U.S. patent application number 11/092132 was filed with the patent office on 2005-10-20 for blade shape creation program and method.
This patent application is currently assigned to Mitsubishi Fuso Truck and Bus Corporation. Invention is credited to Kakishita, Naoya, Kori, Itsuhei.
Application Number | 20050232778 11/092132 |
Document ID | / |
Family ID | 35096455 |
Filed Date | 2005-10-20 |
United States Patent
Application |
20050232778 |
Kind Code |
A1 |
Kakishita, Naoya ; et
al. |
October 20, 2005 |
Blade shape creation program and method
Abstract
In a blade shape creation program and method, a blade thickness
function defining equation is constructed by a cubic function as a
first function defining a leading edge blade thickness function on
a leading edge side of a maximum blade thickness point of the blade
thickness function, and a cubic function as a second function
defining a trailing edge blade thickness function on a trailing
edge side of the maximum blade thickness point; is defined, with a
camber line length, a position of maximum blade thickness, a
maximum blade thickness value, a leading edge blade thickness
change rate, a trailing edge blade thickness change rate, a leading
edge blade thickness value, and a trailing edge blade thickness
value being taken as design factors, and has a boundary condition
that the first function and the second function have tangents
continuous with each other at the maximum blade thickness
point.
Inventors: |
Kakishita, Naoya; (Tokyo,
JP) ; Kori, Itsuhei; (Tokyo, JP) |
Correspondence
Address: |
ROSSI, KIMMS & McDOWELL LLP.
P.O. BOX 826
ASHBURN
VA
20146-0826
US
|
Assignee: |
Mitsubishi Fuso Truck and Bus
Corporation
Minato-ku
JP
|
Family ID: |
35096455 |
Appl. No.: |
11/092132 |
Filed: |
March 29, 2005 |
Current U.S.
Class: |
416/223R |
Current CPC
Class: |
Y02T 50/60 20130101;
F01D 5/141 20130101; F04D 29/384 20130101; Y02T 50/673
20130101 |
Class at
Publication: |
416/223.00R |
International
Class: |
B63H 001/26 |
Foreign Application Data
Date |
Code |
Application Number |
Mar 30, 2004 |
JP |
2004-99031 |
Claims
What is claimed is:
1. A blade shape creation program for creating a blade shape on a
space virtually defined by a computer, wherein a blade thickness
function defining equation for defining a blade thickness function
representing a change in a blade thickness to be defined on a cross
section of the blade shape is constructed by a first function which
defines a leading edge blade thickness function on a leading edge
side of a maximum blade thickness point of the blade thickness
function, and a second function which defines a trailing edge blade
thickness function on a trailing edge side of the maximum blade
thickness point of the blade thickness function.
2. The blade shape creation program according to claim 1, wherein
the blade thickness function defining equation has the first
function and the second function each defined by a cubic function,
is defined, with a camber line length of a section of the blade
shape, a position of maximum blade thickness, a maximum blade
thickness value, a leading edge blade thickness change rate, a
trailing edge blade thickness change rate, a leading edge blade
thickness value, and a trailing edge blade thickness value being
taken as design factors, and has a boundary condition that the
first function and the second function have tangents continuous
with each other at the maximum blade thickness point.
3. A blade shape creation method for creating a blade shape on a
virtually defined space, wherein a blade thickness function
defining equation for defining a blade thickness function
representing a change in a blade thickness to be defined on a cross
section of the blade shape is constructed by a first function which
defines a leading edge blade thickness function on a leading edge
side of a maximum blade thickness point of the blade thickness
function, and a second function which defines a trailing edge blade
thickness function on a trailing edge side of the maximum blade
thickness point of the blade thickness function.
4. The blade shape creation method according to claim 3, wherein
the blade thickness function defining equation has the first
function and the second function each defined by a cubic function,
is defined, with a camber line length of a section of the blade
shape, a position of maximum blade thickness, a maximum blade
thickness value, a leading edge blade thickness change rate, a
trailing edge blade thickness change rate, a leading edge blade
thickness value, and a trailing edge blade thickness value being
taken as design factors, and has a boundary condition that the
first function and the second function have tangents continuous
with each other at the maximum blade thickness point.
5. A blade shape creation program for creating a blade shape on a
space virtually defined by a computer, wherein a blade thickness
function defining equation for defining a blade thickness function
representing a change in a blade thickness to be defined on a cross
section of the blade shape is constructed by a first function which
defines a leading edge blade thickness function on a leading edge
side of a maximum blade thickness point of the blade thickness
function, and a second function which defines a trailing edge blade
thickness function on a trailing edge side of the maximum blade
thickness point of the blade thickness function, and in the first
function and the second function of the blade thickness function
defining equation, a value of the blade thickness is calculated
over an entire region of the blade thickness function, and the
calculated blade thickness value is compared with a maximum blade
thickness value set as a design factor to check whether the blade
thickness function has a blade thickness value larger than the
maximum blade thickness value.
6. A blade shape creation program for creating a blade shape on a
space virtually defined by a computer, wherein a blade thickness
function defining equation for defining a blade thickness function
representing a change in a blade thickness to be defined on a cross
section of the blade shape is constructed by a first function which
defines a leading edge blade thickness function on a leading edge
side of a maximum blade thickness point of the blade thickness
function, and a second function which defines a trailing edge blade
thickness function on a trailing edge side of the maximum blade
thickness point of the blade thickness function, and the first
function and the second function of the blade thickness function
defining equation are differentiated to check over an entire region
of the blade thickness function whether the blade thickness
function has a maximum or minimum point or an inflection point at a
position other than a position of maximum blade thickness set as a
design factor.
7. The blade shape creation program according to claim 5, wherein
the blade thickness function defining equation has the first
function and the second function each defined by a cubic function,
is defined, with a camber line length of a section of the blade
shape, a position of maximum blade thickness, a maximum blade
thickness value, a leading edge blade thickness change rate, a
trailing edge blade thickness change rate, a leading edge blade
thickness value, and a trailing edge blade thickness value being
taken as design factors, and has a boundary condition that the
first function and the second function have tangents continuous
with each other at the maximum blade thickness point.
8. The blade shape creation program according to claim 6, wherein
the blade thickness function defining equation has the first
function and the second function each defined by a cubic function,
is defined, with a camber line length of a section of the blade
shape, a position of maximum blade thickness, a maximum blade
thickness value, a leading edge blade thickness change rate, a
trailing edge blade thickness change rate, a leading edge blade
thickness value, and a trailing edge blade thickness value being
taken as design factors, and has a boundary condition that the
first function and the second function have tangents continuous
with each other at the maximum blade thickness point.
9. The blade shape creation program according to claim 5, wherein
results of checking whether the blade thickness function has a
blade thickness value larger than the maximum blade thickness
value, or results of checking whether the blade thickness function
has a maximum or minimum point or an inflection point at a position
other than the position of maximum blade thickness are displayed on
a checklist window.
10. The blade shape creation program according to claim 6, wherein
results of checking whether the blade thickness function has a
blade thickness value larger than the maximum blade thickness
value, or results of checking whether the blade thickness function
has a maximum or minimum point or an inflection point at a position
other than the position of maximum blade thickness are displayed on
a checklist window.
11. A blade shape creation method for creating a blade shape on a
virtually defined space, wherein a blade thickness function
defining equation for defining a blade thickness function
representing a change in a blade thickness to be defined on a cross
section of the blade shape is constructed by a first function which
defines a leading edge blade thickness function on a leading edge
side of a maximum blade thickness point of the blade thickness
function, and a second function which defines a trailing edge blade
thickness function on a trailing edge side of the maximum blade
thickness point of the blade thickness function, and in the first
function and the second function of the blade thickness function
defining equation, a value of the blade thickness is calculated
over an entire region of the blade thickness function, and the
calculated blade thickness value is compared with a maximum blade
thickness value set as a design factor to check whether the blade
thickness function has a blade thickness value larger than the
maximum blade thickness value.
