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1) Write on vehicle vibration,explaining what is meant by terms,modes,and explaining what is eigenvalues and eigenvectors.

2) Write on passenger comfort and ride quality.

## What is Vehicle Vibration?

Vehicle vibration is normally caused by the ground interaction with road roughness, force dynamics, unbalanced wheels, and/or engine problems. Vehicle vibration has become a critical design issue that Mechanical Engineers in the Auto-industry are increasingly undertaking research to succinctly uncover the phenomenon.

However, firstly, we define the following terms:

Modes- or simply stated as mode of vibration refers to the finite ways in which vibration in a body can occur. Each way of vibration will have a distinct frequency range and amplitude. Complex objects can pose great difficulty in accurately determining the characteristics of the vibration modes. However, in vibration analysis, there are techniques that can be used to infinitesimally link the theory to the actual performance (in terms of vibration).

Eigen values-These are special sets of scalars that are normally linked with a system of linear equations. To demonstrate this, Wolfram (2017) gives the following mathematical definition:

Firstly, let A be a linear transformation represented by a matrix A’ such that:

Ax’= λx’…(i)

Where λ is the eigen value and x’ is the eigen vector

Eigen vectors and values are significant in the analysis of mechanical vibrations where the solutions obtained are used to represent the state space of the system, a process known as matrix diagonalization (Wolfram, 2017)

Eigen vectors- This is a paired correspondence of the eigen values hence the eigen vectors are often accompanied by the eigen values as shown in equation (i)

Now, we get back to Vehicle vibration. Notably, vehicle vibration can never be covered without an in-depth look at the major causes of this phenomenon hence the following are the major causes of vehicle vibration (as mentioned earlier):

• Engine Problems

The engine normally has reciprocating and rotating components. Due to unbalanced forces, motion of these components can sometimes be a major cause of engine vibrations. Although designers have integrated some mechanical means to restrict the degrees of freedom, failures in engine firing and reciprocating parts unbalances are often combined to produce a complex source of vibration which varies with engine operating conditions. Additionally, the transmission shaft and crank shaft normally have mountings on them such as couplings. The centre of gravity of these shafts lies somewhere in the middle such that during rotational movements, the shafts would experience centrifugal force. If these forces are not balanced, then the shafts would begin wobbling and further increasing the engine vibration.

The roughness of road surface is another contributor to vehicle vibrations. As the car moves along, the tires interact with the surface such that up and downward motion occur in a repetitive fashion. Although the suspension springs are designed to absorb these vibration shocks, a poorly designed suspension would allow transmission to the passenger couches hence causing greater discomfort. To overcome this, the predisposing surface conditions are normally taken into account so that we end up with vehicles that can actually surmount the rugged terrain with just a little amount of discomfort at play.

• Force dynamics

## Causes of Vehicle Vibration

A balanced state of force systems in the car is one way of ensuring that car vibration is brought under control. The car suspension system and the chassis design would come in handy in this case. However, should this not be done properly then force balance in the car could be far-fetched. As a result of this, the test engineers must always perform rigorous tests to check on the car mechanics both in motion and stationary state.

• Unbalanced wheels

Unbalanced wheels normally cause uneven rotation of the wheels so that a rotation of all the wheels is not synchronized. This may result into serious problems such as loosening of bolts and nuts. Therefore, if this is unchecked then it can lead to fatal injuries especially when car is moving at high speed.

In conclusion, vehicle vibration need not be trivialized as it has proven detrimental to the health of the passengers. It can lead to driver fatigue as prolonged exposure causes the muscles to be less responsive hence characteristically drowsiness would often set in. It can also make the occupant safety to be at stake as vibration is likely to cause accidental disassembly of bolted components such as the wheel and axle. Unfortunately, during high speed drives, the probability of fatal injuries due to prolonged vibration would be higher.

However, as mentioned earlier, engineers have come up with sophisticated tools and methodologies to detect and measure the levels of vibration in the car body. According to Popovi? & Matijevi? (2016) one of these critical whole-body vibration tests is the bump test. This test can be envisaged as one in which a hummer hits an object and the whole object vibrates. The resulting frequency is measured and cross checked to ascertain that it is within the safe range. A series of bump tests are done and in the process the resonance frequency can be measured. However, engine vibrations can be minimized incorporating viscoelastic materials with a higher damping factor. Notably, mechanical system models have been designed to aid in understanding how engine vibrations occur so that reduction techniques can be integrated in the design. For instance, as argued by  Deulgaonkar, Kallurkar & Mattani (2016), constrained layer damping has successfully been applied in the engine design to limit the excessive vibrations. Additionally, tuned viscoelastic damping seems to register more positive results than the constrained layer damping.

Furthermore, there has been advancement in analytical tools; which are normally applied to derive an ideal vibratory system. The resulting models are then used to uncover the performance characteristics of the said system. Admittedly, Design Engineers would often rely on these scientific findings and sometimes even form part of the teams to explore these phenomena so that in the next design phase, a more superior product would result. Transfer Path Analysis is among the analytical techniques that are often applied in these vibration scenarios (Popovi? & Matijevi? , 2016) . The method would enable identification of the paths relative to the total vibration produced by the whole body. In fact, its functionality can be extended to include analysis of engine noise, vibration and harshness (NVH). It enables tracing of the vibrations right from its source (perhaps the engine) down to the transmission (the gears and gearbox) and finally to the passenger seat. These are then summed up by picking on the individual forces and vibrations. Therefore, this would allow complex vibratory systems to be modeled and analyzed easily. However, there are limitations with the method as it cannot exhaustively identify all the vibration hotspots and singularize them; it is practically impossible to do this with the technique.

