US2389067A

US2389067A - Thermal pump

Info

Publication number: US2389067A
Application number: US510148A
Authority: US
Inventors: Edgar M Lieberman
Original assignee: Individual
Current assignee: Individual
Priority date: 1943-11-13
Filing date: 1943-11-13
Publication date: 1945-11-13
Anticipated expiration: 1962-11-13

Description

Nov. 13, 1945. E. M. LIEBERMAN THERMAL PUMP Filed Nov. 13, 1943 2 Sheets-Sheet 1 INVENTOR: Y

AGENT Nov. 13, 1945. l-:.M.l LIEBERMAN THERMAL PUMP Filed NOV. 13, 1943 2 Sheets-Sheefl 2 AGENT Patented Nov. 13, 1945 UNITED STATESv PATENTg oFFlcE THERMAL PUMP Edgar M. Lieberman, Kansas City, Mo.

Application November 13, 1943, Serial No. 510,148

15 Claims.

This invention relates to pumps and more particularly to a thermal pump employing steam or liquid vapor as the motive force for use in elevating or circulating liquids, and has for its principal object to provide a pumping apparatus in which steam or the like is generated and employed to provide motive energy for a reciprocating pump piston.

Other objects of the invention are to provide a combination reciprocating pump and ash type boiler for generating steam in the boiler for reciprocating a pump plunger; to provide a supply of liquid to the boiler in response to reciprocation of the pump plunger; to provide for metering the liquid supply to the boiler; to provide for exhausting the steam from the pump cylinder and boiler to reduce pressure therein; to provide for delivering the exhausted steam from the cylinder and boiler to the liquid intake duct; to provide a steam jet from the pump cylinder for expediting flow through the liquid inlet duct; to provide for condensing the steam in the boiler'by fresh liquid supply to eiect reduction in pressure therein for accelerating the return stroke of the pump piston; to provide a resilient member for expediting the return stroke of the piston; to provide a pump having automatic means for controlling the pumping operation; to provide control of the pump operation responsive to control of the boiler heating flame; and to provide improved elements and arrangements thereof in a thermal pump of the character and for the purpose noted.

In accomplishing these and other objects in the present invention, I have provided improved vdetails of structure, the preferred form of ,which is illustrated in the accompanying drawings wherell'lI Fig. 1 is a detail vertical section through a thermal pump embodying the features of the present invention.

Fig. 2 is a detail vertical section showing a modified arrangement of the pump exhaust passage for delivering the jet to the liquid intake duct.

Fig. 3 is a detail vertical section showing a further modified arrangement of the liquid metering device and boiler for operation of the pump.

Referring more in detail to the drawings:

l designates a pump body which may be formed of metal, plastic or other suitable material and preferably contains all of the operating elements of the apparatus and ow channels therefor.. The body preferably consists of a single block of material provided with a bore 2 adjacent one side thereof and formed from the bottom 3 of the body. The bore forms a cylinder for a reciprocable piston 4 of suitable size to closely nt the walls of the bore 2, said piston being inserted from the bottom of the body and the bore closed by means of a thin metal plug 5 having external threads 6 adapted to engage internal threads 'l in the body for securing said plug therein. The upper end of the bore 2 terminates short of the top 8 of the body as at 9 and is provided with a passage I0 of smaller size than the bore 2 to provide a shoulder I I at the upper end of the bore for a purpose later described. The passage Ill communicates the bore 2 with a head chamber I2 spaced upwardly from the end 9 of the bore 2 and formed by a transverse bore opening from the side I3 of the body and extending through said body to a point approximately midway between the bore 2 and the side I4 of said pump body, the open-end of the chamber I2 being closed by a plug I5 having threads I6 engaging internal threadsl I1 in the end of said chamber.

