Hydraulic pressure as a function of friction coefficient in control system for automatic transmission

A hydraulic control system for shifting an automatic transmission to desired gears by selectively coupling and uncoupling friction coupling elements which controls a shifting pressure necessary to bring a friction coupling element into coupling according to a presumed friction coefficient of the friction coupling element during shifting so as thereby to achieve an intended gear shift over an intended shifting time.

BACKGROUND OF THE INVENTION 
1. Field of the invention 
The resent invention relates to a hydraulic control system for an automatic 
transmission. 
2. Description of Related Art 
Typically, automatic transmissions for automobiles comprise mechanical 
transmission devices or mechanisms and torque convertors. Available engine 
torque from a crankshaft is multiplied and transferred first by a torque 
convertor and subsequently by a mechanical transmission. Such a mechanical 
transmission includes a planetary gearset consisting of a sun gear, a ring 
gear and pinions which changes the path of power flow for gear shift. 
Specifically, in order for mechanical transmission to change gears or the 
path of power flow, the automatic transmission is provided with friction 
coupling elements, such as clutch mechanism for connecting and 
disconnecting the transmission of power to specific gears of the 
mechanical transmission and braking elements for braking specific gears of 
the mechanical transmission. These friction coupling elements and braking 
elements are selectively actuated by hydraulic control so as to perform 
gear shifts. 
In the automatic transmission, if a shifting time which refers to a time 
necessary to complete a gear shift is too short, in other words, if the 
friction coupling element is abruptly actuated by high hydraulic pressure, 
the automatic transmission causes what is called "shift shock." Contrary, 
if the shifting time is too long, i.e. if the friction coupling element is 
slowly actuated by a high hydraulic pressure, there occurs a deterioration 
in the quality of driving. For that reason, in the hydraulic control of 
automatic transmission, the pressure of oil is typically controlled so as 
to complete gear shifts over specified shifting times according to driving 
conditions. 
The shifting time is governed by torque transferred through a friction 
coupling element by which a specific gear shift is made and a coupling 
force of the friction coupling element, i.e. an oil pressure applied to 
the friction coupling element. Specifically, the greater the torque 
transferred through the friction coupling element, the longer the shifting 
time that a gear shift effected by the friction coupling element takes. On 
the other hand, with an increase in oil pressure, the shifting time 
becomes shorter. Consequently, controlling the oil pressure suitably in 
conformity with the torque transferred through the friction coupling 
element enables the automatic transmission to cause a specific gear shift 
achieved by the friction coupling element over a target or intended 
shifting time. 
As it has been proved that a torque transferred through a friction coupling 
element related to a gear shift during shifting is a resultant force from 
a torque transferred to a transmission gear mechanism and an inertia 
caused by a change in rotational speed of a power transfer line to the 
transmission gear mechanism. That is, since a drop in rotational speed 
occurs to the turbine shaft of the torque convertor which is on the input 
side of the transmission gear mechanism, the power transfer line imparts 
to the friction coupling element the force of inertia in the same 
direction as torque of the turbine shaft during a shift-up and, on the 
other hand, in the direction opposite to torque of the turbine shaft 
during a shift-down. On that account, the hydraulic control system is 
adapted to control an oil pressure according to a torque transferred to 
the transmission gear mechanism and the force of inertia of the power 
transfer line to the transmission gear mechanism so as to enable the 
automatic transmission to cause a gear shift over a target shifting time. 
Hydraulic control systems of this kind are known from, for instance, 
Japanese Unexamined Patent Publications Nos. 3-249468 and 4-72099. 
Experiments conducted by the inventors of this application led to the 
conclusion that hydraulic control systems of this kind are hard to cause 
the automatic transmission to achieve gear shifts over a target shifting 
time. 
As shown in FIG. 11, the experimental results prove a comparatively 
adequate correlation which has a friction coefficient of correlation of 
0.96011 between the inertia component pressure and angular deceleration 
.omega.'. On the other hand, as shown in FIG. 11, the correlation between 
the torque component pressure and the input torque Tt has a coefficient of 
correlation of 0.788101, alluding that the torque component pressure is 
less correlated with the input torque Tt. According to the experimental 
results, there is a linear relation between the inertia component pressure 
Tci and angular deceleration .omega.'. However, it is hard to say there is 
a linear relation between the torque component pressure and the input 
torque Tt. In FIG. 12, the measured values seem to be on a curve. If the 
equation (1) represents properly the correlations of line pressure with 
angular acceleration and a torque, they must have a coefficient of 
correlation of 1 (one) and all of the measured values must be exactly on 
straight lines in FIGS. 11 and 12. 
