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Introduction Engineering ModelingAnd Analysis Assignment
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The main content of this assignment is to evaluate the suspension system of the mountain bikes. The mathematical methods and calculation have been executed in this assignment. The relevant statistical models with graphs will also be implemented. The analysis and modeling problems will also be solved. Some engineering principles will be applied as per the requirements of the calculations (Friesen, 2020). The main outcome is related to the suspension system of the mountain bikes. This system can be developed as the main “spring-damper” system. The optimization about the rear vehicles based suspension manly for increasing e ride comfort of the motorbike driver. The main objective to derive the differential equation of second order and make a model for the mountain bike suspension system has been done properly in this assignment. Then the execution of displacement, velocity and acceleration for the analytical solutions also evaluated with damping comparison graphs. The mass of the concentrated wheel has been taken as “M” and the stiffness of the spring is “k”. The damping coefficient and the displacement have been taken as “c” and “x”. The main equation for suspension system has been taken as follow:
The Role of Motorbike Suspension
This paper generally deals with the dynamic and in plane based simulation for motorbike suspension. Such a model is often considered as the visco-elastic based suspension of the rigid body. There are mainly two different kinds of kinematic related excitations that have been considered, such as the hat shape of bump with the uneven road nature mainly by their power based spectral along with density. The results for simulation are used for the stochastically very uneven based road character provided by their power based spectral density along the density.
The motorbike suspension usually serves the primary purposes like providing the comfort to ride, mainly maintaining the comfort and isolation from various vibrations which would be generated by some interaction between the wheel and uneven surfaced roads. The corresponding gripping of the wheel for the transmission of the various needed drawings, the braking as well as lateral forces. The associated degree of comfort generally depends on the application of motorcycles. The comfort for the racing based motorcycles is certainly less important as compared to the motorbike capabilities. The touring based motorcycles are characterized lobby the high requirements of the various comfort. The paper is highlighting the essential concept in modeling, the dynamic analysis along with the optimization for the stiffness and damping properties for main suspension. The optimization about the rear vehicles based suspension manly for increasing e ride comfort of the motorbike driver.
Aim and objectives
Aim
The main aim of this assignment is to get the outcome related to the suspension system of the mountain bike and develop the main “spring-damper” system with mathematical methods and calculation and the relevant statistical models with graphs as per the requirements of the analysis and modeling problems,
Objectives
The main objectives of this assignment and developments are discussed as follows:
- To derive the differential equation of second order and make a model for the mountain bike suspension system
- To execute the displacement, velocity and acceleration for the analytical solutions
- To evaluate the graphs of motion equation, displacement and the generated acceleration of the mountain bikes
- To implement the MATLAB Simulink model based on the suspension system with graphs
- To analyze the response of the changes in damping coefficients with the changes of 60% reduction
Methodology
The main research is related to the mountain bikes and the design of those bikes to clarify the suspension with shock absorption and the efficiency of pedaling. The overall design of the mountain bike has been evaluated to calculate the suspension of the mountain bike. The system has been developed as the main “spring-damper” system. It is related to the MR damper with a shock absorber (Abraham et al. 2022). The mathematical methods and calculations have been executed in this assignment. The relevant statistical models with graphs will also be implemented. The analysis and modeling problems have been also solved. The touring-based motorcycles are characterized lobby high requirements for various comforts.
Damper design method
Some different types of geometric constraints can be evaluated to observe the suspension and dumping area of mountain bikes. The air springs and the MR damper can be changed as per the requirements of the bike (Coyne et al. 2021). The mountain locations can make the linkage in the suspension existing frame. The experimental uses can be dependent on the damper shock absorber and the volume or weight of the rider. The mathematical methods and calculations have been evaluated in this research and a relevant statistical model with graphs can also be implemented. The development of the damping coefficient can be related to the velocity and the MR fluid of subsequent coefficients of the bike (Ongaro, 2021). The main acceleration can be generated through the shock numbers of the microcontroller in the current coil. The executed value of the shock can be converted into analog control between the voltage 0 and 5 Volts. The voltage can be controlled with the current of the amplifier. The control of the voltage can be mounted to the bike and the handlebars of the microcontroller. The main evaluation is related to the frequencies of the damping. The normal frequencies can be used as 10 to 20 Hz. it can give the proper isolation and acceleration to increase the damper current. Some frequency graphs for the response with the initial conditions have been developed. The step count values and impulse response can also be developed though this research. The whole process has been developed and executed using MATLAB codes and Simulink.