The inner end of the chamber I2 intersects a vertical passage I8 preferably formed from the top of the pump and Provided with an enlarged portion I9 adjacent the end of the chamber I2 to provide a shoulder 20 forming a seat for a valve 2 I. The upper end of the enlarged portion of the passage is preferably closed by a plug 22 having threaded engagement with internal threads 23 in said passage. The passage I8 extends through the pump body and is provided with threads 24 at the bottom of said body to receive a pipe or the like 25 having connections with a source of liquid supply (not shown). Adjacent the end of the chamber I2 which is closed by the plug I5 and formed from the top of the pump body is a passage 26 terminating short of the chamber I2 and connected therewith by an opening` 21 of reduced size to form a shoulder and valve seat 28 for a valve 29, the upper end of said passage 26 being threaded as at 30 to receive the threaded end of a pipe 3I preferably connected toa suitable reservoir or circulatory system requiring a liquid supply. .l

The piston 4 is preferably of a. differential type having an upwardly projecting concentric auxiliary piston 32 of such length that as the piston nears the upper limit of its stroke, said auxiliary piston32 will enter a bore 33 extending upwardly in the top 8 of the pump body and terminating adjacent the bottom 33 thereof, the upper end of said bore 36 being closed by a suitable plug 31 threaded therein. The lower end of the bore 36 intersects a lateral bore 38 drilled through the side I4 of the body and having communica.- tion with a chamber 40, the outer end of said bore 38 being closed by a plug 39 threaded therein. It will be understood that the passage I8 is offset relative to the

passages

34, 36 and 38 so that the respective machining operations may be performed and the proper passages intersect to provide flow through the body as will be later described.

The chamber 48 is located intermediate the bore 2 and the intersection between the

bores

38 and 36 and is preferably formed by a, hole drilled from the bottom 3 of the pump and of suitable size to receive a valve 4| adapted to seat on the edges of the passage 38 formed by the chamber 40, said edges forming a valve seat 42 located at the upper end of the chamber 40. The valve is preferably provided with a spring or the like 43 for normally holding said valve in closed position relative to the passage 38. The chamber 40 is provided with a plug 43 threaded therein to close the opening at the bottom of the pump body. The chamber 40 communicates with the bore 2 through a passage 44 in the body I and a port 44' in the side wall of the plug 5. Adjacent the lower end of the piston 4 at the end of its upward travel is a passage 45 preferably drilled from the side I4 of the pump body through the passage I8 and into the bore 2 to provide an exhaust port communicating the bore 2 with the passage I8, the outer end of the passage 45 being closed by a. suitable plug 46.

In order to provide means for expediting the movement of the piston 4 downwardly in the bore 2 a spring 41 is provided in the upper end of the bore 2, said spring having one end engaging the top of the piston 4 and the other the shoulder I I formed by the end of the bore 2 and the passage I0.

The plug forms a heating surface and heat is applied thereto by a flame from a suitable burner 49 such as a gas, oil or kerosene burner having a suitable source of supply of fuel connected thereto by a duct 50 under control of a suitable valve or control 5| The operation of a pumping apparatus constructed as described is as follows:

Assuming that the pipe 25 is connected to a suitable source of liquid, the pipe 3| with a suitable reservoir or circulatory system requiring a liquid supply and the line 50 with a fuel supply, a small quantity of liquid is placed in the cylinder on the plug 5 and the valve or suitable control 5I operated to provide a name 48 for applying heat to the plug 5 to vaporize the liquid in the bore 2, it being understood that the pump may be primed by liquid to be pumped by removal of any of the plugs, but preferably the plugs I5 The piston 4 is normally at the bottom of the bore 2 and resting on the side walls of the plug 5 which forms a stop for the piston due to the resilient force of the spring 41 and the passage 45 closed thereby. The heat from the flame 48 will vaporize the liquid in the plug 5 at the lower end of the bore forming a vapor pressure in said bore to force the piston 4 upwardly therein against the pressure of the spring 41. Upward movement of the piston 4 forces the liquid in the bore above the piston through the passage I8,

chamber I2, and passage 21, lifting the valve 28 to discharge said liquid through the pipe 8|. The bore 33 is open for the majority of the upward stroke of the piston 4 so that liquid will fill the bore 33

passages

84, 36 and 38. However, the valve 4| maintains the passage 38 closed due to the pressure'of the spring 48 andthe vapor pressure in the bore 2.