12. A blade shape creation method for creating a blade shape on a
virtually defined space, wherein a blade thickness function
defining equation for defining a blade thickness function
representing a change in a blade thickness to be defined on a cross
section of the blade shape is constructed by a first function which
defines a leading edge blade thickness function on a leading edge
side of a maximum blade thickness point of the blade thickness
function, and a second function which defines a trailing edge blade
thickness function on a trailing edge side of the maximum blade
thickness point of the blade thickness function, and the first
function and the second function of the blade thickness function
defining equation are differentiated to check over an entire region
of the blade thickness function whether the blade thickness
function has a maximum or minimum point or an inflection point at a
position other than a position of maximum blade thickness set as a
design factor.
13. The blade shape creation method according to claim 11, wherein
the blade thickness function defining equation has the first
function and the second function each defined by a cubic function,
is defined, with a camber line length of a section of the blade
shape, a position of maximum blade thickness, a maximum blade
thickness value, a leading edge blade thickness change rate, a
trailing edge blade thickness change rate, a leading edge blade
thickness value, and a trailing edge blade thickness value being
taken as design factors, and has a boundary condition that the
first function and the second function have tangents continuous
with each other at the maximum blade thickness point.
14. The blade shape creation method according to claim 12, wherein
the blade thickness function defining equation has the first
function and the second function each defined by a cubic function,
is defined, with a camber line length of a section of the blade
shape, a position of maximum blade thickness, a maximum blade
thickness value, a leading edge blade thickness change rate, a
trailing edge blade thickness change rate, a leading edge blade
thickness value, and a trailing edge blade thickness value being
taken as design factors, and has a boundary condition that the
first function and the second function have tangents continuous
with each other at the maximum blade thickness point.
15. The blade shape creation method according to claim 11, wherein
results of checking whether the blade thickness function has a
blade thickness value larger than the maximum blade thickness
value, or results of checking whether the blade thickness function
has a maximum or minimum point or an inflection point at a position
other than the position of maximum blade thickness are displayed on
a checklist.
16. The blade shape creation method according to claim 12, wherein
results of checking whether the blade thickness function has a
blade thickness value larger than the maximum blade thickness
value, or results of checking whether the blade thickness function
has a maximum or minimum point or an inflection point at a position
other than the position of maximum blade thickness are displayed on
a checklist.
Description
CROSS REFERENCE TO RELATED APPLICATION
[0001] The entire disclosure of Japanese Patent Application No.
2004-099031 filed on Mar. 30, 2004, including specification,
claims, drawings and summary, is incorporated herein by reference
in its entirety.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] This invention relates to a blade shape creation program and
method for creating the blade shape of a cooling fan or the
like.
[0004] 2. Description of the Related Art
[0005] When the blade shape of a cooling fan installed in a vehicle
is to be created (drawn) in designing the cooling fan, for example,
the first step is to create (draw) the cross-sectional shapes of a
blade at a plurality of locations in the hub diameter direction of
the blade. Then, based on these cross-sectional shapes of the
blade, the entire shape of the blade (visible outline and exterior
surface) is created (drawn) by spline interpolation or the like. A
method using "Joukowski airfoil" shown, for example, in the
following document is named as one of ordinary methods for drawing
the cross-sectional shape of the blade:
[0006] T. Fujimoto, "2nd Revision of Fluid Dynamics", 2nd Revision,
6th Edition, YOKENDO Co., Ltd., published Jan. 20, 1992, p.
141"
[0007] An outline of this method will be shown in FIGS. 11(a) and
11(b). The "Joukowski airfoil" is an airfoil (cross-sectional shape
of blade) 3 as shown in FIG. 11(b), which is obtained by-the
coordinate transformation (mapping) of a combination of two circles
1 and 2 with centers M and M', as shown in FIG. 11(a), by the
equation (1) offered below. To change the airfoil profile
(cross-sectional shape of blade) in this case, the shapes of the
two circles 1 and 2 before coordinate transformation are adjusted.
The method using "Joukowski airfoil" is one of general methods for
drawing an "average camber curve (camber line)", which is a basic
skeleton of the cross-sectional shape of the blade. According to
this method, the central points of the airfoil (cross-sectional
shape of blade) 3 shown in FIG. 11(b) are connected to draw a
camber line 4. 1 z = + a 2 , a = c 4 ( 1 )
[0008] To improve the performance of the blade (lift performance
and drag performance), it is necessary to change (adjust) the shape
of the section of the blade contour (airfoil) (i.e., blade
profile), and study influence on the performance of the blade. For
this purpose, it is effective to individually change (adjust) a
plurality of design factors (details to be described later), which
determine the blade profile, thereby directly investigating the
degree of contribution of each design factor to the performance of
the blade. Particularly, the ability to change each design factor,
independently of one another, on the leading edge side of a maximum
blade thickness point (see FIG. 3, details to be described later)
of a blade thickness function, which represents a change in the
blade thickness at a section of the blade, and on the trailing edge
side of the maximum blade thickness point would be very effective
for studying the performance of the blade.
[0009] However, conventional methods, such as the method using
"Joukowski airfoil", pose difficulty in changing each design factor
independently. Needless to say, changing each design factor,
independently on the leading edge side and the trailing edge side
of the blade thickness function, is also difficult.
[0010] The present invention has been accomplished in light of the
above-described circumstances. It is an object of the present
invention to provide a blade shape creation program and method
capable of changing a plurality of design factors, which determine
the blade profile (airfoil), on the leading edge side and the
trailing edge side of the blade thickness function, with the
leading edge side and the trailing edge side being separated from
each other, in changing (adjusting) the airfoil.
[0011] It is another object of the present invention to provide a
blade shape creation program and method capable of changing a
plurality of design factors, which determine the blade profile
(airfoil), independently on the leading edge side and the trailing
edge side of the blade thickness function, in changing (adjusting)
the airfoil, and also capable of reliably checking the created
airfoil based on numerical values, without relying on visual
checks.
SUMMARY OF THE INVENTION
[0012] A first aspect of the present invention, for attaining the
above object, is a blade shape creation program for creating a
blade shape on a space virtually defined by a computer, wherein a
blade thickness function defining equation for defining a blade
thickness function representing a change in a blade thickness to be
defined on a-cross section of the blade shape is constructed by a
first function which defines a leading edge blade thickness
function on a leading edge side of a maximum blade thickness point
of the blade thickness function, and a second function which
defines a trailing edge blade thickness function on a trailing edge
side of the maximum blade thickness point of the blade thickness
function.
[0013] A second aspect of the present invention is the blade shape
creation program according to the first aspect, wherein the blade
thickness function defining equation has the first function and the
second function each defined by a cubic function, is defined, with
a camber line length of a section of the blade shape, a position of
maximum blade thickness, a maximum blade thickness value, a leading
edge blade thickness change rate, a trailing edge blade thickness
change rate, a leading edge blade thickness value, and a trailing
edge blade thickness value being taken as design factors, and has a
boundary condition that the first function and the second function
have tangents continuous with each other at the maximum blade
thickness point.
[0014] A third aspect of the present invention is a blade shape
creation method for creating a blade shape on a virtually defined
space, wherein a blade thickness function defining equation for
defining a blade thickness function representing a change in a
blade thickness to be defined on a cross section of the blade shape
is constructed by a first function which defines a leading edge
blade thickness function on a leading edge side of a maximum blade
thickness point of the blade thickness function, and a second
function which defines a trailing edge blade thickness function on
a trailing edge side of the maximum blade thickness point of the
blade thickness function.
