U.S. patent application number 15/877500 was filed with the patent office on 2018-08-02 for analysis method for analyzing deformation of casting in die casting process.
This patent application is currently assigned to TOYOTA JIDOSHA KABUSHIKI KAISHA. The applicant listed for this patent is TOYOTA JIDOSHA KABUSHIKI KAISHA. Invention is credited to Hiroyuki IKUTA, Shoichi TSUCHIYA.
Application Number | 20180214938 15/877500 |
Document ID | / |
Family ID | 61027588 |
Filed Date | 2018-08-02 |
United States Patent
Application |
20180214938 |
Kind Code |
A1 |
TSUCHIYA; Shoichi ; et
al. |
August 2, 2018 |
ANALYSIS METHOD FOR ANALYZING DEFORMATION OF CASTING IN DIE CASTING
PROCESS
Abstract
An analysis method for analyzing deformation of a casting in a
die casting process includes obtaining a first die frictional
stress exerted by a first die on the casting in a mold opening
step, and calculating deformation of the casting in the mold
opening step using the first die frictional stress. A predetermined
frictional coefficient function is selected from a plurality of
frictional coefficient functions based on casting conditions and
lubrication conditions. A frictional coefficient at each portion of
the casting is output by inputting a temperature of a contact
surface between the casting and the first die and a contact surface
pressure therebetween into the selected predetermined frictional
coefficient function. The first die frictional stress acting on
each portion of the casting is obtained by multiplying the contact
surface pressure and the frictional coefficient.
Inventors: |
TSUCHIYA; Shoichi;
(Toyota-shi, JP) ; IKUTA; Hiroyuki; (Nisshin-shi,
JP) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
TOYOTA JIDOSHA KABUSHIKI KAISHA |
Toyota-shi |
|
JP |
|
|
Assignee: |
TOYOTA JIDOSHA KABUSHIKI
KAISHA
Toyota-shi
JP
|
Family ID: |
61027588 |
Appl. No.: |
15/877500 |
Filed: |
January 23, 2018 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
B22D 17/16 20130101;
B22D 17/32 20130101; B22D 17/2236 20130101; B22D 17/22 20130101;
B22D 17/2015 20130101; B22D 17/10 20130101 |
International
Class: |
B22D 17/16 20060101
B22D017/16; B22D 17/22 20060101 B22D017/22; B22D 17/20 20060101
B22D017/20; B22D 17/32 20060101 B22D017/32 |
Foreign Application Data
Date |
Code |
Application Number |
Jan 27, 2017 |
JP |
2017-013217 |
Claims
1. An analysis method for analyzing deformation of a casting in a
die casting process, the die casting process including: a step of
closing a mold by pressing a second die against a first die, and
injecting molten metal into cavities of the first die and the
second die and solidifying the molten metal to form the casting
inside the cavities; and a mold opening step of opening the mold by
separating the second die from the first die with the casting held
in the second die, the analysis method comprising: obtaining a
first die frictional stress exerted by the first die on the casting
in the mold opening step; and calculating deformation of the
casting in the mold opening step using the first die frictional
stress wherein a predetermined frictional coefficient function from
a plurality of different frictional coefficient functions based on
casting conditions and lubrication conditions is selected, and a
frictional coefficient at each portion of the casting is output by
inputting a temperature of a contact surface between the casting
and the first die and a contact surface pressure between the
casting and the first die into the predetermined frictional
coefficient function, and then the first die frictional stress
acting on each portion of the casting is calculated by multiplying
the contact surface pressure exerted by the casting on the first
die and the frictional coefficient.
2. The analysis method according to claim 1, wherein in the mold
opening step, the frictional coefficient is a static frictional
coefficient from a time point at which the mold opening is started
until immediately before a time point at which the second die is
separated from the first die, and the frictional coefficient is a
dynamic frictional coefficient from the time point at which the
second die and the first die are separated from each other until a
time point at which the casting is separated from the second
die.
