerances, the established gaps are greater than a minimum value and also gently load the bottom lobe at the start up, thus δ10 could be selected to be equal to or less than 20% of δ1A. The initial gap on the bottom-lobe is then determined. With this, ω1 is fixed and what left is to iterate for ω2 using equations (9) and (10).
Referring to the example of
Referring again to
gaps 88a-88b=0 (12)
gaps 88c-88d=C1(δ10) (13)
gaps 88e-88f=C2(δ10+δ12) (14)
Because the loading on the lobes 80a-80f is asymmetrical, the equations (12)-(14) are adjusted, as follows, to reestablish a balanced loading condition. In this example, Finite Element Analysis is used determine the imbalanced loads on each of the lobes 80a-80f.
The sizes of the gaps 88a-88e are then established using the following formulas (assuming the left side is higher: FL>FR and FL−FR=ΔF):
Establishing the size of each gap 88a-88f individually accounts for unequal loading on the pressure and suction sides of the blade 34 and the leading and trailing edges.
Referring to
Referring now to
In another example, the disk 32m is crowned. The dimensions of the crown for one of the lobes 80a-80f depends on the load on that lobe 80a-80f.
The dimensions of the crown include a crown drop Cd, a crown radius Cv, and a crown length C1. In this example, the crown drop Cd for the leading edge of the lobe 80e is set up to be less than, or equal to, the differences in load distribution between the leading edge 92 and the trailing edge 96 of the lobes 80e and the stiffness k of the lobes 80e. The following equation represents how the crown drop Cd may be established:
In this example, the subscripts FLE is the average load on the leading edge of the lobe 80e when the blade 34 is in the loaded position, and FLE is the average load on the trailing edge of the lobe 80e when the blade 34 is in the loaded position. The variable k represents the lobe stiffness, and ABS is the absolute value. A person having skill in this art would be able to determine the average loads at these positions using the modeling computer 56.
In this example, the crown length C1 is greater than or equal to the length Cd. and the crown radius Cr is greater than or equal to the crown drop Cd. Typically, C1 (crown length)≧Cr and Cr≧1.5 Ca.)
Features of the disclosed examples include a base of a turbomachine blade that has a relatively balanced load distribution without significantly increasing the size, complexity, and weight of the base or the disk.
The preceding description is exemplary rather than limiting in nature. Variations and modifications to the disclosed examples may become apparent to those skilled in the art that do not necessarily depart from the essence of this disclosure. Thus, the scope of legal protection given to this disclosure can only be determined by studying the following claims.