It is apparent from the above discussion regarding the estimation of a 
target pressure P that the equation (I) is not always precise in order to 
estimate the target pressure P which is sufficiently accurate for 
achievement of a gear shift over an intended shifting time. 
According to a conclusion derived by the considerations by inventors of 
this application, while the kinetic friction coefficient of a friction 
coupling element is considered to change according to an interfacial 
pressure or a relative speed between drive and driven members of the 
friction coupling elements, the prior art hydraulic control system is 
designed and configured on condition that the kinetic friction coefficient 
of a friction coupling element is constant and, consequently, produces 
changes in the target shifting time due to changes in the kinetic friction 
coefficient. In the light of the above considerations, it concluded that 
controlling the line pressure according to changes in the kinetic friction 
coefficients of friction coupling elements cause gear shifts achieved 
exactly over intended shifting times, respectively. Specifically 
describing, in the prior art hydraulic control system for an automatic 
transmission, a line pressure P, which in turn refers to a target shifting 
pressure, is regarded to be given by the following equation (I): 
EQU P=A.multidot..omega.'+B.multidot.Tt+C (I) 
where .omega.' the angular acceleration, i.e. the force of inertia; 
Tt is the torque transferred to the transmission gear mechanism; and 
A, B and C are constants, respectively. 
If the constants A, B and C can be known based on a plurality of 
measurements of these angular acceleration .omega.' and torque Tt and a 
line pressure at which the automatic transmission actually achieves a gear 
shift over an intended shifting time, a target pressure P is obtained for 
various angular acceleration .omega.' and torque Tt. Keeping the line 
pressure at the target pressure P forces the automatic transmission to 
achieve the gear shift over the intended shifting time. 
The inventors made a survey of these factors for gear shifts achieved over 
the intended shifting time and a multiple regression analysis of 64 sets 
of angular acceleration .omega.', input torque Tt and line pressure P was 
done to determine the constants A, B and C which leads to minimum errors. 
According to the equation (I), a part of the whole hydraulic pressure 
corresponding to angular deceleration .omega.', which is referred to as an 
inertia component pressure, is proportional to angular deceleration 
.omega.'. Further, a part of the whole hydraulic pressure corresponding to 
an input torque Tt, which is referred to as a torque component pressure, 
is proportional to an input torque Tt. In other words, there must be a 
linear relation both between the inertia component pressure and angular 
deceleration .omega.' and between the torque component pressure and the 
input torque Tt. The experimental results which were obtained in the way 
described above are shown in FIGS. 11 and 12. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide a hydraulic control 
system for an automatic transmission which achieves a desired gear shift 
accurately over an intended shifting time. 
The above object of the present invention is accomplished by providing a 
hydraulic control system for an automatic transmission which includes 
hydraulically controlled friction coupling elements, such as comprising 
drive and driven plates, selectively coupled and uncoupled to change power 
transfer lines of the automatic transmission so as to shift the automatic 
transmission into desired gears. The hydraulic control system controls to 
develop the shifting pressure, which is necessary to bring the friction 
coupling element into coupling so as to cause a gear shift of the 
automatic transmission to a specific or desired gear, according to a 
friction coefficient of a friction coupling element presumed during a gear 
shift. 
Specifically, the hydraulic control system presumes the friction 
coefficient based on at least one of an interfacial pressure and a 
relative speed between the drive and driven plates of the friction 
coupling element. The hydraulic control system further detects an input 
speed change in rotation (.omega.') of and an input torque (Tt) to the 
automatic transmission and determines the shifting pressure according to a 
function including these speed change and input torque as independent 
variables defined by a first order approximate functional equation, or 
alternatively according to a function including these speed change and 
input torque as independent variables defined by a second order 
approximate functional equation. 
Practically, the shifting pressure P is given by the following first order 
approximate functional equation: 
EQU P=a.sub.1 .multidot.Tt+a.sub.2 .multidot..omega.'+a.sub.3 
.multidot.Tt.multidot..omega.'+a.sub.4 
or alternatively by the following second order approximate functional 
equation: 
EQU P=b.sub.1 .multidot.Tt+b.sub.2 .multidot..omega.'+b.sub.3 
.multidot.Tt.multidot..omega.'+b.sub.4 Tt.sup.2 +b.sub.5 
.multidot..omega.'.sup.2 +b.sub.6 .multidot.Tt.sup.2 
.multidot..omega.'+b.sub.7 .multidot.Tt.multidot..omega.'.sup.2 +b.sub.8 
.multidot.Tt.sup.2 .multidot..omega.'.sup.2 +b.sub.9 
In these equations, a.sub.1 -a.sub.4 and b.sub.1 -b.sub.9 are constants 
depending upon a friction coefficient of the friction coupling element and 
determined experimentally and analytically. 