As the piston 4 approaches the upper end of its stroke, the end of the auxiliary piston 32 enters the bore 33 to apply additional hydraulic pressure therein and the

passages

34, 36 and 38 to overcome the pressure of the spring 43 and the vapor pressure in the bore 2 to discharge a metered quantity of fresh liquid supply to the lower end of the bore 2. As the auxiliary piston I2 enters the bore 33, the lower end of the piston 4 opens the passage 45 to permit exhaust of the vapor pressure in the bore 2 through said passage 45 into the passage I8 to reduce the pressure in said bore 2. The liquid supply entering the bore 2 from the passage 38 further reduces pressure in the bore 2 due to the lower temperature of said liquid supply to effect condensation of some of the vapor in said bore, thereby reducing the pressure in the bore 2 below the piston 4 to cause the piston 4 to move downwardly in said bore closing the passage 45. The pressure of the spring 41 forces the piston on downwardly in the chamber to provide a suction in the upper end of the bore 2 and the chamber I2 which opens the valve 2| and draws a liquid supply through the pipe 25 and passage I8 into the upper end of the bore 2. As the piston 4 moves downwardly on its return stroke, the flame 48 vaporzes additional liquid to again provide pressure in the lower end of the bore 2 to effect upward movement of the piston 4 to pump liquid from the chamber I2 through the discharge valve 28, pipe 3| to the reservoir or circulatory system, and also provides additional liquid supply to the lower end of the bore 2 to provide a continued operation of the apparatus.

Due to the small quantity of liquid supplied to the bore Lover the plug 5, the lower end of the bore 2 acts as a flash type boiler providing a fast action to the apparatus for effecting reciprocation of the pump piston 4 and the vapor pressure in the bore 2 is quickly reduced by exhaust of the pressure through the passage 45 and the reduction of pressure due to the supply of cold liquid through the passage 38. 'I'he vapor being discharged through the passage 45 is condensed by the liquid in the passage I8 thereby maintaining a low pressure in said passage 45 at all times. Control of the flame 48 by means of the valve or control 5| controls the rapidity of the vaporzation of the liquid in the lower end of the bore 2` thereby controlling the speed of the upward movement of the piston 4, the amount of fresh liquid supplied to the bore 2 being automatically controlled as a slower moving piston acting against the resistance of the spring 41 will reduce the amount of opening of portl 45, entry of the auxiliary piston 32 into the bore 33 thereby reducing the amount of fresh liquid supply to the' `either the intake valve 2| or discharge valve 29 may be eliminated.

In the form of the invention shown in Fig. 2 the vapor exhaust passage 52 is arranged at an angle relative to the bore 2 and passage I8 so the vapor pressure being exhausted from the bore 2 at the upper end ofthe piston stroke will be directed substantially in the direction of ow of the liquid through the passaage I8 thereby providing a jet action to increase or aid in the flow of liquid through the passage I8. With this arrangement the pumping apparatus operates substantially in the same manner as described in the preferred forms except for the advantages obtained due to the jet action of the exhaust vapor in increasing the' emciency of the apparatus.

In the form of the invention shown in Fig. 3 the pump body 53 is provided with a cylinder 54 closed by a plug 55; a piston 58 being reciprocable in said cylinder. Said body also includes an intake passage 51 and discharge, passage 58 for ow of liquidto andfrom the. cylinder head chamber 59, said passages being provided with valves 60 and 6IV respectively substantially as in the form shown in Fig. 1.

Threaded into thebody 53 and extending into the head chamber over the cylinder 54 is a guide 62 having a bore 63 adapted to receive-a'pl'ungerl The plunger is providedy with al ring-61 aroundv its upper end to provide a stop for limiting its downward A movement. The portion of the plunger extending through thebore 63 is provided with a groove 58 to provide apassage for liquid into the chamber 66, said groove. terminating slightly below the guide so that a small amount of movement of the plunger closes the lower end of said groove and continued upward movement of the plunger forces liquid from the chamber 56 through a valve 69 into a coil y1I! which serves as a boiler.

The coil is heated by a suitable burner 1| and the heat of the flame therefrom concentrated around the coil by ahcusng 12. The lower end of the coil is connected with the bottom of the plug 55 so that steam or vapor pressure generated in the coil is delivered to the cylinder to effect reciprocation of the piston in substantially the same-manner as in theform shown in Fig. 1. Resistance tothe upward movement of the piston is provided by aispring 13 and the vapor pres sure in .the cylinder is vexhausted through a passage 14 connected with theintake 51. The plunger 54 maybe located any place above the piston 56 and is normally held in the lower position by a spring'15 sleeved over said plunger and having one end bearing on the `guide 62 fand the other endonthehe'adBS. .l -1

It is apparent, therefore,l that an economical and eflicien't thermal pump of simple construction and operation is provided by thepresent invention.

