GB2519161A

GB2519161A - Method of controlling aerodynamic devices in an automotive system during sailing driving

Info

Publication number: GB2519161A
Application number: GB1318135.9A
Authority: GB
Inventors: Paul Kurschewski
Original assignee: GM Global Technology Operations LLC
Current assignee: GM Global Technology Operations LLC
Priority date: 2013-10-14
Filing date: 2013-10-14
Publication date: 2015-04-15
Also published as: GB201318135D0

Abstract

A method is provided for controlling aerodynamic devices, for example an aero shutter or a downforce wing, of an automotive system 100 in a vehicle during sailing driving where an engine 110 of system 100 is stopped allowing the vehicle to coast. During sailing driving, the aerodynamic devices are closed or adjusted, reducing aerodynamic drag, and basic control of the aerodynamic devices is re-established when a time period, which may depend on vehicle speed, expires, sailing driving ceases, for example due to operation of a clutch pedal or an accelerator pedal, or a coolant temperature reaches a predetermined threshold. Advantageously, aerodynamic devices may be closed or adjusted when the vehicle speed exceeds a threshold, for example 4 km/h, and the engine speed is lower than a threshold, for example 100 rpm. Closing or adjusting aerodynamic devices may allow the vehicle to coast for a longer distance, improving fuel economy.

Description

METHOD OF CONTROLLING AERODYNAMIC DEVICES

IN AN AUTOMOTIVE SYSTEM DURING SAILING DRIVING

TECHNICAL FIELD

The present disclosure relates to a method of controlling aerodynamic devices in an automotive system, during sailing driving. The method is particularly suitable for automotive system, with or without hybrid architecture, provided with a controller, configured to automatically stop and start the internal combustion engine.

BACKGROUND

It is known that many automotive systems are provided with a controller, normally an electronic control unit (ECU), which is configured to perform, among other functions, the so called Stop & Start" (or simply 5/8) function. By using said function, the ECU automatically shuts down and restarts the internal combustion engine to reduce the amount of time the engine spends idling, thereby reducing fuel consumption and emissions.

In particular, one of the content of the roadmap of engine manufacturers, aimed to reduce fuel consumption and carbon dioxide (Ca2) emissions, is the extension of the Stop & Start' potential using a soft electrification" to meet Corporate Average Fuel Economy (CAFE) target, foreseen in 2020. CAFE are regulations in the United States, intended to improve the average fuel economy of cars and light trucks. An extended use of the "Stop & Start" function is realized, by stopping the engine not only if the vehicle speed is zero, but also at any vehicle speed, practically when the vehicle speed is lower than a predetermined threshold. The enhanced SIS during such coasting phase is called "Sailing".

Furthermore, automotive system are provided with several aerodynamic devices, in particular modem vehicles are using an active aero shutter, which is fitted to the front grille to control the air flow towards the radiator and inside the engine vane1 thus improving the cooling of the vehicle or its aerodynamic. Normally such device is open at low and intermediate vehicle speeds, while automatically closes at higher speeds to benefit from the aerodynamic advantages. More in general, such economical or sporty vehicles are also provided with front or rear wings, which create a down-force, i.e. a downwards thrust created by the aerodynamic characteristics of a vehicle. The purpose of down-force is to allow a vehicle to travel faster through a corner by increasing the vertical force on the tires, thus creating more grip.

Normally, the creation of down-force by passive devices can only be achieved at the cost of increased aerodynamic drag. Same inconvenience, higher aerodynamic drag, is caused by opened aero shutters.

Therefore, a need exists for a new method of controlling aerodynamic devices in an automotive system, during sailing driving, in other words in a condition during which the aerodynamic devices had not been adjusted so far.

An object of an embodiment of the invention is to provide a method of controlling aerodynamic devices in an automotive system, during sailing driving, with the idea that, closing or adjusting such devices (the aero shutter and any other aerodynamic devices on the vehicle) during sailing extends the coast down time period and therefore improves the fuel consumption.

These objects are achieved by a method and by an automotive system, having the features recited in the independent claims.

The dependent claims delineate preferred and/or especially advantageous aspects.