[0015] A fourth aspect of the present invention is the blade shape
creation method according to the third aspect, wherein the blade
thickness function defining equation has the first function and the
second function each defined by a cubic function, is defined, with
a camber line length of a section of the blade shape, a position of
maximum blade thickness, a maximum blade thickness value, a leading
edge blade thickness change rate, a trailing edge blade thickness
change rate, a leading edge blade thickness value, and a trailing
edge blade thickness value being taken as design factors, and has a
boundary condition that the first function and the second function
have tangents continuous with each other at the maximum blade
thickness point.
[0016] A fifth aspect of the present invention is a blade shape
creation program for creating a blade shape on a space virtually
defined by a computer, wherein a blade thickness function defining
equation for defining a blade thickness function representing a
change in a blade thickness to be defined on a cross section of the
blade shape is constructed by a first function which defines a
leading edge blade thickness function on a leading edge side of a
maximum blade thickness point of the blade thickness function, and
a second function which defines a trailing edge blade thickness
function on a trailing edge side of the maximum blade thickness
point of the blade thickness function; and in the first function
and the second function of the blade thickness function defining
equation, a value of the blade thickness is calculated over an
entire region of the blade thickness function, and the calculated
blade thickness value is compared with a maximum blade thickness
value set as a design factor to check whether the blade thickness
function has a blade thickness value larger than the maximum blade
thickness value.
[0017] A sixth aspect of the present invention is a blade shape
creation program for creating a blade shape on a space virtually
defined by a computer, wherein a blade thickness function defining
equation for defining a blade thickness function representing a
change in a blade thickness to be defined on a cross section of the
blade shape is constructed by a first function which defines a
leading edge blade thickness function on a leading edge side of a
maximum blade thickness point of the blade thickness function, and
a second function which defines a trailing edge blade thickness
function on a trailing edge side of the maximum blade thickness
point of the blade thickness function; and the first function and
the second function of the blade thickness function defining
equation are differentiated to check over an entire region of the
blade thickness function whether the blade thickness function has a
maximum or minimum point or an inflection point at a position other
than a position of maximum blade thickness set as a design
factor.
[0018] A seventh aspect of the present invention is the blade shape
creation program according to the fifth or sixth aspect, wherein
the blade thickness function defining equation has the first
function and the second function each defined by a cubic function,
is defined, with a camber line length of a section of the blade
shape, a position of maximum blade thickness, a maximum blade
thickness value, a leading edge blade thickness change rate, a
trailing edge blade thickness change rate, a leading edge blade
thickness value, and a trailing edge blade thickness value being
taken as design factors, and has a boundary condition that the
first function and the second function have tangents continuous
with each other at the maximum blade thickness point.
[0019] An eighth aspect of the present invention is the blade shape
creation program according to any one of the fifth to seventh
aspects, wherein results of checking whether the blade thickness
function has a blade thickness value larger than the maximum blade
thickness value, or results of checking whether the blade thickness
function has a maximum or minimum point or an inflection point at a
position other than the position of maximum blade thickness are
displayed on a checklist window.
[0020] A ninth aspect of the present invention is a blade shape
creation method for creating a blade shape on a virtually defined
space, wherein a blade thickness function defining equation for
defining a blade thickness function representing a change in a
blade thickness to be defined on a cross section of the blade shape
is constructed by a first function which defines a leading edge
blade thickness function on a leading edge side of a maximum blade
thickness point of the blade thickness function, and a second
function which defines a trailing edge blade thickness function on
a trailing edge side of the maximum blade thickness point of the
blade thickness function; and in the first function and the second
function of the blade thickness function defining equation, a value
of the blade thickness is calculated over an entire region of the
blade thickness function, and the calculated blade thickness value
is compared with a maximum blade thickness value set as a design
factor to check whether the blade thickness function has a blade
thickness value larger than the maximum blade thickness value.
[0021] A tenth aspect of the present invention is a blade shape
creation method for creating a blade shape on a virtually defined
space, wherein a blade thickness function defining equation for
defining a blade thickness function representing a change in a
blade thickness to be defined on a cross section of the blade shape
is constructed by a first function which defines a leading edge
blade thickness function on a leading edge side of a maximum blade
thickness point of the blade thickness function, and a second
function which defines a trailing edge blade thickness function on
a trailing edge side of the maximum blade thickness point of the
blade thickness function; and the first function and the second
function of the blade thickness function defining equation are
differentiated to check over an entire region of the blade
thickness function whether the blade thickness function has a
maximum or minimum point or an inflection point at a position other
than a position of maximum blade thickness set as a design
factor.
[0022] An eleventh aspect of the present invention is the blade
shape creation method according to the ninth or tenth aspect,
wherein the blade thickness function defining equation has the
first function and the second function each defined by a cubic
function, is defined, with a camber line length of a section of the
blade shape, a position of maximum blade thickness, a maximum blade
thickness value, a leading edge blade thickness change rate, a
trailing edge blade thickness change rate, a leading edge blade
thickness value, and a trailing edge blade thickness value being
taken as design factors, and has a boundary condition that the
first function and the second function have tangents continuous
with each other at the maximum blade thickness point.
[0023] A twelfth aspect of the present invention is the blade shape
creation method according to any one of the ninth to eleventh
aspects, wherein results of checking whether the blade thickness
function has a blade thickness value larger than the maximum blade
thickness value, or results of checking whether the blade thickness
function has a maximum or minimum point or an inflection point at a
position other than the position of maximum blade thickness are
displayed on a checklist.
BRIEF DESCRIPTION OF THE DRAWINGS
[0024] The present invention will become more fully understood from
the detailed description given hereinbelow and the accompanying
drawings which are given by way of illustration only, and thus are
not limitative of the present invention, and wherein:
[0025] FIG. 1 is an external outline view of a personal computer
for executing a blade shape creation program according to an
embodiment of the present invention;
[0026] FIG. 2A is a front view of a cooling fan, and FIG. 2B is a
side view of the cooling fan (a view taken in the direction of A in
FIG. 2A);
[0027] FIG. 3 is an explanation drawing of design factors for
determining a blade profile (airfoil), and a coordinate system
(blade thickness function drawing method) used when drawing a blade
thickness function by a cubic function;
[0028] FIG. 4 is a view showing an example of drawing the blade
thickness function when only a leading edge blade thickness change
rate is changed;
[0029] FIG. 5 is a view showing an example of drawing a blade
thickness function in which the blade thickness value of a blade
thickness point other than a set maximum blade thickness point is
greater than the maximum blade thickness value of the maximum blade
thickness point;
[0030] FIG. 6 is a view showing an example of drawing a blade
thickness function which has inflection points at blade thickness
points other than a set maximum blade thickness point;
[0031] FIG. 7 is a view showing an example in which a blade section
extends beyond a hub;
[0032] FIG. 8 is a view showing an example of a checklist
window;
[0033] FIG. 9 is a view showing an example of drawing a blade
thickness function of a shape in which there is no problem in a
maximum blade thickness value;
[0034] FIG. 10 is a view showing an example of drawing a blade
thickness function of a delicate shape in which the blade thickness
value of a blade thickness point other than a set maximum blade
thickness point is slightly greater than the maximum blade
thickness value of the maximum blade thickness point; and
[0035] FIG. 11 is an explanation drawing showing a method of
drawing a blade profile with the use of "Joukowski airfoil".
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0036] Embodiments of the present invention will now be described
in detail with reference to the accompanying drawings. The
application of the blade shape creation program according to the
present invention to the creation of the blade shape of a cooling
fan will be taken as an example for explanation.
[0037] FIG. 1 is an external outline view of a personal computer
for executing the blade shape creation program according to an
embodiment of the present invention. FIG. 2A is a front view of a
cooling fan, and FIG. 2B is a side view of the cooling fan (a view
taken in the direction of A in FIG. 2A).
[0038] As shown in FIG. 1, a personal computer 11 has a computer
body 12, and peripheral instruments connected to the computer body
12, such as a keyboard 13 as an input means, and a display device
14 as a display means, for example, CRT or a liquid crystal
display.