Analytical methods
The research has been done for the implementation of a magnetic damper with activated vibration and isolation. The mountain bike suspension analysis can be executed with the testing of the shaker indication relatively with low frequencies. It can only be possible to control the main response attributes of the shock absorber algorithm. The experimental uses can be dependent on the damper shock absorber and the volume or weight of the rider (Philliberet al. 2022). The mathematical methods and calculations have been evaluated in this research and a relevant statistical model with graphs can also be implemented. The development of the damping coefficient can be related to the velocity and the MR fluid of subsequent coefficients of the bike. Using the MATLAB analysis, the mathematical functions and the models can be represented for the overall acceleration suspension analysis.
Results and Discussion
The first derivation has been executed for the second-order equation which is related to the differential equations. The behavioral graph for this differential equation can be observed through MATLAB graph analysis (Cornoet al. 2021). The commands can be used to derive the order in the values that are taken properly with the MATLAB commands
The above image in Figure 1 has been the analysis of the differential equations in Matlab software. The software analysis had to be used for representing the codes, expressions, as well as parameters. The fact that a new variable t has been included as per the requirement. The modification work focused on the expression y for carrying out a detailed analysis.
The graphical attributes are executed as the response of initial conditions for suspensions and the axes are taken as amplitude and time in seconds. The output of this graph can be looked like the typical graph of damping response for the mountain bike. It can be done through the model implementation and the positions are taken as the results of the analysis (Mohammed, and Alktranee, 2021). The first-order system cannot define the main suspension so the second-order differential equations are considered here to evaluate the graph. The codes are taken for the damping output and the commands are collected to a mat file.
The values for the execution of displacement, velocity, and acceleration for the analytical solutions are also evaluated with damping comparison graphs. The mass of the concentrated wheel has been taken as “M” and the stiffness of the spring is “k”. The damping coefficient and the displacement have been taken as “c” and “x” (Pierce et al. 2022). The whole process has been done for the displacement, velocity, and the acceleration process of mountain bikes. It can be helpful to execute the proper suspensions of the mountain bikes and the executed graphical view can be evaluated to understand the damping frequency and velocity.
The above figure can execute the graph for prominent damping response value. The graphical attributes are executed as the response of initial conditions for suspensions and the axes are taken as amplitude and time in seconds (Zhao et al. 2020). The output of this graph can be looked like the typical graph of damping response for the mountain bike.
The Simulink model has been evaluated for the mountain bike sustainability analysis. The step count and the bloc parameters have been executed as 1 with the step time, the initial value is 1 and the final value is 2. The sample time has been taken as 0 as it has no extra sample times. The main interpretation vector parameters are taken as 1-D and the detection has been executed as the zero crossing enable detection. The following figure can show the view of step time values.
The above image in Figure 6 has been included in the analysis as per the requirement. The analysis of graph had to be used between two variables in Matlab software. A particular Matlab file has been taken into consideration for the damping ratio analysis.
A particular variable “zeta” has been taken into consideration for presenting the data into Matlab file. The normal frequency is selected as 100hz while the Zeta is taken 0.06 since the damping ration is also reduced with 60% and then the impulsive based responses have been simulate and resulted plot have been shown in the above figure.
The above image in Figure 7 has been taken into consideration for presenting the steps in Matlab software. Matlab analysis focused on all the steps and the values for presenting the plots.
The second scope can show the executed response of the Simulink model analysis for the damping and the suspension of the mountain bike (Jibril et al. 2021). The graphical view can represent a different view from the graph collected by the MATLAB commands. The graphical representation has been designed by the simulation model in Matlab software. The software had a Simulink feature, and that particular has been further used for designing out the system model. The above image has been the output of the Simulink model in Matlab software.
The above image in Figure 9 has been used to design a plot in Matlab software. The software analysis focused on the codes as well as expressions for considering two variables Amplitude and Time.
The coding work has been done in the software to ultimately making the design. The amplitude versus time simulation by linear methods has been done and simulation plot is shown in above figure.
Two different types of the impulse response of the velocity and the acceoleratio0n can be executed from Simulink and the MATLAB commands. The acquired graph for the commands has more impulse than the graph executed in Simulink with the same values (Afolayan, 2022). So it can be defined that the graph displacement, velocity, and acceleration are completely different.
