Describe the function of a hydraulic power unit

Transcription

1 Chapter 7 Source of Hydraulic Power Power Units and Pumps 1

2 Objectives Describe the function of a hydraulic power unit and identify its primary components. Explain the purpose of a pump in a hydraulic system. Explain the operation of a basic hydraulic pump. Compare the operating characteristics of positive-displacement and non-positivedisplacement hydraulic pumps. Goodheart-Willcox Co., Inc. 3 Objectives Compare the operating characteristics of rotary and reciprocating hydraulic pumps. Compare the operating characteristics of constant- and variable-volume hydraulic pumps. Explain the principles involved in the operation of a pressure-compensated hydraulic pump. Goodheart-Willcox Co., Inc. 4 2

3 Objectives Describe general construction for each of the various hydraulic pump designs. Explain cavitation and its effect on pump performance and service life. Interpret performance data supplied by a pump manufacturer. Goodheart-Willcox Co., Inc. 5 The power unit: Power Unit Provides energy for the operation of the hydraulic system Moves fluid through the system Provides a safe maximum system operating pressure Assists in maintaining correct system operating temperature and fluid cleanliness Goodheart-Willcox Co., Inc. 6 3

4 Power units are often supplied by manufacturers as a package Power Unit Kim Hotstart Manufacturing Company Goodheart-Willcox Co., Inc. 7 Power Unit A basic power unit consists of: Prime mover to power the system Pump to move fluid Reservoir to store fluid Relief valve or pump compensator to control maximum system pressure Filter to clean the fluid Plumbing to transport fluid to components Goodheart-Willcox Co., Inc. 8 4

5 Power Unit A prime mover may be an electric motor Continental Hydraulics Goodheart-Willcox Co., Inc. 9 Power Unit A prime mover may be an internal combustion engine Deere & Co. Goodheart-Willcox Co., Inc. 10 5

6 Power Unit A coupler connects the prime mover to the pump Goodheart-Willcox Co., Inc. 11 Power Unit The power unit includes a pressure control valve to limit pressure Goodheart-Willcox Co., Inc. 12 6

7 Power Unit Filters and strainers are included in a power unit to remove debris from the fluid Goodheart-Willcox Co., Inc. 13 Basic Pump The basic operating principle that moves fluid through h a pump is similar il in all pumps Enlarging the volume of a chamber allows fluid to enter the pump Reducing the chamber volume moves fluid to the system Inlet and discharge valves or ports control fluid movement through the pump Goodheart-Willcox Co., Inc. 14 7

8 Basic Pump Increasing the size of the pumping chamber moves fluid into the pump Goodheart-Willcox Co., Inc. 15 Basic Pump Reducing the size of the pumping chamber forces fluid idinto the system Goodheart-Willcox Co., Inc. 16 8

9 Basic Pump The maximum pressure developed in a hydraulic system is determined dby: Resistance to fluid flow in the system Force the prime mover can exert Goodheart-Willcox Co., Inc. 17 Basic Pump The output flow rate of a hydraulic pump is dt determined dby: Volume of the pumping chamber Operating speed of the prime mover Goodheart-Willcox Co., Inc. 18 9

10 Basic Pump Classifications Hydraulic pumps can be classified using three basic aspects: Displacement Pumping motion Fluid delivery characteristics Goodheart-Willcox Co., Inc. 19 Basic Pump Classifications Displacement relates to how the output of the pump reacts to system loads Positive-displacement pumps produce a constant output per cycle Non-positive-displacement pumps produce flow variations due to internal slippage Goodheart-Willcox Co., Inc

11 Basic Pump Classifications A non-positive-displacement pump has large internal clearances Allows fluid slippage in the pump Results in varying flow output as system load varies Goodheart-Willcox Co., Inc. 21 Basic Pump Classifications Non-positive-displacement pump Goodheart-Willcox Co., Inc

12 Basic Pump Classifications The basic pumping motions used in hydraulic pumps are: Rotary Reciprocating Goodheart-Willcox Co., Inc. 23 Basic Pump Classifications Gear pumps are rotary pumps Sauer-Danfoss, Ames, IA Goodheart-Willcox Co., Inc