SUMMARY

An embodiment of the disclosure provides a method of controlling aerodynamic devices of an automotive system, during sailing driving conditions, the automotive system comprising an internal combustion engine and a controller for automatically stopping and starting the internal combustion engine, wherein the method comprises the following steps: -applying a sailing driving condition to the automotive system, -closing or adjusting all available aerodynamics devices of the automotive system for a lower aerodynamic drag during a time interval -restoring a basic control of all aerodynamics devices when the time interval is expired or if the sailing driving condition is ended or if a coolant temperature threshold is reached.

Consequently an apparatus is disclosed controlling aerodynamic devices of an automotive system, during sailing driving conditions, the apparatus comprising: -means for applying a sailing driving condition to the automotive system, -means for closing or adjusting all available aerodynamics devices of the automotive system for a lower aerodynamic drag during a time interval -means for restoring a basic control of all aerodynamics devices when the time interval is expired or if the sailing driving condition is ended or if a coolant temperature threshold is reached.

An advantage of this embodiment is that the closing of all aerodynamic devices in the vehicle decreases the air resistance of the vehicle, thus improving fuel consumption and prolonging the duration of the sailing condition.

According to another embodiment, the step of applying a sailing driving condition comprising the following sub-steps: -detecting a coast down driving condition of the automotive system, -applying the sailing driving condition, by stopping the internal combustion engine.

Consequently, the apparatus also comprises means for detecting a coast down driving condition of the automotive system and said means for applying the sailing driving condition are operating by stopping the internal combustion engine.

An advantage of this embodiment is to be properly referred to the coast down driving condition when neither clutch nor accelerator pedal are used by the driver.

According to a further embodiment, all available aerodynamics devices will be closed or adjusted if a vehicle speed is higher than a vehicle speed threshold and an engine speed is lower than an engine speed threshold.

Consequently, said means for closing all available aerodynamics devices are configured to operate if a vehicle speed is higher than a vehicle speed threshold and an engine speed is lower than an engine speed threshold.

An advantage of this embodiment is that the control of the aero shutter, wings and any other aerodynamic device will close them if the vehicle has still a remarkable speed (otherwise it would be no more useful) and the engine speed is very low, in other words the engine is almost shut off.

According to an aspect of this embodiment, the time interval is a function of the vehicle speed, at the time the sailing driving condition is applied.

Consequently, said means for closing or adjusting all available aerodynamics devices of the automotive system during a time interval are configured to operate when the time interval is a function of the vehicle speed, at the time the sailing driving condition is applied.

The higher the vehicle speed is when a sailing driving condition is applied, the longer will be the time interval the aerodynamics devices can stay closed and this is beneficial for the fuel consumption reduction.

According to a further aspect of this embodiment, the sailing driving condition is ended if a clutch or an accelerator pedal of the automotive system is pressed by a driver.

Consequently, said means for restoring a basic control of all aerodynamics devices are configured to detect that the sailing driving condition is ended if a clutch or an accelerator pedal of the automotive system is pressed by a driver.

Of course, the time interval threshold is the longest period the aerodynamic devices can stay closed: if a clutch or an accelerator pedal of the automotive system is pressed by the driver, the sailing condition is ended and the aerodynamic devices must return open, better they should be controlled by an already available basic control.

According to a still further embodiment said aerodynamic devices comprise an aero shutter.

Consequently, said means for closing or adjusting all available aerodynamics devices of the automotive system are configured to operate with an aero shutter.

An advantage of this embodiment is that it can be applied to all economic and sport vehicles provided with aero shutters.

According to still another embodiment, said aerodynamic devices comprise a down-force wing.

Consequently, said means for closing or adjusting all available aerodynamics devices of the automotive system are configured to operate with a down-force wing.

An advantage of this embodiment is that it can be applied to all economic and sport vehicles provided with front wings and/or rear wings.

A still further embodiment discloses an automotive system having at least an aerodynamic device, the automotive system comprising an internal combustion engine and a controller for automatically stopping and starting the internal combustion engine, such controller being configured to carry out the method according to any of the preceding claims.

The method according to one of its aspects can be carried out with the help of a computer program comprising a program-code for carrying out all the steps of the method described above, and in the form of computer program product comprising the computer program.

The computer program product can be embedded in a control apparatus for an internal combustion engine, comprising an Electronic Control Unit (ECU), a data carrier associated to the ECU, and the computer program stored in a data carrier, so that the control apparatus defines the embodiments described in the same way as the method. In this case, when the control apparatus executes the computer program all the steps of the method described above are carried out.

