14/08/2026
A great artical that was recently published and peer reviewed that supports the math and premise of the Suspension Engineers Handbook I wrote earlier in the year
WHY A HYDRAULIC DAMPER MUST BE MODELLED AS A CHANGING FLOW NETWORK
Implications of Wen, Chen and Liu’s multi-scale damper model for motorcycle shim-stack analysis
Hydraulic dampers are often simplified into a small number of independent elements: a bleed circuit controls low-speed damping, a shim stack controls higher-speed damping, and the final damping force is treated as the sum of those contributions.
That representation is useful for basic tuning, but it becomes increasingly inadequate when the objective is to predict real damper behaviour from first principles.
A more physically defensible approach is to treat the damper as a coupled hydraulic and structural network whose dominant flow paths change continuously with pressure differential, piston velocity and valve displacement.
This interpretation is strongly supported by Wen, Chen and Liu (2025), who developed a multi-scale finite-element modelling method for hydraulic dampers operating across low-, medium- and high-velocity conditions.
Their work is particularly important because it does not attempt to force one simplified mathematical representation across the entire operating envelope. Instead, it recognises that the governing physical mechanisms change as the damper progresses from predominantly fixed-or***ce flow to significant valve deflection and fluid-structure interaction.
1. THE CONVENTIONAL SEPARATION BETWEEN “BLEED” AND “SHIM-STACK” DAMPING IS ARTIFICIAL
The familiar workshop explanation is that low-speed damping is controlled primarily by bleed and high-speed damping by the shim stack.
This is directionally useful, but hydraulically incomplete.
At any piston velocity, continuity requires the displaced oil volume to pass through all available flow paths:
Qp = Qb + Qv + Qo + Ql
Where:
Qp = piston-displaced flow
Qb = adjustable or fixed bleed flow
Qv = flow through the deflected shim-valve opening
Qo = other available or***ce or bypass flow
Ql = leakage or secondary flow paths
The critical point is that these quantities are not independent constants.
Each depends, directly or indirectly, on the pressure differential across the valve assembly.
Wen, Chen and Liu demonstrated this explicitly. Under low-velocity conditions, flow was principally controlled by throttling or***ces. Their analysis showed that both or***ce entrance area and or***ce length significantly influenced low-speed damping force.
Once sufficient pressure developed to open the deflecting valve system, however, the distribution of flow changed fundamentally. Most oil progressively transferred from the fixed-or***ce paths to the opening valve gaps.
That means the transition should not be thought of simply as:
BLEED → SHIM STACK
A better representation is:
BLEED DOMINATED → SHARED-FLOW TRANSITION → DEFLECTING-VALVE DOMINATED
The transition itself is part of the damping characteristic.
2. FLOW DISTRIBUTION IS A PRESSURE-DEPENDENT PROBLEM
For a simple bleed or***ce:
Qb = Cd × Ab × √(2ΔP / ρ)
Where:
Cd = discharge coefficient
Ab = effective bleed area
ΔP = pressure differential
ρ = fluid density
A shim valve introduces another restriction, except its effective area changes as the shims deflect.
Av = f(δ)
And:
δ = f(ΔP, shim stiffness, geometry, preload)
Therefore:
Qv = Cdv × Av(ΔP) × √(2ΔP / ρ)
The hydraulic network is now nonlinear in two ways.
Pressure affects flow directly, but pressure also changes the geometry of the valve by deflecting the shim stack.
This produces a feedback loop:
Pressure differential
→ shim force
→ shim deflection
→ valve opening area
→ valve flow
→ revised pressure differential
Or more simply:
ΔP → Fshim → δ → Av → Qv → ΔP
This is fluid-structure interaction.
The valve responds to the oil flow, but the valve movement also changes the oil flow.
3. SHIM-STACK STIFFNESS CANNOT BE CONSIDERED IN ISOLATION
Traditional shim-stack calculations concentrate heavily on structural stiffness.
For a circular shim treated as an annular plate, flexural rigidity can be represented by:
D = E × t³ / [12 × (1 - ν²)]
Where:
E = Young’s modulus
t = shim thickness
ν = Poisson’s ratio
The important relationship is:
D ∝ t³
This explains why relatively small changes in shim thickness can create large changes in stiffness.
But stiffness alone does not determine damping force.
The actual sequence is closer to:
Piston flow
→ pressure differential
→ shim loading
→ shim deflection
→ valve area
→ valve flow
→ new pressure differential
Two shim stacks with similar calculated stiffness can therefore produce different damping curves if they operate with different piston ports, seat diameters, bleed arrangements or downstream restrictions.
Likewise, the same shim stack can behave differently when installed on different piston geometries.
Wen, Chen and Liu found that valve-seat geometry and disc stiffness both materially affected damping in the valve-controlled region.
A shim stack should therefore not simply be considered a spring.
It is a pressure-controlled variable hydraulic restriction.
4. THE VALVE-OPENING THRESHOLD IS A TRANSITION, NOT A SINGLE VELOCITY
The “knee” in a damping curve is often associated with a particular piston velocity.
In reality, the knee emerges from the interaction between:
Piston flow
Pressure differential
Bleed flow
Valve preload
Shim stiffness
Valve opening area
A simplified opening condition can be expressed as:
ΔP × Ae ≥ Fpreload + Felastic
Where Ae is the effective pressure-loaded area.
But even when the shim begins to open, the bleed does not suddenly stop flowing.
Instead:
Qp = Qb + Qv
The proportion of total flow travelling through the shim valve progressively increases.
