ENEM 14015 : Dynamic System Modeling and Control - Multiple Degree of Freedom Systems - MATHEMATICAL MODELS

Internal Code : MAS5134

IT Assignment :

Objectives :  Your project now is to improve the model you developed in Project #2 and again analyse the performance of the motor bike. Part 1 The first improvement in the model to be evaluated will be inclusion of the unsprung mass of the wheels, axles and the stiffness of the tyres. Specifya typical tyre pressure and wheel specifications. Derive or estimate an approximate linear model for the tyres. [*Make an estimate of the tyre properties, again, do not spend time getting ‘good numbers’ it is your analysis that is important. State clearly how you obtain this, you may use experimentation, measurement of existing tyre deflection on vehicle of known mass, you may derive, accuracy is less important than approach.] Assume again linear suspension elements and analyse the two degree of freedom system clearly stating assumptions and limitations of your model, (you may use Linear modelling equations, Matlab and Simulink). Analysis Your analysis will include: An evaluation of suspension performance, vibrations and transients. Minimum scope Your requirement here is to analyse the motorbike as a mechanical system using mathematical modelling and two degree of freedom vibration analysis. Your analysis will include: ? Draw the model schematic of the motorbike. ? Simplify the model to be a two degree of freedom system (vertical motion only—Assume there is no roll or pitch). Draw the 2DOF FBD and write the modelling equations. ? Free vibration response. ? Road surface induced vibration. Assume road speeds up to 100 kph. Assume a simplified corrugation shape and a set of realistic road corrugation depths and wavelengths. ? Determine resonant frequencies. ? Produce plots of magnification factor and transmissibility factor. ? Laplace transform of the modelling equations. From these equations develop transfer functions describing the system. Produce a Bode plots for the system. Reflection and discussion Compare with your Bode diagrams with plots of magnification factor and transmissibility factor. Reflect again on the differences, advantages and disadvantages of frequency domain analysis (Laplace, frequency response etc.) verses time domain (simulation, time series output etc.). Discuss the differences between the project 2 1DOF model and your new 2DOF model. Discuss your 2DOF resonances, magnitude of responses at resonance and controlling resonant amplitudes. Part 2 The second improvement in the model to be evaluated will be inclusion of a pitch degree of freedom, then the addition of more  translational degrees of freedom. In addition to the information you have from earlier problems you will need to estimate moments of inertia data as best you can from the dimenstion and mass data. The last part of your task will be to examine performance over a jump ramp as shown in Figure 1 using your simulink model. Analysis :  Your analysis will include: ? An evaluation of the natural frequencies and mode shapes for the motorbike suspension. ? Simulation over the jump ramp. Minimum scope ? Create a schematic, FBD and modelling equation for a 2DOF model for only the pitch and translation DOF's of the motorbike body ? Find the natural frequencies and mode shapes for a 2DOF model for only the pitch and translation DOF's of the motorbike body. ? Develop a 2DOF Simulink model of the pitch and translational DOF's. ? Now extend your model to include the mass and stiffness of the tyres and convert your model into a three mass model with 4DOF's. Create the schematic, FBD and modelling equations and find the find the natural frequencies and mode shapes. ? Develop a Simulink model of the three mass model with 4DOF's. ? Add non-linearities and damping to the Simulink model to make it more reflective of the real situation. ? Use the Simulink model to get an indication of the vehicle performance over the jump ramp. (Do a jump simulation first for a 1DOF model from Project 2, then your 2DOF translational model in Part 1, and the 2DOF pitch and translational model). Then finally if you have time attempt the ramp jump for the 4DOF simulink model. Reflection and discussion

• Discuss and compare the differences between the single, two and multiple degree of freedom models results
• Discuss the free flight behaviour of the bike over the jump and the simulation of ground contact forces. Discuss any shortfalls of \RXU model or suspension design.
• Discuss any ways to improve the accuracy of the model or the performance of the bike's suspension.