3. The analysis method according to claim 1, wherein an amount of
movement that the casting moves in the mold opening step from a
time point at which the mold opening is started until a time point
at which the casting is separated from the second die is obtained
based on a draft of the first die and amounts of elastic
deformation of the first die and the casting, and the amounts of
elastic deformation of the first die and the casting are obtained
using moduli of elasticity of the first die and the casting, the
moduli of elasticity of the first die varying with a temperature of
the first die, the moduli of elasticity of the casting varying with
a temperature of the casting.
4. The analysis method according to claim 1, wherein the die
casting process further includes a mold releasing step of releasing
the casting from the second die after the mold opening step, and
the analysis method further comprises obtaining a second die
frictional stress exerted by the second die on the casting when an
ejector pin is thrust out of the cavity of the second die in the
mold releasing step, and calculating deformation of the casting in
the mold releasing step using the second die frictional stress.
Description
INCORPORATION BY REFERENCE
[0001] The disclosure of Japanese Patent Application No.
2017-013217 filed on Jan. 27, 2017 including the specification,
drawings and abstract is incorporated herein by reference in its
entirety.
BACKGROUND
1. Technical Field
[0002] The present disclosure relates to an analysis method for
analyzing deformation of a casting in a die casting process.
2. Description of Related Art
[0003] Japanese Patent Application Publication No. 07-009522
discloses an injection molding process simulation method that
involves sequentially conducting analyses of filling, fluid flow
under hold pressure, and cooling in an injection molding process,
and calculating a temperature change of a molding material
undergoing the injection molding process etc., and thus calculating
the amount of shape deformation of a final product etc. In the
cooling analysis, temperature boundary conditions are changed
according to a state of contact between a surface of a molding and
a surface of a mold. This injection molding process simulation
method can be used to obtain a distribution of stress acting on a
part of a product, and estimate mold release resistance up to mold
opening based on this stress distribution, the area of a part of
the product in contact with the mold, and a coefficient of friction
between the product and the mold.
SUMMARY
[0004] The present inventors have conceived of applying the method
disclosed by JP 07-009522 A to analyzing melt flow, a mold
temperature distribution, and casting solidification in a die
casting process, and thereby calculating deformation of a casting
after the casting is released from a mold. We have found room for
improvement in the accuracy of such an analysis of deformation of a
casting after its release from a mold.
[0005] An analysis method for analyzing deformation of a casting in
a die casting process according to the present disclosure improves
the accuracy of an analysis of casting deformation.
[0006] An aspect of the present disclosure relates to an analysis
method for analyzing deformation of a casting in a die casting
process including: a step of closing a mold by pressing a second
die against a first die, and injecting molten metal into cavities
of the first die and the second die and solidifying the molten
metal to form a casting inside the cavities; and a mold opening
step of opening the mold by separating the second die from the
first die with the casting held in the second die. An aspect of the
present disclosure includes: obtaining a first die frictional
stress exerted by the first die on the casting in the mold opening
step, and calculating deformation of the casting in the mold
opening step using the first die frictional stress. A predetermined
frictional coefficient function from a plurality of different
frictional coefficient functions based on casting conditions and
lubrication conditions is selected, and a frictional coefficient at
each portion of the casting is output by inputting a temperature of
a contact surface between the casting and the first die and a
contact surface pressure between the casting and the first die into
the selected predetermined frictional coefficient function; and
then the first die frictional stress acting on each portion of the
casting is calculated by multiplying the contact surface pressure
exerted by the casting on the first die and the frictional
coefficient. According to this configuration, the first die
frictional stress exerted by the first die on the casting during
mold opening can be taken into account in analyzing deformation of
the casting. The value of the first die frictional stress varies
according to the casting conditions, the lubrication conditions,
the temperature of the contact surface between the casting and
first die, and the contact surface pressure between the casting and
the first die, and agrees with actual frictional stress in an
actual test of deformation of a casting in a die casting process.
Therefore, the accuracy of an analysis of casting deformation can
be improved.
[0007] In the mold opening step, the frictional coefficient may be
a static frictional coefficient from a time point at which the mold
opening is started until immediately before a time point at which
the second die is separated from the first die, and the frictional
coefficient may be a dynamic frictional coefficient from the time
point at which the second die and the first die are separated from
each other until a time point at which the casting is separated
from the second die. According to this configuration, the first die
frictional stress can be obtained in the mold opening step by using
either a static frictional coefficient .mu.0 or a dynamic
frictional coefficient .mu.1 depending on the time point in the
step. Thus, the value of the first die frictional stress agrees
with actual frictional stress in an actual test of deformation of a
casting in a die casting process, so that the accuracy of an
analysis of casting deformation can be further improved.