Valve-flow fraction:
Qv / Qp
Bleed-flow fraction:
Qb / Qp
The knee is therefore a FLOW REDISTRIBUTION REGION rather than a simple switching point.
5. BLEED REMAINS PART OF THE SYSTEM AFTER THE SHIM STACK OPENS
For parallel hydraulic paths:
Qtotal = Q1 + Q2 + Q3 + …
Every available pathway contributes according to its instantaneous hydraulic resistance.
A useful way to describe bleed authority is:
Bleed flow fraction = Qb / Qtotal
Likewise:
Valve flow fraction = Qv / Qtotal
These values change with:
piston velocity,
pressure differential,
clicker position,
shim displacement,
oil properties,
and valve geometry.
The damper therefore does not possess one flow path.
It contains a network of competing flow paths whose relative authority changes continuously.
6. REBOUND ADJUSTER BACKFLOW DURING COMPRESSION
This becomes particularly important in motorcycle shocks.
In a design without effective directional separation, compression movement may produce flow not only through the intended compression circuit but also through portions of the rebound-adjuster circuit.
Therefore:
Compression piston flow =
compression valve flow
* compression bleed flow
* rebound-circuit backflow
* other secondary flow
Or:
Qcompression = Qcompression-valve + Qcompression-bleed + Qrebound-backflow + Qother
If rebound backflow is not zero, then changing the rebound adjuster can alter the pressure required to achieve a given compression piston velocity.
Damper force is fundamentally related to pressure:
Fd ≈ ΔP × Ap
where Ap is the effective piston area.
Therefore a flow path through the rebound circuit can influence compression damping even though the adjuster is labelled “rebound”.
There is nothing mysterious about this cross-talk.
It is a hydraulic-network effect.
The more useful engineering question is:
During compression, which hydraulic paths connect the high-pressure and low-pressure control volumes, and what percentage of the displaced flow passes through each?
7. WHY SEPARATOR VALVES MATTER
A separator valve changes the topology of the hydraulic circuit according to flow direction.
Without effective separation:
Qtotal = Qintended + Qunintended
With effective directional separation:
Qunintended → approximately zero
This increases hydraulic independence between compression and rebound circuits.
The important design question is therefore not simply:
“Does the damper have a separator valve?”
The better question is:
“At what operating conditions does cross-flow become large enough to materially alter the intended damping characteristic?”
We can define a cross-flow ratio:
Cross-flow ratio = Qcross / Qtotal
If:
Qcross / Qtotal > Qb
However, that does not automatically mean the other flow paths are irrelevant.
Valve-seat geometry, shim stiffness and available port area become increasingly influential.
REGIME 4 — WHOLE-SYSTEM HIGH-FLOW BEHAVIOUR
At high piston velocities the result can additionally become influenced by:
piston-port capacity,
maximum valve lift,
flow contraction,
turbulence,
cavitation margin,
reservoir pressure,
oil aeration,
check-valve behaviour,
secondary flow paths,
pressure recovery,
and fluid/gas compressibility.
At this point it becomes particularly dangerous to interpret the damping curve purely as “shim-stack stiffness”.
11. THE ENGINEERING CONSEQUENCE
The major lesson from Wen, Chen and Liu is not simply that CFD or fluid-structure interaction can model a damper more accurately.
The deeper lesson is:
THE GOVERNING MECHANISM OF A HYDRAULIC DAMPER CHANGES ACROSS ITS OPERATING ENVELOPE.
For motorcycle suspension, the complete process is:
PISTON MOTION
→ REQUIRED DISPLACED FLOW
→ FLOW-PATH DISTRIBUTION
→ PRESSURE FIELD
→ SHIM DEFORMATION
→ NEW FLOW AREAS
→ REDISTRIBUTED FLOW
→ REVISED PRESSURE FIELD
→ DAMPING FORCE
That feedback loop is the real damper.
Shim-stack calculations remain extremely valuable, but they represent only the structural part of a substantially larger coupled problem.
CONCLUSION
Wen, Chen and Liu provide strong contemporary support for moving beyond the idea that hydraulic damping can always be reduced to an isolated bleed equation at low velocity and an isolated shim-stiffness calculation at higher velocity.
Their work demonstrates that fixed restrictions dominate one region, deformable valves increasingly dominate another, and the transition between them involves a fundamental redistribution of flow.
For motorcycle suspension engineering, this concept extends naturally to base valves, mid-valves, rebound adjusters, bleed circuits, check valves and separator valves.
These components should be regarded as parts of one pressure-driven hydraulic network.
Changing one component changes flow distribution.
Changed flow alters pressure.
Changed pressure alters shim loading.
Changed shim loading alters valve opening.
Changed valve opening redistributes flow again.
That feedback loop is the system we are actually trying to model.
The next step in high-fidelity motorcycle damper analysis is therefore not simply a better shim-stack equation.
It is the integration of plate theory, pressure-dependent valve displacement, bleed and adjuster flow, directional valve behaviour, whole-system continuity and dyno validation into one coupled model.
That is the point at which suspension tuning begins to move from empirical stack comparison toward predictive suspension engineering.
REFERENCE
Wen, H., Chen, X. and Liu, X. (2026), “A novel multi-scale finite element modeling method for high-precision analysis of hydraulic damper dynamics characteristics under full-operating conditions”, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 240, No. 8, pp. 5330–5359. First published online 16 September 2025. DOI: 10.1177/09544070251368420.