[0039] The computer body 12 is equipped with a CPU, a hard disk
(HD) drive, and a compact disk (CD) drive, and the CPU executes a
blade shape creation program P (software) stored in storage media
such as HD and CD. The blade shape creation program P is a program
for creating a blade shape on a space virtually defined by the
personal computer 11. This program can change a plurality of design
factors, which determine a blade profile (sectional shape of a
blade; airfoil), independently of each other, in changing the blade
profile, although details of the program will be described
later.
[0040] The keyboard 13 is used to enter data for execution of the
blade shape creation program P into the computer body 12. The
display device 14 is used for displaying on a display screen 15 the
data entered from the keyboard 13 into the computer body 12, and
the results of execution of the blade shape creation program P in
the computer body 12. For example, the display device 14 displays a
checklist window 16 (details to be described later).
[0041] FIGS. 2A and 2B show an example of a cooling fan loaded on a
vehicle. A cooling fan 21 illustrated in FIGS. 2A and 2B comprises
a plurality of (eight in the illustrate example) blades 23 provided
on an outer peripheral surface 22a of a cylindrical hub 22. The
cooling fan 21 has a rotating shaft (not shown) connected, for
example, to a rotating shaft of an engine of the vehicle, and
rotationally driven thereby. In the side view of FIG. 2B, each
blade 23 is provided on the outer peripheral surface 22a of the hub
such that its chord is inclined at a predetermined blade
inclination angle with respect to a hub center axis B (see FIG. 7).
The exterior shape of the blade 23 is not limited to the
illustrated one, but is available in various types.
[0042] In creating (drawing) the blade shape of each blade 23 of
the cooling fan 21 for designing the cooling fan 21, the present
embodiment is arranged to execute the blade shape creation program
P on the personal computer 11, thereby deriving a blade thickness
function representing a change in the blade thickness in a blade
section, and creating (drawing) a blade profile having a blade
thickness calculated by the blade thickness function in connection
with a separately designated camber line.
[0043] The blade thickness function creation capability (program),
blade thickness function checking capability (program), and
checklist window display capability (program) of the blade shape
creation program P will be described in detail based on FIGS. 3 to
10.
[0044] FIG. 3 is an explanation drawing of design factors for
determining a blade profile (airfoil), and a coordinate system
(blade thickness function drawing method) used when drawing a blade
thickness function by a cubic function. FIG. 4 is a view showing an
example of drawing the blade thickness function when only a leading
edge blade thickness change rate is changed. FIG. 5 is a view
showing an example of drawing an airfoil and a blade thickness
function in which the blade thickness value of a blade thickness
point other than a set maximum blade thickness point is greater
than the maximum blade thickness value of the maximum blade
thickness point. FIG. 6 is a view showing an example of drawing and
airfoil and a blade thickness function which have inflection points
at blade thickness points other than a set maximum blade thickness
point. FIG. 7 is a view showing an example in which a blade section
extends beyond a hub. FIG. 8 is a view showing an example of a
checklist window. FIG. 9 is a view showing an example of drawing an
airfoil and a blade thickness function of a shape in which there is
no problem in a maximum blade thickness value. FIG. 10 is a view
showing an example of drawing an airfoil and a blade thickness
function of a delicate shape in which the blade thickness value of
a blade thickness point other than a set maximum blade thickness
point is slightly greater than the maximum blade thickness value of
the maximum blade thickness point.
[0045] The blade thickness function creation capability of the
blade shape creation program P will be described first of all.
[0046] In providing the blade thickness function creation (drawing)
capability, the following seven design factors (1) to (7) were
selected as optimal (basic) design factors for determining the
blade profile (airfoil) (see FIG. 3):
[0047] (1) Camber line length Lc
[0048] (2) Position of maximum blade thickness x.sub.Tmax
[0049] (3) Maximum blade thickness value y.sub.Tmax
[0050] (4) Leading edge blade thickness change rate .alpha.
[0051] (5) Trailing edge blade thickness change rate .beta.
[0052] (6) Leading edge blade thickness value Tf
[0053] (7) Trailing edge blade thickness value Tb
[0054] As shown in FIG. 3, a camber line 31 is a line formed by
connecting the centers of blade thicknesses B of a blade section
(airfoil) 32, and a camber line length Lc refers to the length of
the camber line 31. The blade thickness B of the blade section 32
is a blade thickness in a direction perpendicular to a tangent to
the camber line 31 at each camber point SP on the camber line 31. A
blade thickness function 33 represents a change in the blade
thickness B, namely, a change over the range from a leading edge
31a of the camber line 31 (leading edge 32a of the blade section
32) to a trailing edge 31b of the camber line 31 (trailing edge 32b
of the blade section 32). The leading edge 31a of the camber line
31 is a site where airflow enters, while the trailing edge 31b of
the camber line 31 is a site where airflow exits.
[0055] To express the blade thickness function 33 by an x-y
coordinate system, a coordinate axis representing the position of
the camber line 31 in the camber line length direction is
designated as an x-axis, the leading edge 31a of the camber line 31
is taken as the origin of the x-axis, and a coordinate axis
representing the magnitude of the blade thickness B is designated
as a y-axis. A maximum blade thickness value y.sub.Tmax is the
maximum value of the blade thickness B. Each point on the blade
thickness function 33 is called a blade thickness point BP and, of
these blade thickness points BP's, the point at which the blade
thickness B takes the maximum blade thickness value y.sub.Tmax is
called a maximum blade thickness point BPM. In the x-y coordinate
system, the blade thickness B is expressed by the y-coordinate, and
refers to the length of a perpendicular dropped from each blade
thickness point BP on the blade thickness function 33 to the
x-axis. The position of maximum blade thickness x.sub.Tmax is the
position in the camber line direction (x-axis direction) at which
the blade thickness B takes the maximum blade thickness value
y.sub.Tmax.
[0056] A leading edge blade thickness change rate .alpha. is the
change rate of the blade thickness B at the leading edge 33a of the
blade thickness function 33, and refers to an angle which a tangent
33c at the leading edge 33a of the blade thickness function 33
makes with a line 34a parallel to the x-axis. A trailing edge blade
thickness change rate .beta. is the change rate of the blade
thickness B at the trailing edge 33b of the blade thickness
function 33, and refers to an angle which a tangent 33d at the
trailing edge 33b of the blade thickness function 33 makes with a
line 34b parallel to the x-axis. A leading edge blade thickness
value Tf is the value of the blade thickness B at the leading edge
33a of the blade thickness function 33. The leading edge blade
thickness value Tf may be zero when a leading edge portion of the
blade section 32 is arcuate. Alternatively, the leading edge blade
thickness value Tf may be some value when the leading edge portion
is flat, as in the illustrated example. A trailing edge blade
thickness value Tb is the value of the blade thickness B at the
trailing edge 33b of the blade thickness function 33. The trailing
edge blade thickness value Tb may be zero when a trailing edge
portion of the blade section 32 is at an acute angle.
Alternatively, the trailing edge blade thickness value Tb may be
some value when the trailing edge portion is flat, as in the
illustrated example.
[0057] An equation for defining the blade thickness function 33,
which represents a change in the blade thickness B to be defined on
the cross section 32 of the blade shape, is constructed by a first
function which defines a leading edge blade thickness function on
the leading edge side of the maximum blade thickness point BPM of
the blade thickness function 33, and a second function which
defines a trailing edge blade thickness function on the trailing
edge side of the maximum blade thickness point BPM on the blade
thickness function 33. That is, as shown in FIG. 3, the blade
thickness function 33 is divided into a leading edge side and a
trailing edge side, with the maximum blade thickness point BPM as a
boundary. A cubic function of an equation (2) is selected as a
first function which defines (represents) a leading edge blade
thickness function 33A on the leading edge side of the maximum
blade thickness point BPM, while a cubic function of an equation
(3) is selected as a second function which defines (represents) a
trailing edge blade thickness function 33B on the trailing edge
side of the maximum blade thickness point BPM.
y.sub.L=a.sub.Lx.sub.L.sup.3+b.sub.Lx.sub.L.sup.2+c.sub.Lx.sub.L+d.sub.L
(2)
y.sub.T=a.sub.Tx.sub.T.sup.3+b.sub.Tx.sub.T.sup.2+c.sub.Tx.sub.T+d.sub.T
(3)
[0058] The reason for selecting the cubic functions as the first
function and the second function is that the aforementioned seven
design factors are selected as the optimal design factors
determining the shape of the blade section 32 (the shape of the
blade thickness function 33), whereby the eight constraints (1) to
(8) to be indicated below can be set based on these design factors.
