The present invention relates to crankshafts to be mounted in reciprocating
engines such as automotive engines, marine engines, and multiple purpose engines used
in, for example, power generators and a design method of these crankshafts.
BACKGROUND ART
[0002]
A reciprocating engine requires a crankshaft for converting the reciprocating
motion of pistons in cylinders to rotational motion so as to extract power. Crankshafts
are generally categorized into two classes: the type manufactured by die forging and the
type manufactured by casting. Especially for multiple cylinder engines, the firstly
mentioned die forged crankshafts, which are excellent in strength and stiffness, are often
employed.
[0003]
FIG. 1 is a schematic side view of an example of a common crankshaft for a
multiple cylinder engine. A crankshaft 1 shown in FIG. 1 is designed to be mounted in
a 4-cylinder engine and includes: five journals Jl to J.5; four crank pins P1 to P4; a front
part Fr, a flange Fly and eight crank arms A1 to A8 (hereinafter also referred to simply as
\'arms1') that connect the journals J1 to J.5 and the crank pins P1 to P4 to each other.
The crankshaft 1 is configured such that all of the eight crank arms A1 to A8 are formed
integrally with counterweights Wl to W8 (hereinafter also referred to as "weights"),
respectively, and is referred to as a 4-cylinder 8-counterweight crankshaft.
[0004]
Hereinafter, when the journals J1 to J.5, the crank pins PI to P4, the crank anns
A1 to A8, and the counterweights Wl to W8 are each collectively referred to, the
reference character "J" is used for the journals, "P" for the crank pins, "A" for the crank
arms, and "W" for the counterweights. A crank pin P and a pair of crank arms A
(including the counterweights W) which connect with the crank pin P are also
collectively referred to as a "throw".
[0005]
The journals J, the front part Fr, and the flange F1 are arranged coaxially with
the center of rotation of the crankshaft 1. The crank pins P are arranged at positions
eccentric with respect to the center of rotation of the crankshaft 1 by half the distance of
the piston stroke. The journals J are supported by the engine block by means of sliding
bearings and serve as the central rotation axis. The big end of a connecting rod
(hereinafter referred to as "conrod") is coupled to the crank pin P by means of a sliding
bearing, and a piston is coupled to the small end of the conrod by means of a piston pin.
The front part Fr is a front end portion of the crankshaft 1. To the front part Fr, a
damper pulley 2 to drive a timing belt, a fan belt or the like is fitted. The flange F1 is a
rear end portion of the crankshaft 1. To the flange Fly a flywheel 3 is fitted.
[0006]
In an engine, fuel explodes within cylinders. The combustion pressure
generated by the explosion causes reciprocating motion of the pistons, which is
converted into rotational motion of the crankshaft 1. In this regard, the combustion
pressure acts on the crank pins P of the crankshaft 1 via the conrod and is transmitted to
the journals J via the respective crank arms A connecting to the crank pins P. In this
process, the crankshaft 1 rotates while repetitively undergoing elastic deformation.
[0007]
The bearings that support the journals of the crankshaft are supplied with
lubricating oil. In response to the elastic deformation of the crankshaft, the oil film
pressure and the oil film thickness in the bearings vary in correlation with the bearing
load and the journal center orbit. Furthermore, depending on the surface roughness of
the journals and the surface roughness of the bearing metal in the bearings, not only the
oil film pressure but also local metal-to-metal contact occurs. Ensuring a sufficient oil
film thickness is important in order to prevent seizure of the bearings due to lack of
lubrication and to prevent local metal-to-metal contact, thus affecting the fuel economy
performance.
[OOOS]
In addition, the elastic deformation accompanied with the rotation of the
crankshaft and the movements of the center orbit of the journals within the clearances of
the bearings cause an offset of the center of rotation, and therefore affect the engine
vibration (mount vibration). Furthermore, the vibration propagates through the vehicle
body and thus affects the noise in the vehicle and the ride quality.
[0009]
In order to improve such engine performance properties, there is a need for a
crankshaft that is lightweight and is high in stiffness with the ability to resist
deformation.
[OOl 01
FIG. 2 is a graph indicating a curve showing the pressure in a cylinder of a
four-cycle engine. In FIG. 2, when the position of the crankshaft where the crank pin
comes to a top dead point in a compression process is considered as a reference (point
of crank angel 8 of 0 degrees), an explosion occurs immediately after the top dead point
in the compression process. Accordingly, the pressure in the cylinder becomes a
maximum combustion pressure when the crank angle 8 becomes about 8 to 20 degrees.
The crankshaft is subjected to the load of pressure in the cylinder (combustion pressure)
as shown in FIG. 2, and also subjected to the load of centrifugal force of rotation. The
design of the crankshaft aims to improve the flexural rigidity and the torsional rigidity,
thereby achieving deformation resistance against these loads, along with weight
reduction.
[OOll]
In designing a crankshaft, generally, the main specifications such as the journal
diameter, the crank pin diameter, and the piston stroke are firstly determined. The
point that can undergo design changes to ensure sufficient flexural rigidity and torsional
rigidity after determination of the main specifications is only the shape of the crank
arms. Thus, the design of the crank arm shape is an important factor affecting the
performance of the crankshaft. Strictly speaking, as described above, the crank arms
mean the oval portions connecting the journals and the crank pins to each other and do
not include the portions serving as counterweights.
[OO 121
Japanese Patent No. 4998233 (Patent Literature 1) discloses a technique of
making recess grooves in the crank pin-side surface and the journal-side surface of each
crank arm, in the center, aiming at an increase in flexural rigidity, an increase in
torsional rigidity and also a reduction in weight of the crankshaft. The technique
disclosed in Patent Literature 1 provides a design method of a crank arm, focusing on a
reduction in weight and an increase in stiffness of each crank arm in the state where the
crank angle 9 is 0 degrees (that is, in the state where the crank pin is in the top dead
point in the compression process). In other words, the design method shows how to
reduce the weight of the crank arm while achieving a given target value of stiffness in
the state where the crank angle 9 is 0 degrees. Also, the design method shows how to
increase the stiffness of the crank arm while achieving a given target value of weight
reduction.