13 Basic Pump Classifications Piston pumps are reciprocating pumps Reciprocating piston movement Goodheart-Willcox Co., Inc. 25 Basic Pump Classifications In a rotary pump, the pumping action is produced dby revolving components In a reciprocating pump, the rotating motion of the pump input shaft is changed to reciprocating motion, which then produces the pumping action Goodheart-Willcox Co., Inc

14 Basic Pump Classifications Hydraulic pumps are classified as either fixed or variable ibl delivery dli Fixed-delivery pumps have pumping chambers with a volume that cannot be changed; the output is the same during each cycle In variable-delivery designs, chamber geometry may be changed to allow varying flow from the pump Goodheart-Willcox Co., Inc. 27 Basic Pump Classifications Gear pumps are fixed-delivery pumps Courtesy of Eaton Fluid Power Training Goodheart-Willcox Co., Inc

15 Basic Pump Classifications Piston pumps may be designed as variabledli delivery pumps Courtesy of Eaton Fluid Power Training Goodheart-Willcox Co., Inc. 29 Basic Pump Classifications When selecting a pump for a circuit, factors that t must be considered d are: System operating pressure Flow rate Cycle rate Expected length of service Environmental conditions Cost Goodheart-Willcox Co., Inc

16 Pump Design, Operation, Gear pumps are positive-displacement, fixeddli delivery, rotary units Gear pumps are produced with either external or internal gear teeth configurations Goodheart-Willcox Co., Inc. 31 Pump Design, Operation, Gear pumps are commonly used Goodheart-Willcox Co., Inc

17 Pump Design, Operation, Pumping action of gear pumps results from unmeshing and meshing of the gears As the gears unmesh in the inlet area, low pressure causes fluid to enter the pump As the pump rotates, fluid is carried to the pump discharge area When the gears mesh in the discharge area, fluid is forced out of the pump into the system Goodheart-Willcox Co., Inc. 33 Pump Design, Operation, Gear pumps are available in a wide variety of sizes Flow outputs from below 1 gpm to 150 gpm Pressure rating range up to 3000 psi Goodheart-Willcox Co., Inc

18 Pump Design, Operation, The gerotor pump design is an internal-gear pump Uses two rotating, gear-shaped elements that form sealed chambers The chambers vary in volume as the elements rotate Fluid comes into the chambers as they are enlarging g and is forced out as they decrease in size Goodheart-Willcox Co., Inc. 35 Pump Design, Operation, The gerotor is a common internal-gear design Goodheart-Willcox Co., Inc

19 Pump Design, Operation, Gerotor operation Goodheart-Willcox Co., Inc. 37 Pump Design, Operation, Gerotor operation Goodheart-Willcox Co., Inc

20 Pump Design, Operation, Gerotor operation Goodheart-Willcox Co., Inc. 39 Pump Design, Operation, Gerotor operation Goodheart-Willcox Co., Inc

21 Pump Design, Operation, Vane pumps are positive-displacement, fixed or variable ibl delivery, dli rotary units. Design is commonly used in industrial applications Delivery can range up to 75 gpm Maximum pressure of about 2000 psi Goodheart-Willcox Co., Inc. 41 Pump Design, Operation, Vane pump consists of a slotted rotor, fitted with moveable vanes, that rotates within a cam ring in the pump housing Rotor is off center in the ring, which creates pumping chambers that vary in volume as the pump rotates As chamber volume increases, pressure decreases, bringing fluid into the pump As volume decreases, fluid is forced out into the system Goodheart-Willcox Co., Inc

22 Pump Design, Operation, Operation of a typical vane pump Goodheart-Willcox Co., Inc. 43 Pump Design, Operation, Parts of a typical vane pump Courtesy of Eaton Fluid Power Training Goodheart-Willcox Co., Inc

23 Pump Design, Operation, Vane pump may be pressure unbalanced or pressure bl balanced Unbalanced has only one inlet and one discharge, which places a side load on the shaft Balanced has two inlets and two discharges opposite each other, creating a pressure balance and, therefore, no load on the shaft Goodheart-Willcox Co., Inc. 45 Pump Design, Operation, Piston pumps are positive-displacement, fixedibl li reciprocating units or variable-delivery, Several variations Many provide high volumetric efficiency (90%), high operating pressure (10,000 psi or higher), and high-speed operation Goodheart-Willcox Co., Inc

