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Automobile

1. 1. BIRLA INSTITUTE OF TECHNOLOGY ASSIGNMENT ON AUTOMOBILE ENGINEERINGTitle : –Braking of vehicle on curved path. Submitted By Nitesh Prasad (BE/1183/08) Mechanical Engineering 8th Semester
2. 2. Acknowledgement Braking of vehicle is an important concept of automobileand is also related to my area of interest. I would like tothank our Automobile Engg. teacherProf. S K Sinhasir,for giving me such topic as assignment. Without hisguidelines, support, direction and time to time help Icould not bring this project in its present form.I am also thankful to BIT library,lan facility andforemostmy friends who helped me a lot and providedme resources for building up the project.Once again thanks to all. Submitted By:- Nitesh Prasad (BE/1183/08) Mechanical Engineering 8th Semester
3. 3. Motion of a vehicle in a bend curve path:-Motion along a curved path can be analyzed in terms of circular motion.We all experience motion along a curved path in our daily life. The motion is not exactly a circularmotion. However, we can think of curved path as a sequence of circular motions of different radii.As such, motion of vehicles like that of car, truck etc, on a curved road can be analyzed in terms ofthe dynamics of circular motion. Clearly, analysis is done for the circular segment with the smallestradius as it represents the maximum curvature. It must be noted that "curvature" and "radius ofcurvature" are inverse to each other. Motion along a curved path Figure 1One common experience, in this respect, is the experience of a car drive, which is negotiating a sharpturn. If a person is sitting in the middle of the back seat, she/he holds on the _xed prop to keep theposture steady and move along with the motion of the car. If the person is close to the farther side(from the centre of motion) of the car, then she/he leans to the side of the car to become part of themotion of the car.In either of the two situations, the requirement of centripetal force for circular motion is fulfilled.The bottom of the body is in contact with the car and moves with it, whereas the upper part of thebody is not.When she/he leans on the side of the car away from the center of motion, the side of the car appliesnormal force, which meets the requirement of centripetal force. Finally, once the requirement ofcentripetal force is met, the complete body is in motion with the car. Motion along a curved path Figure 2: The person presses by side of the car.The direction in which the body responds to curved motion is easy to find by just thinking whatwould be the natural direction of motion of the free part of the body. In the example discussed above,the body seeksto move straight, but the lower part in contact with car moves along curved pathhaving side way componentof motion (towards centre). The result is that the upper part is away from
4. 4. the centre of curvature of the curved path. In order to keep the body upright an external force in theradial direction is required to be applied on the body.Braking of vehicle moving on curved pathWhile moving along a curved path a vehicle comes under the influence of centrifugal force, whichtries to move it outward. This action ofcentrifugal force is made futile by side forces acting at thetyres in the direction reverse to that of centrifugal force. When the vehicle is braked while movingalong a curved path, the frictional forces between the tyres and the road become more complex.Referring to Fig.Let W = weight of the vehicle, NC = radius of curved path, m Figure 3. Forces acting on a vehicle during braking while moving on a curved path (plan view).As the radius of the curved path is very large compared to the dimensions of the vehicle, P and Q areassumed to be parallel. Similarly brakingforceFf and Fr are also parallel.For simplification, it is assumed that the forces at the vehicle wheels are compressed into a singleforce on a single plane passing through the centreof gravity neglecting the rolling effect on the wheelreactions due to centrifugal action and turning tendency during braking caused by unequal forces atinner and outer wheels.Referring Fig. let R is the vertical load on the wheel and i is the coefficient of adhesion. A part ofthe frictional force ui resists the side-slip and the rest is utilized for braking as shown in the figure. Itis quite clear from this that the braking capacity of a vehicle is reduced while moving along a curved
5. 5. path. Finally it can be concluded from this figure that if the value of n is very high then vehiclemoving above a certain speed may overturn before it slides sideways.Stability Criteria of vehicle on curved pathAccording to the robust stability criterion, it results that the vehicle is stable as it is shown in the fig.bellowFig.The stability limit of the vehicle on a curved path.The curve from the fig. above represents the stability limit of the studied vehicle, that means if thevehicle has a small velocity and a brakeage angle of the wheel such that the point corresponding tothe respective coordinates is under the curve, then the motion on the specified trajectory is stable andif the point is above the curve then the motion is unstable.From the performed analysis, it results that the vehicle is stable until a 110 km/h velocity when thebrakeage angle reaches the value of 10o, at the value of 15° of the brakeage angle the stability is atits limit for the same velocity, and when the wheels have more than 15o the instability tendencygrows more, until the value 25o of the brakeage angle when the stability is lost at velocities less than90 km/h.The original mathematical model with six freedom degrees is without Approximations thiscontributing to the exactness of the results obtained. The stability criterion applied is also an originalapproach regarding this type of application due to the higher degree of difficulty of the Liapunovfunction finding. It is important to notice that this criterion shows the tendency of loosing thestability, this means that it indicates exactly the conditions when the vehicle starts loosing adherenceor contact with soil for at least one of the wheels.