[0008] The amount of movement that the casting moves in the mold
opening step from the time point at which the mold opening is
started until the time point at which the casting is separated from
the second die may be obtained based on a draft of the first die
and the amounts of elastic deformation of the first die and the
casting, and the amounts of elastic deformation of the first die
and the casting may be obtained using the moduli of elasticity of
the first die and the casting, the modulus of elasticity of the
first die varying with a temperature of the first die, the modulus
of elasticity of the casting varying with a temperature of the
casting. According to this configuration, the amounts of elastic
deformation of the first die and the casting can be obtained using
the moduli of elasticity of the first die and the casting according
to their respective temperatures, and moreover, the amount of
movement that the casting moves in the mold opening step from the
time point at which the mold opening is started until the time
point at which the casting is separated from the second die can be
obtained. Thus, the value of the first die frictional stress agrees
with actual frictional stress in an actual test of deformation of a
casting in a die casting process, so that the accuracy of an
analysis of casting deformation can be further improved.
[0009] The die casting process may further include a mold releasing
step of releasing the casting from the second die after the mold
opening step, and the analysis method may further include obtaining
a second die frictional stress exerted by the second die on the
casting when an ejector pin is thrust out of the cavity of the
second die in the mold releasing step, and calculating deformation
of the casting in the mold releasing step using the second die
frictional stress. According to this configuration, the second die
frictional stress exerted by the second die on the casting can be
taken into account in obtaining deformation of the casting in the
mold releasing step. The accuracy of an analysis of casting
deformation can be further improved by taking into account both the
obtained casting deformation in the mold releasing step and the
casting deformation in the mold opening step.
[0010] The analysis method for analyzing deformation of a casting
in a die casting process according to the present disclosure can
improve the accuracy of an analysis of casting deformation.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] Features, advantages, and technical and industrial
significance of exemplary embodiments of will be described below
with reference to the accompanying drawings, in which like numerals
denote like elements, and wherein:
[0012] FIG. 1 is a flowchart showing a method for analyzing
deformation of a casting in a die casting process according to the
embodiment;
[0013] FIG. 2 is the flowchart showing the method for analyzing
deformation of a casting in a die casting process, and a block
diagram showing calculation items, according to the embodiment;
[0014] FIG. 3 is a schematic view showing an analysis model that is
used in the method for analyzing deformation of a casting in a die
casting process according to the embodiment;
[0015] FIG. 4 is a main part of a table showing casting conditions
and lubrication conditions that is used in the method for analyzing
deformation of a casting in a die casting process according to the
embodiment;
[0016] FIG. 5 is a graph showing a frictional coefficient .mu.
relative to a contact surface temperature and a contact surface
pressure;
[0017] FIG. 6 is a schematic view showing a boundary surface
between a casting and a mold in a mold opening step;
[0018] FIG. 7 is a schematic view showing the boundary surface
between the casting and the mold in the mold opening step;
[0019] FIG. 8 is a schematic view showing the boundary surface
between the casting and the mold in the mold opening step; and
[0020] FIG. 9 is a graph showing a specific example of stress and a
frictional coefficient relative to the amount of movement of the
casting.
DETAILED DESCRIPTION OF EMBODIMENTS
[0021] A method for analyzing deformation of a casting in a die
casting process according to the embodiment will be described with
reference to FIG. 1 to FIG. 9. FIG. 1 is a flowchart showing the
method for analyzing deformation of a casting in a die casting
process according to the embodiment. FIG. 2 is the flowchart
showing the method for analyzing deformation of a casting in a die
casting process, and a block diagram showing calculation items,
according to the embodiment. FIG. 3 is a schematic view showing an
analysis model that is used in the method for analyzing deformation
of a casting in a die casting process according to the embodiment.