BRIEF DESCRIPTION OF THE DRAWINGS

The various embodiments will now be described, by way of example, with reference to the accompanying drawings, in which: Figure 1 schematically represents a hybrid powertrain of a motor vehicle.

Figure 2 shows in more details an internal combustion engine belonging to the hybrid powertrain of figure 1.

Figure 3 is a section A-A of the internal combustion engine of figure 2.

Figure 4 is a high level flowchart of a method of controlling aerodynamic devices of an automotive system, according to an embodiment of the present invention.

Figure 5 is a more detailed flowchart of the method of controlling aerodynamic devices of an automotive system, according to several embodiments of the present invention.

DETAILED DESCRIPTION OF THE DRAWINGS

Some embodiments may include a motor vehicle automotive system 100, as shown in Figures 1, that comprises an internal combustion engine (ICE) 110, in this example a diesel engine, a transmission (a manual transmission 510 in the example of Fig. 1), a motor-generator electric unit (MGU) 500, an electric energy storage device (battery) 600 electrically connected to the MGU 500, and an electronic control unit (ECU) 450. The hybrid powertrain architecture has at least a direct electric drive axle.

As shown in Figures 2 and 3, the ICE 110 has an engine block 120 defining at least one cylinder 125 having a piston 140 coupled to rotate a crankshaft 145. A cylinder head 130 cooperates with the piston 140 to define a combustion chamber 150.

A fuel and air mixture (not shown) is disposed in the combustion chamber 150 and S ignited, resulting in hot expanding exhaust gasses causing reciprocal movement of the piston 140. The fuel is provided by at least one fuel injector 160 and the air through at least one intake port 210. The fuel is provided at high pressure to the fuel injector 160 from a fuel rail 170 in fluid communication with a high pressure fuel pump 180 that increase the pressure of the fuel received from a fuel source 190.

Each of the cylinders 125 has at least two valves 215, actuated by a camshaft 135 rotating in time with the crankshaft 145. The valves 215 selectively allow air into the combustion chamber 150 from the port 210 and alternately allow exhaust gases to exit through a port 220. In some examples, a cam phaser 155 may selectively vary the timing between the camshaft 135 and the crankshaft 145.

The air may be distributed to the air intake port(s) 210 through an intake manifold 200.

An air intake duct 205 may provide air from the ambient environment to the intake manifold 200. In other embodiments, a throttle body 330 may be provided to regulate the flow of air into the manifold 200. In still other embodiments, a forced air system such as a turbocharger 230, having a compressor 240 rotationally coupled to a turbine 250, may be provided. Rotation of the compressor 240 increases the pressure and temperature of the air in the duct 205 and manifold 200. An intercooler 260 disposed in the duct 205 may reduce the temperature of the air. The turbine 250 rotates by receiving exhaust gases from an exhaust manifold 225 that directs exhaust gases from the exhaust ports 220 and through a series of vanes prior to expansion through the turbine 250. The exhaust gases exit the turbine 250 and are directed into an exhaust system 270. This example shows a variable geometry turbine (VGT) with a VGT actuator 290 arranged to move the vanes to alter the flow of the exhaust gases through the turbine. In other embodiments the turbocharger 230 may have a fixed geometry and/or include a waste gate actuator 290.

The exhaust system 270 may include an exhaust pipe 275 having one or more exhaust aftertreatment devices 280. The aftertreatment devices may be any device configured to change the composition of the exhaust gases. Some examples of aftertreatment devices 280 include, but are not limited to, catalytic converters (two and three way), oxidation catalysts, lean NOx traps, hydrocarbon adsorbers, selective catalytic reduction (SCR) systems, and particulate filters. Other embodiments may include an exhaust gas recirculation (EGR) system 300 coupled between the exhaust manifold 225 and the intake manifold 200. The EGR system 300 may include an EGR cooler 310 to reduce the temperature of the exhaust gases in the EGR system 300. An EGR valve 320 regulates a flow of exhaust gases in the EGR system 300.

The hybrid powertrain 100 may further include a controller, for example an electronic control unit (ECU) 450, in communication with one or more sensors and/or devices associated with the ICE 110 and equipped with a data carrier 460. The ECU 450 may receive input signals from various sensors configured to generate the signals in proportion to various physical parameters associated with the ICE 110 and the MGU 500.

