vehicle dynamics week 10a

Questions:

1. What is the difference between deterministic and stochastic models/methods? Which one would you use to study road profiles
2. Explain Fourier transform in your own words
3. Explain PSD in your own words
4. What are the three main aspects of suspension performance evaluation that we discussed
5. How many degrees of freedom does the quarter car model have? What are they?
6. ISO ride metric filters for ride comfort are different for different axis (x,y,z). Why do you think they are this way?
7. You have decided to switch to aluminum wheels from steel wheels when designing a suspension system. What effect would this have on vibration isolation?
8. Your shock absorbers are worn, leaking fluid and cannot deliver the desired damping. What effect does this have on the rattle space?
9. Explain pitch and bounce oscillation centers
10. What is one potential disadvantage of performing subjective ride measurements?

Answers:

4. In deterministic models, the output of the model is fully determined by the parameter values and the initial conditions. Stochastic models possess some inherent randomness. The same set of parameter values and initial conditions will lead to an ensemble of different outputs.stochastic models on the other hand, can allow for certain degree of uncertainty while providing its prediction that's why it should be used for modeling road roughness
5. Fourier Transform says that any signal which varies periodically could be represented by a combination of sine and cosine waves.Fourier transform is a mathematical transform which decomposes a function (often a function of time, or a signal) into its constituent frequencies. The term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of time.There is also an inverse Fourier transform that mathematically synthesizes the original function from its frequency domain representation, as proven by the Fourier inversion theorem.
6. Psd is composed of three main parts:Power refers to the fact that the magnitude of the PSD is the mean-square value of the signal being analyzed. the mean-square value of any quantity has become known as the power of that quantity.

   Spectral refers to the fact that the PSD is a function of frequency. The PSD represents the distribution of a signal over a spectrum of frequencies just like a rainbow represents the distribution of light over a spectrum of wavelengths (or colors).

   Density refers to the fact that the magnitude of the PSD is normalized to a single bandwidth.

   So in short: Power spectral density function (PSD) shows the strength of the variations(energy) as a function of frequency

   PSD is useful measure of road roughness because every profile has special and unique psd plot, all roads show the comprehensive drop in amplitude with spatial frequency(Spatial Frequency defines as the cycles/meter whereas temporal frequency is cycles/sec). This simply reflects the fact that deviations in the road surface about hundreds of feet in length may have amplitudes of inches, whereas those only a few feet in length are normally only fractions of an inch in amplitude.

7. Three main aspect of Suspension Performance evaluation through Ride Models are:

• Vibration Isolation - Vibration can be isolated through ride models by varying unprung mass, spring rate and damping coefficient of the system to reduce vibration by reducing transmissibility ratio in low, mid and high frequency range. TR is nothing but a sprung mass deflection measure with respect to ground deflection.
• Suspension Travel and Rattle Space - Suspension travel is the relative deflection of sprung mass and unsprung mass w.r.t ground deflection thus in this we have to reduce this ratio for low, mid and high frequency range. Rattle space has to be tuned for the packaging purpose. Rattle space is the space required by the suspension during jounce and rebound motion.
• Road Holding - Road Holding means how much the tyre deflected during dynamic condition. To improve road holding capability we have to reduce unsprung mass deflection w.r.t ground deflection by varying unsprung mass, shock stiffness, damping coefficient in low,mid, and high frequency.

5. Quarter car model has 2 dof as it has 2 mass (Sprung and Unsprung mass) which move relative to each other vertically and hence two equation of motion can be written to predict the deflection of each masses.
6. Because in the human body, vibrations perception and reaction is depended upon the area and direction of vibration over full human body. The vibration comfort or fatigue limits are not same everywhere of the body, like torsa,legs,foot have different vibration limits level. Thats why ISO has made the limits on the basis of transverse and vertical vibration by considering the variable perception level at different areas of human body.
7. Alluminium has the less density than steel so Al is lighter that Steel which reduces the unsprung mass. the reduction of unsprung mass provides the better vibration isolation in mid frequency range but it will increase the Transmissibilty ratio in high frequency.
8. If dampers are not working as desired then the suspension travel will be difficult to control as it will give a sudden rise in relative deflection of sprung and unsprung mass at low and at high frequency. Which could create a packaging issue as the rattle space is increased due to increase in travel.
9. Bounce Oscillation center is the point about which body will have a motion corresponding to its bounce natural frequency. Pitch Oscillation center is the point about which body will have a pitch motion corresponding to its pitch natural frequency.If the Oscillation centers lie outside the wheelbase then it is a Bounce Oscillation center and if it lies inside the wheelbase then it is known as Pitch oscillation center.

10. In subjective ride measurements we require group of trained evaluators and observers and percieve vibrations and provide meaningful information. But, in this method the degree of difference in ride quality cannot be quantitatively determined. Subjective results has to match with objective testing results. Its difficult to convert subjective outcomes into mathematical models. Subjective testing also has the degree of human error and results varies with person to person which could results in confusion among engineers and challenging at the same time.