24 Pump Design, Operation, A basic piston pump consists of a housing that supports a pumping mechanism and a motionconverting mechanism Pumping mechanism is a block containing cylinders fitted with pistons and valves Motion converter changes rotary to reciprocating motion via cams, eccentric ring, swash plate,or bent-axis designs Rotating the pump shaft causes piston movement that pumps the fluid Goodheart-Willcox Co., Inc. 47 Pump Design, Operation, Piston pump classification is based on the relationship lti between bt the axes of fthe power input shaft and piston motion Axial Radial Reciprocating Goodheart-Willcox Co., Inc

25 Pump Design, Operation, Axial piston pumps use two design variations: Inline Bent axis Goodheart-Willcox Co., Inc. 49 Pump Design, Operation, Inline has the cylinder block and pistons located on the same axis as the pump input shaft Pistons reciprocate against a swash plate Very popular design used in many applications Goodheart-Willcox Co., Inc

26 Pump Design, Operation, An inline axial-piston pump The Oilgear Company Goodheart-Willcox Co., Inc. 51 Pump Design, Operation, Bent axis has the cylinder block and pistons set at an angle to the input shaft Geometry of the axis angle creates piston movement Considered a more rugged pump than inline Manufactured in high flow rates and maximum operating pressures Goodheart-Willcox Co., Inc

27 Pump Design, Operation, A bent-axis axial-piston pump Goodheart-Willcox Co., Inc. 53 Pump Design, Operation, Radial piston pumps have the highest continuous operating pressure capability of any of the pumps regularly used in hydraulic systems Models are available with operating pressure ratings in the 10,000 psi range Goodheart-Willcox Co., Inc

28 Pump Design, Operation, Two variations of radial piston pumps: Stationary-cylinder design uses springs to hold pistons against a cam that rotates with the main shaft of the pump Rotating-cylinder design uses centrifugal force to hold pistons against a reaction ring When the main shaft is rotated, each piston reciprocates, causing fluid to move through the pump Goodheart-Willcox Co., Inc. 55 Pump Design, Operation, A stationary-cylinder radial-piston pump Goodheart-Willcox Co., Inc

29 Pump Design, Operation, Large, reciprocating-plunger pump designs were widely used when factories had a central hydraulic power source Today, plunger pumps are typically found in special applications requiring high-pressure performance Goodheart-Willcox Co., Inc. 57 Pump Design, Operation, Screw pumps have pumping elements that consist itof one, two, or three rotating tti screws As the screws rotate, fluid is trapped and carried along to the discharge of the pump The design of screw pumps allows them to operate at a very low noise level Goodheart-Willcox Co., Inc

30 Pump Design, Operation, A typical screw pump Goodheart-Willcox Co., Inc. 59 Pump Design, Operation, The lobe pump is a close relative of the gear pump Two three-lobed, gear-shaped units are often used to form the pumping element Output flow is larger than a gear pump of comparable bephysical ysc size ebecause useof pumping p chamber geometry Lower pressure rating than gear pumps Tend to have a pulsating output flow Goodheart-Willcox Co., Inc

31 Pump Design, Operation, Operation of a lobe pump Goodheart-Willcox Co., Inc. 61 Pump Design, Operation, Centrifugal pumps are non-positivedisplacement units Use centrifugal force generated by a rotating impeller to move fluid Large clearances between the impeller and the pump housing allow internal pump slippage when resistance to fluid flow is encountered in the system Typically used in hydraulic systems as auxiliary fluid transfer pumps Goodheart-Willcox Co., Inc

32 Pump Design, Operation, Operation of a centrifugal pump Goodheart-Willcox Co., Inc. 63 Pump Design, Operation, Propeller and jet pumps are non-positive- displacement pumps Sometimes used to transfer fluid within hydraulic systems Propeller pump consists of a rotating propellershaped pumping element Jet pump creates flow by pumping fluid through a nozzle concentrically located within a venturi Goodheart-Willcox Co., Inc

33 Pump Design, Operation, Construction of a propeller pump Goodheart-Willcox Co., Inc. 65 Pump Design, Operation, Construction of a jet pump Goodheart-Willcox Co., Inc