That is, of the following eight constraints (1) to (8), the four
constrains (1), (3), (5) and (7) can be set for the leading edge
side of the blade thickness function 33, while the other four
constrains (2), (4), (6) and (8) can be set for the trailing edge
side of the blade thickness function 33. In accordance with these
constraints, therefore, the respective coefficients (a.sub.L,
b.sub.L, c.sub.L, d.sub.L, a.sub.T, b.sub.T, C.sub.T, d.sub.T) of
the cubic functions of the equations (2) and (3) can all be
uniquely determined. The constrains (1) to (4) are the constraints
concerned with the transit points of the blade thickness function
33, while the constraints (5) to (8) are the constraints about the
gradient of the tangents at the transit points of the blade
thickness function 33.
[0059] If the number of the design factors (constraints) is small,
quadratic functions may be used as the first and second functions.
If the number of the design factors (constraints) is large,
functions of fourth or higher order may be used. However, if the
number of the design factors (constraints) is small, sufficient
adjustment of an airfoil cannot be made. Too large a number of the
design factors (constraints) would wastefully render the equations
of the functions complicated. Thus, it would be best to select, as
the first function and the second function, cubic functions which
are suitable for the seven design factors (camber line length Lc,
position of maximum blade thickness x.sub.Tmax, maximum blade
thickness value y.sub.Tmax, leading edge blade thickness change
rate .alpha., trailing edge blade thickness change rate .beta.,
leading edge blade thickness value Tf, trailing edge blade
thickness value Tb) optimal as design factors for determining the
blade profile (airfoil).
[0060] (1) When x.sub.L=0, y.sub.L=Tf: Leading edge position
(leading edge blade thickness value)
[0061] (2) When x.sub.T=Lc, y.sub.T=Tb: Trailing edge position
(camber line length, trailing edge blade thickness value)
[0062] (3) When x.sub.L=x.sub.Tmax, y.sub.L=y.sub.Tmax: Position of
maximum blade thickness, maximum blade thickness value
[0063] (4) When x.sub.T=x.sub.Tmax, y.sub.T=y.sub.Tmax: Position of
maximum blade thickness, maximum blade thickness value
[0064] (5) When x.sub.L=0, dy.sub.L/dx.sub.L=tan .alpha.: Leading
edge blade thickness change rate
[0065] (6) When x.sub.T=Lc, dy.sub.T/dx.sub.T=tan(-.beta.):
Trailing edge blade thickness change rate
[0066] (7) When x.sub.L=x.sub.Tmax, dy.sub.L/dx.sub.L=0: Position
of maximum blade thickness (gradient of tangent)
[0067] (8) When x.sub.T=x.sub.Tmax, dy.sub.T/dx.sub.T=0: Position
of maximum blade thickness (gradient of tangent)
[0068] The constraint (1) is a constraint on the leading edge
position of the blade thickness function 33 (leading edge blade
thickness value Tf) for the equation (2). When x.sub.L=0, namely,
at the position of the leading edge 33a of the blade thickness
function 33, the blade thickness value y.sub.L=Tf. The constraint
(2) is a constraint on the trailing edge position of the blade
thickness function 33 (camber line length Lc, trailing edge blade
thickness value Tb) for the equation (3). When x.sub.T=Lc (camber
line length), namely, at the position of the trailing edge 33b of
the blade thickness function 33, the blade thickness value
y.sub.T=Tb. The constraint (3) is a constraint on the position of
maximum blade thickness x.sub.Tmax and the maximum blade thickness
value y.sub.Tmax of the blade thickness function 33 for the
equation (2). The constraint (4) is a constraint on the position of
maximum blade thickness x.sub.Tmax and the maximum blade thickness
value y.sub.Tmax of the blade thickness function 33 for the
equation (3). The constraint (5) is a constraint on the leading
edge blade thickness change rate .alpha. of the blade thickness
function 33 for the equation (2), namely, a constraint on the
gradient of the tangent at the position of the leading edge 33a of
the blade thickness function 33. The constraint (6) is a constraint
on the trailing edge blade thickness change rate .beta. of the
blade thickness function 33 for the equation (3), namely, a
constraint on the gradient of the tangent at the position of the
trailing edge 33b of the blade thickness function 33.
[0069] The constraint (7) is a constraint on the gradient of the
tangent at the position of maximum blade thickness x.sub.Tmax,
i.e., at the maximum blade thickness point BPM of the blade
thickness function 33, for the equation (2). The constraint (8) is
a constraint on the gradient of the tangent at the position of
maximum blade thickness x.sub.Tmax, i.e., at the maximum blade
thickness point BPM of the blade thickness function 33, for the
equation (3). Under the constrains (7) and (8), the gradient of the
tangent at the position of maximum blade thickness x.sub.Tmax
(maximum blade thickness point BPM) is zero, i.e.,
dy.sub.L/dx.sub.L=0. This is because unless the gradient of the
tangent at the position of maximum blade thickness x.sub.Tmax
(maximum blade thickness point BPM) is zero, the value of the blade
thickness B (y.sub.L, y.sub.T) at the set maximum blade thickness
point BPM is not maximal. The constrains (7) and (8) also mean that
the maximum blade thickness value at the position of maximum blade
thickness x.sub.Tmax (maximum blade thickness point BPM) is
similarly y.sub.Tmax, and the gradient of the tangent
(dy.sub.L/dx.sub.L, dy.sub.T/dx.sub.T) is similarly zero, showing
that the equation (2) of the first function and the equation (3) of
the second function have the boundary condition that their tangents
are continuous with each other at the maximum blade thickness point
BPM.
[0070] Based on the above constraints (1) to (8), the respective
design factors (camber line length Lc, position of maximum blade
thickness x.sub.Tmax, maximum blade thickness value y.sub.Tmax,
leading edge blade thickness change rate .alpha., trailing edge
blade thickness change rate .beta., leading edge blade thickness
value Tf, trailing edge blade thickness value Tb) are set (changed)
independently of each other to find the respective coefficients
(a.sub.L, b.sub.L, c.sub.L, d.sub.L, a.sub.T, b.sub.T, c.sub.T,
d.sub.T) of the cubic functions of the equations (2) and (3). By so
doing, the leading edge blade thickness function 33A can be defined
(drawn) based on the cubic function of the equation (2), and the
trailing edge blade thickness function 33B can be defined (drawn)
based on the cubic function of the equation (3). By combining the
cubic functions of the equations (2) and (3), the whole of the
blade thickness function 33 can be defined (drawn).
[0071] The relationships between the respective coefficients
(a.sub.L, b.sub.L, c.sub.L, d.sub.L, a.sub.T, b.sub.T, c.sub.T,
d.sub.T) of the cubic functions of the equations (2) and (3) and
the respective design factors (camber line length Lc, position of
maximum blade thickness x.sub.Tmax, maximum blade thickness value
y.sub.Tmax, leading edge blade thickness change rate .alpha.,
trailing edge blade thickness change rate .beta., leading edge
blade thickness value Tf, trailing edge blade thickness value Tb)
are as indicated by the equations (4) to (11) offered below. To
avoid the complexity of the indications of the equations, the
equations (9), (10) and (11) for b.sub.T, c.sub.T and d.sub.T
include a.sub.T. However, since a.sub.T is a function involving
only the design factors as in the equation (8), b.sub.T, c.sub.T
and d.sub.T can also be regarded as functions composed of the
design factors alone.
