Hydraulic Power Unit: Pump Flow, Motor kW, Cylinder Force and Speed

The hydraulic relationships follow Muncie Power, Understanding Truck Mounted Hydraulic Systems, attached pp. 5–7 and 17–18 (printed pp. 3–5 and 15–16). With all units converted explicitly:

• $A_b=\pi D^2/4$, $A_r=\pi d^2/4$, $A_a=A_b-A_r$.
• $Q=V_g n\eta_v$. Shaft rpm is converted to revolutions per second before multiplying displacement.
• $p_{in}=p_w-\Delta p_s$; $F_{ext}=\eta_c(p_{in}A_b-p_bA_a)$ and $F_{ret}=\eta_c(p_{in}A_a-p_bA_b)$.
• $v_{ext}=Q/A_b$, $v_{ret}=Q/A_a$, $t=L/v$. Exhaust flows are $Q A_a/A_b$ on extension and $Q A_b/A_a$ on retraction.
• $\eta_p=\eta_v\eta_{hm}$, $P_h=p_wQ$, $P_{shaft}=P_h/\eta_p$, $P_{electrical}=P_{shaft}/\eta_m$. Delivered flow already includes volumetric efficiency, so power divides by the overall pump efficiency, not by hydromechanical efficiency alone. The motor rating calculation uses $p_{peak}=p_{rel}(1+a)$ and the chosen sizing margin.

The rod screening method is ideal Euler column theory, as described by AHP Merkle and Hänchen: $I=\pi d^4/64$, $L_{eff}=KL_{col}$, $F_E=\pi^2 EI/L_{eff}^2$. AHP gives K = 2, 1, 0.699 and 0.5 and recommends a safety factor of at least 5. The displayed allowance is $\min(F_E,f_yA_r)/S_b$. It is compared with $p_{peak}A_b$, conservatively taking zero opposing pressure and no friction credit. This tool adds a conservative elastic-range warning when $F_E/A_r>f_y/2$; this is a screening assumption, not a manufacturer's certified limit.

The reservoir heuristic comes from Suyog Hydrosystems: use a residence allowance of about 3–5 minutes. Here $V_{base}=Qt_{res}$, $V_{swing}=A_rL$ and $V_{tank}=(V_{base}+V_{swing})/(1-f_{space})$. Muncie attached p. 21 describes approximately 80% usable capacity; the 20% default is illustrative and must be checked against the real tank.

Main-circuit moving heat is derived here by energy conservation: useful work in a full cycle is $F_{ext}L+F_{ret}L$; divide by travel time, then subtract from working shaft power. The elapsed-time average adds main-circuit moving losses and stalled-relief shaft power in their entered time fractions; the main pump is stopped during the remaining time. All stalled shaft demand at the allowed peak is conservatively assigned to oil. The tool requires a separate, continuously operated tank-to-tank cooler circulation pump and fan, following HYDAC attached p. 1. Cylinder and relief return lines go directly to the tank. Actual off-line flow is zero when its pump/fan operation is disabled. Circulation-pump shaft power is $P_{circ}=\Delta p_{loop}Q_{loop}/\eta_{loop}$; conservatively all of it becomes oil heat, including its hydraulic work dissipated in the loop. This is added continuously to the estimated main-circuit heat. A known heat-load input bypasses the estimate and must already include circulation-pump heating and any other sources. After verified passive heat rejection is subtracted, apply HYDAC's 1.1 contamination factor (attached pp. 5–6): $P_{cool}=1.1\max(0,P_{heat}-P_{pass})$ and $C_{req}=P_{cool}/(T_{oil}-T_{air})$ for positive duty. When $P_{cool}=0$, $C_{req}=0$ directly, including equal oil and air temperatures. Positive duty requires $T_{oil}>T_{air}$ and continuous off-line pump/fan operation with positive oil flow. Available capacity is $C_{cool}\max(0,T_{oil}-T_{air})$ only while that circulation is available; otherwise it is zero. The entered coefficient must correspond to the actual off-line flow, not cylinder return flow.

The travel chart uses exactly $[0,t_{ext},t_{cycle}]$. With constant speed on each stroke, these three points describe both straight segments and include the full-stroke reversal exactly.

• One fixed-displacement pump and one double-acting, single-stage cylinder with a solid circular rod. The same delivered inlet flow and working pump pressure apply in both directions. There is no regeneration or flow sharing.
• Pump efficiencies are constant estimates at the specified duty. Supplied ratings and material strengths are user inputs, not claims about a particular catalogue component. The 355 MPa rod strength is illustrative; use a certified value.
• Force efficiency represents cylinder friction only. Cylinder leakage, compressibility, acceleration, breakaway friction, cushion zones, load variation, gravity return and side loading are omitted.
• Cooling duty assumes complete powered strokes. The remaining time after moving and stalled fractions is main pump stopped. The separate circulation pump and cooler fan continue to run. An idling or unloaded main pump, a counterbalance valve, braking, process heat or other actuators require an independently assessed heat load. In known-heat mode that value includes the circulation pump, so its calculated loss is not added again.
• Main-pump losses and all circulation-pump shaft demand are conservatively counted as oil heat. Electric motor and fan losses are dissipated externally and excluded; the main motor sizing does not include their separate electrical demands. Passive heat rejection is valid only at the chosen temperatures; enter zero if unknown.
• The cooler is an independent off-line unit with continuous tank-to-tank circulation. Its coefficient must come from its actual performance curve at the entered off-line flow, viscosity, fan speed, air conditions and oil-to-air approach. A larger tank is not a substitute for heat rejection.
• Diagram dimensions are schematic. The animation shows an immediate valve reversal and no dwell; thermal duty fractions are separate.
• The equations for pressure force, continuity, energy balance and axial yield are derived from physical definitions. Reservoir volume is a heuristic and Euler buckling is an idealized screen.

Use for preliminary steady hydraulic power-unit sizing and troubleshooting within the real components' pressure, speed, temperature, viscosity and inlet limits. The load determines working pressure; a relief setting does not automatically produce that pressure during motion. Relief opening pressure, full-flow override, tolerances, return pressure and pressure spikes must be checked on the selected valve. The pressure-rating ceiling does not cover intensification from externally driven or trapped cylinder loads.

A rod utilization below 1 is meaningful only if the elastic-range condition also holds and the idealized end restraints are justified. Short/intermediate columns, hollow or threaded rods, telescopic cylinders, eccentric loads, combined bending, fatigue and the complete cylinder/guide/mounting assembly require a manufacturer or detailed structural check. Do not use the Euler result to approve lifting or personnel-support equipment.

The reservoir estimate excludes the initial system fill, accumulators, foaming, thermal expansion, special fluids, inclination and suction-port layout. Verify minimum oil level, return diffuser, air release, filtration and pump inlet conditions separately. Cooler duty is an average heat balance with a separate, continuously operated off-line pump and fan. The result cannot be applied to an in-line cooler supplied only by intermittent cylinder or relief return flow. A time-dependent temperature check is still needed for large fluctuations or long heat pulses. Verify oil/seal temperature ratings and the off-line circuit's pressure drops, pump inlet conditions, component pressure ratings, bypass and independent pressure protection. The main-circuit pressure-rating checks do not certify the separate cooling circuit.

The metric/US selector converts supported pressure, geometry, force, speed, power and temperature fields. Pump flow and tank volume have explicit US companion results; known flow can be entered directly in either L/min or US gal/min. The circuit annotations and chart axes use the explicitly printed metric units. Installation and electrical work must be performed by qualified people. This calculation is not a complete hydraulic safety-system or installation design.