34 Additional Design Features of Pumps Some basic pump designs can be modified to allow the unit to produce variable flow outputs t at constant operating speeds This is achieved by including pump elements that allow the volume of the pumping chamber to be changed, either manually or by pressuresensing devices Goodheart-Willcox Co., Inc. 67 Additional Design Features of Pumps Unbalanced-vane pumps can be designed to produce variable flow outputs t A cam ring moves in relation to the center of the rotor No flow output is produced when the centers of the ring and rotor are concentric Flow increases as the centers move apart Goodheart-Willcox Co., Inc

35 Additional Design Features of Pumps A variable-flow, unbalanced-vane pump Goodheart-Willcox Co., Inc. 69 Additional Design Features of Pumps Axial- and radial-piston pumps can include variable ibl flow output t Variable flow is created by varying the length of the piston stroke Inline design varies the angle of the swash plate Bent-axis design varies the angle between the cylinder barrel and pump input shaft Radial-piston design uses a moveable reaction ring Goodheart-Willcox Co., Inc

36 Additional Design Features of Pumps Pressure compensation allows a pump to sense system pressure and vary pumping chamber volume Provides only sufficient fluid to maintain the desired system operating pressure When system resistance is low, the pump produces maximum flow Goodheart-Willcox Co., Inc. 71 Additional Design Features of Pumps When system load increases, the pump adjusts and supplies only sufficient flow to maintain the desired operating pressure When the actuator stalls, fluid flow only sufficient to compensate for system leakage is produced Reduces the time the prime mover must spend producing maximum flow against maximum system pressure Reduces energy consumption Goodheart-Willcox Co., Inc

37 Additional Design Features of Pumps Pressure compensation reduces energy consumption Goodheart-Willcox Co., Inc. 73 Additional Design Features of Pumps Pressures that occur in a hydraulic system exert force on all of fthe internal surfaces of pumps and other components Pressure differences within a pump can cause uneven loads on bearings Pressure balancing delivers pressurized fluid to critical locations to counteract these forces Helps reduce wear and improve sealing between components Goodheart-Willcox Co., Inc

38 Additional Design Features of Pumps System pressure can be used to help create a seal Goodheart-Willcox Co., Inc. 75 Additional Design Features of Pumps Dual pumps are two pumps housed in a single case and ddi driven by a single prime mover Some units include integral valving to provide relief and unloading capabilities Typical application is a high-low circuit where a large cylinder quickly extends followed by highpressure clamping Goodheart-Willcox Co., Inc

39 Additional Design Features of Pumps A dual-pump design Sauer-Danfoss, Ames, IA Goodheart-Willcox Co., Inc. 77 Pump and Power Unit Design and Operating Considerations Manufacturers supply considerable information about their pumps: General specifications Performance data Installation drawings Application information Goodheart-Willcox Co., Inc

40 Pump and Power Unit Design and Operating Considerations Careful analysis of these sheets provides the dtildif detailed information needed ddfor selecting, installing and operating a hydraulic pump Goodheart-Willcox Co., Inc. 79 Pump and Power Unit Design and Operating Considerations The size of the prime mover is established by the peak power needed d during the system operating cycle Determining peak power requires careful system analysis as changes in actuator loads, pump efficiency, operating temperature, and fluid viscosity will change the power need Goodheart-Willcox Co., Inc

41 Pump and Power Unit Design and Operating Considerations Horsepower is defined as 33,000 foot pounds of work per minute In a hydraulic system, pressurized fluid is moved instead of an object The formula for general hydraulic horsepower is: pounds of the fluid moved per minute pressure in feet of head 33,000 foot pounds per minute Goodheart-Willcox Co., Inc. 81 Pump and Power Unit Design and Operating Considerations The pounds of fluid moved for use in the general lhydraulic horsepower formula is calculated as: pump flow rate in gallons per minute weight of water specific gravity of the fluid gallons in a cubic foot of fluid Goodheart-Willcox Co., Inc

42 Pump and Power Unit Design and Operating Considerations The pressure in feet of head for use in the general lhydraulic horsepower formula is calculated as: system pressure in pounds per square inch number of square inches in a square foot weight of a cubic foot of water specific gravity of the system fluid Goodheart-Willcox Co., Inc. 83 Pump and Power Unit Design and Operating Considerations The general hydraulic formula can be reduced: pump flow rate system pressure 1714 Stated in mathematical form: gpm psi 1714 or gpm psi Goodheart-Willcox Co., Inc

