Vertical Tyre Axle Rate Given Roll Rate Of Suspension With Anti-Roll Bar Calculator

Formula Used:

\[ K_w = \frac{\frac{K_{\Phi} \times K_t \times (t_R^2)/2}{K_t \times (t_R^2)/2 - K_{\Phi}} - R_{arb}}{(T_s^2)/2} \]

Roll Rate (KΦ):

N·m/rad

Tyre Vertical Rate (Kt):

N/m

Rear Track Width (tR):

Roll Rate of Anti-Roll Bar (Rarb):

N·m/rad

Spring Track Width (Ts):

Wheel Centre Rate (Kw):

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1. What is Wheel Centre Rate?

Wheel Centre Rate is the vertical force acting on the tire per unit vertical displacement at the location along the spindle corresponding to the wheel centerline, measured relative to the chassis. It's a crucial parameter in vehicle suspension design that affects ride comfort and handling characteristics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ K_w = \frac{\frac{K_{\Phi} \times K_t \times (t_R^2)/2}{K_t \times (t_R^2)/2 - K_{\Phi}} - R_{arb}}{(T_s^2)/2} \]

Where:

\( K_w \) — Wheel Centre Rate (N/m)
\( K_{\Phi} \) — Roll Rate or Roll stiffness (N·m/rad)
\( K_t \) — Tyre Vertical Rate (N/m)
\( t_R \) — Rear Track Width (m)
\( R_{arb} \) — Roll Rate of Anti-Roll Bar (N·m/rad)
\( T_s \) — Spring Track Width (m)

Explanation: This formula calculates the wheel centre rate by considering the suspension geometry, tire characteristics, and anti-roll bar contribution to the overall roll stiffness.

3. Importance of Wheel Centre Rate Calculation

Details: Accurate wheel centre rate calculation is essential for optimizing vehicle suspension performance, ensuring proper ride comfort, handling stability, and tire contact with the road surface under various driving conditions.

4. Using the Calculator

Tips: Enter all values in appropriate units (N·m/rad for roll rates, N/m for spring rates, and meters for track widths). Ensure all values are positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between wheel rate and spring rate?
A: Spring rate is the stiffness of the spring itself, while wheel rate is the effective spring rate at the wheel, considering suspension geometry and leverage ratios.

Q2: How does anti-roll bar affect wheel centre rate?
A: The anti-roll bar contributes to the overall roll stiffness and affects how the suspension responds to body roll, which is accounted for in the wheel centre rate calculation.

Q3: Why is track width important in this calculation?
A: Track width affects the leverage and moment arms in the suspension system, directly influencing how forces are transferred and how the suspension responds to inputs.

Q4: Can this formula be used for front suspension?
A: While the formula is presented for rear suspension, similar principles apply to front suspension, though specific geometry factors may differ.

Q5: What are typical values for wheel centre rate?
A: Wheel centre rate values vary significantly depending on vehicle type, but typically range from 20,000 to 60,000 N/m for passenger vehicles.