With the hydraulic control system of the invention, because the shifting 
pressure is determined according to an input torque and a speed change in 
rotation of the automatic transmission and a presumed friction coefficient 
of a friction coupling element which includes drive and driven plates 
brought into friction coupling, it is accurately maintained at an optimum 
level for an intended shifting time even when there occurs a change in an 
actual friction coefficient. Together, the presumption of friction 
coefficient is made based on at least interfacial pressure and relative 
speed between the drive and driven plates of the friction coupling 
element, leading to more accurate shifting pressure control, i.e. a more 
accurate achievement of a gear shift over an intended shifting time. 
In addition, the shifting pressure is given by the first order approximate 
functional polynomial or alternatively by the second order approximate 
functional polynomial, which includes an input torque and a speed change 
in rotation of the automatic transmission as independent variables. This 
results in a simplified logic of shifting pressure control.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring now to the drawings in detail, and in particular, to FIGS. 1 and 
2, an automotive vehicle 1 shown as a type having a front engine 3 and 
front drive wheels 2a and 2b, is equipped with an automatic transmission 4 
controlled by a hydraulic control system in accordance with a preferred 
embodiment of the present invention. Engine output torque is transferred 
to front drive wheels 2a and 2b through drive axles 6a and 6b, 
respectively, via the automatic transmission 4 and a differential 5. These 
engine 3 and automatic transmission 4 are consolidated in operation and 
controlled by a control unit (ECU) 70 which comprises a microcomputer and 
memories. For controlling the consolidated operation of the engine 4 and 
the automatic transmission 4, there are provided various sensors including 
a vehicle speed sensor 71, a throttle position sensor 72, an air flow 
sensor 73, an engine speed sensor 74, an engine temperature sensor 75, a 
turbine speed sensor 76, a transmission output speed sensor 77, a shift 
position sensor 78, an oil temperature sensor 79. The control unit 70 
receives signals from these sensors 71-79 representative of related 
physical quantities and provides for various valves of a hydraulic control 
unit 60, which will be described later, including gear shift control 
solenoid valves 61 and a line pressure control duty solenoid valve 62, and 
ignition plugs 7 control signals, respectively. All these sensors 71-79 
may take any type well known in the automobile art. In this instance, 
during a gear shift, a timing of ignition of the respective cylinder is 
controlled so as to reduce the engine output torque. 
As shown in FIG. 2, the automatic transmission 4 cooperates with a torque 
convertor 20 disposed between and connecting the engine 3 and a 
transmission gear mechanism 30 so as to multiply and transfer the engine 
output torque to the transmission gear mechanism 30. The torque convertor 
20, only schematically shown, consists of a pump 22 and a turbine 23, 
disposed face to face, and a stator 25, all of which are disposed in a 
casing 21. The pump 22 is secured to the casing 21 directly connected to 
an output shaft 8 of the engine 3. The turbine 23 has a hollow turbine 
shaft 27 which in turn transmits power from the torque convertor 20 to the 
transmission gear mechanism 30. The torque convertor 20 is equipped with a 
one-way clutch 24, connected between the stator 25 and a transmission 
housing 9, and a lock-up clutch 26 disposed between the convertor casing 
21 and the turbine 23 for coupling directly the engine output shaft 8 and 
the turbine 23 together. A special lightweight oil is utilized to transmit 
the engine output torque from the pump 22 to the turbine 23. A shaft 10 
passes through the hollow turbine shaft 27 so as to connecting the engine 
output shaft 8 to an oil pump 11 disposed on one end of the automatic 
transmission 4 remote from the engine 3. 
The transmission gear mechanism 30 comprises a planetary gear set, which 
may be of, for instance, a Rabinyo type. The planetary gear set consists 
of a sun gear 31 having a small diameter (which is referred to as a small 
sun gear), a sun gear 32 having a diameter larger than the small sun gear 
31 (which is referred to as a large sun gear), a carrier 35 carrying a 
plurality of short pinions 33 and a long pinion 34 for rotation, and a 
ring gear 36. The small sun gear 31 and the large sun gear 33, disposed 
axially behind the small sun gear 31, are fitted for rotation to the 
turbine shaft 27. The short pinions 33 are disposed at regular angular 
separations and between and in mesh with the front part of the long pinion 
34 and small sun gear 31. The long pinion 34 is in mesh, on one hand, with 
the large sun gear 32 at its front part and, on the other hand, with the 
ring gear 36. 
