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

Formula Used:

\[ Tyre Vertical Rate = \frac{Roll Rate \times (Roll Rate of Anti-Roll Bar + Wheel Centre Rate \times (Spring Track Width^2)/2)}{(Roll Rate of Anti-Roll Bar + Wheel Centre Rate \times (Spring Track Width^2)/2 - Roll Rate) \times (Rear Track Width^2)/2} \]

\[ Kt = \frac{K\Phi \times (Rarb + Kw \times (Ts^2)/2)}{(Rarb + Kw \times (Ts^2)/2 - K\Phi) \times (tR^2)/2} \]

Roll Rate (KΦ):

N·m/rad

Roll Rate of Anti-Roll Bar (Rarb):

N·m/rad

Wheel Centre Rate (Kw):

N/m

Spring Track Width (Ts):

Rear Track Width (tR):

Tyre Vertical Rate (Kt):

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1. What is Tyre Vertical Rate?

Tyre Vertical Rate is the spring rate controlled by the tyre compound, sidewall stiffness and operating pressure. It represents the vertical force acting on the tire per unit vertical displacement.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Kt = \frac{K\Phi \times (Rarb + Kw \times (Ts^2)/2)}{(Rarb + Kw \times (Ts^2)/2 - K\Phi) \times (tR^2)/2} \]

Where:

\( Kt \) — Tyre Vertical Rate (N/m)
\( K\Phi \) — Roll Rate (N·m/rad)
\( Rarb \) — Roll Rate of Anti-Roll Bar (N·m/rad)
\( Kw \) — Wheel Centre Rate (N/m)
\( Ts \) — Spring Track Width (m)
\( tR \) — Rear Track Width (m)

Explanation: This formula calculates the tyre vertical rate based on the suspension system's roll characteristics and geometric parameters.

3. Importance of Tyre Vertical Rate Calculation

Details: Accurate tyre vertical rate calculation is crucial for vehicle suspension design, ride comfort analysis, and handling performance optimization. It helps engineers understand how the tyre contributes to the overall suspension stiffness.

4. Using the Calculator

Tips: Enter all values in appropriate units (N·m/rad for roll rates, N/m for rates, m for track widths). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What factors affect tyre vertical rate?
A: Tyre compound, sidewall stiffness, operating pressure, and temperature all influence the tyre vertical rate.

Q2: How does tyre vertical rate affect vehicle performance?
A: It affects ride comfort, handling characteristics, and overall suspension behavior, particularly in response to road irregularities.

Q3: Can this calculation be used for both front and rear suspensions?
A: While the formula uses rear track width in the notation, it can be adapted for front suspension by using appropriate track width values.

Q4: What are typical values for tyre vertical rate?
A: Values vary significantly based on tyre type and size, but typically range from 100-500 N/mm for passenger vehicles.

Q5: How accurate is this calculation compared to physical testing?
A: This provides a theoretical estimation. For precise applications, physical testing under controlled conditions is recommended.