[00 1 31
Japanese Patent Application Publication No. 10-1 69637 (Patent Literature 2)
discloses a method for calculating an optimal distribution of mass moments of the
counterweights by using the three-moment equation in the Strength of Materials. The
technique disclosed in Patent Literature 2 provides a method including approximating a
crankshaft to stepped round-bar beams and adjusting the distribution of mass moments
of the counterweights in accordance with the stiffness of the crank arms and the mass
moments of the crank arms to minimize the loads on the journals. In other words,
according to the method, the stiffness of each crank arm is determined by taking a
prepared value or in another way, and thereafter, the distribution of mass moments of a
plurality of counterweights (for example, eight counterweights in a case of a 4-cylinder
and 8-counterweight crankshaft) is adjusted so that the loads on the bearings of the
journals can be minimized.
CITATION LIST
PATENT LITERATURE
[00 141
Patent Literature 1 : Japanese Patent No. 4998233
Patent Literature 2: Japanese Patent Application Publication No. 10-1 69637
SUMMARY OF INVENTION
TECHNICAL PROBLEM
[0015]
As shown in FIG. 2, the pressure in the cylinder becomes a maximum
combustion pressure not when the crank angle 8 is 0 degrees but when the crank angle 8
is about 8 to 20 degrees. Accordingly, the crank pin is loaded with the maximum
combustion pressure via the conrod when the crank angle 8 is about 8 to 20 degrees.
In this moment, the load direction of the combustion pressure onto the crank pin is a
direction from the axis of the piston pin (the axis of the small end of the conrod) to the
axis of the crank pin. Accordingly, the maximum combustion pressure is applied to
the crank arm not in the direction along a line connecting the axis of the crank pin to the
axis of the journal (hereinafter referred to as "crank arm centerline") but in a direction
inclined from the crank arm centerline.
[00 161
The crank arm design method disclosed in Patent Literature 1 is based on the
premise that a maximum load due to a maximum combustion pressure is applied to the
crank arm in the state where the crank arm 8 is 0 degrees. In other words, this method
is based on the premise that the maximum load is applied in the direction along the
crank arm centerline. Then, the crank arm shape obtained by the technique disclosed
in Patent Literature 1 does not fit for reality. Therefore, the crank arm shape is not
necessarily appropriate for an improvement in stiffness and a reduction in weight. In
the first place, the technique disclosed in Patent Literature 2 is not intended to improve
the stiffness of a crank arm.
[0017]
The present invention has been made in view of the above circumstances. An
object of the present invention is to provide a crankshaft for reciprocating engines
which has an increased flexural rigidity fit for reality and a reduced weight, and a design
method of the crankshaft.
SOLUTION TO PROBLEM
[0018]
The present invention is to solve the above-described problems, and the gist of
the present invention is a crankshaft for reciprocating engines as described in the
following section (I) and a crankshaft design method as described in the following
section (11).
[0019]
(I) A crankshaft of the present embodiment includes: journals that define a
central axis of rotation; crank pins that are eccentric with respect to the journals; crank
arms connecting the journals to the crank pins; and counterweights integrated with the
crank arms, wherein when the crankshaft is mounted in the reciprocating engine, a load
due to combustion pressure is applied to each of the crank pins via a connecting rod in a
direction from an axis of a piston pin to an axis of the crank pin.
Each of the crank arms has an asymmetric shape with respect to a crank arm
centerline connecting the axis of each of the crank pins to an axis of each of the journals,
and
Each of the crank arms has a maximum flexural rigidity at a point of time when
the load onto each of the crank pins due to the combustion pressure reaches a
maximum.
When each of the crank arms is divided by the crank arm centerline into a right
arm portion and a left arm portion,
in each section of each of the crank arms on a plane perpendicular to the crank
arm centerline at a position outward of the axis of the crank pin, an area moment of
inertia of one of the right and the left arm portions that is in a side that is subjected to
the maximum load is greater than an area moment of inertia of the other arm portion
that is in a side opposite to the side that is subjected to the maximum load, and
in each section of each of the crank arms on a plane perpendicular to the crank
arm centerline at a position inward of the axis of the crank pin, the area moment of
inertia of the arm portion that is in the side opposite to the side that is subjected to the
maximum load is greater than the area moment of inertia of the arm portion that is in the
side that is subjected to the maximum load.
[0020]
The crankshaft may be configured such that
in each section of each of the crank arms on a plane perpendicular to the crank
arm centerline at a position outward of the axis of the crank pin, a maximum thickness
of the arm portion that is in the side that is subjected to the maximum load is greater
than a maximum thickness of the arm portion that is in the side opposite to the side that
is subjected to the maximum load, and
in each section of each of the crank arms on a plane perpendicular to the crank
arm centerline at a position inward of the axis of the crank pin, the maximum thickness
of the arm portion that is in the side opposite to the side that is subjected to the
maximum load is greater than the maximum thickness of the arm portion that is in the
side that is subjected to the maximum load.
[002 I ]
Also, the crankshaft may be configured such that
in each section of each of the crank arms on a plane perpendicular to the crank
arm centerline at a position outward of the axis of the crank pin, a width of the arm
portion that is in the side that is subjected to the maximum load is greater than a width
of the arm portion that is in the side opposite to the side that is subjected to the
maximum load, and
in each section of each of the crank arms on a plane perpendicular to the crank
arm centerline at a position inward of the axis of the crank pin, the width of the arm
portion that is in the side opposite to the side that is subjected to the maximum load is
greater than the width of the arm portion that is in the side that is subjected to the
maximum load.
[0022]
(11) A crankshaft design method of the present embodiment is a method for
designing the crankshaft described in the section (I), and the design method includes
designing the shape of each of the crank arms to be asymmetric with respect to
the crank arm centerline such that at the point of time when the maximum load due to
the combustion pressure is applied, the crank arm has a maximum flexural rigidity in a
direction from which the maximum load is applied, thereby meeting a target rigidity,
and such that the crank arm meets a target weight.
[0023]
The crankshaft design method may include designing the shape of each of the
crank arm to allow for minimization of weight of the crank arm under a condition that
the flexural rigidity of the crank arm in the direction from which the maximum load due
to the combustion pressure is applied is fixed.