43 Pump and Power Unit Design and Operating Considerations Prime mover power actually required for the operation of a system will be greater than that calculated using the general hydraulic horsepower formula This is because of power losses in both the prime mover and the pump Internal leakage Internal friction Goodheart-Willcox Co., Inc. 85 Pump and Power Unit Design and Operating Considerations Internal leakage: Caused by clearances in the pump resulting from manufacturing tolerances and component wear Expressed as volumetric efficiency Volumetric efficiency is calculated as: actual pump flow rate theoretical pump flow rate 100 Goodheart-Willcox Co., Inc

44 Pump and Power Unit Design and Operating Considerations Internal friction: Caused by bearings, close contact of machined surfaces, fluid viscosity, and turbulence Expressed as mechanical efficiency Mechanical efficiency is calculated as: theoretical horsepower needed to operate the pump actual horsepower required to operate the pump 100 Goodheart-Willcox Co., Inc. 87 Pump and Power Unit Design and Operating Considerations Overall efficiency of a pump considers all energy losses in the unit Combines the volumetric and mechanical efficiency ratings Overall efficiency is calculated as: volumetric efficiency mechanical efficiency 100 Goodheart-Willcox Co., Inc

45 Pump and Power Unit Design and Operating Considerations Required prime mover input horsepower is equal lto the calculated ltdgeneral lhd hydraulic horsepower for the system divided by the overall efficiency of the pump: gpm psi 1714 overall efficiency Goodheart-Willcox Co., Inc. 89 Pump and Power Unit Design and Operating Considerations All of the fluid used in the operation of a hydraulic system enters the system through the inlet line of the pump The low pressure differential between the system reservoir and pump inlet can create problems Cavitation Air entrainment Goodheart-Willcox Co., Inc

46 Pump and Power Unit Design and Operating Considerations Cavitation is caused when inlet line pressure drops below the vapor pressure of the fluid and bubbles form Reduces lubricity of the system fluid Collapsing bubbles produce severe shock waves that can damage pump parts Collapsing bubbles also produce noisy pump operation Goodheart-Willcox Co., Inc. 91 Pump and Power Unit Design and Operating Considerations Factors that influence the point at which a liquid id begins to form a vapor: Chemical makeup of the liquid Pressure applied on the liquid Temperature of the liquid Goodheart-Willcox Co., Inc

47 Pump and Power Unit Design and Operating Considerations Point at which liquid begins to form vapor depends on system pressure, temperature, and fluid characteristics Goodheart-Willcox Co., Inc. 93 Pump and Power Unit Design and Operating Considerations Entrained air is air suspended in fluid Enters the inlet line through leaks Can produce a result similar to cavitation Testing inlet line pressure can help indicate which condition exists High negative pressure (vacuum) indicates cavitation Pressure closer to 0 psi may indicate entrained air Goodheart-Willcox Co., Inc

48 Pump and Power Unit Design and Operating Considerations The inlet line of the pump must be carefully sized and configured to eliminate cavitation and air entrainment Fluid velocity in the line should not exceed 4 feet per second Lines should be no smaller than the diameter of the pump inlet fitting Strainer and inlet line filters must not restrict fluid flow Goodheart-Willcox Co., Inc. 95 Review Question Name the five functions of a hydraulic system power unit. A. Provide the energy for the operation of the system, B. move fluid through the system, C. limit the maximum pressure of the system, D. aid in maintaining i i proper system operating temperature, and E. aid in maintaining fluid cleanliness Goodheart-Willcox Co., Inc

49 Review Question The device that is used to move fluid through a hydraulic system is called the. pump Goodheart-Willcox Co., Inc. 97 Review Question During the phase of basic pump operation, the pressure in the pumping chamber is below atmospheric pressure. intake Goodheart-Willcox Co., Inc

50 Review Question In a centrifugal pump, the primary element of the pumping mechanism is called a(n). impeller Goodheart-Willcox Co., Inc. 99 Review Question A(n) valve found in some power units is set at a pressure slightly higher than the normal system operating pressure for protection if the relief valve fails. safety Goodheart-Willcox Co., Inc

51 Review Question Describe how variable flow can be achieved in an unbalanced-vane bl pump. By incorporating a moveable cam ring. Goodheart-Willcox Co., Inc. 101 Review Question The pressure-compensating feature of a hydraulic pump is available only on those pump designs that are also capable of -flow delivery. variable Goodheart-Willcox Co., Inc

