Calculating Stiffness of Springs/Suspensions for Inclined Suspension

In summary, the conversation discusses calculating the stiffness of springs/suspensions in different scenarios such as inclined suspension and independent suspension. The derivation of roll stiffness is also explained, with the formula being T_{\phi} = 0.5 K_{s} s^{2} \phi. For independent suspensions, the same formula applies but K_{s} is replaced with the wheel rate and s with the track width. For straight axles with inclined springs, the roll rate is multiplied by the cosine of the inclination angle.
  • #1
Vincent Mazzo
5
0
Hello guys

How can I calculate the following stiffness of the springs/suspensions in the case of inclined suspension (angle between suspension and axle)?

I know that the lateral separation of the springs causes them to develop a roll resisting moment proporcional to the difference roll angle between the body and the axle.

And in the case of independent suspension? How substitute the rate at the wheel for K_s and use the tread as the separation distance?

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  • #2
Derivation of the roll stiffness:

The reaction torque ([itex]T_{\phi}[/itex]) can be found with the spring force ([itex]F_{s}[/itex]) times the lever arm length ([itex]s/2[/itex]) for both springs:

[itex]T_{\phi} = 2 \times F_{s} \frac{s}{2} = F_{s} s[/itex]

The spring force is equal to the spring rate times the spring compression (or extension) based on the roll angle ([itex]\phi[/itex]) and lever arm length ([itex]s/2[/itex]):

[itex]F_{s} = K_{s} \phi \frac{s}{2} [/itex]

Which leads to:

[itex]T_{\phi} = 0.5 K_{s} s^{2} \phi[/itex]

Since roll stiffness is defined as the amount of torque per roll angle:

[itex]K_{\phi} = \frac{T_{\phi}}{\phi} = 0.5 K_{s} s^{2}[/itex]

So for independent suspensions, the same procedure applies. All you have to do is to replace [itex]K_{s}[/itex] with the http://enderw88.wordpress.com/automotive-theory/spring-rate-theory/" and [itex]s[/itex] with the track width (where the wheel rates are acting).

For the straight axle with inclined springs, multiply the roll rate by the cosine of the inclination angle (see the wheel rate link above, same concept).
 
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FAQ: Calculating Stiffness of Springs/Suspensions for Inclined Suspension

1. What is the purpose of calculating the stiffness of a spring/suspension?

The stiffness of a spring or suspension is a measure of its resistance to deformation when a force is applied. It is an important parameter in designing and optimizing suspension systems to ensure proper handling, stability, and comfort of a vehicle.

2. How is the stiffness of a spring/suspension calculated?

The stiffness of a spring or suspension can be calculated by dividing the applied force by the resulting displacement. This can be done experimentally by measuring the force and displacement with specialized equipment, or it can be calculated using mathematical equations and models.

3. What factors affect the stiffness of a spring/suspension?

The stiffness of a spring or suspension is affected by various factors such as the material properties of the spring, the number of coils, the diameter of the wire, and the angle of the spring. Additionally, the orientation and arrangement of the springs in the suspension system also play a role in determining the overall stiffness.

4. How does the inclination of a suspension affect its stiffness?

The inclination or angle of a suspension refers to the angle at which the suspension is mounted to the vehicle. This angle can significantly affect the stiffness of the suspension as it changes the direction and magnitude of the forces acting on the suspension components. A higher inclination angle typically results in a stiffer suspension, while a lower angle results in a more compliant suspension.

5. Why is it important to calculate the stiffness of a spring/suspension for inclined suspensions?

Calculating the stiffness of a spring or suspension for an inclined suspension is crucial because it allows for proper design and optimization of the suspension system for the specific vehicle and intended use. It ensures that the suspension is capable of handling the required load and providing the desired level of performance and comfort. Additionally, calculating the stiffness can also help identify and troubleshoot any potential issues with the suspension system.

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