Mathematical Modelling of the Rear Drive Unit of a Lightweight Vehicle for Sensitivity Analysis of Vibration

2016 ◽  
Author(s):  
Jiewei Lin ◽  
Yi Qiu
Keyword(s):  
Mathematical Model ◽  
Adverse Effect ◽  
Sensitivity Analysis ◽  
Vertical Vibration ◽  
Fractional Factorial ◽  
Design Stage ◽  
Design Parameters ◽  
Mass Reduction ◽  
Drive Unit ◽  
Car Body

Lightweight technology is applied in the automobile industry because mass reduction is beneficial in improving fuel efficiency and reducing CO2 emissions. Apart from the car body and the power unit (the two heaviest parts of a vehicle), the driveline also has potential for a reduction in weight. The driveline transfers power to the wheels and plays an important role in the vehicle system. Vibration is induced by the road input and by unbalanced forces transmitted through the driveline to the car body. Mass reduction in the driveline could influence the dynamic behaviour of a vehicle but it is not yet clear how mass reduction affects vibration of the driveline, the vehicle ride and NVH performance — important considerations when designing a lightweight driveline. In the prototype design stage, a mathematical model provides a more flexible and less costly method of optimising the system dynamics. In this paper, a 14 degree-of-freedom mathematical model is developed to study the dynamics of a rear drive unit (RDU). The system consists of a rear differential gearbox, left and right constant velocity joints and driveshafts, a rear sub-frame, and bushings between the RDU and the sub-frame and between the sub-frame and the car body. Excitations from the rear wheels, rear suspensions, and input shaft were considered. The vertical acceleration at the rear sub-frame was calculated and correlated with a calibrated multi-body dynamic model of the vehicle developed in a parallel study. Using a fractional factorial design with the vehicle travelling on a smooth road at various speeds, a sensitivity analysis was carried out with the developed mathematical model to identify the contributions of the mass properties of the RDU and the bushing parameters to the vibration at the centre of gravity (COG) of the rear sub-frame. Results indicate that the effects of design parameters on the rear sub-frame vibration vary according to the vehicle speed. For vibration at the rear sub-frame, the most influential factors are the masses of the rear differential gearbox and the driveshaft, and the stiffness of the front right bushings between the RDU and the sub-frame. The stiffness of the front left bushing between the RDU and the sub-frame also has considerable effect on the subsystem response but only at higher speeds. Reducing the mass of the CV joint is beneficial in decreasing the vertical vibration at the COG of the rear sub-frame, while reductions in masses of the gearbox and the driveshafts tend to slightly increase the vertical vibration at the same location. However, the adverse effect brought by lightweight differential gearbox and driveshafts on vibration is relatively small that may be hardly detected by passengers. The adverse effect (if any) can be compromised by adjusting the stiffness of the front bushings between the gearbox and the sub-frame.

scholarly journals VORTEX DEVICES OF THE DIESEL AIR SUPPLY SYSTEM: MATHEMATICAL MODEL OF AERODYNAMIC PROCESSES

2020 ◽  
Vol 17 (1) ◽  
pp. 110-120
Author(s):  
R. V. Yakimushkin
Keyword(s):  
Mathematical Model ◽  
Rational Design ◽  
Particle Dynamics ◽  
Supply System ◽  
Design Stage ◽  
Design Parameters ◽  
Classical Dynamics ◽  
Effective Parameters ◽  
Air Supply ◽  
Dynamics Method

Introduction. The calculation of effective indicators of the vortex ejector used in the diesel air supply system is a pressing task as it allows significantly reducing time for determination of rational design parameters at the design stage. One of the modifications of the particle dynamics method is a promising direction, allowing with high physical adequacy, “from the first principles,” to model aerodynamic processes in vortex devices. Therefore, the purpose of the paper is to develop a mathematical model of a vortex ejector.Materials and methods. The paper discussed a method of the mathematical simulation of ejection and ejection flows in a vortex ejector. The proposed modification of the particle dynamics method allowed describing aerodynamic processes with the help of simple laws of classical dynamics, and modeling them with the help of software of the Delphi 7 System. The author presented differential equations, which were solved by the Runge-Kutt method of the second order. As a result of the solution, the authors determined paths of air elements movement in the vortex ejector, which allowed estimating effective parameters of vortex devices.Results. To study the model, the author developed a program with the possibility to set geometric parameters of the vortex ejector in the interface window and to display the current values of the process parameters.Discussion and conclusions. Proposed mathematical model and computer program make it possible to quantify efficiency of vortex devices at their design stage. The advantage of the proposed mathematical model lies in more accurate calculation of vortex flow parameters from the vortex ejector design and physical properties of ejecting and ejecting flows.Financial transparency: the author has no financial interest in the presented materials or methods. There is no conflict of interest.