What I claim and desire to secure by Letters Patent is:

l. In a pumping apparatus of the character described, a pump body having a chamber therein, a, piston reciprocable in said chamber, inlet and outlet connections in one end ofthe chamber for movement of liquid to and from said chamber in response to reciprocation of said piston, means for applying vapor pressure to the other end of the chamber for effecting movement of the pisment of said piston, and means actuated by reciprocation of said piston for metering liquid to be vaporized to form the vapor pressure in' said chamber for causing the reciprocation to be continuous. y

2. In a pumping apparatus of the character described, a pump body having a chamber therein, a piston reciprocable in the chamber, means connecting one end of the chamber with a source of liquid supply, a liquid outlet connected with'said end of the chamber, means operative responsive to reciprocation of the piston in the chamber for delivering a quantity of liquid to the other end of the chamber, means for applying heat to said other end of the chamber for vaporizing the liquid therein, applying vapor pressure to the piston for moving same toward the first named end of the chamber to force the liquid therein through the outlet connection, means for controlling the vapor pressure in said chamber for eiecting reciprocation of the piston therein, and means actuated by reciprocation of said'pistonfor metering liquid to lbe vaporizedto form the vapor pressure in said chamber for causingthe reciprocation to befcontinuous.

in, a piston reciprocable in said chamber, zinlet and outlet connections in one end of the chamber for movement of liquid-to and from vsaid chamber in response to reciprocation of4 said piston, means for applying vapor pressureV to the other endpf the chamber for effecting movement of thev piston in one direction, means for applying heat-to said other end of the chamber, means controlled by said movement of the piston for reducing vapor pressure in the chamber and reverse movement of said piston, an exhaust line extending atan angle communicating with said chamber and controlled by said movement of the piston for exhausting the vapor pressure in the chamber, and resilient means in the chamber for resisting action of the Vapor pressure on the piston. c 4

4. In a pumping apparatus of the character described, a pump body having a chamber therein, a piston reciprocable in said chamber, inlet and outlet connections in one end oi the chamber for movement of liquid to and from said chamber in response to reciprocation of said piston, means operative in response to reciprocation of said piston for delivering liquid to the other end of said chamber, means for vaporizing the liquid in said other end of the chamber for applying vapor pressure to the piston for eiectingmovement thereof in one direction,an exhaust line extending to an angle communicating with said chamber and controlled Aby said movement of the piston for exhausting the Vapor pressure in the chamber, and spring means in the chamber for effecting reverse movement of the piston'whenfthe vapor pressure is exhausted therefrom.

5. In a pumping apparatus of the character described, a pump body having a chamber therein, a piston reciprocable in said chamber, means connecting one end of the chamber lwith the source of liquid supply, a liquid outlet connected with said end of the chamber, meansoperative responsive. to reciprocationof the piston in the chamber for delivering aquantty of l'quid to the other end of the chamber, means for applying heat to said other end of the chamber for vaporizing the liquid therein for applying vapor pressure to thepiston for moving same toward the first named end of the chamber to force the liquid 3. In a pumping apparatus -of the character described, a pump body having a'chamber-there- Kflcontrolled means connecting one end of the chamber with a source of liquid supply, valve controlled outlet connected with said end of the chamber, a relatively small amount of liquid in the other end of the chamber, means for applying heat to said other end of the chamber for vaporizing the liquid therein for applying vapor pressure to the piston for moving same toward the first named end of the chamber to force the liquid therein through the outlet connection, and an auxiliary piston actuated by the first named piston and extending toward the first named end of said chamber, said pump body having a bore therein communicating with the chamber, said auxiliary piston being adapted to enter said bore as the iirst named piston approaches the end of its movement toward the rst named end of the chamber to force a quantityy of liquid into said bore, said pump body having a valve controlled passage therein communicating the bore with the second named end 0f the chamber whereby liquid forced into the bore is delivered to said chamber to replenish the supply of liquid therein.