ADVANTAGEOUS EFFECTS OF INVENTION
[0024]
In the crankshaft according to the present invention, the crank arm has a shape
that is asymmetric with respect to the crank arm centerline, reflecting reality.
Therefore, the flexural rigidity of the crank arm is increased with high reliability, and at
the same time, a reduction in weight of the crank arm can be achieved.
BRIEF DESCRIPTION OF DRAWINGS
[0025]
[FIG. I] FIG. 1 is a schematic side view of an example of a common crankshaft
for a multiple cylinder engine.
[FIG. 21 FIG. 2 is a graph indicating a curve showing the pressure in a cylinder
of a four-cycle engine.
[FIG. 31 FIG.3 is a schematic diagram illustrating a method for evaluating the
flexural rigidity of a crank arm.
[FIG. 41 FIGS. 4(a) and 4(b) are schematic diagrams illustrating a method for
evaluating the torsional rigidity of a crank arm, wherein FIG. 4(a) is a side view of a
throw, and FIG. 4(b) is a front view thereof in the axial direction.
[FIG. 51 FIGS. 5(a) and 5(b) are schematic diagrams showing the shape of a
crank arm of a conventional crankshaft.
[FIG. 61 FIGS. 6 (a) to 6(c) are schematic diagrams showing an example of the
shape of a crank arm of a crankshaft of the present embodiment.
[FIG. 71 FIG. 7 is a conceptual diagram illustrating the latitude of the design
parameter for stiffness of the crank arm of the crankshaft of the present embodiment.
[FIG. 81 FIG. 8 is an illustration showing the geometric relationship between
the crank arm and the conrod of the crankshaft at the point of time when the load of
combustion pressure reaches a maximum.
[FIG. 91 FIG. 9 is a graph showing the correlation between the crank angle 8 at
the point of time when the load of combustion pressure reaches a maximum and the
maximum load angle a.
[FIG. 101 FIG. 10 is a schematic view showing another example of the
geometric relationship between the crank arm and the conrod at the point of time when
the load of combustion pressure reaches a maximum.
[FIG. 111 FIG. 11 is a flowchart showing an example of the outline of design of
the crank arm of the crankshaft of the present embodiment.
[FIG. 121 FIGS. 12(a) and 12(b) are diagrams showing examples of beam
shapes according to the beam theory in the Strength of Materials, wherein FIG. 12(a)
shows a rectangular cross-sectional beam, and FIG. 12(b) shows a beam with a reduced
weight.
[FIG. 131 FIGS. 13(a) to 13(c) are diagrams showing a crank arm having a
laterally asymmetric shape in accordance with the concept of a lightweight beam shown
by Fig. 12(b).
[FIG. 141 FIG. 14 is a chart showing design of the crank arm shape such that
the crank arm has a maximum flexural rigidity at the point of time when the load of
combustion pressure reaches a maximum.
[FIG. 151 FIG. 15 is a chart showing that an objective function to minimize the
weight is equivalent to an objective function to maximize the flexural rigidity in the
crank arm design outline shown in FIG. 11.
[FIG. 161 FIGS. 16(a) to 16(c) are diagrams showing an example of the shape
of the crank arm of the crankshaft of the present embodiment.
[FIG. 171 FIGS. 17(a) to 17(c) are diagrams showing another example of the
shape of the crank arm of the crankshaft of the present embodiment.
[FIG. 181 FIGS. 18(a) to 18(c) are diagrams showing another example of the
shape of the crank arm of the crankshaft of the present embodiment.
[FIG. 191 FIGS. 19(a) to 19(c) are diagrams showing an example of the shape
of a crank arm of a conventional crankshaft.
[FIG.20] FIG. 20 is a graph showing the comparison between the flexural
rigidity of the crank arm of the present embodiment shown by FIGS. 16(a) to 16(c) and
the flexural rigidity of the conventional crank arm shown by FIGS. 19(a) to 19(c).
[FIG. 211 FIG. 21 is a graph showing the comparison between the weight of a
throw including the crank arm of the present embodiment shown by FIGS. 16(a) to
16(c) and the weight of a throw including the conventional crank arm shown by FIGS.
19(a) to 19(c).
DESCRIPTION OF EMBODIMENTS
[0026]
Embodiments of the crankshaft for reciprocating engines according to the
present invention, and a design method thereof will hereinafter be described.
[0027]
1. Basic Techniques to Consider in Designing Crankshaft
1 - 1. Flexural Rigidity of Crank Arm
FIG. 3 is a schematic diagram illustrating a method for evaluating the flexural
rigidity of a crank arm. As shown in FIG. 3, in each throw of the crankshaft, a load F
of combustion pressure generated by the ignition and explosion in the cylinder is
applied to the crank pin P via a conrod. Since the journals J at the both ends of each
throw are supported by bearings, the load F is transmitted to the journal bearings from
the crank pin P via the crank arms A. Thus, each of the crank arms A is put into a state
of being subjected to a load of three-point bending, and a bending moment M acts on
the crank arm A. Accordingly, in each crank arm A, compressive stress occurs at the
outside in the thickness direction (the side adjacent to the journal J), and tensile stress
occurs at the inside in the thickness direction (the side adjacent to the crank pin P). In
this moment, the flexural rigidity Mc of the crank arms A counteracts the stresses. The
flexural rigidity Mc, and the flexural rigidity Mt of the whole one throw including the
flexural rigidity of the crank pin and the flexural rigidity of the journals can be
evaluated as shown by the following formula (1).
[0028]
Mt = Flu . . . (1)
wherein, F represents a load of combustion pressure applied to the crank pin,
and u represents a displacement of the crank pin center with respect to the axial
direction in the load direction of combustion pressure.