The automatic transmission 4 cooperates with various hydraulically 
controlled clutch element and brake elements which are selectively 
actuated so as to provide various drive ranges and forward and reverse 
gears or gear ratios, such as 1st-4th gears in a drive (D) range, 1st-3rd 
gears in a second speed (S) range, 1st and 2nd gear in a low speed (L) 
range, and a reverse (R) range in addition to park (P) and neutral (N) 
gears. These clutch element and brake elements are actuated by means of 
the hydraulic control unit 60. 
The clutch and brake elements include hydraulically controlled, friction 
coupling or braking elements 41-46 and electromagnetically controlled 
one-way clutches 51 and 52. A forward (FWD) clutch 41, which is one of the 
friction coupling elements, and a first (1ST) one way clutch 51 are 
disposed in series between the turbine shaft 27 and the small sun gear 31. 
Further, a coast (CST) clutch 42, which is one of the friction coupling 
elements, is disposed in parallel with respect to these forward clutch 41 
and first one way clutch 51 between the turbine shaft 27 and the small sun 
gear 31. A 3-4 clutch 43, which is one of the friction coupling elements, 
is disposed between the turbine shaft 27 and the carrier 35. A reverse 
(RVS) clutch 44, which is one of the friction coupling elements, is 
disposed between the turbine shaft and the large sun gear 32. A 2-4 brake 
45 of a type having a brake band, which is one of the friction braking 
elements, is disposed between the large sun gear 32 and the reverse clutch 
44. Further, a low reverse (LRV) brake 46, which is another one of the 
friction braking elements, is disposed between the carrier 35 and the 
transmission housing 9. In parallel with the low reverse brake 46 there is 
disposed a second (2ND) one way clutch 52 between the carrier 35 and the 
transmission housing 9 which counters reaction from the carrier 35. The 
transmission gear mechanism 30 further includes an output gear 12 
connected to the ring gear 36 through which it transmits the engine output 
torque to the front drive wheels 2a and 2b via the differential 5. 
These friction coupling elements 41-46 and one-way clutches 51 and 52 are 
selectively operated by means of the hydraulically controlled solenoid 
valves 61 and 62 of the hydraulic control unit 60 so as to place the 
transmission gear mechanism 30 into desired ranges and gears, i.e. the 
first (1st) to fourth (4th) gears in the drive (D) range, the first (1st) 
to third (3rd) gears in the second speed (S) range, the first (1st) and 
second (2nd) gears in the low speed (L) range, the park (P) range and the 
neutral (N) range, as shown in Table I in which a circle indicates that 
each specific element is coupled or locked. 
TABLE I 
______________________________________ 
ONE-WAY 
CLUTCH BRAKE CLUTCH 
Range / Gear 
FWD CST 3/4 RVS 2/4 LRV 1ST 2ND 
______________________________________ 
Park (P) 
Reverse (R) .smallcircle. 
.smallcircle. 
Neutral (N) 
Drive 1st .smallcircle. .smallcircle. 
.smallcircle. 
(D) 2nd .smallcircle. .smallcircle. 
.smallcircle. 
3rd .smallcircle. 
.smallcircle. 
.smallcircle. .smallcircle. 
4th .smallcircle. 
.smallcircle. 
.smallcircle. 
Second 
1st .smallcircle. .smallcircle. 
.smallcircle. 
(S) 2nd .smallcircle. 
.smallcircle. 
.smallcircle. 
.smallcircle. 
3rd .smallcircle. 
.smallcircle. 
.smallcircle. .smallcircle. 
Low 1st .smallcircle. 
.smallcircle. .smallcircle. 
.smallcircle. 
.smallcircle. 
(L) 2nd .smallcircle. 
.smallcircle. .smallcircle. 
.smallcircle. 
______________________________________ 
Referring to FIG. 3, the hydraulic circuit of the hydraulic control unit 
60, shown partly, has valves, such as a regulator valve 63 for regulating 
oil discharged by the oil pump 11 to a predetermined line pressure, a 
modulator valve 64 for providing for the regulator valve 63 a control 
pressure and a reducing valve 66 for reducing hydraulic pressure to a 
specified level of pressure. Hydraulic pressure is supplied by the oil 
pump 11 to the reducing valve 66 through a main pressure line 65 and, 
after reduced to a specified level, to the modulator valve 64 through a 
pressure line 67. The control pressure is supplied by the modulator valve 
64 to the regulator valve 63 at its intensifying port 63a through a 
control pressure line 68. Further, pilot pressure is supplied to the 
modulator valve 64 at its control port 64a through a pilot pressure line 
69 branching off from the pressure line 67. The duty solenoid valve 62 is 
installed in the pilot pressure line 69 so as to develop a pilot pressure 
according to its duty rate at the control port 64a of the modulator valve 
64. The hydraulic pressure at the specified level is regulated by the 
modulator valve according to the pilot pressure, i.e. the duty rate of the 
duty solenoid valve 62 and directed as a control pressure to the regulator 
valve 63. With the hydraulic circuit thus structured, the regulator valve 
63 develops a line pressure regulated according to the duty rate of the 
duty solenoid valve 62. 
