Damper Plots

Why do we need it ?

• Understanding the implications of different speed groups (low, mid, and high speeds) on suspension performance aids in fine-tuning the suspension for optimal handling and control.

What is it ?

• Force (y-axis- Newtons) vs. Velocity (x-axis- mm/sec) or Force vs. Displacement(mm)

• A good damper plot graph helps in understanding how the force changes with the displacement or velocity. It provides insights into how effectively the damper can reduce vibrations and prevent excessive movement

• There are typically two types of damper plots:  Force-Velocity Plot: This type of plot shows the force exerted by the damper against the velocity of the object. It helps to understand how the force varies with the speed of the movement. (how speed affects the suspension)  Force-Displacement Plot: This plot displays the force exerted by the damper against the displacement of the object. It helps to understand how the force varies with the distance the object has moved from its equilibrium position. (how turning, hitting curbs, etc. affect suspension)

Using Linear Potentiometers and Accelerometers for Reading Data

• How to use Linear Potentiometers on the Car to get a Damper Plot?

• For measuring we need to position the linear Potentiometers on the correct suspension points on the car.
• The reading that we get in Voltage can be converted into Displacement in millimeters using the formula: o Displacement (mm) = Voltage * Conversion Factor. where the Conversion Factor depends on the specific characteristics of the potentiometer and its installation. o We can graph the Force vs Displacement Damper Plot graph if we know the Force (we get from Accelerometers). o Velocity (mm/sec) = (displacement2 - displacement1) / (time2 - time1). Where displacement2 and displacement1 are the displacements at two different time points, and time2 and time1 are the corresponding time values.

• How to use Accelerometers on the Car to get Damper Plots?

• Attach the Accelerometers on the car’s body or suspension correctly to measure the acceleration.
• Use the measured Acceleration reading from the Accelerometer to calculate Force: o Force (N) = Mass (kg) * Acceleration (m/s^2). Make sure to account for the mass of the specific parts of the car to which the accelerometer is

attached. o If you have velocity data, integrate the acceleration data to get velocity data, and then use this data to plot Force vs. Velocity. o Velocity (m/s) = Acceleration (m/s^2) * TimeInterval (sec).

• Other Points to consider while using Data: o Ensure that the units are consistent (e.g., force in Newtons, displacement in millimeters, and velocity in millimeters per second). o Ensure that the sensors are calibrated and securely mounted to avoid any inaccuracies in the measurements. o Account for any external factors that may affect the readings, such as temperature, vibration, or other environmental conditions. o Verify the accuracy of the conversion factors and the mass of the components involved.

Calculations

Damper Plots are Velocity (x) vs Damping force exerted by the damper (y) calculating velocity: Vi = Vi-1 + Ai * Time interval between measurements Sample Code for calculating velocity using accelerometers:

import numpy as np

def calculate_velocity(accelerations, time_intervals):
    """
    Calculate velocity from acceleration data.

    :param accelerations: DataFrame of acceleration values.
    :param time_intervals: DataFrame column for time values.
    :return: List of velocity values.
    """
    velocities = [0]  # starting with an initial velocity of 0
    for i in range(1, len(accelerations)):
        # Velocity = Previous Velocity + (Acceleration * Time Interval)
        velocity = velocities[i-1] + accelerations[i] * time_intervals[i]
        velocities.append(velocity)
    return velocities

accelerations = [0.5, 0.6, 0.55, 0.4, 0.3]  # Accelerations in m/s^2
time_stamps = [0, 1, 2, 3, 4]  # Time stamps in seconds

time_intervals = np.diff(time_stamps)

velocities = calculate_velocity(accelerations, time_intervals)

print("Velocities:", velocities)

def calculate_velocity(displacements, time_stamps):
    """
    Another method of calculating velocity from displacement data.

    :param displacements: List or array of displacement values. Displacement values will need to be calculated for this to work, this will be the difference in position between the starting point and its positions at each interval, this will also need to be a new DF
    :param time_stamps: List or array of time stamps.
    :return: List of velocity values.
    """
    velocities = []
    for i in range(1, len(displacements)):
        delta_x = displacements[i] - displacements[i - 1]
        delta_t = time_stamps[i] - time_stamps[i - 1]
        velocity = delta_x / delta_t
        velocities.append(velocity)
    return velocities

def estimate_damping_force(velocities, damping_coefficient):
    """
    Estimate the damping force using the damping coefficient and velocity.

    :param velocities: List or array of velocity values.
    :param damping_coefficient: Damping coefficient (constant).
    :return: List of estimated damping forces.
    """
    damping_forces = [damping_coefficient * v for v in velocities]
    return damping_forces

After these are found we simply need to plot them