7. In a pumping apparatus of the character described, a pump body having a chamber therein, a piston reciprocable in said chamber, valve controlled means connecting one end of the chamber with a source of liquid supply, valve controlled outlet connected with said end of the chamber, a relatively small amount of liquid in the other end ofthe chamber, means for app-1ying heat to said other end of the chamber for vaporzing the liquid therein for applying vapor pressure to the piston for moving same toward the rst named end of the chamber to force the liquid therein through the outlet connection, and an auxiliary piston actuated by the first named piston and extending toward the first named end of said chamber, said pump body having a bore therein communicating With the chamber, said auxiliary piston being adapted to enter said bore as the first named piston approaches the end of its movement toward the rst named end of the chamber to force a quantity of liquid into said bore, said pump body having a valve controlled passage therein communicating the bore with the second named end 0f the chamber whereby liquid forced into the bore is delivered to said chamber to replenish the supply of liquid therein, the liquid delivered by the passage eiecting a reduction in temperature and condensation of the vapor in the chamber to reduce the pressures therein.

8. In a pumping apparatus of the character described, a pump body having a chamber therein, a piston reciprocable in said chamber, valve controlled means connecting one end of the chamber with a source of liquid supply, valve controlled outlet connected with said end of the chamber, a, relatively small amount of liquid in the other end of the chamber, means for applying heat to said other end of the chamber for vaporizing the liquid therein for applying vapor pressure to the piston for moving same toward the iirst named end of the chamber to force the liquid therein through the outlet connection, and an auxiliary piston actuated by the rst named piston and extending toward the iirst named end of said chamber, said pump body having a bore therein communicating with the chamber, said auxiliary piston being adapted to enter said bore as the first named piston approaches the end of its movement toward the first named end of the chamber to force a quantity of liquid into said bore, said pump body having a valve controlled passage therein communicating the bore with the second named end of the chamber whereby liquid forced into the bore is delivered to said chamber to replenish the supply of liquid therein, the liquid delivered-by the passage effecting a reduction in temperature and condensation of the vapor in the chamber to reduce the pressures therein, said pump body having an exhaust passage therein communicating the chamber with the means connected with a liquid supply for exhausting and reducing the vapor pressure in the chamber after a predetermined piston travel.

9. In a pumping apparatus of the character described, a pump body having a chamber therein, a piston reciprocable in said chamber, valve controlled means connecting one end of the chamber with a source of liquid supply, valve controlled outlet connected with said end of the chamber, a relatively small amount of liquid in the other end of the chamber, means for applying heat to said other end of the chamber for vaporizing the liquid therein for applying vapor pressure to the piston for moving same toward the first named end of the chamber to force the liquid therein through the outlet connection, an auxiliary piston actuated by the rst named piston and extending toward the first named end of said chamber, said pump body having a bore therein communicating With the chamber, said auxiliary piston being adapted to enter said bore as the rst named piston approaches the end of its movement toward the iirst named end of the chamber to 'force a quantity of liquid into said bore, said pump body having a valve controlled passage therein communicating the bore with the second named end of the chamber whereby liquid forced into the bore is delivered to said chamber to replenish the supply of liquid therein, the liquid delivered by the passage effecting a reduction in temperature and condensation of the vapor in the chamber to reduce the pressures therein, said pump having an exhaust passage therein communicating the chamber with the means connected with a liquid supply for exhausting and reducing the vapor pressure in the chamber after a predetermined piston travel; and resilient means in the chamber for resisting action of the vapor pressures on the piston and effecting reverse movement of said piston when the vapor pressure in the chamber is reduced.

I 10. In an apparatus of the character described, a body having a chamber therein, a second chamber having communication with the first named Chamber, a liquid supply to said body, means for metering a quantity of liquid to said second named chamber, a coil for heating said liquid and vaporizing said liquid in the second named chamber for applying vapor pressure to the iirst named chamber, piston means movable in one direction responsive to the vapor pressure in the chamber, exhaust means communicating with said rst named chamber and controlled by movement of said piston means for exhausting the vapor pressure at an angle in the respective chambers for effecting reverse movement of said piston means, and means for effecting reverse movement of the piston after the vapor pressure acting on the piston is reduced.

1l. In a pumping apparatus of the character described, a pump body having a chamber therein, a piston reciprocable in the chamber, means connecting one end of said chamber with a source of liquid supply, a liquid outlet connected with saidend of the chamber, said liquid outlet including a guide carrying a plunger having a longitudinal slot therein and having its lower end engageable with said piston upon upward stroke of the piston, a vapor chamber formingmeans connected with .the other end of said chamber, means operative responsive to reciprocation of the piston for delivering a quantity of liquid to said vapor chamber forming means, means for applying heat to said chamber forming means for vaporizing the liquid therein and applying the vapor pressure to the piston for moving same toward the iirst named end of the chamber to force the liquid therein through the outlet connection, means for controlling the vapor pressure in said chamber ior eilecting reciprocation of the piston, and means for effecting reverse movement of the piston after the vapor pressure acting on the piston is reduced.

