Vertical Tyre Axle Rate Given Roll Rate Calculator

Formula Used:

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

Roll Rate (KΦ):

N·m/rad

Tyre Vertical Rate (Kt):

N/m

Rear Track Width (tR):

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 and analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( K_w \) — Wheel Centre Rate (N/m)
\( K_{\Phi} \) — Roll Rate (N·m/rad)
\( K_t \) — Tyre Vertical Rate (N/m)
\( t_R \) — Rear Track Width (m)
\( T_s \) — Spring Track Width (m)

Explanation: This formula calculates the effective vertical stiffness at the wheel center based on roll characteristics, tire properties, and geometric dimensions of the suspension system.

3. Importance of Wheel Centre Rate Calculation

Details: Accurate calculation of wheel centre rate is essential for proper suspension tuning, ride comfort analysis, handling characteristics prediction, and overall vehicle dynamics optimization.

4. Using the Calculator

Tips: Enter all values in appropriate units (Roll Rate in N·m/rad, Tyre Vertical Rate in N/m, Track Widths in meters). All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between wheel centre rate and spring rate?
A: Spring rate is the stiffness of the spring itself, while wheel centre rate is the effective vertical stiffness at the wheel center, which includes the effects of suspension geometry and leverage ratios.

Q2: Why is roll rate important in this calculation?
A: Roll rate represents the suspension's resistance to body roll and directly influences how vertical forces are distributed across the suspension system.

Q3: How does track width affect wheel centre rate?
A: Track width affects the leverage ratios in the suspension system, which in turn influences the effective wheel centre rate calculation.

Q4: What are typical values for wheel centre rate?
A: Wheel centre rate values vary significantly depending on vehicle type, but typically range from 20-100 N/mm for passenger vehicles.

Q5: Can this formula be used for both front and rear suspensions?
A: While the formula is generally applicable, specific suspension designs may require modifications to account for different geometry and component arrangements.