In order for the automatic transmission 4 to achieve a gear shift over an 
intended or target shifting time, the control unit 70 controls the duty 
rate of the duty solenoid valve 62 according to an input torque to the 
transmission gear mechanism 30, the force of inertia of the power transfer 
line to the transmission gear mechanism 30, which is represented by a 
change in turbine speed, and the kinetic friction coefficient of a 
friction coupling element which is coupled or uncoupled during the 
specific gear shift so that the regulator valve 63 develops a desired line 
pressure in the hydraulic control unit 60. 
FIG. 4 is a block diagram illustrating a conceptualized principle of the 
line pressure control which the control unit performs. At a functional 
block F1, a target shifting time is determined based on a change in 
rotational speed of the transmission gear mechanism 30, i.e. a change in 
turbine speed, between before and after a gear shift (which is hereafter 
referred to as a speed change for simplicity), and an input torque to the 
transmission gear mechanism 30, i.e. a torque of the turbine shaft 27 
(which is hereafter referred to as an input torque for simplicity). The 
input torque is calculated in an ordinary way well known in the art based 
on engine load or throttle position, engine speed, ignition timing on 
condition that there occurs no torque drop during a gear shift. 
While, as the shifting time becomes short, the vehicle responds fast and 
satisfactorily to gear shifting, improving the quality of driving during 
the gear shift, nevertheless, there occurs during up-shifting such a 
phenomenon that the transmission gear mechanism 30 causes a momentary rise 
in output torque due to the force of inertia of the power transfer line to 
the transmission gear mechanism 30 and the torque rise is enhanced with a 
reduction in the shifting time. Because a massive torque rise is apt to 
produce a shift shock, it is always imprudent and undesirable to shorten 
the shifting time excessively. Contrarily, a prolonged shifting time 
causes aggravation of the responsiveness of the vehicle to the gear 
shifting or the quality of driving of the vehicle. Accordingly, it is 
typical to establish a target shifting time according to driving 
conditions so as to be best for preventing an occurrence of a substantial 
shift shock and providing the intended quality of driving. Target shifting 
times are mapped with speed change and input torque as parameters and 
stored in a memory of the control unit 70. 
Subsequently, at a function block F2, angular acceleration of the 
transmission gear mechanism 30 at the input side (which is hereafter 
referred to as input angular acceleration for simplicity) is calculated by 
dividing a speed change by the shifting time. As well known in the art, 
letting the moment of inertia of the power transfer line to the 
transmission gear mechanism 30 be I, the moment of force N of the power 
transfer line, i.e. the force of inertia to the friction coupling element 
related the gear shift during shifting is given by the following equation: 
EQU N=I.multidot..omega.' 
Since the moment of inertia I is invariable, the force of inertia N is 
proportional to and determined unconditionally based only the angular 
acceleration .omega.'. At functional block F3, an inertia component 
pressure Tci necessary to absorb the force of inertia N caused due to the 
moment of inertia I of the power transfer line to the transmission gear 
mechanism 30 is determined. 
As was previously described, since the force of inertia caused due to the 
moment of inertia I of the power transfer line to the transmission gear 
mechanism 30 acts on the friction coupling element during shifting, a 
coupling pressure, i.e. a line pressure, necessary to couple the friction 
coupling element related to the gear shift must be regulated according to 
the force of inertia. The inertia component pressure Tci is determined 
based on the angular acceleration .omega.' to which the force of inertia N 
is proportional. In this instance, an inertia component pressure Tci is 
previously given in a table with angular acceleration as a parameter and 
stored in a memory of the control unit 70. 
At function block F4, simultaneously with the determination of an inertia 
component pressure Tci, a target input torque transferred to the 
transmission gear mechanism 30 is calculated in the case where a gear 
shift is performed on condition that the torque drop control is induced. 