FIG. 4 is a main part of a table showing casting conditions and
lubrication conditions that is used in the method for analyzing
deformation of a casting in a die casting process according to the
embodiment. FIG. 5 is a graph showing a frictional coefficient .mu.
relative to a contact surface temperature and a contact surface
pressure. FIG. 6 to FIG. 8 are schematic views showing a boundary
surface between a casting and a mold in a mold opening step. FIG. 9
is a graph showing a specific example of stress and a frictional
coefficient relative to the amount of movement of the casting.
[0022] In the method for analyzing deformation of a casting in a
die casting process according to the embodiment, casting
deformation is calculated by computer aided engineering (CAE) using
the die casting process shown in FIG. 3 as a model. A wide variety
of numerical analysis techniques can be used in this analysis
method. For example, various methods including a finite volume
method, finite difference method, finite element method, and
particle method can be used in a melt flow analysis. A plurality of
types of these numerical analysis techniques may be used in
combination as necessary. This model includes molten metal (not
shown), a casting P1, a fixed die 1 (a first die), a movable die 2
(a second die), a sleeve 3, and a plunger 4. In the die casting
process shown in FIG. 3, the casting P1 is formed by solidifying
the molten metal (not shown) using the fixed die 1, the movable die
2, the sleeve 3, and the plunger 4. For example, a die casting
aluminum alloy can be used for the molten metal and the casting P1.
The fixed die 1 and the movable die 2 are installed in a casting
machine (not shown) and their respective actions are controlled.
The sleeve 3 and the plunger 4 are components of this casting
machine. The sleeve 3 is held in a predetermined position, and the
plunger 4 is held so as to be able to reciprocate inside the sleeve
3 in an axial direction of the sleeve 3.
[0023] The die casting process will be specifically described.
First, the mold is closed by pressing the movable die 2 against the
fixed die 1 into close contact. A cavity C1 of the fixed die 1 and
a cavity C2 of the movable die 2 are butted together, and thus the
cavities C1, C2 having the same or almost the same shape as the
casting P1 are formed. The molten metal is poured through a molten
metal inlet 3c of the sleeve 3, and the plunger 4 is pushed in
toward the movable die 2, and thus the molten metal is injected to
fill the cavities C1, C2. After filling, a predetermined pressure
is applied to the molten metal, and the molten metal is solidified
in this state. When the molten metal has solidified and the casting
P1 has been formed, the volume of the casting P1 has become smaller
than the volume of the molten metal due to solidification shrinkage
and thermal shrinkage. As a result of the solidification shrinkage
and the thermal shrinkage, an air gap (clearance) is left at an
interface between the casting P1 and the cavity C 1 of the fixed
die 1 and at an interface between the casting P1 and the cavity C2
of the movable die 2. The mold is opened by separating the movable
die 2 from the fixed die 1 with the casting P1 held in the movable
die 2. The casting P1 is released from the movable die 2 by pushing
the casting P1 out of the cavity C2 of the movable die 2 using
ejector pins 21 that can be thrust out of the cavity C2 toward an
outside of the movable die 2, in other words, toward the fixed die
1. Thus, the casting P1 is formed.
[0024] First, the melt flow analysis is conducted (melt flow
calculation step ST1). Specifically, first, the mold is closed by
pressing the movable die 2 against the fixed die 1. The flow of the
molten metal from when the molten metal is poured through the
molten metal inlet 3c of the sleeve 3 with the mold closed until
when the molten metal is injected to fill the cavities C1, C2 as
the plunger 4 is pushed in toward the movable die 2 is
calculated.
[0025] Next, temperature distributions in the fixed die 1 and the
movable die 2 are calculated (mold temperature distribution
calculation step ST2). Specifically, the temperature distributions
in the fixed die 1 and the movable die 2 from a time point at which
the molten metal is poured through the molten metal inlet 3c of the
sleeve 3 until a time point at which the molten metal is injected
to fill the cavities C1, C2 and solidified under pressure are
calculated.
[0026] Next, solidification shrinkage of the molten metal is
calculated (solidification shrinkage calculation step ST3).
Specifically, solidification shrinkage resulting when the molten
metal solidifies in the cavities of the fixed die 1 and the movable
die 2 and the casting P1 is formed is calculated.