100291
1-2. Torsional Rigidity of Crank Arm
FIGS. 4(a) and 4(b) are schematic diagrams illustrating a method for evaluating
the torsional rigidity of a crank arm, wherein FIG. 4(a) is a side view of a throw, and
FIG. 4(b) is a front view thereof in the axial direction. The crankshaft rotates about the
journal J, which causes a torsional torque T as shown in FIGS. 4(a) and 4(b). Thus, it
is necessary to enhance the torsional rigidity of the crank arms A in order to ensure
smooth rotation against the torsional vibrations of the crankshaft without causing
resonance. The torsional rigidity of each throw greatly depends on the torsional
rigidity of the crank arms A in a case where the diameters of the crank pin P and the
journals J have been determined. The torsional rigidity Tc of the crank arms A, and the
torsional rigidity Tt of the whole one throw including the torsional rigidity of the crank
pin and the torsional rigidity of the journals are given by the following formula (2).
[0030]
Tt = Tly . . . (2)
wherein, T represents a torsional torque, and y represents a torsion angle.
[003 11
For these reasons, it is necessary to design a crankshaft to increase both the
flexural rigidity and the torsional rigidity of the crank arms. It is to be noted that the
counterweights W seldom contribute to the flexural rigidity and the torsional rigidity.
Accordingly, the increases in flexural rigidity and in torsional rigidity dominantly
depend on the shape of the crank arms A and do not depend on the shape of the
counterweights W. The counterweights W mainly serve to balance the mass by
adjusting the position of the center of mass and the mass.
[0032]
2. Crankshaft of Present Embodiment and Design Method Thereof
2- 1. Outline
FIGS. 5(a) and 5(b) are schematic diagrams showing the shape of a crank arm
of a conventional crankshaft. FIG. 5(a) is a front view of the crank arm in the axial
direction, and Fig. 5(b) is a side view thereof. As shown in FIGS. 5(a) and 5(b), the
crank arm A of the conventional crankshaft has a shape laterally symmetric with respect
to the crank arm centerline Ac connecting the axis PC of the crank pin P to the axis Jc of
the Journal J. In other words, the crank arm A includes a right arm portion Ar and a
left arm portion Af that are symmetric with respect to the crank arm centerline Ac.
This is because the shape of a crank arm A has been conventionally designed in the
premise that the maximum load on the crank arm A due to the maximum combustion
pressure is applied in the direction along the crank arm centerline Ac.
[0033]
On the other hand, each crank arm of the crankshaft of the present embodiment
has the following features.
FIGS. 6(a) to 6(c) are schematic diagrams showing an example of the shape of
the crank arm of the crankshaft of the present embodiment. FIG. 6(a) is a perspective
view of a throw, FIG. 6(b) is a sectional view thereof on a plane perpendicular to the
crank arm centerline at a position C-C' as indicated in FIG. 6(a), and FIG. 6(c) is a
sectional view thereof on a plane perpendicular to the crank arm centerline at a position
D-D' different from the position C-C' as indicated in Fig. 6(a). The position C-C'
shown by FIG. 6(b) is a position that is outward of the axis of the crank pin. The
position D-D' shown by FIG. 6(c) is a position that is inward of the axis of the crank pin.
As is clear from FIGS. 6(a) and 6(b), the crank arm A of the crankshaft of the present
embodiment has an asymmetric shape with respect to the crank arm centerline Ac. In
other words, the right arm portion Ar and the left arm portion Af of the crank arm A are
asymmetric with respect to the crank arm centerline Ac.
[0034]
Thus, according to the present embodiment, the shape of the crank arm A is
designed in the premise, reflecting reality, that the maximum load due to the maximum
combustion pressure is applied to the crank arm A in the state where the crank angle 8 is
about 8 to 20 degrees. In short, the crank arm shape is designed in the premise that the
maximum load is applied in a direction inclined at an angle a from the crank arm
centerline Ac. The shape of the crank arm A is designed by varying the right arm
portion Ar and the left arm portion Af independently of each other such that the crank
arm A has a maximum flexural rigidity in the direction in which the maximum load is
applied, thereby meeting the target rigidity. It is also necessary to design the shape of
the crank arm A such that the crank arm A meets the target weight.
[0035]
In the following paragraphs, the angle of the direction in which the combustion
pressure is applied to the crank arm A (the direction from the axis of the piston pin to
the axis of the crank pin) to the crank arm centerline Ac will sometimes be referred to as
a load angle P. Among such load angles P, the load angle at which the maximum load
due to the maximum combustion pressure is applied when the crank angle 8 is about 8
to 20 degrees will sometimes be referred to as a maximum load angle a.
[0036]
FIG. 7 is a conceptual diagram illustrating the latitude of the design parameter
for stiffness of the crank arm of the crankshaft of the present embodiment.
[0037]
As shown in FIGS. 6(b) and 6(c), the right arm portion Ar of the crank arm A
of the crankshaft of the present embodiment is extracted for consideration, and the left
arm portion Af of the crank arm A of the crankshaft of the present embodiment is
extracted for consideration. In this case, as shown in Fig. 7, the flexural rigidity Mc of
the whole crank arm A is the sum of the flexural rigidity "Mr12" of the right arm portion
Ar and the flexural rigidity "Mf12" of the left arm portion Af. Similarly, the torsional
rigidity Tc of the whole crank arm A is the sum of the torsional rigidity "Tr12" of the
right arm portion Ar and the torsional rigidity "Tf12" of the left arm portion Af.
[0038]
In FIG. 7, the flexural rigidity Mp and the torsional rigidity Tp of a crank arm
A of a conventional crankshaft are also indicated. Since each crank arm A of the
conventional crankshaft has a laterally symmetric shape, there is only one design
parameter. Accordingly, the flexural rigidity Mp and the torsional rigidity Tp
correspond to the design parameter on a one-to-one basis. Once the design parameter
has been selected, there is no latitude for a combination of the flexural rigidity Mp and
the torsional rigidity Tp.
[0039]
In the crankshaft according to the present embodiment, on the other hand, since
the shape of the right arm portion Ar and the shape of the left arm portion Af of the
crank arm A differ from each other, there are two design parameters. Accordingly, the
flexural rigidity "Mr12" and the torsional rigidity "Tr12" of the right arm portion Ar, and
the flexural rigidity "Mf12" and the torsional rigidity "Tf12" of the left arm portion Af
can be selected independently of each other. The sum of these rigidities becomes the
stiffness of the whole asymmetric crank arm A. This provides more parameter options
for stiffness design that also allows for weight reduction of the crankshaft.