The torque drop control is performed to cause a drop or fall in engine 
output torque during shifting in order to prevent a momentary rise in 
transmission output torque caused by the force of inertia, which acts on 
the transmission gear mechanism 30 in the same direction as the input 
torque, due to the moment of inertia I of the power transfer line to the 
transmission gear mechanism 30. Target input torque are mapped with 
angular acceleration and input torque as parameters and stored in a memory 
of the control unit 70. At function block F5, a torque component pressure 
Tct, which is necessary to develop a coupling force in conformity with an 
input torque to the transmission gear mechanism 30, is subsequently 
determined based on the target input torque which has been determined in 
consideration of a torque drop. Torque component pressure Tct are mapped 
according to target input pressure as a parameter and stored in a memory 
of the control unit 70. Based on these inertia component pressure Tci, 
torque component pressure Tct, speed change in rotation of the friction 
coupling element related to a specific gear shift, the friction 
coefficient .mu. of the friction coupling element related to the gear 
shift is corrected at function block F6. This friction coefficient .mu. is 
used to determine a shifting pressure necessary to cause the gear shift at 
function block F7. More specifically describing, the friction coefficient 
.mu. is estimated based on both, or otherwise either one, of an 
interfacial pressure between drive and driven clutch plates of the 
friction coupling element in an axial direction and a relative speed 
between them. Finally, the shifting pressure is further corrected as an 
eventual target line pressure is established according to the temperature 
of oil of the transmission at function F8. With the line pressure control, 
a target line pressure is set according to the friction coefficient .mu. 
of a friction coupling element to which the pressure is applied, so as to 
cause a gear shift over an exact target shifting time. 
While the shifting pressure is set or calculated after and based on the 
estimation of the friction coefficient .mu., a calculation may be made 
based on the input torque and the angular acceleration to obtain the 
shifting pressure which has been tempered with the effect of friction. 
Since the interfacial pressure is proportional to the shifting pressure P, 
and the relative speed can be substituted by angular acceleration 
.omega.', the friction coefficient .mu. is given by the following function 
of independent variables P and .omega.' (2): 
EQU .mu.=g(P, .omega.') (2) 
The force of friction (.mu..multidot.A.multidot.P) acting on the friction 
coupling element is given by the following function of independent 
variables, such as an input torque Tt and angular acceleration .omega.' 
(3): 
EQU .mu..multidot.A.multidot.P=h(Tt, .omega.') (3) 
where A is the area of surface of clutch plates of the friction coupling 
element. 
From functions (2) and (3), 
EQU g(P, .omega.').multidot.A.multidot.P=h(Tt, .omega.') (4) 
Since independent variables in the function (4) are P, Tt and .omega.', the 
following function (5) is theoretically derived from the function (6): 
EQU P=f(Tt, .omega.') (5) 
However, since it is generally impossible to derive the function (5) from 
the function (6) by algebraic transformation, the shifting pressure P is 
approximated by a Maclaurin expansion polynomial including independent 
variables, such as an input torque Tt and angular acceleration .omega.'. 
The shifting pressure P may be given by a first order approximation 
polynomial. 
EQU P=a.sub.1 .multidot.Tt+a.sub.2 .multidot..omega.'+a.sub.3 
.multidot.Tt.multidot..omega.'+a.sub.4 (6) 
In the equation (6), a.sub.1 -a.sub.4 are constants determined according to 
the friction coefficient .mu. of the friction coupling element and 
obtained experimentally and analytically. 
Alternatively, the shifting pressure P may be given by a second order 
approximation polynomial. 
EQU P=b.sub.1 .multidot.Tt+b.sub.2 .multidot..omega.'+b.sub.3 
.multidot.Tt.multidot..omega.'+b.sub.4 .multidot.Tt.sup.2 +b.sub.5 
.multidot..omega.'.sup.2 +b.sub.6 .multidot.Tt.sup.2 
.multidot..omega.'+b.sub.7 .multidot.Tt.multidot..omega.'.sup.2 +b.sub.8 
.multidot.Tt.sup.2 .multidot..omega.'.sup.2 +b.sub.9 (7) 
In the equations (6) and (7), a.sub.1 -a.sub.4 and b.sub.1 -b.sub.9 are 
constants which are experimentally and analytically determined according 
to the friction coefficient .mu. of the friction coupling element. 
From the results of experiments and analyses conducted by the inventors, it 
concluded that the second order approximation polynomial may be 
practically simplified and expressed as follows: 
EQU P=c.sub.1 .multidot.Tt+c.sub.2 .multidot..omega.'+c.sub.3 
.multidot.Tt.multidot.Tt+c.sub.4 (8) 
In the equation (8), c.sub.1 -c.sub.8 are constants which are 
experimentally and analytically determined according to the friction 
coefficient .mu. of the friction coupling element. 