[0072] As the following equations (4) to (7) show, the respective
coefficients (a.sub.L, b.sub.L, c.sub.L, d.sub.L) of the equation
(2) for the cubic function on the leading edge side can be uniquely
determined by determining the position of maximum blade thickness
x.sub.Tmax, maximum blade thickness value y.sub.Tmax, leading edge
blade thickness change rate .alpha., and leading edge blade
thickness value Tf as the design factors. As the following
equations (8) to (11) show, the respective coefficients (a.sub.T,
b.sub.T, c.sub.T, d.sub.T) of the equation (3) for the cubic
function on the trailing edge side can be uniquely determined by
determining the camber line length Lc, position of maximum blade
thickness x.sub.Tmax, maximum blade thickness value y.sub.Tmax,
trailing edge blade thickness change rate .beta., and trailing edge
blade thickness value Tb as the design factors. The procedure for
deriving the following relational expressions (4) to (11) will be
described later. 2 a L = - 2 y T max + x T max tan + T f x T max 3
( 4 ) b L = y T max - T f x T max 2 - tan x T max - x T max ( - 2 y
T max + x T max tan + T f x T max 3 ) ( 5 ) c L = tan ( 6 ) d L = T
f ( 7 ) a T = - ( L c - x T max ) tan ( - ) + 2 y T max - 2 T b ( x
T max - L c ) 3 ( 8 ) b T = - 3 2 ( L c + x T max ) a T + tan ( - )
2 ( L c - x T max ) ( 9 ) c T = a T ( 1 2 L c 2 + 2 L c x T max + 1
2 x T max 2 ) - ( 10 ) 1 L c - x T max ( ( L c + x T max ) tan ( -
) 2 + y T max - T b ) d T = 1 6 ( x T max 3 - 2 x T max L c 2 - 5 x
T max 2 L c ) a T + ( 11 ) x T max x T max - L c ( x T max tan ( -
) 6 - 2 3 ( ( L c + x T max ) tan ( - ) 2 + y T max - T b ) + x T
max - L c x T max y T max )
[0073] The blade thickness function 33, which has been created
(drawn) by the cubic functions of the equations (2) and (3), is
combined with the camber line 31 created (drawn) beforehand. That
is, the values of the blade thickness B (y.sub.L, y.sub.T) at the
respective blade thickness points BP of the blade thickness
function 33 are added to the respective camber points SP of the
camber line 31 in a direction perpendicular to the tangents at the
respective camber points SP. As a result, the shape of the blade
section 32 is created (drawn). Such a shape of blade section (blade
profile) is created (drawn) at each of a plurality of locations in
the hub diameter direction of the blade. Based on the resulting
blade profiles, spline interpolation is performed to create (draw)
a spline curve (visible outline of the blade) and a spline surface
(exterior surface of the blade), thereby creating (drawing) the
entire shape of the blade (external diameter line, external
diameter surface). In this case, the camber line 31 may be created
by the aforementioned method using the "Joukowski airfoil", or may
be created by any method.
[0074] According to the present embodiment, as described above,
under the blade shape creation program P, which creates a blade
shape on a space virtually defined by the personal computer 11, the
equation for defining the blade thickness function 33, which
represents a change in the blade thickness B to be defined on the
section 32 of the blade shape is composed of the first function
(cubic function) which defines the leading edge blade thickness
function 33A on the leading edge side of the maximum blade
thickness point BPM of the blade thickness function 33, and the
second function (cubic function) which defines the trailing edge
blade thickness function 33B on the trailing edge side of the
maximum blade thickness point BPM of the blade thickness function
33. Thus, with the exception of the design factors concerning the
maximum blade thickness point at the boundary between the first
function and the second function (i.e., position of maximum blade
thickness x.sub.Tmax, maximum blade thickness value y.sub.Tmax),
the design factors on the leading edge side of the blade thickness
function 33 and those on the trailing edge side of the blade
thickness function 33 can be independently set (changed) by the
first function and the second function. Thus, the influence of each
design factor on the site of flow can be systematically studied.
This facilitates tuning of the site of flow, and enables an airfoil
of higher performance to be developed. In connection with the
maximum blade thickness point BPM on the boundary between the first
function and the second function, it goes without saying that the
first function and the second function are equal to each other in
terms of the position of maximum blade thickness x.sub.Tmax and the
maximum blade thickness value y.sub.Tmax, with their tangents at
BPM continuing, and the gradients of the tangents being zero.
[0075] In the present embodiment, in particular, the seven design
factors (camber line length Lc, position of maximum blade thickness
x.sub.Tmax, maximum blade thickness value y.sub.Tmax, leading edge
blade thickness change rate .alpha., trailing edge blade thickness
change rate .beta., leading edge blade thickness value Tf, trailing
edge blade thickness value Tb) were selected as optimal design
factors for determining the blade profile (airfoil) and the cubic
functions of the equations (2) and (3) were selected as the first
function and the second function suited for these design factors.
Thus, the respective design factors can be changed independently of
each other. This makes it possible to directly grasp the degree of
influence which each design factor exerts on the performance of the
blade (lift performance and drag performance) (i.e., the degree of
contribution to blade performance).
[0076] For example, FIG. 4 shows an example of the blade thickness
function 33 created (drawn), with only the leading edge blade
thickness change rate .alpha. being changed in three different
ways, and an example of the blade section 32 created (drawn) based
on the blade thickness function 33 and the camber line 31. In FIG.
4, only the leading edge blade thickness change rate .alpha. is
changed, and the other design factors (camber line length Lc,
position of maximum blade thickness x.sub.Tmax, maximum blade
thickness value y.sub.Tmax, trailing edge blade thickness change
rate .beta., leading edge blade thickness value Tf, trailing edge
blade thickness value Tb) are not changed. Thus, the influence of
the leading edge blade thickness change rate .alpha. on the
performance of the blade can be grasped directly. Since each design
factor can be changed independently of one another in this manner,
the influence of each design factor on the site of flow can be
systematically studied. Hence, tuning of the site of flow becomes
easy, and an airfoil with higher performance can be developed.
[0077] The procedure for deriving the relationships between the
respective coefficients (a.sub.L, b.sub.L, c.sub.L, d.sub.L,
a.sub.T, b.sub.T, c.sub.T, d.sub.T) in the cubic functions of the
equations (2) and (3) and the design factors (camber line length
Lc, position of maximum blade thickness x.sub.Tmax, maximum blade
thickness value y.sub.Tmax, leading edge blade thickness change
rate .alpha., trailing edge blade thickness change rate .beta.,
leading edge blade thickness value Tf, trailing edge blade
thickness value Tb) will be shown.