[0040]
In short, while in a conventional crankshaft, the stiffness of each crank arm is
represented by the flexural rigidity Mp and the torsional rigidity Tp, in the crankshaft of
the present embodiment, the stiffness of each crank arm is represented by the following
formulae (3) and (4). Thus, in the crankshaft of the present embodiment, the right
portion and the left portion of each crank arm can be designed independently of each
other, and the crankshaft of the present embodiment has the advantage of having greater
latitude of design choice.
[004 11
Flexural Rigidity: Mc = (Mr+Mf)/2 . . . (3)
Torsional Rigidity: Tc = (Tr+Tf)/2 . . . (4)
[0042]
By appropriately selecting the shapes of the right portion and the left portion of
the crank arm independently of each other for the purpose of reducing the weight, it is
possible that the asymmetric crank arm has greater stiffness than the conventional
symmetric crank arm as shown by the following expressions (5) and (6). In short, this
provides the advantage of greater latitude of design choice for a reduction in weight and
an increase in stiffness.
[0043]
Mc = (Mr+Mf)/2 > Mp . . . (5)
Tc = (Tr+Tf)/2 > Tp . . . (6)
[0044]
FIG. 8 is an illustration showing the geometric relationship between the crank
arm and the conrod of the crankshaft at the point of time when the load of combustion
pressure reaches a maximum. FIG. 9 is a graph showing the correlation between the
crank angle 0 at the point of time when the load of combustion pressure reaches a
maximum and the maximum load angle a. With regard to the bending load, the time
when the combustion pressure in the cylinder reaches a maximum is the point of time
when the crank angle 0 becomes about 8 to 20 degrees by slight rotation of the
crankshaft from the top dead point in the compression process.
[0045]
As shown in FIG. 8, the crank arm A is subjected to the maximum load Fmax
of the maximum combustion pressure in the direction inclined at the maximum load
angle a from the crank arm centerline Ac. The maximum load angle a is determined
as an external angle of a triarigle defined by one angle and two sides, that is, defined by
the crank angle "8" at the point of time when the load of the maximum combustion
pressure is applied the distance "Ls/2", a half of the piston stroke Ls (the distance
between the axis PC of the crank pin P and the axis Jc of the journal J), and the distance
"LC" between the axis 4Sc of the small end 4s of the conrod 4 (the axis of the piston
pin) and the axis PC of the crank pin P. Accordingly, the arm A is subjected to a
bending load at the maximum load angle a (about 10 to a little over 20 degrees), which
is a little greater than the crank angle 9 (about 8 to 20 degrees), to the crank arm
centerline Ac (see Fig. 9).
[0046]
FIG. 10 shows another example of the geometric relationship between the
crank arm and the conrod at the point of time when the load of combustion pressure is
the maximum. In the engine shown by Fig. 10, the axis Jc of the journal J (the rotation
axis of the crankshaft) is offset from the central axis of the cylinder. Alternatively, the
axis Jc of the journal J is located on the central axis of the cylinder, but the axis of the
piston pin is offset from the central axis of the cylinder. In such a case, the maximum
load angle a is determined geometrically from a triangle defined in a similar way to the
triangle defined in the case of Fig. 8 and the amount of offset Lo.
[0047]
2-2. Design Outline
For design of a crank arm to increase the stiffness, actually, it is possible to use
a non-parametric shape optimization software. With such a non-parametric shape
optimization software, it is possible to design a crank arm of a laterally asymmetric
shape having an increased flexural rigidity and an increased torsional rigidity by using,
as a model, a crank arm to be subjected to a maximum bending load applied at a
maximum load angle a of about 10 to a little more than 20 degrees, by setting flexural
rigidity as the object function and by setting weight as the limiting condition.
[0048]
Alternatively, a cut-and-try approach may be used to design the crank arm. In
the cut-and-try approach, a plurality of crank arms, each having a laterally asymmetric
shape, are formed as models, and each of the models undergoes an FEM analysis while
being subjected to a bending load applied at the maximum load angle a and a torsional
torque. Then, the best model that achieves the target stiffness is selected. In this case,
it is possible to obtain a crank arm with an approximately optimized shape.
[0049]
The use of a non-parametric shape optimization software provides a crankshaft
with a reduced weight and an increased stiffness by a more theoretical extreme value
method, and therefore, a non-parametric shape optimization software has the advantage
of bringing a better result. Whatever approach is used for the design, it is essential to
design the crank arm to have a laterally asymmetric shape and to have a maximum
flexural rigidity against a bending load applied at the maximum load angle a.
[OOSO]
FIG. 11 is a flowchart showing an example of the outline of design of the crank
arm of the crankshaft of the present embodiment. Here, a non-parametric shape
optimization software is used. First, a crank arm of a crankshaft is set as the design
region, and a bending load Fmax is applied to an analysis model of a throw at a
maximum load angle a. Next, a limitation is imposed on the shape of the crank arm.
Specifically, allowable ranges are set on the maximum radius of rotation, the draft angle
in a case of a forged crankshaft and the like, from a standpoint of design and
manufacturing limitation.
[OOSl]
In the optimization analysis, an increase in flexural rigidity is set as the object
function, and an analysis is conducted to increase the flexural rigidity as much as
possible with the initial analysis model used as a reference. In this regard, the limiting
condition is a reduction in the weight of the crank arm, and the amount of weight
reduction from the weight of the initial model is set up. When a reduction in weight is
intended, the weight reduction is specified in the form of a weight reduction of minus
X% relative to the initial model.
[0052]
In repeated computation, the shape of the crank arm is changed bit by bit so as
to reduce the weight, that is, to meet the limiting condition first. Once the limiting
condition (weight reduction) is met, next, the shape of the crank arm is changed bit by
bit so as to increase the flexural rigidity, which is the object function, while maintaining
the limiting condition.