[0027] Next, the air gap is calculated (air gap calculation step
ST4). As described above, the air gap (clearance) is left at the
interface between the casting P1 and the cavity C1 of the fixed die
1 and at the interface between the casting P1 and the cavity C2 of
the movable die 2, as the molten metal and the casting P1 undergo
thermal shrinkage and solidification shrinkage upon solidification
of the molten metal inside the cavities C1, C2 of the fixed die 1
and the movable die 2. For example, the position, size, and range
of this air gap, and a time point at which it occurs are
calculated. Specifically, the form of heat migration at the
interface between the molten metal or the casting P1 and the fixed
die 1 and the form of heat migration at the interface between the
molten metal or the casting P1 and the movable die 2 change from
heat conduction to heat transfer. A time point at which this change
in the form of heat migration occurs is calculated (see FIG.
2).
[0028] Next, changes in product cooling conditions, changes in a
product temperature distribution, and changes in a product strength
distribution are calculated in the order mentioned based on the
result of the above air gap calculation, and deformation of the
casting P1 inside the fixed die 1 and the movable die 2 (see FIG.
2), for example, the amount of deformation at each time point and
each portion of the casting P1 is calculated. Next, changes in the
mold temperature distribution that are changes in the temperature
distributions in the fixed die 1 and the movable die 2 are
calculated based on the time point at which the form of heat
migration changes. Changes in product residual stress are
calculated using the calculated changes in the mold temperature
distribution and the above-mentioned changes in the product cooling
conditions. Thus, the amount of deformation due to release of
residual stress (see FIG. 2) can be obtained.
[0029] Next, a contact surface pressure N is calculated based on
the residual stress (contact surface pressure calculation step
ST5). The contact surface pressure N is a pressure with which each
portion of the casting P1 presses each contact portion of the
cavity C1 of the fixed die 1 and the cavity C2 of the movable die
2.
[0030] As can be seen by referring to the following Formula 1, the
contact surface pressure N may be represented by a function f2 of
an amount of movement Lmove and a contact surface temperature
Temp:
N=f2(Lmove, Temp) (Formula 1)
[0031] Finally, casting deformation after mold opening is
calculated (post-mold opening casting deformation calculation step
ST6).
[0032] First, in the mold opening step, deformation of the casting
P1 from time point T0 at which mold opening is started until time
point T2 at which the casting P1 is separated from the fixed die 1
is obtained using a fixed die frictional stress F, a temperature
distribution in the casting P1, and a product strength distribution
in the casting P1 (mold opening step-caused casting deformation
calculation step ST61).
[0033] The relation among the fixed die frictional stress F, the
frictional coefficient .mu., and the contact surface pressure N
satisfies the following Formula 2:
F=.mu..times.N (Formula 2)
[0034] As shown in FIG. 9, the relation among a fixed die
frictional stress F0, a frictional coefficient .mu.0, and a contact
surface pressure N0 when the amount of movement Lmove is zero
satisfies the following Formula 2A:
F=.mu.0.times.NO (Formula 2A)
[0035] The relation among the fixed die frictional stress F, a
frictional coefficient 0, and the contact surface pressure N when
the amount of movement Lmove is larger than zero satisfies the
following Formula 2B:
F=.mu.1.times.N (Formula 2B)
[0036] Frictional Coefficient .mu.
[0037] Here, the frictional coefficient .mu. is obtained.
Specifically, first, casting conditions and lubrication conditions
are determined, and thereby a frictional coefficient function is
selected. A plurality of different types of frictional coefficient
functions are obtained in advance by conducting a casting
experiment under predetermined casting conditions and predetermined
lubrication conditions. For each casting condition and each
lubrication condition, the frictional coefficient functions include
a frictional coefficient function f0 for a static frictional
coefficient and a frictional coefficient function f1 for a dynamic
frictional coefficient. Input variables of the frictional
coefficient function are the contact surface temperature Temp and
the contact surface pressure N, and an output variable thereof is
the frictional coefficient .mu.. In other words, when the contact
surface temperature Temp and the contact surface pressure N are
input into the frictional coefficient function, this frictional
coefficient function outputs the frictional coefficient More
specifically, as shown in FIG. 4, various manufacturing conditions
including the casting conditions and the lubrication conditions are
selected. The casting conditions and the lubrication conditions are
determined in advance according to a product to be manufactured.