Cumulative Microslip in Conrod Big End Bearing System

2006 ◽  
Author(s):  
Jean-Louis Ligier ◽  
Nicolas Antoni
Keyword(s):  
Sensitivity Analysis ◽  
Gas Pressure ◽  
Design Stage ◽  
Physical Parameters ◽  
Mass Reduction ◽  
Combustion Gas ◽  
Automotive Engines ◽  
Mechanical Assemblies ◽  
Material Theory ◽  
Bearing System

High combustion gas pressure and mass reduction of modern automotive engines have generated new problems in mechanical assemblies. For example, it is now common to observe bearing shell rotation in the conrod of automotive prototype engines at the design stage. The consequence is sometimes the seizure of the bearing due to the presence of the joint face relief in the loaded area. Physically, the bearing shell rotation results from cumulated microslip between the bearing and the conrod. To have a better physical approach of the phenomenon and propose design recommendations, we have performed analyses based on the strength of material theory and numerical modellings. These tools permit us to obtain simple models allowing an easier mechanical understanding as well as an analysis of sensitivity to different parameters. The main results presented in this paper are: • The basic description of the phenomenon, • The modelling of the conrod, its sensitivity to deformation and numerical validation, • The analysis of the microslip between the bearing shell and the conrod, • The sensitivity analysis with respect to conception and physical parameters.

scholarly journals Effect of Different Design Parameters on the Cyclic Response of Reduced Beam Sections (RBS) Moment Connections

2021 ◽  
Author(s):  
Syed Asad Abbus Naqvi
Keyword(s):  
Sensitivity Analysis ◽  
Statistical Design ◽  
Fractional Factorial ◽  
Design Parameters ◽  
Dissipated Energy ◽  
Northridge Earthquake ◽  
Initial Stiffness ◽  
Moment Connections ◽  
Cyclic Response ◽  
Rbs Connections

After the 1994 Northridge earthquake, research has been conducted to develop new types of beamcolumn moment connections, such as Reduced Beam Section (RBS) connections. This study performs a sensitivity analysis of the cyclic response of RBS connections using detailed finite element simulation. The significance of the effect of twenty-one factors is assessed using a statistical design of experiment method. The input factors are related to the material properties or the geometry of the beam-column connection. A two-level fractional factorial design is used to create factor combinations for the sensitivity analysis. The cyclic response of RBS connections is assessed in terms of five response variables, including: the total dissipated energy, initial stiffness, strength degradation rate, maximum moment capacity and rupture index at 7.5% storey drift. The sensitivity analysis results show that the beam depth has the greatest influence on the cyclic response of RBS connections.

Analytical Robust Design of a Gear Milling Machine Headstock

2010 ◽  
Vol 37-38 ◽  
pp. 162-165 ◽  
Author(s):  
Yong Liang Chen ◽  
Shuang Liu ◽  
Han Tao Wang ◽  
Pei Hua Gu
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Robust Design ◽  
Optimization Model ◽  
Functional Performance ◽  
Geometric Design ◽  
Design Parameters ◽  
Milling Machine ◽  
Robust Analysis ◽  
Rayleigh Method

Headstock is a key component of gear milling machine. The dynamic functional performance of the headstock is usually influenced by uncertainties of both geometric and non-geometric design parameters. A new mathematical model to represent relationships among first frequency and design parameters of the headstock were derived with Rayleigh method. Then, a larger-the-better and smaller-the-better robust analysis and optimization model was developed. The sensitivity analysis results show that height of the headstock makes a great impact on the first frequency. Through robust optimizations, the first frequency is scaled up by 3.35 percent while minimizing the variance of the first frequency.

scholarly journals Development of the mathematical model for the process of oil raw materials pressing