[0053]
The flexural rigidity is increased to the maximum, and it is judged whether the
flexural rigidity has reached a (local) maximum value. The local maximum value is
defined as a value of flexural rigidity when the object function (flexural rigidity) no
longer changes, and when the flexural rigidity becomes this state, it is judged that the
computation has been converged. In this moment, the crank arm achieves the target
reduced weight and also achieves the target high flexural rigidity such that the crank
arm theoretically has a maximum flexural rigidity against the maximum bending load
applied at the maximum load angle a. The shape of the crank arm satisfying these
conditions are laterally asymmetric with respect to the crank arm centerline.
[0054]
2-3. Specific Examples
2-3-1. Maximization of Flexural Rigidity as Object Function
In order to design a crank arm to have a maximum flexural rigidity at the point
of time when a bending load is applied at a maximum load angle a, it is a necessary
condition that the crank arm has an asymmetric shape. In the following, simple
specific examples based on Strength of Materials are given. However, the examples
do not exclusively represent the shape of the crank arm.
[0055]
(A) Fundamental Knowledge from Strength of Materials
With regard to flexural rigidity, based on the fundamental knowledge from
Strength of Materials, a rectangular beam is given as an example. The relationship
between the flexural rigidity and the area moment of inertia of the beam is shown by the
following formulae (7) to (9). The relationship shown in the formulae indicates that
increasing the area moment of inertia results in an increase in flexural rigidity.
[0056]
Flexural rigidity: E x I ... (7)
Area moment of inertia: I = (1112) x b x h3 ... (8)
Flexural displacement: v = k(Ml(E x I)) ... (9)
where the cross section of the crank arm is assumed to be rectangular, b
represents the width of the crank arm, h represents the thickness of the crank arm, E
represents the Young's modulus, M represents the bending moment, and k represents the
shape factor.
[0057]
With respect to torsional rigidity, on the other hand, based on the fundamental
knowledge from Strength of Materials, a round bar is given as a simple example. The
relationship between the torsional rigidity and the polar area moment of inertia of the
beam is shown by the following formulae (10) to (12). The relationship shown in the
formulae indicates that increasing the polar area moment of inertia of the beam by
forming the beam to have a circular cross sectional shape results in an increase in
torsional rigidity, which is desired. In this regard, placing materials (mass) far from
the axis of torsion provides an increase in polar area of moment of inertia.
Accordingly, a preferred way to increase the torsional rigidity and at the same time to
reduce the weight is to arrange a large amount of mass in a circle with a large radius of
which center point lies on the axis of torsion or alternatively to arrange the mass in a
circle. Here, the direction of the design guideline is given.
[005S]
Torsional rigidity: Tly ... (10)
Polar area moment of inertia: J = (~132)x d4 ... (1 1)
Torsion angle: y = T x LI(G x J) ... (12)
where L represents the axial length, G represents the modulus of rigidity, d
represents the radius of the round bar, and T represents the torsional torque.
[0059]
Generally, crank arms of a crankshaft are required to have a high flexural
rigidity. Also, practically, crank arms are required to have a high torsional rigidity.
Therefore, it is preferred to increase the flexural rigidity of the crank arms and
concurrently increase the torsional rigidity of the crank arms. However, the increase in
torsional rigidity is an additional improvement, and in the following, the torsional
rigidity will not particularly be discussed.
[0060]
(B) Description of Laterally Asymmetric Crank Arm Shape Allowing for Weight
Lightness and High Stiffness against Bending
As described above, the maximum bending load is applied to the crank arm in
the direction inclined at the maximum load angle a from the crank arm centerline.
From this viewpoint, it is an effective way to modify a beam-like crank arm having a
reduced weight and high stiffness into a laterally asymmetric shape. The reason will
be described in the following.
[0061]
FIGS. 12(a) and 12(b) show examples of beam shapes according to the beam
theory in Strength of Materials. FIG. 12(a) shows a rectangular beam, and FIG. 12(b)
shows a beam that is reduced in weight. A crank arm will hereinafter be considered
simply in terms of Strength of Materials, based on the beam theory. In consideration
of receiving a bending load, the two-dimensional shape of the most lightweight beam
(having a constant board thickness t) that is high in stiffness and low in deformability is
not a rectangular beam having a constant board width B as shown in FIG. 12(a) but a
lightweight beam of which board width B simply increases from the load point to the
fixed end as shown in FIG. 12(b).
[0062]
FIGS. 13(a) to 13(c) show a crank arm having a laterally asymmetric shape in
accordance with the concept for weight reduction of a beam shown by Fig. 12(b). FIG.
13(a) is a perspective view, and FIGS. 13(b) and 13(c) are sectional views on planes
perpendicular to the crank arm centerline. FIG. 13(b) is a sectional view at a position
outward of the axis of the crank pin, that is, a sectional view at a position shifted from
the axis of the crank pin in the direction away from the journal. FIG. 13(c) is a
sectional view at a position inward of the axis of the crank pin, that is, a sectional view
at a position shifted from the axis of the crank pin in the direction toward the journal.
A crank arm A as shown by FIG. 8 or 10 which is subjected to the maximum bending
load applied from the direction inclined at the maximum load angle a from the crank
arm centerline is considered to be a crank arm as shown by Fig. 13(a) that is a laminate
of a plurality of beams with a board thickness of t. By configuring each of the
plurality of beams to be a lightweight beam as shown by FIG. 12(b) of which board
thickness B simply increases toward the fixed end, a crank arm A that is the most
lightweight and high in stiffness can be obtained.
[0063]
When the crank arm A is cut along planes perpendicular to the crank arm
centerline Ac as shown in FIG. 13(a), geometrically, the sections are laterally
asymmetric shapes with respect to the crank arm centerline Ac as shown by FIGS. 13(b)
and 13(c). Specifically, the crank arm A is divided into a right arm portion Ar and a
left arm portion Af with the crank arm centerline Ac marking the border therebetween,
and the right arm portion Ar and the left arm portion Af are asymmetric with respect to
the crank arm centerline Ac.
[0064]
Configuring the crank arm A to be laterally asymmetric is an efficient way to
provide a lightweight crank arm A of which stiffness is increased sufficiently to resist
against the maximum bending load applied to the crank arm A at the maximum load
angle a. Various asymmetric shapes are possible as the shape of the crank arm A.