52 Review Question The type of pump that delivers the best pulse- free flow of fluid throughout the full range of operating speeds uses a(n) pumping mechanism design. screw Goodheart-Willcox Co., Inc. 103 Review Question A condition known as exists when bubbles bbl of vapor begin to appear in the inlet line of a pump. This is caused when the inlet pressure is too far below atmospheric pressure. cavitation Goodheart-Willcox Co., Inc

53 Review Question Overall efficiency and volumetric efficiency is typically found din the section of pump information sheets. performance data Goodheart-Willcox Co., Inc. 105 Glossary Application information Information supplied by a manufacturer describing conditions and limits of operation in which a product may be expected to successfully operate. Axial piston pump A hydraulic pump using a design in which the reciprocating motion of the pistons is parallel to the power input shaft. Goodheart-Willcox Co., Inc

54 Glossary Balanced-vane pump p A hydraulic vane pump using a design with two inlet and outlet chambers that balance the load forces on the bearings of the pump rotor shaft. Goodheart-Willcox Co., Inc. 107 Glossary Cavitation The formation of gas within a liquid stream that occurs when pressure drops below the vapor pressure of the liquid; may result in excessive noise and pump damage. The condition in a hydraulic pump can result from restricted inlet flow or excessive oil viscosity. Goodheart-Willcox Co., Inc

55 Glossary Dual pump A design in which two pumps are built into a single case. The pumps may be rated at different pressures and flow outputs to provide additional flexibility. Fixed-delivery pump Any hydraulic pump p design that has a nonadjustable fluid delivery rate. Goodheart-Willcox Co., Inc. 109 Glossary Gear pump A hydraulic pump design that uses gears to move fluid through the pumping chamber of the component. Gears may have internal or external teeth. Goodheart-Willcox Co., Inc

56 Glossary General hydraulic horsepower A computed figure used in hydraulic systems based on fluid flow and pressure. Equal to fluid flow weight in pounds per minute multiplied by the pressure in feet of head divided by 33,000 foot pounds per minute. Goodheart-Willcox Co., Inc. 111 Glossary Gerotor design A common internal-gear pump or motor design. The pumping chamber of these units has two gear-shaped elements that form varying-size chambers as they rotate. Goodheart-Willcox Co., Inc

57 Glossary Impeller The rotating component of a dynamic compressor or impeller pump. Energy is increased in the fluid as centrifugal force causes flow through the unit. Goodheart-Willcox Co., Inc. 113 Glossary Mechanical efficiency The theoretical horsepower needed to operate a pump or compressor divided by the actual horsepower required. Non-positive-displacement pump A pump p that does not have a variable-volume pumping chamber. An impeller or other device is used to move the fluid. The inertia of that fluid movement produces pressure when flow is resisted. Goodheart-Willcox Co., Inc

58 Glossary Power unit The unit in a hydraulic system that provides energy for the system, moves fluid through the system, provides a safe maximum limit of system pressure, and maintains desired system temperature and fluid cleanliness. Goodheart-Willcox Co., Inc. 115 Glossary Radial-piston pump A positive-displacement t piston pump design in which the pistons are located in a cylinder block or housing that is perpendicular to the power input shaft. Goodheart-Willcox Co., Inc

59 Glossary Reciprocating pump One of a variety of pump designs using reciprocating pistons to move fluid. The drive mechanisms vary, but a reciprocating piston moves the fluid against resistance from the system actuator. Goodheart-Willcox Co., Inc. 117 Glossary Screw pump A pump unit that uses intermeshing screws to form chambers that linearly move hydraulic oil through the pump. The design provides a continuous, positive displacement of the oil. Goodheart-Willcox Co., Inc

60 Glossary Stationary-cylinder design A radial-piston hydraulic pump design in which a cam operates pistons located in a fixed cylinder block. Swash plate An inclined disk in a hydraulic axial-piston pump p or motor that causes the pistons to reciprocate. Goodheart-Willcox Co., Inc. 119 Glossary Vapor pressure The pressure at which a liquid will begin to form a vapor. Vapor pressure varies with fluid type and formulation. Goodheart-Willcox Co., Inc

61 Glossary Volumetric efficiency A ratio of the volume of air admitted to a compressor cylinder at a given temperature and pressure to the full displacement of the cylinder. Goodheart-Willcox Co., Inc