[0078] First, the relations between the respective coefficients
(a.sub.L, b.sub.L, c.sub.L, d.sub.L) of the cubic function equation
(2) on the leading edge side of the blade thickness function and
the design factors are derived in accordance with the following
procedure:
[0079] From the equation (2) and the constraint (1),
d.sub.L=T.sub.f (12)
[0080] From the equation (2),
dy.sub.L/dx.sub.L=3a.sub.Lx.sub.L.sup.2+2b.sub.Lx.sub.L+c.sub.L
(13)
[0081] From the equation (13) and the constrain (5),
c.sub.L=tan .alpha. (14)
[0082] From the equation (2) and the constraint (3), the equation
(12) and the equation (14),
y.sub.Tmax=a.sub.L.multidot.x.sub.Tmax.sup.3+b.sub.L.multidot.x.sub.Tmax.s-
up.2+x.sub.Tmax.multidot.tan .alpha.+T.sub.f (15)
[0083] Both sides are multiplied by 2 to give
2y.sub.Tmax=2a.sub.L.multidot.x.sub.Tmax.sup.3+2b.sub.L.multidot.x.sub.Tma-
x.sup.2+2x.sub.Tmax.multidot.tan .alpha.+T.sub.f (16)
[0084] From the equation (13) and the equation (14), as well as the
constraint (7),
0=3a.sub.L.multidot.x.sub.Tmax.sup.2+2b.sub.L.multidot.x.sub.Tmax+tan
.alpha. (17)
[0085] Both sides are multiplied by x.sub.Tmax to obtain
0=3a.sub.L.multidot.x.sub.Tmax.sup.3+2b.sub.L.multidot.x.sub.Tmax.sup.2+x.-
sub.Tmax.multidot.tan .alpha. (18)
[0086] Subtraction of the equation (18) from the equation (16)
gives
2y.sub.Tmax=-a.sub.L.multidot.x.sub.Tmax.sup.3+x.sub.Tmax.multidot.tan
.alpha.+T.sub.f 3 a L = - 2 y T max + x T max tan + T f x T max 3 (
19 )
[0087] From the equation (15), 4 b L = y T max - T f x T max 2 -
tan x T max - a L x T max = y T max - T f x T max 2 - tan x T max -
x T max ( - 2 y T max + x T max tan + T f x T max 3 ) ( 20 )
[0088] Next, the relations between the respective coefficients
(a.sub.T, b.sub.T, c.sub.T, d.sub.T) of the cubic function equation
(3) on the trailing edge side of the blade thickness function and
the design factors are derived in accordance with the following
procedure:
[0089] From the equation (3),
dy.sub.T/dx.sub.T=3a.sub.T.multidot.x.sub.T.sup.2+2b.sub.T.multidot.x.sub.-
T+c.sub.T (21)
[0090] From the equation (21) and the constraint (6)
tan(-.beta.)=3a.sub.T.multidot.L.sub.c.sup.2+2b.sub.T.multidot.L.sub.c+c.s-
ub.T (22)
[0091] From the equation (21) and the constraint (8),
0=3a.sub.T.multidot.x.sub.Tmax.sup.2+2b.sub.T.multidot.x.sub.Tmax+c.sub.T
(23)
[0092] Subtraction of the equation (23) from the equation (22)
gives 5 tan ( - ) = 3 a T ( L c 2 - x T max 2 ) + 2 b T ( L c - x T
max ) b T = - 3 2 ( L c + x T max ) a T + tan ( - ) 2 ( L c - x T
max ) ( 24 )
[0093] From the equation (3) and the constraint (2),
T.sub.b=a.sub.T.multidot.L.sub.c.sup.3+b.sub.T.multidot.L.sub.c.sup.2+c.su-
b.T.multidot.L.sub.c+d.sub.T (25)
[0094] From the equation (3) and the constraint (4),
y.sub.Tmax=a.sub.T.multidot.x.sub.Tmax.sup.3+b.sub.T.multidot.x.sub.Tmax.s-
up.2+c.sub.T.multidot.x.sub.Tmax+d.sub.T (26)
[0095] Subtraction of the equation (26) from the equation (25)
gives
T.sub.b-y.sub.Tmax=a.sub.T.multidot.(L.sub.c.sup.3-x.sub.Tmax.sup.3)+b.sub-
.T.multidot.(L.sub.c.sup.2-x.sub.Tmax.sup.2)+c.sub.T.multidot.(L.sub.c-x.s-
ub.Tmax) (27)
[0096] Substitution of the equation (24) into the equation (27),
followed by arrangement, yields 6 c T = a T ( 1 2 L c 2 + 2 L c x T
max + 1 2 x T max 2 ) - 1 L c - x T max ( ( L c + x T max ) tan ( -
) 2 + y T max - T b ) ( 28 )
[0097] Subtraction of (the equation (26).times.3) from (the
equation (23).times.x.sub.Tmax) gives 7 d T = - x T max 2 3 b T - 2
x T max 3 c T + y T max ( 29 )
[0098] Substitution of b.sub.T and c.sub.T into the equation (29)
followed by arrangement, yields 8 d T = 1 6 ( x T max 3 - 2 x T max
L c 2 - 5 x T max 2 L c ) a T + x T max x T max - L c ( x T max tan
( - ) 6 - 2 3 ( ( L c + x T max ) tan ( - ) 2 + y T max - T b ) + x
T max - L c x T max y T max ) ( 30 )
[0099] Substitution of b.sub.T, c.sub.T and d.sub.T into the
equation (23), followed by arrangement, yields 9 a T = - ( L c - x
T max ) tan ( - ) + 2 y T max - 2 T b ( x T max - L c ) 3 ( 31
)
[0100] Next, the blade thickness function checking capability and
the checklist window display capability in the blade shape creation
program P will be described.
[0101] In creating (drawing) the blade thickness function 33 by the
blade shape creation program P (cubic functions of the equations
(2) and (3)), the following cases may be encountered, depending on
a combination of the seven design factors (camber line length Lc,
position of maximum blade thickness x.sub.Tmax, maximum blade
thickness value y.sub.Tmax, leading edge blade thickness change
rate .alpha., trailing edge blade thickness change rate .beta.,
leading edge blade thickness value Tf, trailing edge blade
thickness value Tb) determining the blade profile (airfoil), even
if the eight constraints (1) to (8) to be satisfied are fulfilled:
There may be a blade thickness function, like the blade thickness
function 33 illustrated in FIG. 5, which, at a blade thickness
point BP other than a set maximum blade thickness point BPM, has a
value of blade thickness B (y.sub.L, x.sub.L) greater than a
maximum blade thickness value y.sub.Tmax at the set maximum blade
thickness point BPM. There may be another blade thickness function,
like the blade thickness function 33 illustrated in FIG. 6, which,
at blade thickness points BP other than the set maximum blade
thickness point BPM, has inflection points (may have a maximum or
minimum point).
[0102] Under the blade shape creation program P, therefore, a
numerical check is made for such cases (i.e., whether a blade
thickness value greater than the set maximum blade thickness value
is present, and whether a maximum or minimum point or an inflection
point is present at a blade thickness point other than the set
maximum blade thickness point) at the time of creating the blade
thickness function 33. A further check is performed of whether the
blade section 32 does not extend beyond the hub 22. The results of
these checks are displayed on the checklist window. A concrete
procedure is as follows:
[0103] <Method of Checking Whether a Blade Thickness Value
Greater than a Set Maximum Blade Thickness Value is Present>
[0104] In the first function (cubic function) and the second
function (cubic function) of the blade thickness function defining
equation, whose coefficients were determined by setting the design
factors (constraints), the value of the blade thickness B (y.sub.L,
x.sub.L) is calculated over the entire region of the blade
thickness function 33 in the camber line direction (x-axis
direction of FIG. 3). That is, in connection with the cubic
function of the equation (2), each coefficient is determined based
on the design factors (constrains), and then a blade thickness
value y.sub.L at each position (each blade thickness point BP) over
the range from x.sub.L=0 to x.sub.L=x.sub.Tmax is calculated. In
connection with the cubic function of the equation (3) as well,
each coefficient is determined based on the design factors
(constrains), and then a blade thickness value y.sub.T at each
position (each blade thickness point BP) over the range from
x.sub.T=x.sub.Tmax to x.sub.T=Lc is calculated.
[0105] These calculated blade thickness values y.sub.L and y.sub.T
are compared with the maximum blade thickness value y.sub.Tmax set
as a design factor to check whether the blade thickness function 33
has blade thickness values y.sub.L and y.sub.T greater than the
maximum blade thickness value y.sub.Tmax.