For example, designing the crank arm A, with the load angle P used as a parameter and
varied, to have a maximum flexural rigidity at the point of time when the load angle P
becomes the maximum load angle a (that is, at the point of time when the load due to
the combustion pressure reaches a maximum) as shown in Fig. 14 is the most efficient
way to obtain a lightweight crank arm A with no excess volume. Thereby, the crank
arm A is the most lightweight and high in stiffness, and the crankshaft can deliver the
best possible performance.
[0065]
In this regard, as shown in FIG. 13(b), on a cross section at a position outward
of the axis of the crank pin, the area moment of inertia of the left arm portion Af that is
in the side that is subjected to the maximum load is greater than the area moment of
inertia of the right arm portion Ar that is in the side opposite to the side that is subjected
to the maximum load. Also, as shown in FIG. 13(c), on a cross section at a position
inward of the axis of the crank pin, the area moment of inertia of the right arm portion
Ar that is in the side opposite to the side that is subjected to the maximum load is
greater than the area moment of inertia of the left arm portion Af that is in the side that
is subjected to the maximum load.
[0066]
2-3-2. Minimization of Weight as Object Function
As described above, designing a crank arm to have a minimum weight under
the condition that the flexural rigidity of the crank arm at the point of time when a
bending load is applied thereto at the maximum load angle a is fixed is equivalent to
designing the crank arm to have a maximum flexural rigidity at the point of time when a
bending load is applied thereto at the maximum load angle a. In short, minimizing the
weight as an object function is another expression of maximizing the flexural rigidity.
Optimal design in either of these ways provides the same crank arm shape, which means
that the requirements are the same.
[0067]
FIG. 15 is a chart indicating that in the outline of design of a crank arm shown
in FIG. 11, setting minimization of weight as the object function is equivalent to setting
maximization of flexural rigidity as the object function. FIG. 15 shows two
approaches to optimal design of a crank arm: an approach where an increase in stiffness
is set as the limiting condition, and a reduction in weight is set as the object function
(right side in FIG. 15), and an approach where these are interchanged, that is, a
reduction in weight is set as the limiting condition, and an increase in stiffness is set as
the object function (left side in FIG. 15). These approaches to optimal design provide
the same shape as the finally converged and designed shape though different processes.
For example, either of the approaches provides, as the finally converged and designed
shape, the same crank arm shape with a reduction in weight by minus B % and an
increase in stiffness by A %.
[0068]
2-3-3. Examples of Crank Arm Shape
FIGS. 16(a) to 16(c) are diagrams showing an example of the shape of a crank
arm of a crankshaft of the present embodiment. FIGS. 17(a) to 17(c) and 18(a) to
18(c) are diagrams showing other examples thereof. Any of the figures provided with
a reference symbol (a) is a perspective view of a throw, and any of the figures provided
with a reference symbol (b) is a sectional view on a plane perpendicular to the crank
arm centerline at a position C-C'. Further, any of the figures provided with a reference
symbol (c) is a sectional view on a plane perpendicular to the crank arm centerline at a
position D-D', which is different from the position C-C'. The position C-C' shown by
the figures provided with the reference symbol (b) is a position that is outward of the
axis of the crank pin. The position D-D' shown by the figures provided with the
reference symbol (c) is a position that is inward of the axis of the crank pin.
[0069]
Each of the crank arms shown by FIGS. 16(a) to 16(c), FIGS. 17(a) to 17(c)
and FIGS. 18(a) to 18(c) is lightweight and high in stiffness, and has an asymmetric
shape with respect to the crank arm centerline Ac. These crank arm shapes are derived
along the design outline by use of a non-parametric shape optimization software as
shown by FIG. 11 under the condition that a bending load is applied at the maximum
load angle a. Specifically, the shape of the crank arm A is designed to be laterally
asymmetric with respect to the crank arm centerline Ac such that the crank arm A has a
maximum flexural rigidity at the point of time when the load on the crank pin due to the
combustion pressure reaches a maximum. Thus, the crank arm A has a laterally
asymmetric shape with respect to the crank arm centerline Ac. Further, as shown by
the figures provided with the reference symbol (b), in a section at a position outward of
the axis of the crank pin P, the area moment of inertia of the left arm portion Af that is in
the side that is subjected to the maximum load is greater than the area moment of inertia
of the right arm portion Ar that is in the side opposite to the side that is subjected to the
maximum load. Also, as shown by the figures provided with the reference symbol (c),
in a section at a position inward of the axis of the crank pin P, the area moment of
inertia of the right arm portion Ar that is in the side opposite to the side that is subjected
to the maximum load is greater than the area moment of inertia of the left arm portion
Af that is in the side that is subjected to the maximum load.
[0070]
With regard to the crank arm A shown by FIGS. 16(a) to 16(c), in a section at a
position outward of the axis of the crank pin P, the maximum thickness Baf of the left
arm portion Af is greater than the maximum thickness Bbr of the right arm portion Ar
(see FIG. 16(b)), and in a section at a position inward of the axis of the crank pin P, the
maximum thickness Baf of the left arm portion Af is smaller than the maximum
thickness Bar of the right arm portion Ar (see FIG. 16(c)).
[007 11
The crank arm A shown by FIGS. 17(a) to 17(c) is a modification of the crank
arm A shown by FIGS. 16(a) to 16(c). The difference is as follows. With regard to
the crank arm A shown by FIGS. 17(a) to 17(c), in a section at a position outward of the
axis of the crank pin P, the width Wf of the left arm portion Af is greater than the width
Wr of the right arm portion Ar (see FIG. 16(b)), and in a section at a position inward of
the axis of the crank pin P, the width Wf of the left arm portion Af is smaller than the
width Wr of the right arm portion Ar (see FIG. 16(c)).
[0072]
The crank arm A shown by FIGS. 18(a) to 18(c) is a modification of the crank
arm A shown by FIGS. 17(a) to 17(c). The difference is as follows. With regard to
the crank arm A shown by FIGS. 18(a) to 18(c), the maximum thickness is laterally
symmetric with respect to the crank arm centerline Ac.
[0073]
The conventional crank arm A shown by FIGS. 19(a) to 19(c), however, has a
laterally symmetric shape with respect to the crank arm centerline Ac.