The MGU 500 is an electric machine, namely an electro-mechanical energy converter, which is able either to convert electricity supplied by the battery 600 into mechanical power (i.e., to operate as an electric motor) or to convert mechanical power into electricity that charges the battery 600 (i.e.1 to operate as electric generator). In greater details, the MGU 500 may comprise a rotor, which is arranged to rotate with respect to a stator, in order to generate or respectively receive the mechanical power. The rotor may comprise means to generate a magnetic field and the stator may comprise electric windings connected to the battery 600, or vice versa. If the MGU 500 operates as electric motor, the battery 600 supplies electric currents in the electric windings, which interact with the magnetic field to set the rotor in rotation. Conversely, when the MGU 500 operates as electric generator, the rotation of the rotor causes a relative movement of the electric wiring in the magnetic field, which generates electrical currents in the electric windings. The MGU 500 may be of any known type, for example a permanent magnet machine, a brushed machine or an induction machine. The MGU 500 may also be either an asynchronous machine or a synchronous machine.

The rotor of the MGU 500 may comprise a coaxial shaft 505, which is mechanically is connected with other components of the hybrid powertrain 100, so as to be able to deliver or receive mechanical power to and from the final drive of the motor vehicle. In this way, operating as an electric motor, the MGU 500 can assist or replace the ICE 110 in propelling the motor vehicle, whereas operating as an electric generator, especially when the motor vehicle is braking, the MGU 500 can charge the battery 600. In the present example, the MGU shaft 505 is connected with the ICE crankshaft 145 through a transmission belt 510, similarly to a conventional alternator starter. In order to switch between the motor operating mode and the generator operating mode, the MGU 500 may be equipped with an appropriate internal control system.

In order to carry out these methods, the ECU 450 is in communication with one or more sensors and/or devices associated with the ICE 110, the MGU 500 and the battery 600.

The ECU 450 may receive input signals from various sensors configured to generate the signals in proportion to various physical parameters associated with the ICE 110, the MGU 500 and the battery 600. The sensors include, but are not limited to, a mass airflow and temperature sensor 340, a manifold pressure and temperature sensor 350, a combustion pressure sensor 360, coolant temperature sensor 380 (which, in case the engine coolant circuit is provided with a switchable water pump 381, can also provide the information of switching off the pump 361, for example, during engine startup), oil temperature sensor 385, a fuel rail pressure sensor 400, a camshaft position sensor 410, a crankshaft position sensor 420, exhaust pressure and temperature sensors 430, an EGR temperature sensor 440, a sensor 445 of a position of an accelerator pedal 446, and a measuring circuit capable of sensing the state of charge of the battery 600.

Furthermore, the ECU 450 may generate output signals to various control devices that are arranged to control the operation of the ICE 110 and the MGU 500, including, but not limited to, the fuel injectors 160, the throttle body 330, the EGR Valve 320, the VGT actuator 290, the cam phaser 155, and the above mentioned internal control system of the MGU 500. Note, dashed lines are used to indicate communication between the ECU 450 and the various sensors and devices, but some are omitted for clarity.

Tuming now to the ECU 450, this apparatus may include a digital central processing unit (CPU) in communication with a memory system and an interface bus. The CPU is configured to execute instructions stored as a program in the memory system, and send and receive signals to/from the interface bus. The memory system may include various storage types including optical storage, magnetic storage, solid state storage, and other non-volatile memory. The interface bus may be configured to send, receive, and modulate analog and/or digital signals to/from the various sensors and control devices.

The program may embody the methods disclosed herein, allowing the CPU to carryout out the steps of such methods and control the ICE 110 and the MGU 500.

The program stored in the memory system is transmitted from outside via a cable or in a wireless fashion. Outside the automotive system 100 it is normally visible as a computer program product, which is also called computer readable medium or machine readable medium in the art, and which should be understood to be a computer program code residing on a carrier, said carrier being transitory or non-transitory in nature with the consequence that the computer program product can be regarded to be transitory or non-transitory in nature.

An example of a transitory computer program product is a signal, e.g. an electromagnetic signal such as an optical signal, which is a transitory carrier for the computer program code. Carrying such computer program code can be achieved by modulating the signal by a conventional modulation technique such as QPSK for digital data, such that binary data representing said computer program code is impressed on the transitory electromagnetic signal. Such signals are e.g. made use of when transmitting computer program code in a wireless fashion via a WiFi connection to a laptop.

