Automotive Science and Engineering

---

In this article, rubber bumpers of Double - Wishbone suspension system have been modeled and analyzed. The objective of the present work is to predict the performance of these products during deformation, represent an optimum method to design, obtain stiffness characteristic curves and utilize the results in the automotive suspension dynamic analysis. These parts are nonlinear and exhibit large deformation under loading. They have an important role to limit the motion of wheels and absorb energy. In this study, nonlinear FE model using ABAQUS software was used to obtain the bumper load - displacement curve. Then a laboratory test was done on the bumper to get this curve. The comparison between numerical and experimental results shows a good adaptation. A less than 2 percent difference has been observed between them. Thus, we can use this numerical method to simulate bumpers easily and accurately.

---

Nonlinear hunting speeds of railway vehicles running on a tangent track are analytically obtained using Hopf bifurcation theory in this paper. The railway vehicle model consists of nonlinear primary yaw dampers, nonlinear flange contact stiffness as well as the clearance between the wheel flange and rail tread. Linear and nonlinear critical speeds are obtained using Bogoliubov method. A comprehensive parametric study is then carried out and effects of different parameters like the magnitudes of lateral clearance, damping values, wheel radius, bogie mass, lateral stiffness and the track gauge on linear and nonlinear hunting speeds are investigated.

---

In this paper, a complete model of an electro hydraulic driven dry clutch along with its performance evaluation has elucidated. Through precision modeling, a complete nonlinear physical and full order sketch of clutch has drawn. Ultimate nonlinearities existent in the system prohibits it from being controlled by conventional linear control algorithms and to compensate the behavior of the system mainly during gearshift procedure, a nonlinear control program has been developed and tested. A unique approach to estimating clamp force has been adopted which makes the system comparable to a real world and full-physical one. Based on this type of modeling, the control approach is a true and feasible, ready-to-implement program which is based only on reality. The clutch model has been validated against experiments and great agreement has been attained since, every fine point has been taken into account and nothing is out of representation unless it is not crucial to system performance. The nonlinear control program does the control task very well and administrates the system in the desired trajectory.

---

Nonlinear vibration of parabolic springs employed in suspension system of a freight car has been studied in this paper. First, dynamical behavior of the springs is investigated by using finite element method and the obtained results are then used in vibration analysis of a railway freight car. For this purpose, dynamics of a parabolic spring subjected to a cyclic excitation has been studied in the frequency range of 2 to 15 Hz. By utilizing an experimental setup, equivalent static and dynamic stiffness and damping of the spring have been obtained and compared with theoretical results. Different classes of rail irregularities are taken into account to excite the vehicle. Bond Graph method is employed to extract the equations of motion of the system and validity of the obtained equations is investigated. Finally, a parametric study is carried out and the influence of vehicle velocity and rail irregularity on vertical acceleration of the freight car has been examined.

---

In cruise control systems, the performance of the controller is important. Hence, in order to have accurate results, the nonlinear behavior of a vehicle model should also be considered. In this article, a vehicle with a nonlinear model is controlled by using a nonlinear method. The nonlinear term of the model is the generated torque of engine, which is a polynomial equation. In addition, feedback linearization is used as a nonlinear method in order to design two parallel controllers to control the movement of the vehicle. These two parallel controllers are used to control braking and gas pedals which are in charge of the angular velocity of the wheels. To check the performances of controllers, first, each controller is used separately. Finally, two parallel controllers are used to track the reference signal. Comparison between results shows that the designed controller is able to reduce the convergence time of about 10 seconds. This improvement is near 35% in comparison with near studies. In addition, it can reduce the error between the velocity of the vehicle and the values of the reference signal that results in more safety for passengers.

---

In this study, a multi-objective differential evolution with fuzzy inference-based dynamic adaptable mutation factor with hybrid usage of non-dominated sorting and crowding distance (MODE-FM) is utilized for Pareto optimization of a 5-degree of freedom nonlinear vehicle vibration model considering the five conflicting functions simultaneously, under different road inputs. The significant conflicting objective functions that have been observed here are, namely, vertical seat acceleration, vertical forward tire velocity, vertical rear tire velocity, relative displacement between sprung mass and forward tire and relative displacement between sprung mass and rear tire. Different road inputs are, namely, double-bump, stationary random road and non-stationary random road. It is exhibited that the optimum solutions of 5-objective optimization contain those of 2-objective optimization and, as a result, this important matter creates more options for optimal design of nonlinear vehicle vibration model.

---

In this paper, the consensus of second-order nonlinear self-driving vehicle convoys (SDVCs) is studied. We assume that each self-driving vehicle (SDV) communicates only with one front and one rear SDVs. Each SDV’s nonlinear dynamics consisting of the rolling resistance and the air drag force is a function of SDV’s speed and is investigated in SDVC’s modeling and consensus design. Since the speed is bounded, all vehicles’ nonlinearities are also bounded. Due to engine saturation of each SDV, the control input is limited. We involve this limitation by introducing the arctan(.) function to control protocol. The inter-SDV’s distances are assumed to be constant during motion. The distance tracking error associated with each SDV is defined as distance between it and the leading SDV. The error dynamics of the proposed SDVC is derived after applying the consensus law to each SDV. To prove the internal stability, the Lyapunov theorem is employed. We will prove that under this consensus algorithm, the SDVC will be internal stable. To validate the effectiveness of this method, a SDVC comprising a leading and 6 following SDVs will be studied. It will be verified that under the proposed consensus law, all the SDVs reach a unique consensus.

---

The turn-around task is one of the challenging maneuvers in automated driving which requires intricate decision making, planning and control, concomitantly. During automatic turn-around maneuver, the path curvature is too large which makes the constraints of the system severely restrain the path tracking performance. This paper highlights the path planning and control design for single and multi-point turn of autonomous vehicles. The preliminaries of the turn-around task including environment, vehicle modeling, and equipment are described. Then, a predictive approach is proposed for planning and control of the vehicle. In this approach, by taking the observation of the road and vehicle conditions into account and considering the actuator constraints in cost function, a decision is made regarding the minimum number of steering to execute turn-around. The constraints are imposed on the speed, steering angle, and their rates. Moreover, the collision avoidance with road boundaries is developed based on the GJK algorithm. According to the simulation results, the proposed system adopts the minimum number of appropriate steering commands while incorporating the constraints of the actuators and avoiding collisions. The findings demonstrate the good performance of the proposed approach in both path design and tracking for single- and multi-point turns.