ASSESSMENT REGARDING THE EQUATION W = PV (WORK = PRESSURE x VOLUME) AS IT RELATES TO THE WORKING CAPABILITY OF PRESSURISED S APPLIED IN THE CONVENTIONAL PISTON AND THE DIAMOND-SHAPED PREPARED BY: David Strain analystsofpneumatic@bellnet.ca http://www.apscontrols.ca (905) 640-2333 (1-800-646-8414)
EXECUTIVE SUMMARY The fluid equation WORK = PRESSURE x VOLUME (W = PV) applies to the linear fluid performance regarding conventional piston actuators. In these cases work input = work output (WI = WO). The fluid equation WORK = PRESSURE x VOLUME (W = PV) does not apply to the non-linear fluid performance regarding diamond-shaped actuators. In the initial stages of the diamond-shaped actuators stroke, work input is less than work output (WI < WO). Many engineer/scientists have tested the physical model concluding this fact. Diamond-shaped actuators are more efficient than conventional piston actuators in the early stages of the diamond-shaped actuators stroke. PATENTED APPLICATION CONCEPT 10 PSIG 15 10 20 5 25 0 30 DIAMOND-SHAPED DIRECTION OF NET WORK VC1 SHAFT SHAFT PISTON VC2 15 10 20 5 25 0 30 10 PSIG PRESSURE SOURCE FLOW (TYPICAL) FORCE X > FORCE Y CUSHION TANK The diamond-shaped actuator expends 85% of its work potential generating its own source of fluid, pumping fluid from the piston actuator. The remaining 15% of the diamond-shaped actuator s work potential may be extracted, addressing work requirements other than producing its own fluid source. 15% net work achieved = ((force X force Y ) x travel) VC1 (volume change one) < VC2 ( volume change two) i
REPORT S PURPOSE Present information illustrating: -1- The equation W = PV applies to the linear fluid performance in conventional piston actuators, but does not apply to fluid performance in diamond-shaped actuators. -2- The diamond-shaped actuator performance is non-linear as it progresses through its stroke regarding the work/pressure/volume relationship. -3- Diamond-shaped actuators are more efficient than conventional piston actuators in the early stages of the diamond-shaped actuators stroke. CONTENTS Page one -- Page two -- Graph illustrating linear power characteristics regarding conventional piston actuators. Graph illustrating non-linear power characteristics regarding diamondshaped actuators. Page three -- Graph illustrating the efficiency difference between conventional piston actuators and diamond-shaped actuators. Page four -- Summary ii
EQUILIBRIUM PRESSURE REGARDING CONVENTIONAL PISTON S WITH BOUNDARY FACES OF 23.953 IN² AND A CONSTANT LOAD OF 59.75 POUNDS.2.4.6.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 69.12 WG (2.494 PSI) PRESSURE APPLIED TO PISTON S 23.953 IN² BOUNDARY FACE AT EQUILIBRIIUM INCHES OF LIFT AT EQUILIBRIUM LOAD 59.75# LOAD 59.75# LOAD 59.75# PISTON FORCE < 59.75# PISTON FORCE = 59.75# PISTON FORCE > 59.75# FULLY RETRACTED EQUILIBRIUM FULLY DRIVEN PRESSURE PRESSURE PRESSURE < 69.12 WG (2.494 PSI) = 69.12 WG (2.494 PSI) > 69.12 WG (2.494 PSI) LOAD FORCES PISTON TO ANY POINT IN PISTON S LIFTS LOAD TO PISTON S MINIMUM STROKE STROKING RANGE PISTON S MAXIMUM STROKE The above graph illustrates that a piston with a constant load of 59.75 pounds and a boundary face of 23.953 IN² requires a pressure of 69.12 WG (2.494 PSI), maintaining equilibrium at all points in its stroke. If another piston actuator receives an identical volume of fluid as the above example, with a boundary face twice as large (2 x 23.953 IN² = 47.906 IN²), its force is doubled; however, the stroke is one-half. Travelling one-half the distance of the above piston actuator, while producing double the force, generates exactly the same amount of work as the illustrated piston The fluid equation W = PV applies to conventional piston actuators regarding work, pressure and volume. The relationship is linear. The work input required for each.5 stroke for the illustrated piston is: W = PV = 2.494 PSI x (.5 x 23.953 IN²) = 2.494 PSI x 11.9765 IN³ = 29.87 in/lb PAGE ONE