In case of a non-transitory computer program product the computer program code is embodied in a tangible storage medium. The storage medium is then the non-transitory carrier mentioned above, such that the computer program code is permanently or non-permanently stored in a retrievable way in or on this storage medium. The storage medium can be of conventional type known in computer technology such as a flash memory, an Asic, a CD or the like.

Instead of an ECU 450, the automotive system 100 may have a different type of processor to provide the electronic logic, e.g. an embedded controller, an onboard computer, or any processing module that might be deployed in the vehicle.

According to an embodiment of the present invention, the automotive system 100 (or more in general the motor vehicle) as described above, is provided with a start and stop device, which is controlled by the ECU and can automatically stop the engine. The automotive system is also provided with at least one aerodynamic device. For example, the motor vehicle can be provided with an aero shutter device in the radiator grille, to improve the cooling of the radiator and the engine vane. On the other hand, the motor vehicle can be equipped with some dawn-force wings (front wing and/or rear wing) to improve the vehicle stability. Such aerodynamics devices are well known and for these reason are not shown in the enclosed drawings.

Figure 4 shows a high level flowchart according to a preferred embodiment of the present method. To control aerodynamic devices during sailing driving conditions, the method is based on the followings. After starting the engine S400, a sailing driving condition is applied 8410 to the automotive system. Then, during sailing, all available aerodynamics devices (aero shutters, down-force wings and any others) of the automotive system are closed S420 during a predetermined time interval tthr. Finally, a basic control of all aerodynamics devices is restored 8440 when the time interval is expired or if the sailing driving condition is ended or if a coolant temperature threshold Tthr is reached 8430. The method cyclically is repeated from the engine start condition.

As mentioned, the start and stop device is controlled by the ECU and can automatically stop the engine, either if the vehicle speed is zero but also (and this is the case related to the present method) if the vehicle speed is higher than zero and the vehicle is in the so called coast down condition.

Therefore and with reference to Fig. 5, starting from a vehicle having 8500 a constant driving or a constant acceleration, a coast down driving condition of the automotive system 100 is detected 5510 if the vehicle drives without the driver is pressing the accelerator pedal. The ECU can decide 8520 to use sailing, in other words to shut off the engine 5530 with the transmission in the neutral gear condition and the clutch completely released.

Then, the control of the aerodynamic devices will be able to close them if the sailing can be defined "active" 5540 or, in more clear words, if a vehicle speed V is higher than a vehicle speed threshold Vthr and an engine speed n is lower than an engine speed threshold nthr. This means the vehicle has still a remarkable speed (otherwise it would be no more useful to close aerodynamic devices) and the engine speed is very low, in other words the engine is almost shut off. As an example, the vehicle speed should be higher than 4 km/h and the engine speed should be lower than 100 rpm.

Then the ECU will check if the aero shutter and the other aerodynamic devices are closed 5550: if yes, no other action shall be taken 8560, other than ensure closing for a calibrated time interval. On the other hand, if the devices are open, the controller will close S570 them for a calibrated maximum time interval. The time interval tthr is a function of the vehicle speed V, when the sailing driving condition is applied. The higher is the vehicle speed when a sailing driving condition is applied. the longer will be the time interval the aerodynamics devices can stay closed.

The sailing driving condition is ended S580 if a clutch 510 or an accelerator pedal 446 of the automotive system is pressed by the driver. In that case, the basic control of the aerodynamic devices is restored 8590.

The idea to close the aero shutter or any other aerodynamic device during sailing improves the fuel consumption and extends the coast down time period. If a vehicle is equipped with an aero shutter in the radiator grille it is possible to close the aero shutter during this sailing event to profit from a belier aerodynamic and to amplify this positive effect on fuel consumption. This positive effect will be higher with rising vehicle speeds.

Summarizing, the present method allows remarkable benefits. Due to better aerodynamic with closed aerodynamic devices (aero shutter and/or wings) the coast down time period of the vehicle will rise, especially for higher vehicle speeds. That means to have a longer sailing event during which the engine is shut off. Therefore the engine can be restarted later than without closed aerodynamic devices. This effect leads to a better fuel consumption.