For example, the casting conditions shown in FIG. 4 include (1) M/T
(manual transmission) case, (2) A/T (automatic transmission) case,
and (3) O/P (oil pan). When these items (1) to (3) are determined,
the casting conditions shown in FIG. 4 are specifically the
material of the mold, the surface material of the mold, the surface
roughness of the mold, the material of an alloy composing the
casting, the surface state of the casting, the degree of vacuum,
the atmosphere, etc. More specifically, the casting conditions are
the modulus of elasticity and the plastic flow stress of the mold
and those of the alloy composing the casting, a shape imparted from
a surface of the mold to the casting by casting, etc. The moduli of
elasticity here may respectively vary according to the temperatures
of the mold and the alloy.
[0038] The lubrication conditions shown in FIG. 4 include (1) BASE
lubrication A, (2) MIT (manual transmission) case lubrication A
revised, and (3) A/T (automatic transmission) case lubrication CC.
The lubrication conditions shown in FIG. 4 are, for example, the
type of a mold release agent, the dilution ratio of the mold
release agent, the amount of application of the mold release agent,
and dryness. The dryness refers to whether water remains on a
surface of the mold.
[0039] For example, when the condition (1) (1) is determined, the
frictional coefficient functions f0, f1 are selected. As shown in
FIG. 5, the frictional coefficient functions f0, f1 are functions
that have the contact surface temperature Temp and the contact
surface pressure N as input variables and the frictional
coefficient .mu. as an output variable. Curves CL1 to CL3 shown in
FIG. 5 each represent changes in the frictional coefficient .mu. in
the case where the contact surface temperature Temp is at a
predetermined value and the contact surface pressure N is within a
predetermined range, and these curves are a part of a curve of the
frictional coefficient function f1 showing the value of the
frictional coefficient .mu. that is the output variable
thereof.
[0040] As shown in FIG. 6, at time point T0 at which mold opening
is started or at time point T0 immediately before mold opening,
each portion of the casting P1 presses each portion of the fixed
die 1 with the contact surface pressure N, while each portion of
the fixed die 1 exerts a reactive force Nr on each portion of the
casting P1 in reaction to the contact surface pressure N of the
casting P1. The casting P1 and the fixed die 1 are pressing each
other and neither moves. A static frictional coefficient .mu.0 is
used as the coefficient of friction between the casting P1 and the
fixed die 1, from time point T0 at which mold opening is started
until immediately before time point T1 immediately after the start,
i.e., time point T1 at which the movable die 2 (see FIG. 3) is
released from close contact with the fixed die 1 and separated from
the fixed die 1. The contact surface temperature Temp and the
contact surface pressure N at each portion are input into the
frictional coefficient function f0 for the static frictional
coefficient, and the corresponding static frictional coefficient
.mu.0 at that portion is output.
[0041] At time point T1 immediately after mold opening is started,
the fixed die 1 tries to pull the casting P1 with a fixed die
frictional stress F1, but the movable die 2 pulls the casting P1
with a force F2 larger than the fixed die frictional stress F1.
Thus, the casting P1 is held in the movable die 2 and pulled in a
direction away from the fixed die 1, so that the casting P1 moves.
Although the casting P1 moves relative to the fixed die 1, both the
casting P1 and the fixed die 1 undergo elastic deformation and
press each other while in contact with each other. A dynamic
frictional coefficient .mu.1 is used as the coefficient of friction
between the casting P1 and the fixed die 1, from time point T1 at
which the movable die 2 (see FIG. 3) is released from close contact
with the fixed die 1 and separated from the fixed die 1 until time
point T2 at which the casting P1 is released from close contact
with the fixed die 1 and separated from the fixed die 1. The
contact surface temperature Temp and the contact surface pressure N
at each portion are input into the frictional coefficient function
f1 for the dynamic frictional coefficient, and the corresponding
dynamic frictional coefficient .mu.1 at that portion is output.