## Techniques used to measure and control Vehicle Vibration

In conclusion, therefore, vehicle vibration still presents an interesting arena for research engineers and scientists do explore further. But what is encouraging is that their efforts are causing further advancement in the vehicle vibration control technologies.

Passenger comfort and ride quality are often two critical parameters that enhances acceptance from customers and ultimately lead to repeat purchases on the side of the buyers (Shirahatt, A, Prasad, P & Panzade, P. (2 008). The entire design of the vehicle greatly determines the performance levels of these two factors. Many a research engineers have attempted to study different vehicle models with the aim of establishing the degree of comfort and ride quality in those automobiles. This section will focus on such design factors that can affect the comfort and ride quality of the vehicle. Notably, central to this is the engine design.

In the engine, where masses spin, rotate and reciprocate at menacingly higher speeds, coupled with out-of-balance mechanisms, it is inevitable for the car to remain smooth in motion. However, inasmuch as engineers do attempt to deaden the engine vibration, passengers are still likely to be affected by discomfort arising from the engine motion. However, there are mechanisms such as the suspension springs that are supposed to ensure these vibrations are absorbed while insignificant proportions are normally allowed to leak through (Rafa?Burdzik & Dole?ek, 2012). Surprisingly, as mentioned earlier, vehicles moving in rough road surfaces are likely to have the passengers experience the discomfort that comes as a result of repetitive up and down motion as the tyres interact with the ground surface. In fact, if unchecked using modern sophisticated alignment tools, some of the wheels are normally misaligned in the process. Consequently, during high-speed rides, the vehicle vibration increases tenfold as the masses in the wheels are out-of-balance while they are being span at greater velocities. Therefore, ride quality in such a case would grossly be affected.

Secondly, engine noises also greatly contribute to passenger discomfort. Admittedly, however, this is an area that engineers have greatly worked on. The silencer technology currently available in some of these vehicles is top notch. The hybrid muffler design that has successfully been installed and tested in the formula one car has received great positive reviews from the ordinary motorist. Many automakers have also responded with even better and affordable muffler design. For instance, companies like Volvo and Porche resorted to install the KERS technology (which in full means: Kinetic Energy Recovery System); the said technology quickly recovers the kinetic energy that would be lost due to braking and is used elsewhere or stored. Hence the technology conserves the environment and also boosts the auto-power. Consequently, the exhaust noise is considerably reduced in the process; that is the reason why most Volvo cars have recorded greater ratings in performance level and ride quality. However, the technology is said to be very expensive to implement hence it is mostly used in formula one cars.

## Passenger Comfort and Ride Quality

Thirdly, the onboard air conditioning levels also play a key role in determining the passenger comfort. Due to changing weather conditions, whereby at one time, it is raining and therefore surrounding air-conditions change and sometimes later, it is oven-hot. All of these conditions need to be integrated in the design of the car body and interior. Suppose one carries out a survey to uncover the passenger comfort levels as far as onboard air-conditioning is concerned, many would be surprised by the result. A number of motorist and passengers are not really in need of the air-conditioning system as it is only one sided in terms of functionality; it cools down the temperatures in the car. However, car owners are craving for a dual-purpose kind of air-conditioning system where the system can serve the passengers both in winter and summer season without necessarily having to install another device. However, there are heat warmers that handle that functionality; unfortunately, they are dependent on the heat from the car engine. Besides, it normally takes time before the device can supply warm air. So, one would ask: what about during cold state when the engine shuts down? Therefore, an innovative design solution could as well be needed in this area; perhaps one can configure a way of capturing the heat during active rides so that it can be expended during engine shutoffs and therefore the car interior remains in a desirable state.

Admittedly, as mentioned earlier, the interior design also comes in handy. From the leg room to the size of the car furniture, the interior design of a car is another reason why passengers would either feel comfortable or uncomfortable. However, space economy in car manufacturing is among key design considerations. For every unit amount of space left in the car, there are costs to be incurred indirectly. Optimized design techniques are therefore normally employed so that space does not go to waste and the parts are correctly located to minimize complexities during assembly.

Therefore, in conclusion, as discussed above, passenger comfort and ride quality are essential customer requirements that must be integrated in the design. Importantly, the engine design must be such that it does not cause serious discomfort and irritation due to perhaps too much noise or vibrations being transmitted. Notably, however, engine car technology is still greatly advancing; with every subsequent car rollouts there are normally improvements in the car performance features.

References

Wolfram. (2017). MathWorld. Available at: https://mathworld.wolfram.com/Eigenvalue.html

Rafa?Burdzik, R& Dole?ek, R. (2012).  Research of Vibration Distribution in Vehicle Constructive. Number 4(Volume 7). Available at: https://pernerscontacts.upce.cz/28_2012/Burdzik.pdf

Shirahatt, A, Prasad, P & Panzade, P. (2008) .Optimal Design of Passenger Car Suspension for Ride and Road Holding. Available at: https://www.scielo.br/pdf/jbsmse/v30n1/a10v30n1.pdf

Winberg, M. (2005).Noise and Vibration Control of Combustion Engine Vehicles. Available at: https://www.diva-portal.org/smash/get/diva2:837892/FULLTEXT01.pdf

Deulgaonkar ,V, Kallurkar, P,  & Mattani, A.G. (2016). Review and Diagnostics of noise and vibrations in automobiles. Available at: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.416.3157&rep=rep1&type=pdf

Popovi?, D & Matijevi?,V. (2016). Overview of Modern Contributions in Vehicle Noise and Vibration Refinement with Special Emphasis on Diagnostics. Available at: https://www.mas.bg.ac.rs/_media/istrazivanje/fme/vol45/3/18_dmatijevic_et_al.pdf

Peters, J.D. (no year).What’s up with Bump Testing. Available at: https://www.ctconline.com/pdf/pubTechPapers/13-Bump%20Testing.pdf

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