Viscous Damper and Dynamic Response Calculator

How to use

1. Select Capillary damper, Annular squeeze, Pressure / Couette, Response from displacement, Response from force, or Hydraulic cushion.
2. Enter every displayed input in its shown unit. Diameters, lengths, gaps, and amplitudes use mm; viscosity uses Pa·s. Use positive magnitudes. For annular modes require R₀>R₁; for the cushion use 0≤ε≤1.
3. Select Calculate, or edit a field for immediate updating. Reset returns to the capillary example.
4. Read the canonical result and supporting quantities together. Damping coefficients relate viscous force to velocity; impulse, amplitudes, force, pressure, and stopping stroke retain the displayed units.
5. Correct warnings before interpretation. Check laminar-flow conditions, cavitation, leakage, compressibility, temperature-dependent viscosity, pressure limits, and structural loads independently.
6. Do not use these models for turbulent/non-Newtonian flow, gas-charged dampers, nonlinear valve stacks, seal friction, cavitating motion, detailed transient control, or final safety/code qualification.

Worked example

1. Select Capillary damper and enter R₀=20 mm, d=2 mm, L=20 mm, and η=0.01 Pa·s. 2. Calculate. Expected C=0.80 kN·s/m and I₀=16.08 N·s. 3. The coefficient screens the viscous-force slope; confirm the capillary Reynolds number before using it.

Equations used

Capillary damper: C = 128πηLR₀⁴/d⁴; I₀ = CL.

Annular squeeze damper: C = 6πηL(R₀²−R₁²)²/(R₀h₀³); I₀ = CL/2.

Pressure and Couette flow: Cₚ = 6πηLR₀³/h₀³; C꜀ = 2πηLR₀/h₀.

Harmonic response: ω = 2πf. From Xmax: Vmax=ωXmax and Fmax=CVmax. From Fmax: Vmax=Fmax/C and Xmax=Fmax/(ωC).

Hydraulic cushion: Qᵣ = 1 + 1.5ε²; c₁=6πη(R₀²−R₁²)²Qᵣ/(R₀h₀³); L=√(2mV₀/c₁); xmax=√(2V₀m/(3c₁)); Fmax=−c₁²xmax³/(2m)+V₀c₁xmax; pmax=Fmax/[π(R₀²−R₁²)].

R₀ and R₁ are outer and inner effective diameters, d is capillary diameter, L is active length or computed stopping stroke by mode, h₀ is radial gap, η is dynamic viscosity, C is damping coefficient, I₀ is normalized impulse, f is frequency, ω is angular frequency, Xmax/Vmax/Fmax are positive amplitudes, m is moving mass, V₀ is positive entry speed, ε is relative eccentricity (0 concentric, 1 contact), Qᵣ is the eccentricity flow factor, c₁ is the cushion coefficient, and pmax is peak pressure. Internal SI units are m, Pa·s, N, kg, and s; displayed values preserve two-decimal rounding.

Theory and method

These screening relations combine laminar capillary or thin-annular viscous resistance with the linear damper law F=Cv. The harmonic modes assume a sinusoid and no spring or inertial force. The cushion mode balances a simplified velocity-dependent hydraulic resistance against the incoming mass to estimate stopping stroke, maximum force, and pressure.

Assumptions and limits: Newtonian incompressible fluid, constant temperature and viscosity, laminar fully developed flow, rigid smooth geometry, uniform clearance, negligible leakage outside the modeled path, no fluid inertia/compliance/cavitation, and no seal friction. Small gaps produce cubic sensitivity; tolerance and thermal growth require explicit review. Validate Reynolds number and pressure/temperature limits for the actual fluid and hardware.

Reference: A. van Beek, Advanced Engineering Design: Lifetime Performance and Reliability, viscous damping calculation collection; use a current fluid-mechanics or hydraulic-system reference for capillary/annular resistance and transient design.

Continue in TriboSolver to refine pressure, clearance flow, thermal-viscosity effects, and transient response.

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