2018 ◽  
Vol 7 (2.13) ◽  
pp. 145
Author(s):  
Ainura Kairbayeva ◽  
Vitalii Vasilenko ◽  
Seit Dzhinguilbayev ◽  
Lyazzat Baibolova ◽  
Larisa Frolova
Keyword(s):  
Mathematical Model ◽  
Chemical Interaction ◽  
Raw Materials ◽  
Screw Press ◽  
Design Stage ◽  
Design Parameters ◽  
Single Screw ◽  
Porous Skeleton ◽  
The Mathematical Model ◽  
Oil Filtration

The mathematical model for the process of oily raw materials pressing with single-screw oil press has been developed, which makes it possible to calculate the main design parameters of an oil press for extracting oil from oil crop seeds.This model of pressing describes the process of moving meal in the pressure zone and expression of oil in the pressing cage of the screw press, taking into account the following assumptions: porous skeleton and oil have the same density, they have no chemical interaction, the process of oil filtration occurs under isothermal conditions with laminar conditions of motion.The developed mathematical model corresponds to physical meaning of the occurring phenomena and can be used to analyze the work of active presses, and at the design stage. 

The Sensitivity Analysis of Engine Mounting System’s Inertial Parameters Based on the Orthogonal Test

2011 ◽  
Vol 338 ◽  
pp. 440-445
Author(s):  
Fang Hua Lei ◽  
Ning Sun ◽  
Wei Lin Tang
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Orthogonal Test ◽  
Vibration Characteristics ◽  
Design Parameters ◽  
Quality Level ◽  
Test Plan ◽  
Inertial Parameters ◽  
Engine Mount ◽  
The Individual

This paper analyze the variation of the inertial parameters of the powertrain based on the orthogonal test, and their effect on the vibration characteristics of the system. Then the paper designs a test plan of the two levels orthogonal test with 6 facts by establishing a mathematical model of 6-dof in engine-mount system. We spend 8 times having done the orthogonal computation with MATLAB. The experiment results bring us the average of the changes of two levels decoupling owned by the mounting system's 6 rank inherent characteristics on each direction .And this changes are caused by the fluctuating of inertial parameters. Finally, we analyze the variation of the rotational inertial and the inertial integrated parameters, and their influence on the quality level of the sensitivity on the all decoupling parameters in engine-mounting system on each direction. Combined with the calculation examples in the thesis, we discuss the individual inertial parameters of the engine-mounting system ，which is the crucial design parameters of sensitivity analysis, and have provided a parameter basis for the design of engine-mounting system.

scholarly journals A Consistent Procedure Using Response Surface Methodology to Identify Stiffness Properties of Connections in Machine Tools

Materials ◽  
2018 ◽  
Vol 11 (7) ◽  
pp. 1220 ◽  
Author(s):  
Jesus-Maria Hernandez-Vazquez ◽  
Iker Garitaonandia ◽  
María Fernandes ◽  
Jokin Muñoa ◽  
Luis Lacalle
Keyword(s):  
Finite Element ◽  
Response Surface ◽  
Machine Tools ◽  
Computational Cost ◽  
Fractional Factorial ◽  
Dynamic Responses ◽  
Design Stage ◽  
Design Parameters ◽  
Regression Equations ◽  
Design Variables

Accurate finite element models of mechanical systems are fundamental resources to perform structural analyses at the design stage. However, uncertainties in material properties, boundary conditions, or connections give rise to discrepancies between the real and predicted dynamic characteristics. Therefore, it is necessary to improve these models in order to achieve a better fit. This paper presents a systematic three-step procedure to update the finite element (FE) models of machine tools with numerous uncertainties in connections, which integrates statistical, numerical, and experimental techniques. The first step is the gradual application of fractional factorial designs, followed by an analysis of the variance to determine the significant variables that affect each dynamic response. Then, quadratic response surface meta-models, including only significant terms, which relate the design parameters to the modal responses are obtained. Finally, the values of the updated design variables are identified using the previous regression equations and experimental modal data. This work demonstrates that the integrated procedure gives rise to FE models whose dynamic responses closely agree with the experimental measurements, despite the large number of uncertainties, and at an acceptable computational cost.