12. In an apparatus of the character described, a body having a chamber therein, means connected with said chamber for forming a vapor pressure therein, means for exhausting and condensing the vapor pressure in the chamber, a piston reciprocable in said chamber in response to alternate formation, exhaust and condensation of the vapor pressure in the chamber acting on the piston, means actuated by reciprocation of said piston for metering liquid' to be vaporized to form the vapor pressure in said chamber for causing the reciprocation tobe continuous, and an auxiliary piston actuated by the rst named pisa valve controlled passage therein communicating'the bore with the lower end of the chamber whereby liquid forced into the bore is delivered to said chamber to replenish the supply of liquid therein.

14. In an apparatus of the character described, a body having a chamber therein, means connected with'sid chamber for forming a vapor pressure therein, means for exhausting and condensing the vapor pressure in the chamber, a piston reciprocable in vsaid chamber in response to alternate formation, exhaust and condensation of the vapor pressure in the chamber acting on the piston, means actuated by reciprocation of said piston for metering liquid to be vaporized to form the vapor pressure in said chamber for causingk the reciprocation to be continuous, andan auxiliary piston actuated by the first named piston and extending toward the upper end of said chamber, said body having a bore therein communicating with the chamber, said auxiliary piston being adapted to enter said bore as the first named piston approaches the end of its movement toward the upper end of the chamber to foce a. quantity of liquid into said bore, said body having a valve controlled passage therein communieating the bore with the lower end of the chamber whereby liquid forced into the bore is deliveredto said chamber to replenish the supply of liquid therein, the liquid delivered by the passage eiecting the reduction in temperature and condensation of the vapor in the 'chamber to reduce the pressures therein.

15. In an apparatus of the character described, a body havnga chamber therein, means connected with said chamber for forming a vapor ton and extending toward' the upper end of said chamber,said body having a bore therein communicating with the chamber, said auxiliary piston being adapted to enter said bore as the rst named piston approaches the end of its movement toward the upper end of the chamber to force a quantity of liquid into said bore.

13. In an apparatus of the character described, a body having a chamber therein, means connected with said chamber for forming a vapor pressure therein, means for exhausting and condensing the vapor pressure in the chamber, a piston reciprocable in said chamber in response to alternate formation, exhaust and condensation of the vapor pressure in the chamber acting on the piston, means actuated by reciprocation of said piston for metering liquid to be vaporized to form the vapor pressure in said chamber for causing the reciprocation to be continuous, and an auxiliary piston actuated by the rst named piston and extending toward the upper end of said chamber, said body having a bore therein communicating with the chamber, said auxiliary piston being adapted to enter said bore as the rst named piston approaches the end of its movement toward the upper end of the chamber'to forcea quantity of vliquid into said bore, said body having pressure therein, means for exhausting and condensing the vapor pressure in the chamber, a piston reciprocable in said chamber in response to alternate formation, exhaust and condensatiom of the vapor pressure in the chamber acting on the piston, means actuated 4.by reciprocation of said piston for metering liquid to be vaporlzed to form the vapor pressure in said chamber forl causing the reciprocation to be continuous, and an auxiliary piston actuated by the rst named piston and extending toward the upper end of, said chamber, said body having a bore therein l communicating with the chamber, said auxiliary piston being adapted to enter said bore as the first named piston approaches the end of its movement toward the upper end of the chamber to force a quantity of liquid into said bore, said body having a valve controlled passage therein communicating the bore with the lower end of the chamber whereby liquid forced into the bore is delivered to said chamber to replenish the supply of liquid therein, the liquid delivered by the. passage eiecting the reduction in temperature and condensation of the vapor in the chamber to reduce the pressures therein, saidl body having an exhaust passage therein communicating the chamber with the means connected with a liquid l supply for exhausting and reducingvthe'vapor pressure inthe chamber lafter a predetermined piston travel. g

EDGAR M. LIEBERMAN.