[0074]
FIG. 20 is a graph showing the comparison between the flexural rigidity of the
crank arm of the present embodiment shown by FIGS. 16(a) to 16(c) and the flexural
rigidity of the conventional crank arm shown by FIGS. 19(a) to 19(c). FIG. 21 is a
graph showing the comparison between the weight of a throw including the crank arm
of the present embodiment shown by FIGS. 16(a) to 16(c) and the weight of a throw
including the conventional crank arm shown by FIGS. 19(a) to 19(c). In each of the
graphs, the comparison is shown by a proportion with the value of the conventional
crank arm or throw assumed to be a reference (1 00 %).
[0075]
As is clear from FIG. 20, the flexural rigidity of the crank arm of the present
embodiment is greater than that of the conventional crank arm. As is clear from FIG.
21, the weight of a throw including the crank arm of the present embodiment is smaller
than that of a throw including the conventional crank arm. In conclusion, a crank arm
having an asymmetric shape, like the crank arm of the present embodiment, is
lightweight and high in flexural rigidity.
[0076]
As thus far described, the crankshaft of the present embodiment is configured
to fit for reality, and specifically, each crank arm of the crankshaft is configured to be
asymmetric with respect to the crank arm centerline. Thereby, the crankshaft is
improved in flexural rigidity with high reliability and at the same time, is reduced in
weight. Such a crankshaft can be obtained effectually by a design method of the
present embodiment.
[0077]
The present invention is applicable to crankshafts to be mounted in a variety of
reciprocating engines. Specifically, the engine may have any number of cylinders as
well as four cylinders, for example, two cylinders, three cylinders, six cylinders, eight
cylinders or ten cylinders, and even more cylinders. The cylinder arrangement may be
of any type, for example, in-line type, V-type, opposed type or the like. The fuel for
the engine may be of any kind, for example, gasoline, diesel, biofuel or the like. Also,
the engines include a hybrid engine consisting of an internal-combustion engine and an
electric motor.
INDUSTRIAL APPLICABILITY
[0078]
The present invention is capable of being effectively utilized in crankshafts to
be mounted in a variety of reciprocating engines.
DESCRIPTION OF REFERENCE SYMBOLS
[0094]
1 : crankshaft
J, J 1 to J5: journal
Jc: axis of journal,
P, P1 to P4: crank pin
PC: axis of crank pin
Fr: front part
FI: flange
A, A1 to AS: crank arm
Ac: crank arm centerline
Ar: right arm portion
Af: left arm portion
W, W 1 to W8: counterweight
2: damper pulley
3: flywheel
4: connecting rod
4s: small end
4Sc: axis of small end (axis of piston pin)

We claim:
1. A crankshaft for a reciprocating engine, the crankshaft comprising:
journals that define a central axis of rotation;
crank pins that are eccentric with respect to the journals;
crank arms connecting the journals to the crank pins; and
counterweights integrated with the crank arms,
wherein when the crankshaft is mounted in the reciprocating engine, a load due
to combustion pressure is applied to each of the crank pins via a connecting rod in a
direction from an axis of a piston pin to an axis of the crank pin;
wherein each of the crank arms has an asymmetric shape with respect to a
crank arm centerline connecting the axis of each of the crank pins to an axis of each of
the journals;
wherein each of the crank arms has a maximum flexural rigidity at a point of
time when the load onto each of the crank pins due to the combustion pressure reaches a
maximum; and
wherein when each of the crank arms is divided by the crank arm centerline
into a right arm portion and a left arm portion,
in each section of each of the crank arms on a plane perpendicular to the crank
arm centerline at a position outward of the axis of the crank pin, an area moment of
inertia of one of the right and the left arm portions that is in a side that is subjected to
the maximum load is greater than an area moment of inertia of the other arm portion
that is in a side opposite to the side that is subjected to the maximum load, and
in each section of each of the crank arms on a plane perpendicular to the crank
arm centerline at a position inward of the axis of the crank pin, the area moment of
inertia of the arm portion that is in the side opposite to the side that is subjected to the
maximum load is greater than the area moment of inertia of the arm portion that is in the
side that is subjected to the maximum load.
2. The crankshaft for a reciprocating engine according to claim I,
wherein in each section of each of the crank arms on a plane perpendicular to
the crank arm centerline at a position outward of the axis of the crank pin, a maximum
thickness of the arm portion that is in the side that is subjected to the maximum load is
greater than a maximum thickness of the arm portion that is in the side opposite to the
side that is subjected to the maximum load; and
wherein in each section of each of the crank arms on a plane perpendicular to
the crank arm centerline at a position inward of the axis of the crank pin, the maximum
thickness of the arm portion that is in the side opposite to the side that is subjected to
the maximum load is greater than the maximum thickness of the arm portion that is in
the side that is subjected to the maximum load.
3. The crankshaft for a reciprocating engine according to claim 1 or 2,
wherein in each section of each of the crank arms on a plane perpendicular to
the crank arm centerline at a position outward of the axis of the crank pin, a width of the
arm portion that is in the side that is subjected to the maximum load is greater than a
width of the arm portion that is in the side opposite to the side that is subjected to the
maximum load; and
wherein in each section of each of the crank arms on a plane perpendicular to
the crank arm centerline at a position inward of the axis of the crank pin, the width of
the arm portion that is in the side opposite to the side that is subjected to the maximum
load is greater than the width of the arm portion that is in the side that is subjected to the
maximum load.
4. A method for designing the crankshaft for a reciprocating engine according to
any one of claims 1 to 3, including
designing the shape of each of the crank arms to be asymmetric with respect to
the crank arm centerline such that at the point of time when the maximum load due to
the combustion pressure is applied, the crank arm has a maximum flexural rigidity in a
direction from which the maximum load is applied, thereby meeting a target rigidity,
and such that the crank arm meets a target weight.
5. A method for designing the crankshaft according to claim 4, comprising
designing the shape of each of the crank arms to allow for minimization of
weight of the crank arm under a condition that the flexural rigidity of the crank arm in
the direction from which the maximum load due to the combustion pressure is applied is
fixed.