Robust Design Applied to Concurrent Parameter and Tolerance Selection

2000 ◽  
Author(s):  
Rahul Gupta ◽  
Chang-Xue Jack Feng
Keyword(s):  
Data Analysis ◽  
Factorial Design ◽  
Robust Design ◽  
Statistical Data ◽  
Fractional Factorial Design ◽  
Fractional Factorial ◽  
Design Approach ◽  
Design Stage ◽  
Design Parameters ◽  
Statistical Data Analysis

Abstract This research discusses the robust design method for reducing cost and improving quality using the fractional factorial design approach. Robust design is proposed by Professor Genichi Taguchi to determine the optimum configuration of design parameters for better performance, higher quality and lower cost. The philosophy Taguchi recommends is sound and should be included in the quality improvement process of any organization. However, some methods of statistical data analysis and some approaches to the design of experiments, which he advocates, are unnecessarily complicated and sometimes ineffective. His sound engineering concepts can be combined with more efficient and effective experimental design and statistical data analysis methods. This is demonstrated by simultaneously optimizing the nominal value and the tolerances for a nonlinear RL electric circuit using the fractional factorial design approach instead of the Taguchi orthogonal array approach. Another contribution of this research is the incorporation of manufacturing cost data into the design stage.

scholarly journals Effect of Different Design Parameters on the Cyclic Response of Reduced Beam Sections (RBS) Moment Connections

2021 ◽  
Author(s):  
Syed Asad Abbus Naqvi
Keyword(s):  
Sensitivity Analysis ◽  
Statistical Design ◽  
Fractional Factorial ◽  
Design Parameters ◽  
Dissipated Energy ◽  
Northridge Earthquake ◽  
Initial Stiffness ◽  
Moment Connections ◽  
Cyclic Response ◽  
Rbs Connections

After the 1994 Northridge earthquake, research has been conducted to develop new types of beamcolumn moment connections, such as Reduced Beam Section (RBS) connections. This study performs a sensitivity analysis of the cyclic response of RBS connections using detailed finite element simulation. The significance of the effect of twenty-one factors is assessed using a statistical design of experiment method. The input factors are related to the material properties or the geometry of the beam-column connection. A two-level fractional factorial design is used to create factor combinations for the sensitivity analysis. The cyclic response of RBS connections is assessed in terms of five response variables, including: the total dissipated energy, initial stiffness, strength degradation rate, maximum moment capacity and rupture index at 7.5% storey drift. The sensitivity analysis results show that the beam depth has the greatest influence on the cyclic response of RBS connections.

FEATURES OF APPLICATION OF SMALL RECONNAISSANCE ROBOT

2019 ◽  
pp. 29-38 ◽  
Author(s):  
R. Zinko ◽  
P. Kazan ◽  
D. Khaustov ◽  
O. Bilyk
Keyword(s):  
Mathematical Model ◽  
Armed Forces ◽  
Climatic Conditions ◽  
Design Stage ◽  
Experimental Sample ◽  
Single Trial ◽  
Test Cycle ◽  
Military Equipment ◽  
The Mathematical Model ◽  
Human Losses

A small intelligence robot (SSR) is a special military intelligence means. It is used to obtain information about the enemy - the collection of intelligence, the search for targets and target indication, observation of the situation, etc. The use of a small intelligence robot is assumed in various natural and climatic conditions: in temperate terrain, on soils with low bearing capacity, at low temperatures, in the desert, on sandy and marshy soils, on rocky soils, in elevated temperature and dustiness of air, and also in conditions highlands In the article an overview of modern developments of remotely controlled robotic military complexes, principles of their construction and perspective directions of development in the armed forces are reviewed. The issues of robotization of existing weapons and military equipment are considered. Every sample of a SSR used in combat action must possess all combat characteristics at once in an optimal ratio between them, ensuring its maximum effectiveness. Ignoring any of the properties or enhancing one property at the expense of others will not enable the full realization of the small surveillance robot. It is reasonable to select the relevant properties at the design stage, using the possibilities of mathematical modeling. The set of tactical and technical characteristics of the SSR allowed forming this. Its characteristics determine the scope and possibilities of application. The mathematical model of the SSR motion is written in the Matlab Simulink environment. Recorded mathematical model of SSR motion, formed single test cycle and input data allowed to conduct computer simulation of motion in possible conditions of operation of small surveillance robot.The single trial cycle presented contains a set of individual sites and reproduces the testing test cycle of a real polygon. On the basis of the developed tactical and technical characteristics of the SSR, the experimental sample was made. An example of the use of SSR for the intelligence of the settlement and at keeping the node of barriers has been provided. The efficiency of performing intelligence units’ tasks and reducing the risk of human losses are shown.

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