Q: How should I read the vibration transmissibility chart?

The transmissibility T = |x_s / x_road| is the ratio of body displacement to road displacement. A peak occurs near the sprung mass natural frequency f_n1 (typically 1–2 Hz). A second peak appears at the unsprung (wheel hop) natural frequency f_n2 (typically 10–15 Hz). At frequencies well above f_n1, the transmissibility drops below 1 (isolation region), meaning the suspension absorbs vibration. Higher damping ratio reduces the peaks but increases transmissibility in the isolation region.

Q: Why is tire contact force (road holding) important?

When the tire contact force drops below the static load (m_s + m_u)·g, the tire loses grip with the road (tire liftoff). Braking and cornering performance depend on contact force, so the closer the minimum contact force is to zero, the worse the handling stability. A Tyre Dynamic Load Coefficient (dynamic load variation divided by static load) below 0.3 is typically desired. The quarter-car model can evaluate minimum tire contact force as a road holding index.

Question 1

What is the quarter-car model?

Accepted Answer

The quarter-car model represents 1/4 of the vehicle body mass as the sprung mass m_s, and the tire/wheel/axle assembly as the unsprung mass m_u, forming a 2-DOF system. The sprung mass is supported by the suspension spring (k_s) and shock absorber (c), while the unsprung mass connects to the road via the tire (k_t). Although simpler than a full-vehicle model, it is widely used as a fundamental tool for quantitatively evaluating the trade-off between ride comfort and handling stability.

Question 2

How is the optimal damping coefficient for a shock absorber determined?

Accepted Answer

The design parameter is the damping ratio ζ relative to the critical damping coefficient c_c = 2√(k_s · m_s). Typical passenger cars use ζ ≈ 0.2–0.3 for ride comfort priority and ζ ≈ 0.3–0.5 for handling stability priority. Too low ζ causes excessive body oscillation (underdamped); too high ζ reduces road-following ability. ISO 2631 defines a_w < 0.315 m/s² as comfortable.

Question 3

How should I read the vibration transmissibility chart?

Accepted Answer

The transmissibility T = |x_s / x_road| is the ratio of body displacement to road displacement. A peak occurs near the sprung mass natural frequency f_n1 (typically 1–2 Hz). A second peak appears at the unsprung (wheel hop) natural frequency f_n2 (typically 10–15 Hz). At frequencies well above f_n1, the transmissibility drops below 1 (isolation region), meaning the suspension absorbs vibration. Higher damping ratio reduces the peaks but increases transmissibility in the isolation region.

Question 4

Why is tire contact force (road holding) important?

Accepted Answer

When the tire contact force drops below the static load (m_s + m_u)·g, the tire loses grip with the road (tire liftoff). Braking and cornering performance depend on contact force, so the closer the minimum contact force is to zero, the worse the handling stability. A Tyre Dynamic Load Coefficient (dynamic load variation divided by static load) below 0.3 is typically desired. The quarter-car model can evaluate minimum tire contact force as a road holding index.

Shock Absorber / Vehicle Suspension Analysis

Theory (2-DOF Model)