[0042] Thus, the static frictional coefficient .mu.0 and the
dynamic frictional coefficient .mu.1 are respectively represented
by the following Formulae 3 and 4:
.mu.0=f0 (N, Temp) (Formula 3)
.mu.1=f1 (N, Temp) (Formula 4)
[0043] Next, a method of obtaining the length of time from time
point T0 at which mold opening is started until time point T2 at
which the casting P1 is released from close contact with the fixed
die 1 and separated from the fixed die 1, and an amount of movement
Lmove1 of the casting P1 from time point T0 to time point T2, based
on an amount of elastic deformation L1 of the casting P1 and an
amount of elastic deformation L2 of the fixed die 1 will be
described. As shown in FIG. 7, the relation among the amount of
elastic deformation L1 of the casting P1, a modulus of elasticity
E1 (T) of the casting P1, the contact surface pressure N, and a
contact area S satisfies the following Formula 5. The modulus of
elasticity E1 is a function having a temperature T of the casting
P1 as an input variable:
L1=E1(T).times.N/S (Formula 5)
[0044] The relation among the amount of elastic deformation L2 of
the fixed die 1, a modulus of elasticity E2 (T) of the fixed die 1,
the contact surface pressure N, and the contact area S satisfies
the following Formula 6. The modulus of elasticity E2 is a function
having a temperature T of the fixed die 1 as an input variable:
L2=E2(T).times.N/S (Formula 6)
[0045] Using the above Formulae 5 and 6, the amount of elastic
deformation L1 of the casting P1 and the amount of elastic
deformation L2 of the fixed die 1 are obtained.
[0046] As shown in FIG. 8, from time point T0 at which mold opening
is started, the casting P1 is pulled in the direction away from the
fixed die 1, which increases the amount of movement Lmove of the
casting P1. The amount of movement Lmove reaches the predetermined
amount of movement Lmove1. Here, both the amount of elastic
deformation L1 of the casting P1 and the amount of elastic
deformation L2 of the fixed die 1 decrease to substantially zero.
The casting P1 and the fixed die 1 are merely in contact with each
other, or are slightly separated from each other, without pressing
each other. The relation among the amount of movement Lmove1 (see
FIG. 9), the amount of elastic deformation L1 of the casting P1,
the amount of elastic deformation L2 of the fixed die 1, and a
draft .theta. of the fixed die 1 (see FIG. 7) satisfies the
following Formula 7. The amount of movement Lmove1 can be obtained
using Formula 7.
Lmove1=(L1+L2)/tan.theta. (Formula 7)
[0047] The relation among the amount of movement Lmove1, a velocity
V2 of the movable die 2, and a length of time T02 from time point
T0 to time point T2 described above satisfies the following Formula
8. The length of time T02 can be obtained using Formula 8.
T02=Lmove1/V2 (Formula 8)
[0048] The frictional stress F exerted by the fixed die 1 on a
predetermined portion of the casting P1 during mold opening can be
obtained by multiplying the frictional coefficients .mu.0, .mu.1
and the contact surface pressure N at the predetermined portion.
The frictional stress F is a mold opening resistance due to the
contact surface pressure of the fixed die 1 (see FIG. 2). The
contact surface pressure N tends to decrease as the amount of
movement Lmove increases. A specific example of the contact surface
pressure N is a linear function that has the amount of movement
Lmove as a variable and has a negative slope. For example, when the
amount of movement Lmove is zero and the contact surface pressure N
is N0, a specific example of the contact surface pressure N is
represented by the following Formula 9:
N=N0-(N0/Lmove1).times.Lmove (Formula 9)
[0049] Here, FIG. 9 shows a specific example of the frictional
coefficient .mu., the fixed die frictional stress F, and the
contact surface pressure N relative to the amount of movement Lmove
at a predetermined portion of the casting P1.