If the equation (8) is proper, by determining the constants c.sub.1 
-c.sub.4 based on a plurality of measurements of these shifting pressure 
P, input torque Tt and angular acceleration .omega.' experimentally 
obtained in the event of a gear shift achieved over a target shifting 
time, the shifting pressure P which is tempered with the effect of 
friction according to an input torque Tt and angular acceleration .omega.' 
is known from the equation (8). Accordingly, if keeping the line pressure 
at the shifting pressure P, the gear shift is caused over the target 
shifting time. 
In view of the above analysis, the constants c.sub.1 -c.sub.4, such as 
leading to minimum errors, were determined by a multiple regression 
analysis of the actual measurements of input torque Tt and angular 
acceleration .omega.' which are plotted in FIGS. 10 and 11. Here, if the 
equation (8) is proper, the component pressure of the shifting pressure P 
must be proportional to the respective related factors, i.e. angular 
acceleration .omega.', an input torque Tt and a square input torque 
Tt.sup.2, respectively, and consequently, the correlation between each 
component pressure and the related factor must be linear. 
The correlations of the component pressure to the respective factors having 
been obtained based on the actual measurements of an input torque Tt and 
angular acceleration .omega.' are shown in FIGS. 7-9. As apparent from 
these figures, these correlations have coefficients of 0.971002, 0.971001 
and 0.933570, respectively, which are sufficiently large to be regarded as 
linear. Accordingly, it is proved that the equation (8) provides a target 
shifting pressure considerably accurate for achieving a gear shift over a 
target shifting time. 
In the line pressure control, a target line pressure such as having been 
tempered with the effect of friction of a friction coupling element 
relating to a specific gear shift is determined without actually finding 
the friction coefficient of the friction coupling element, enabling the 
gear shift to be achieved over a target shifting time. 
Referring to FIG. 5, which is a flow chart of a line pressure control 
sequence routine which the control unit 70 performs during, for instance, 
a schedule-up gear shift taking place upon an occurrence of a rise in 
vehicle speed, when a schedule-up gear shift commences and control 
proceeds to step S1 where various signals provided by the sensors 71-79 
are read. At step S2, a prospective turbine speed change .DELTA.Nt, which 
refers to a prospective change in rotational speed Nt of the turbine 23 
between before and after the gear shift, is calculated according to the 
following equation (9): 
EQU .DELTA.Nt=Nt-No.multidot.Go (9) 
where 
No is the output rotational speed of the transmission gear mechanism 30; 
and 
Go is the gear ratio after gear shift. 
Subsequently, a calculation is made at step S3 to determine a turbine 
torque Tt according to the following equation (10): 
EQU Tt=Te.multidot.K.sub.1 .multidot.(Nt/Ne) (10) 
where 
Te is the engine output torque; 
K.sub.1 is the coefficient of torque multiplication of the torque convertor 
20; and 
Ne is the rotational speed of the engine 3. 
The engine torque Te is determined based on engine speed, the amount of 
intake air and an ignition time in a manner well known to those skilled in 
the art. 
After the calculations of these prospective turbine speed change .DELTA.Nt 
and turbine torque Tt, a decision is made at step S4 as to whether a 
torque down flag Ftd is up or set to a state of "1" which indicates that 
the torque down control is permitted. The torque down control takes place 
when, for instance, the engine temperature sensor 75 detects temperatures 
of the engine 3 which indicate warming up of the engine 3. If the answer 
to the decision is "YES," a torque down shifting time map f.sub.1, which 
defines shifting times with parameters such as turbine torque Tt, 
prospective turbine speed changes .DELTA.Nt and types of gear shifts Lm, 
is searched to find a target shifting time Ts for a gear shift during 
torque down control at step S5. Subsequently, at step S6, a target angular 
acceleration Am is given by a calculation according to the following 
equation (11): 
EQU Am=.vertline..DELTA.Nt/Ts.vertline. (11) 
Then, at step S7, a target turbine torque map f.sub.2, which defines target 
turbine torque with parameters such as turbine torque Tt, turbine speed Nt 
and angular acceleration Am, is searched to find a target turbine torque 
Tm. 
On the other hand, if the answer to the decision concerning the torque down 
flag Ftd made at step S4 is "NO," this indicates that the torque down 
control is prohibited, then, after finding a target shifting time Ts by 
searching a torque down shifting time map f.sub.5 for non-torque down 
control at step S8 and, subsequently, calculating a target angular 
acceleration Am according to the following equation (11) at step S9, the 
turbine torque Tt is set as a target turbine torque Tm at step S10. In 
this instance, the target shifting time Ts for a specific gear shift is 
predetermined to be longer in the non-torque down shifting time map 
f.sub.5 than in the torque down shifting time map f.sub.1. 