A complete Simulink model has been implemented as per the requirement s of the assignment and the system can execute the graphs with two scopes (scope 1 and scope 2). The diagram has been shown in the figure above with proper names and attributes values.
The mass component of spring damping mass system is added to simulate the required code in Matlab simulation and then obtaining the essential simulation plots.
The mass attached with system is of 25kg and 70kg while the coefficient of damping is reduced by 60% and hence taken as 2000*0.06, i.e 120. The constant taken as 350 and 7000 for the determination of values of G1 and G2.
The commands are used for the response of displacements, velocity and acceleration and it has been shown in the figure above. The graphical view has been shown also in the figure as follows:
The above image in Figure 14 has been used to design a plot in Matlab software. Matlab had all the important codes as well as insights for designing the plot. The comparison of position, velocity and acceleration for the given system have been analyzed and then simulated by using Matlab software and the resultant plots is shown in above figure.
In the end, the response displacements have been executed with two comparison graph. It has been evaluated with the “Van Der Pol equation”. The comparison can be detected as it has two graphical lines with red and blue color.
Conclusions
The assignment is based on such models that can be often considered as the visco-elastic based suspension of the rigid body. There are mainly two different kinds of kinematic related excitations that have been considered. The main outcome is related to the suspension system of the mountain bikes. This system can be developed as the main “spring-damper” system. The mathematical methods and calculation have been executed in this assignment. The relevant statistical models with graphs will also be implemented. The analysis and modeling problems have been also solved. The touring based motorcycles are characterized lobby the high requirements of the various comfort. The associated degree of comfort generally depends on the application of motorcycles. The comfort for the racing based motorcycles is certainly less important as compared to the motorbike capabilities. This assignment can highlight the essential concept in modeling, the dynamic analysis along with the optimization for the stiffness and damping properties for main suspension. The optimization about the rear vehicles based suspension manly for increasing e ride comfort of the motorbike driver.
References
Abraham, E., Klemp, D., Cryder, J., Alsinan, S., Spencer, T. and Coyne, A., 2022. Bike Suspension Preliminary Proposal.
Afolayan, D.O., 2022. Modeling and Implementation of PID Controller for Efficient EV Suspension Energy Harvesting (Doctoral dissertation, Tennessee Technological University).
Corno, M., Panzani, G., Catenaro, E. and Savaresi, S.M., 2021. Modeling and analysis of a bicycle equipped with in-wheel suspensions. Mechanical Systems and Signal Processing, 155, p.107548.
Free SampleCoyne, A., Klemp, D., Abraham, E., Cryder, J., Alsinan, S. and Spencer, T., 2021. Mountain Bike Suspension Capstone Final Report.
Devys, S., Bertin, D. and Rao, G., 2019. Does changing the bike frame influence pedal force pattern in mountain bike cyclists?. Science & Sports, 34(5), pp.e279-e287.
Friesen, J.R., 2020. Mountain bike rear suspension design: Utilizing a magnetorheological damper for active vibration isolation and performance (Doctoral dissertation, Western Carolina University).
Jibril, M., Tadese, M. and Hassen, N., 2021. Control of Nonlinear Active Suspension System Based on Fuzzy Model Predictive Controller. Journal of Theory and Practice of Engineering Science ISSN, 2790, p.1505.
Mohammed, M. and Alktranee, M.H., 2021, February. Parametric analysis of vehicle suspension based on air spring and MR damper with semi-active control. In Journal of Physics: Conference Series (Vol. 1773, No. 1, p. 012022). IOP Publishing.
Ongaro, A., 2021. Characterization and analysis of an electromechanical suspension for mountain bikes.
Results and DiscussionPhilliber, T.J., Shaffer, R.M., Ruiz, D.M. and Ringrose, J.M., 2022. MTB DAQ-Mountain Bike Data Acquisition System.
Pierce, R. Scott, Caleb Whitener, and SudhirKaul, 2022. "Semi-Active Damping for Off-Road Bicycle Suspension: An Experimental Study." In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 51852, p. V008T10A054. American Society of Mechanical Engineers, 2018.
Zhao, L., Yu, Y. and Results and DiscussionZhou, C., 2020. Dynamic modeling, simulation and experimental investigation on cycling-trainers equipped with suspensions considering human biomechanical characteristics. Journal of Vibroengineering, 22(5), pp.1228-1239.