[0106] <Method of Checking Whether a Maximum, Minimum or
Inflection Point other than a Set Maximum Blade Thickness Point is
Present>
[0107] The first function (cubic function) and the second function
(cubic function) of the blade thickness function defining equation,
whose coefficients were determined by setting the design factors
(constraints), are subjected to differentiation (differentiation of
first order, or differentiation of second or higher order). By so
doing, whether the blade thickness function 33 has a maximum or
minimum point or an inflection point at a position other than the
position of maximum blade thickness x.sub.Tmax (blade thickness
point BP other than the maximum blade thickness point BPM) set as a
design factor is checked over the entire region of the blade
thickness function 33.
[0108] For example, in the first function (cubic function) and the
second function (cubic function) of the blade thickness function
defining equation, whose coefficients were determined by setting
the design factors (constraints), the gradient of the tangent to
the blade thickness function 33 (dy.sub.L/dx.sub.L,
dy.sub.T/dx.sub.T) is calculated over the entire region of the
blade thickness function 33 in the camber line direction (x-axis
direction of FIG. 3). That is, in connection with the cubic
function of the equation (2), each coefficient is determined based
on the design factors (constrains), and then the gradient of the
tangent (dy.sub.L/dx.sub.L) at each position (each blade thickness
point BP) over the range from x.sub.L=0 to x.sub.L=x.sub.Tmax is
calculated. In connection with the cubic function of the equation
(3) as well, each coefficient is determined based on the design
factors (constrains), and then the gradient of the tangent
(dy.sub.T/dx.sub.T) at each position (each blade thickness point
BP) over the range from x.sub.T=x.sub.Tmax to x.sub.T=Lc is
calculated. Then, a check is made of whether the positivity or
negativity of the sign of the calculated gradient of the tangent
(dy.sub.L/dx.sub.L, dy.sub.T/dx.sub.T) is reversed before and after
a position other than the set position of maximum blade thickness
(blade thickness point BP other than the maximum blade thickness
point BPM) (namely, whether there is a maximum or minimum
point).
[0109] <Method for Checking Whether the Blade Section Does Not
Extend Beyond the Hub>
[0110] A check is made of whether the blade section 32, created
(drawn) based on the blade thickness function 33 by the blade
thickness function defining equation (cubic function), does not
extend beyond the hub 22 in a side view (plan view), when its
inclination angle with respect to the hub center axis B is also
taken into consideration. FIG. 7 shows an example in which a
leading edge portion C of the blade section 32 extends beyond the
hub 22 in a side view (plan view) of the cooling fan.
[0111] <Method for Display of Checklist Window>
[0112] The results of the checks made by the above checking methods
are displayed on a checklist window 16 on a display screen 15 as
shown in FIG. 8. Curve-1 to Curve-3 in a column of the checklist
window 16 represent blade thickness functions created (drawn) for
the blade section at each position of the blade in the hub diameter
direction. The number of the created blade thickness functions is
not limited to 3 in the illustrated example, but may be 2 or 4 or
more in accordance with the shape of the blade to be created.
[0113] Error-1 to Error-4 in a row of the checklist window 16
represent items checked by the above-described checking methods.
Error-1 shows the results of the check of whether the blade
thickness function 33 as a whole has a blade thickness value
greater than the set maximum blade thickness value. When values
y.sub.L and y.sub.T greater than the maximum blade thickness value
y.sub.Tmax are not present, a judgment "no problem" is made, and a
circle ".largecircle." meaning no problem is displayed. If blade
thickness values y.sub.L and y.sub.T greater than the maximum blade
thickness value y.sub.Tmax are present, this means that the
conditions for setting (preconditions) the maximum blade thickness
value and the position of maximum blade thickness are not
fulfilled. Since a judgment "problematical" is made, "warning" is
displayed.
[0114] Error-2 shows the results of the check of whether the
leading edge blade thickness function 33A has a maximum or minimum
point or an inflection point. When there is no maximum or minimum
point or no inflection point, a judgment "no problem" is made, and
a circle ".largecircle." meaning no problem is displayed. If there
is a maximum or minimum point or an inflection point, the presence
of a maximum or minimum point or an inflection point on the leading
edge side (leading edge blade thickness function 33A) is considered
to affect, often adversely, the performance of the blade. Thus, a
judgment "problematical" is made, and "warning" is displayed.
Error-3 shows the results of the check of whether the trailing edge
blade thickness function 33B has a maximum or minimum point or an
inflection point. When there is no maximum or minimum point or no
inflection point, a judgment "no problem" is made, and a circle
".largecircle." meaning no problem is displayed. If there is a
maximum or minimum point or an inflection point, "caution" is
displayed. The reason why "caution", rather than "warning," is
displayed here is that the presence of a maximum or minimum point
or an inflection point on the trailing edge side (trailing edge
blade thickness function 33B) does not necessarily exert an adverse
influence on the performance of the blade, but is rather considered
to exert a favorable influence on the performance of the blade.
Anyway, a display of "caution" enables the developer to recognize
reliably that a maximum or minimum point or an inflection point is
present.
[0115] Error-4 shows the results of the check of whether the blade
section 32 does not extend beyond the hub 22. When the blade
section 32 does not extend beyond the hub 22, a judgment "no
problem" is made, and a circle ".largecircle." meaning no problem
is displayed. If the blade section 32 extends beyond the hub 22,
this is not necessarily a problem, and it suffices to have the
developer recognize that the blade section 32 extends beyond the
hub 22. Thus, "caution" is displayed.
[0116] A "Close" button 42 displayed on the display screen 16 of
FIG. 8 is a button to be pushed (for example, to be clicked by a
mouse) for closing (erasing) the checklist window 16.
[0117] According to the present embodiment described above, in the
first function (cubic function) and the second function (cubic
function) of the blade thickness function defining equation, the
value of the blade thickness B (y.sub.L, y.sub.T) is calculated
over the entire region of the blade thickness function 33. This
calculated blade thickness value (y.sub.L, y.sub.T) is compared
with the maximum blade thickness value y.sub.Tmax set as a design
factor to check whether the blade thickness function 33 has a blade
thickness value (y.sub.L, y.sub.T) greater than the maximum blade
thickness value y.sub.Tmax. Hence, the presence or absence of a
delicate blade thickness value (y.sub.L, y.sub.T), which is
difficult to confirm visually, can be numerically checked with
reliability when creating the blade thickness function 33. Thus,
the efficiency of blade development increases. For example, the
blade thickness function 33 of FIG. 9 poses no problem about blade
thickness values. In regard to the blade thickness function 33 of
FIG. 10, on the other hand, a value of the blade thickness B
(y.sub.L) at a blade thickness point BP nearer to the leading edge
is slightly larger than a maximum blade thickness value y.sub.Tmax
at the set maximum blade thickness point BPM. The problem of such a
delicate blade thickness value (y.sub.L) can be checked
reliably.
[0118] According to the present embodiment, moreover, the first
function (cubic function) and the second function (cubic function)
of the blade thickness function defining equation are
differentiated. By so doing, whether the blade thickness function
33 has a maximum or minimum point or an inflection point at a
position other than the position of maximum blade thickness set as
a design factor is checked over the entire region of the blade
thickness function 33. Hence, the presence or absence of a maximum
or minimum point or an inflection point, which is difficult to
confirm visually, can be numerically checked with reliability when
creating the blade thickness function 33. Thus, the efficiency of
blade development increases.
[0119] According to the present embodiment, moreover, the results
of the checks of whether the blade thickness function has a greater
blade thickness value than the maximum blade thickness value,
whether the blade thickness function has a maximum or minimum point
or an inflection point at a blade thickness point other than the
maximum blade thickness point, and whether the blade section does
not extend beyond the hub are displayed on the checklist window 16.
Accordingly, these checking results are clear at a glance, and the
efficiency of blade development increases.
[0120] While the present invention has been described by the above
embodiment, it is to be understood that the invention is not
limited thereby, but may be varied or modified in many other ways.
Such variations or modifications are not to be regarded as a
departure from the spirit and scope of the invention, and all such
variations and modifications as would be obvious to one skilled in
the art are intended to be included within the scope of the
appended claims.
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