While at least one exemplary embodiment has been presented in the foregoing summary and detailed description, it should be appreciated that a vast number of variations exist. It should also be appreciated that the exemplary embodiment or exemplary embodiments are only examples, and are not intended to limit the scope, applicability, or configuration in any way. Rather, the foregoing summary and detailed description will provide those skilled in the art with a convenient road map for implementing at least one exemplary embodiment, it being understood that various changes may be made in the function and arrangement of elements described in an exemplary embodiment without departing from the scope as set forth in the appended claims and their legal equivalents.

REFERENCE NUMBERS

automotive system internal combustion engine engine block 125 cylinder cylinder head camshaft piston crankshaft 150 combustion chamber cam phaser fuel injector fuel rail fuel pump 190 fuel source intake manifold 205 air intake pipe 210 intake port 215 valves 220 port 225 exhaust manifold 230 turbocharger 240 compressor 245 turbocharger shaft 250 turbine 260 intercooler 270 exhaust system 275 exhaust pipe 280 aftertreatment devices 290 engine air actuator, turbocharger actuator (waste gate or VGT actuator) 300 exhaust gas recirculation system 310 EGR cooler 320 exhaust gas actuator, EGR valve actuator, EGR valve 330 throttle body 340 mass airflow and temperature sensor 350 manifold pressure and temperature sensor 360 combustion pressure sensor 380 coolant temperature and level sensors 381 switchable water pump 385 lubricating oil temperature and level sensor 390 metal temperature sensor 400 fuel rail pressure sensor 410 cam position sensor 420 crank position sensor 430 exhaust pressure and temperature sensors 440 EGR temperature sensor 445 accelerator position sensor 446 accelerator pedal 450 controller I ECU 460 memory system 500 motor-generator electric unit 505 MGU shaft 510 clutch and manual transmission 600 battery Tøu coolant temperature threshold tthr time interval V vehicle speed Vmr vehicle speed threshold n engine speed n1 engine speed threshold 8400 step 8410 step 8420 step S430 step 8440 step 8500 step 8510 step 8520 step 8530 step 8540 step 8550 step 8560 step 8570 step 8580 step 8590 step

Claims

CLAIMS1. Method of controlling aerodynamic devices of an automotive system (100), during sailing driving conditions, the automotive system comprising an internal combustion engine (110) and a controller (450) for automatically stopping and starting the internal combustion engine (110), wherein the method comprises the following steps: -applying a sailing driving condition to the automotive system, -closing or adjusting all available aerodynamics devices of the automotive system for a lower aerodynamic drag during a time interval (tth1) -restoring a basic control of all aerodynamics devices when the time interval (tmr) is expired or if the sailing driving condition is ended or if a coolant temperature threshold (Tthr) is reached.
2. Method according to claim 1, wherein the step of applying a sailing driving condition comprising the following sub-steps: -detecting a coast down driving condition of the automotive system (100), -applying the sailing driving condition, by stopping the internal combustion engine (110).
3. Method according to claim I or 2, wherein all available aerodynamics devices will be closed or adjusted if a vehicle speed (V) is higher than a vehicle speed threshold (Vmr) and an engine speed (n) is lower than an engine speed threshold (nthr).
4. Method according to claim 3, wherein the time interval (tthf) is a function of the vehicle speed (V), at the time the sailing driving condition is applied.
5. Method according to any of the preceding claims, wherein the sailing driving condition is ended if a clutch (510) or an accelerator pedal (446) of the automotive system is pressed by a driver.
6. Method according to any of the preceding claims, wherein said aerodynamic devices comprise an aero shutter.
7. Method according to any of the preceding claims, wherein said aerodynamic devices comprise a down-force wing.
8. Automotive system (100) having at least an aerodynamic device, the automotive system comprising an internal combustion engine (110) and a controller (450) for automatically stopping and starting the intemal combustion engine (110), such controller being configured to carry out the method according to any of the preceding claims.
9. A non-transitory computer program comprising a computer-code suitable for performing the method according to any of the claims 1-7.
10. Computer program product on which the non-transitory computer program according to claim 9 is stored.
11. Control apparatus for an internal combustion engine, comprising an Electronic Control Unit (450), a memory system (460) associated to the Electronic Control Unit (450) and a non-transitory computer program according to claim 9 stored in the memory system (460).