67 DIAMOND-SHAPED EQUILIBRIUM POINTS AT VARIOUS PRESSURES WITH A CONSTANT 59.75# LOAD 66 65 64 63 WG PRESSURE APPLIED TO DIAMOND-SHAPED (2.875" LIFT, 65.9"WG) (2.675" LIFT, 63"WG) V = 68.005 IN³ V = 63.383 IN³ 62 61 60 59 WG TO 61.7 WG (2.500 LIFT, 61.7 WG) (2.413" LIFT, 61"WG) V = 59.318 IN³ V = 57.291 IN³ 59 58 DIAMOND-SHAPED S PERFORMANCE LINE (2" LIFT, 59"WG) V = 47.618 IN³ V = 41.725 IN³ 57 56 WG TO 58 WG V = 11.854 IN³ V = 11.7 IN³ LIFT =.5 LIFT =.5 56 (1.25" LIFT, 56"WG) V = 29.871 IN³ 1.25 TO 1.75 2.0 TO 2.5 55 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 INCHES OF LIFT AT EQUILIBRIUM WITH A CONSTANT 59.75# LOAD The above graph illustrates the equilibrium performance of our test model with a constant 59.75 pound load. 2.625" DIAMOND-SHAPED 9.125" ANCHORED 9.125" ANCHORED 2.625" VARYING PRESSURE The table below presents data regarding two segments of travel: each being one half inch. SEGMENT TRAVEL VOLUME CHANGE LOAD PRESSURE LOW HIGH AVERAGE 1.25-1.75.5 11.854 IN³ 59.75 lb 56 WG 58.0 WG 57.00 WG 2.00-2.50.5 11.700 IN³ 59.75 lb 59 WG 61.7 WG 60.35 WG The output is equal regarding both segments of travel, each lifting 59.75 lb through.5. (W=FD) W = 59.75 lb x.5 in = 29.87 in/lb The input work for one segment from 1.25 to 1.75 is: (W=PV) 57 WG (2.057 PSI) x 11.854 IN³ = 24.38 in/lb The work input for the segment from 2.0 to 2.5 is: (W=PV) 60.35 WG (2.178 PSI) x 11.7 IN³ = 25.48 in/lb NOTE: The work output for both segments is equal (29.87 in/lb), maintaining equilibrium, but the work inputs are different (24.38 in/lb and 25.48 in/lb). PAGE TWO
EQUILIBRIUM COMPARISON REGARDING THE DIAMOND-SHAPED AND THE CONVENTIONAL PISTON 69.12 67 66 69.12 WG EQUILIBRIUM PRESSURE REQUIRED AT ALL POINTS OF PISTON S STROKE (2.875" LIFT, 65.9"WG) 65 64 63 62 61 60 59 WG PRESSURE APPLIED TO DIAMOND AND PISTON (2.675" LIFT, 63"WG) (2.500 LIFT, 61.7 WG) (2.413" LIFT, 61"WG) (2" LIFT, 59"WG) DV = 68.005 IN³ PV = 68.865 IN³ DV = 63.383 IN³ PV = 64.074 IN³ DV = 59.318 IN³ PV = 59.882 IN³ DV = 57.291 IN³ PV = 57.990 IN³ DV = 47.618 IN³ PV = 47.906 IN³ 58 57 56 DIAMOND-SHAPED S PERFORMANCE CURVE (1.25" LIFT, 56"WG) DV = DIAMOND S VOLUME PV = PISTON S VOLUME DV = 41.725 IN³ PV = 41.918 IN³ DV = 29.871 IN³ PV = 29.941 IN³ 55 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 INCHES OF LIFT AT EQUILIBRIUM WITH A CONSTANT 59.75# LOAD CONVENTIONAL PISTON CONSTANT 59.75 LB FORCE 2.625" DIAMOND-SHAPED 9.125" ANCHORED 9.125" ANCHORED 2.625" CONSTANT PRESSURE OF 69.12 WG (2.494 PSI) VARYING PRESSURE The table below presents the efficiency comparison regarding equilibrium with an equal load of 59.75 pounds on both the piston actuator and the diamond-shaped actuator. TRAVEL PISTON EQUILIBRIUM PRESSURE DIAMOND EQUILIBRIUM PRESSURE DIAMOND S ADVANTAGE 1.250 69.12 WG (2.4944 PSI) 56.0 WG 18.98% 1.750 58.0 WG 16.08% 2.000 59.0 WG 14.64% 2.413 61.0 WG 11.75% 2.500 61.7 WG 10.73% 2.675 63.0 WG 8.85% 2.875 65.9 WG 4.66% NOTE: The piston actuator requires the same pressure of 69.12 WG (2.494 PSI) at all points in its travel, maintaining the equilibrium force of 59.75 pounds to match the 59.75 pound load. The diamond actuator requires varying pressures during its illustrated travel maintaining an equilibrium force of 59.75 pounds matching the 59.75 pound load. PAGE THREE
SUMMARY -1- The equation W = PV defines fluid performance regarding conventional piston actuators. The work input for every.5 of the example conventional piston actuator s travel requires 29.87in/lb of work. The input work matches the output work of 29.87 in/lb. The relationship is linear. -2- The equation W = PV does not define fluid performance regarding diamond-shaped actuators. The two example.5 travel segments of our model produced identical work output of 29.87 in/lb, but their work input was different, being 24.38 in/lb and 25.48 in/lb. Both the volume and pressure were different for each travel segment. In this case W = W; however, PV for the first segment of travel PV for the second segment of travel. WORK SUMMARY OF EXAMPLE S STYLE TRAVEL RANGE WORK RELATIONSHIP CONVENTIONAL PISTON ANY.5 OF DRIVE WORK IN = WORK OUT (29.87 in/lb) (29.87 in/lb) DIAMOND-SHAPED.5 (1.25 TO 1.75 ) WORK IN WORK OUT (24.38 in/lb) (29.87 in/lb) DIAMOND-SHAPED.5 (2.00 TO 2.5 ) WORK IN WORK OUT (25.48 in/lb) (29.87 in/lb) -3- The diamond-shaped actuator achieves more work relative to a conventional piston actuator with identical fluid input, regarding both pressure and volume. This occurs only during the first portion of the diamond-shaped actuator s travel. -4- The diamond-shaped actuator is more efficient than the conventional piston actuator, at varying magnitudes, depending on the angle variation of the diamond-shaped actuator s walls. -5- This is the main corner stone regarding the patented invention DIAMOND-SHAPED POWERED LINKAGE, SYSTEM AND ENGINE. The efficiency differential produces a work differential, allowing the diamond-shaped actuator to attain its complete source of fluid via pumping the fluid from the conventional piston actuator. The diamond-shaped actuator expends approximately 85% of its work potential generating the total fluid requirement of that action. The diamond-shaped actuator experiences a surplus work potential of approximately 15% after generating its own total fluid requirement relating to each stroke. PAGE FOUR