After the determination of a target turbine torque Tm either at step S7 or 
at step S10, a torque component pressure Tct and an inertia component 
pressure Tci are found by searching a torque component pressure map 
f.sub.3 and an inertia component pressure map f.sub.4, respectively, at 
step S11. As was described previously, the torque component pressure Tct 
used herein refers to a pressure necessary to generate a coupling force of 
a friction coupling element corresponding to an input torque to the 
transmission gear mechanism 30 and the inertia component pressure Tci used 
herein refers to a pressure necessary to absorb the force of inertia N 
caused due to the moment of inertia I of the power transfer line to the 
transmission gear mechanism 30. The torque component pressure map f.sub.3 
defines torque component pressure Tct according to target turbine torque 
Tm and types of gear shifts Lm as parameters. Similarly, the inertia 
component pressure map f.sub.4 defines inertia component pressure Tci 
according to target angular acceleration Am and types of gear shifts Lm as 
parameters. 
At step S12, a target line pressure PL is found by searching a target line 
pressure map f.sub.u according to a torque component pressure Tct and an 
inertia component pressure Tci as parameters. The target line pressure map 
f.sub.u is given experimentally and analytically as a function after 
consideration of the friction coefficient of the friction coupling element 
related to a specific gear shift. As was described previously, because, 
though the friction coefficient is basically determined according to an 
interfacial pressure and a relative speed between the clutch plates of a 
friction coupling element, the interfacial pressure is given as a function 
of a torque component pressure and a function of an inertia component 
pressure Tct and the relative speed is given as a function of inertia 
component pressure Tci, the target line pressure which has been tempered 
with the effect of friction is given as a function of these inertia 
component pressure Tct and inertia component pressure Tci as independent 
variables. 
Finally, at step S13, control signals are provided to control the line 
pressure so as to develop the target line pressure PL and the engine 
output torque by regulating an ignition time so as to provide for the 
turbine the target turbine torque Tm. 
The line pressure control may be changed so as to determine target line 
pressure PL according to a preliminary target line pressure Pa. 
FIG. 6 is a flow chart of another line pressure control sequence routine 
which the control unit 70 performs during, for instance, a schedule-up 
gear shift taking place upon an occurrence of a rise in vehicle speed. 
This line pressure control sequence routine takes just the same steps 
S1-S10 as the previous sequence routine shown in FIG. 5 in order to 
calculate the target turbine torque Tm. In the line pressure control 
sequence routine, the preliminary target line pressure Pa is given by the 
following equation (12): 
EQU Pa=a.multidot.Am+b.multidot.Tm+c.multidot.Tm.sup.2 +d (12) 
In the equation (12), a-d are constants which are experimentally and 
analytically determined according to the friction coefficient .mu. of the 
friction coupling element. The equation (12) is a second order 
approximation polynomial simplified and basically similar to the equation 
(8), in which target angular acceleration Am and target turbine torque Tm 
are substituted for the angular acceleration .omega.' and input torque Tt 
in the equation (8), respectively. 
After the determination of a target turbine torque Tm either at step S7 or 
at step S10, a preliminary target line pressure Pa is calculated at step 
S11A. Subsequently, at step S12A, an eventual target line pressure PL is 
obtained by performing a correction of the preliminary target line 
pressure Pa according to the friction coefficient of the friction coupling 
element and a change of the friction coefficient due to types of gear 
shifts. The eventual target line pressure PL is corrected by the following 
equation (13): 
EQU PL=Pa.multidot.{.mu.(Lm, To)+.DELTA..mu.(Lm)} (12) 
The friction coefficient .mu. is defined in a map according to the type of 
gear shift Lm and the temperature To of oil as parameters. The change 
.DELTA..mu. in the friction coefficient is defined in a map according to 
the type of gear shift Lm and determined by learning. The correction of 
the preliminary target line pressure Pa is made on one hand to compensate 
the line pressure for a change in viscosity of the oil due to temperature 
changes and, on the other hand, to cope with a change in characteristics 
of the hydraulic control unit 60 due to aging. 
At step S13, control signals are provided to control the line pressure so 
as to develop the target line pressure PL and the engine output torque by 
regulating an ignition time so as to provide for the turbine the target 
turbine torque Tm. 
With the line pressure control according to the above described embodiments 
of the present invention, a friction coupling element is brought into 
friction coupling with the line pressure having been tempered with the 
effect of friction of the friction coupling element, achieving a gear 
shift accurately over the target shifting time. 
It is to be understood that although the present invention has been 
described with regard to preferred embodiments thereof, various other 
embodiments and variants may occur to those skilled in the art, which are 
within the scope and spirit of the invention, and such other embodiments 
and variants are intended to be covered by the following claims.