[0050] The die casting process may further include a mold releasing
step of releasing the casting P1 held in the movable die 2 from the
movable die 2 after the mold opening step. In this mold releasing
step, the casting P1 is released from the movable die 2 by pushing
out the casting P1 using the ejector pins 21 (see FIG. 3) that can
be thrust out of the cavity C2 of the movable die 2. In the mold
releasing step, as necessary, deformation of the casting P1 from
time point T2 at which the casting P1 is separated from the fixed
die 1 until a time point at which the casting P1 is released from
the movable die 2 may be obtained using a movable die frictional
stress, the temperature distribution in the casting P1, and the
product strength distribution in the casting P1 (mold releasing
step-caused casting deformation calculation step ST62). In this
step, for example, the movable die frictional stress exerted by the
movable die 2 on the casting P1 through the ejector pins 21 can be
calculated in the same manner as the fixed die frictional stress F1
in the mold opening step-caused casting deformation calculation
step ST61. Casting deformation in the mold releasing step can be
obtained based on this calculated movable die frictional stress
along with the deformation of the casting P1 due to the fixed die
frictional stress F etc. and the deformation of the casting P1
inside the mold (see FIG. 2), and the amount of deformation due to
release of residual stress (see FIG. 2) that are obtained in the
air gap calculation step ST4 and the contact surface pressure
calculation step ST5. Casting deformation after mold opening may be
obtained based on the casting deformation in the mold opening step
and the casting deformation in the mold releasing step.
[0051] Thus, deformation of the casting P1 after mold opening can
be calculated. In the method for analyzing deformation of a casting
in a die casting process according to the embodiment described
above, the frictional coefficient function based on the casting
conditions and the lubrication conditions is used, and this
frictional coefficient function has the contact surface pressure
and the contact surface temperature as input variables. Thus, the
fixed die frictional stress F exerted by the fixed die 1 on a
predetermined portion of the casting P1, i.e., the mold opening
resistance due to the contact surface pressure of the fixed die 1,
can be analyzed using the value of the frictional coefficient
according to the casting conditions, the lubrication conditions,
the contact surface pressure, and the contact surface temperature.
Therefore, the result of an analysis of casting deformation agrees
well with the result of a test of casting deformation after
ejection and release from a mold in a die casting process, so that
the accuracy of the analysis of casting deformation can be
improved.
[0052] In the method for analyzing deformation of a casting in a
die casting process according to the embodiment described above, as
the coefficient of friction between the casting P1 and the fixed
die 1, the static frictional coefficient .mu.0 is used at time
point T0 at which mold opening is started, and the dynamic
frictional coefficient .mu.1 is used from time point T1 at which
the movable die 2 is separated from the fixed die 1 after the start
of mold opening until time point T2 at which the casting P1 is
separated from the fixed die 1. Thus, the mold opening resistance
due to the contact surface pressure of the fixed die 1 can be
analyzed using the frictional coefficient according to the time
point in mold opening. Therefore, the accuracy of an analysis of
casting deformation can be further improved.
[0053] In the method for analyzing deformation of a casting in a
die casting process according to the embodiment described above,
the time for which the fixed die frictional stress F is exerted on
the casting P1 while the movable die 2 is moving and the magnitude
of this fixed die frictional stress F may be obtained by varying
material properties, mainly the modulus of elasticity, based on the
temperatures of the movable die 2 in motion, the fixed die 1, and
the casting P1. The mold opening resistance due to the contact
surface pressure of the fixed die 1 can be analyzed using the
moduli of elasticity E1, E2 according to the temperatures of the
fixed die 1 and the casting P1. As described above, the moduli of
elasticity E1, E2 significantly affect the amounts of elastic
deformation L1, L2. When the amounts of elastic deformation L1, L2
are large, a large fixed die frictional stress F tends to act on
the casting P1 for a prolonged time. The moduli of elasticity E1,
E2 according to the temperatures of the fixed die 1 and the casting
P1 are considered as values closer to the actual phenomenon of
casting deformation. Therefore, the accuracy of an analysis of
casting deformation can be further improved.
[0054] In the method for analyzing deformation of a casting in a
die casting process according to the embodiment described above,
casting deformation after mold opening due to mold release
resistance caused by the ejector pins 21 can be obtained based on
the deformation of the casting P1 due to the fixed die frictional
stress F, the deformation of the casting P1 inside the mold (see
FIG. 2), and the amount of deformation due to release of residual
stress (see FIG. 2). Therefore, the accuracy of an analysis of
casting deformation can be further improved.
[0055] The present disclosure is not limited to the above
embodiment but can be modified as appropriate within the scope of
the gist of the disclosure.
* * * * *