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Fluid Power Engineering, Industrial & Mobile Hydraulic Cylinders & Regenerative Valves

Hydraulic Cylinder Push/Pull Force & Regenerative Speed Formula

Calculate Full-Bore Push Force (kN), Annular Rod-End Pull Force (kN), Normal Extension Speed (mm/s), Retraction Speed (mm/s), and Regenerative Fast-Approach Speed (mm/s).

Routing rod-end oil back into the cap port speeds cylinder advance 2.78x—by acting solely on the piston rod cross-section!

A single-rod double-acting hydraulic cylinder of Piston Bore Diameter D (mm) and Chrome Rod Diameter d (mm) has asymmetric effective areas: Full Cap Area A_cap = (PI() / 4) * D^2 mm² vs Annular Rod-End Area A_ann = (PI() / 4) * (D^2 - d^2) mm²! Under relief/pump pressure P (bar = 0.1 MPa = 0.1 N/mm²), Theoretical Extension Push Force is F_push = (0.1 * P * A_cap) / 1,000 kN whereas Retraction Pull Force drops to F_pull = (0.1 * P * A_ann) / 1,000 kN; inversely, under constant pump flow Q (L/min = Q * 10^6 / 60 mm³/s), Normal Extension Speed v_ext = (Q * 10^6 / 60) / A_cap mm/s is slower than Retraction Speed v_ret = (Q * 10^6 / 60) / A_ann mm/s! Switching in a Regenerative Valve ties cap and rod ports together at equal pressure P so displaced rod-annulus oil recycles directly into the cap end—boosting Fast-Approach Extension Speed to v_regen = (Q * 10^6 / 60) / A_rod_shaft (acting solely on rod area PI()*d^2/4!) while trading force down to F_regen = 0.1 * P * A_rod_shaft!

Verify on a 100 mm Bore / 60 mm Heavy-Rod Hydraulic Press Cylinder—Bore_Diameter D = 100.0 mm (B2), Rod_Diameter d = 60.0 mm (B3), System_Pressure P = 210.0 bar (B4), and Pump_Flow Q = 45.0 L/min (B5): Full-Bore Push Force hits 164.93 kN (E2), Annular Pull Force equals 105.56 kN (E3), Normal Extension Speed is 95.49 mm/s vs 149.21 mm/s Retraction (E4 shows Normal Extension = 95.49 mm/s), and Engaging Regenerative Fast-Approach surges Extension Speed 2.78x to 265.26 mm/s (E5)!

Hydraulic Cylinder KPI (Bore D=100 mm, Rod d=60 mm, P=210 bar, Q=45 L/min)FormulaVerified Output
Full-Bore Push Force Fpush (kN)(0.1 * P_bar * (PI()/4 * D^2)) / 1000164.93 kN
Annular Rod Pull Force Fpull (kN)(0.1 * P_bar * (PI()/4 * (D^2-d^2)))/1000105.56 kN (84.12 kN @ d = 70 mm rod)
Normal Extension Speed vext (mm/s)(Q_L_min * 1e6 / 60) / (PI()/4 * D^2)95.49 mm/s
Regenerative Fast-Advance (mm/s)(Q_L_min * 1e6 / 60) / (PI()/4 * d^2)265.26 mm/s (194.88 @ d = 70 mm rod)

ISO 3320 Hydraulic Cylinder Force, Asymmetric Speed & Regenerative Flow Formula

Validate Bore D > 10 mm, Rod 0 < d < 0.90 * D (rod cannot fill or exceed cylinder bore!), Pressure P in (0, 700] bar, and Pump_Flow Q > 0 L/min!

=LET(br_d, B2, rd_d, B3, pr_b, B4, fl_l, B5, IF(OR(br_d <= 10, rd_d <= 0, rd_d >= 0.9 * br_d, pr_b <= 0, pr_b > 700, fl_l <= 0), "Invalid Cylinder Input", LET(ar_s, (PI() / 4) * (rd_d ^ 2), ROUND(((fl_l * 1000000) / 60) / ar_s, 2))))

Oversized Anti-Buckling 70 mm Rod Area-Ratio Check (Set Rod Diameter d = 70.0 mm)

Upgrade to a 2:1-class anti-buckling 70.0 mm chrome rod (B3 = 70.0): Full-Bore Push Force E2 (164.93 kN) and Normal Extension Speed E4 (95.49 mm/s) are unchanged, Annular Pull Force E3 drops to 84.12 kN, and Regenerative Advance Speed E5 settles at 194.88 mm/s (nearly matching retraction speed 187.24 mm/s for symmetric cycle times)!

=IF(ISTEXT(E5), E5, ROUND((0.1 * B4 * ((PI() / 4) * ((B2 ^ 2) - (B3 ^ 2)))) / 1000, 2))

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