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Taşıtlara etkiyen kuvvetler ve taşıt titreşimleri

Taşıtlara etkiyen kuvvetler ve taşıt titreşimleri

##### Dosyalar

##### Tarih

1995

##### Yazarlar

Çelikkaya, Ruhi

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

##### Özet

Bu çalışmada, lastik tekerlekli araçların dinamiği ele alına rak, hareket halindeki bir araca etkiyen kuvvetler incelenmiş, ta şıt titreşimleri ve geometrik yol düzgünsüzlerinin hesaplama ve öl çüm yöntemleri hakkında bilgiler verilmiştir. Birinci bölümde konuya giriş yapılarak problem tanıtılmıştır. İkinci bölümde araç dinamiği hakkında temel bilgiler verilmiş, hareket halindeki bir araca etkiyen kuvvetler tanıtılmıştır. Üçüncü bölümde lastik tekerlekli bir araçta motorun devir sa yısı ve momenti ile diferansiyel ve vites kutusunun çevrim oranla rından faydalanılarak tekerlek momenti, tekerlek çevre kuvveti ve tekerlek hızının bulunması gösterilmiş ve örnek bir kamyon için bu değerler hesaplanmıştır. Dördüncü bölümde seyir dirençleri tanıtılarak hesaplanma yön temleri gösterilmiş ve örnek kamyon için seyir dirençleri hesaplana rak seyir diyagramı çizilmiştir. Seyir dirençlerinin diğer etkenle rin yanısıra özellikle taşıdın ağırlığı ve hızıyla arttığı ve yolun özelliklerinden de çok etkilendiği ortaya çıkmıştır. Beşinci bölümde lastik tekerlekli araçların altı serbestlik dereceli bir yay-kütle sistemi olduğu kabulüyle taşıt titreşimleri incelenerek titreşim frekansının hesaplanması gösterilmiş, bu fre kansı hesaplayan bilgisayar programı verilerek örnek bir taşıt için hesaplanmıştır. İnsan organlarının öz frekans sınırları içinde bu lunan titreşimler (2-10 Hz arası) tehlikeli olmaktadır. Altıncı bölümde araç dinamiği, seyir dirençleri ve taşıt titre şimlerini önemli ölçüde etkileyen geometrik yol düzgünsüzlükleri ele alınarak, bunların etkileri ve ölçüm yöntemleri hakkında bilgi veril miştir. Sonuç ve öneriler bölümünde ise seyir dirençlerini azaltmak için uygulanacak bazı tedbirlerle, geometrik yol düzgünsüzlükleri- nin ölçümünün öneminden bahsedilmiştir.

Researching vehicle dynamics is a v/ery important step to provide vehicle development. Vehicle dynamics examines the forces acting on a hihg-speed motor vehicle. Vehicle dynamics in its broadest sense encompasses all forms of conveyans-ships. airplanes, railroad trains, as well as rubber-tired vehicle. The principles involved in the dynamics of these many types of vehicles are divers and extensive. İn this thesis, vehicle dynamics is explained in basic terms, the forces acting on a high-speed motor and rubber tired vehicle are introduced, the forces where the tires contact the road and movement resistance are calculatedand movement diagram is drawn. After that, the vibrations of venicies are examined. The effects of the road surface roughness are explained and methods of road profile measuring systems are introduced. İt has often been said that the primary forces by which a high-Speed motor vehicle is controlled are developed in four patches- each the size of a man's hand-where the tires contact the road. This is indeed the case. A knowledge of the the forces and moments generated by pneumatic (rubber) tires at the ground is essential to understanding highway vehicle dynamics. Inasmuch as the performance of a vehicle-the motions accomplished in accelerating, braking and ride- is a response to forces imposed, much of the study of vehicle dynamics must involve the study of how and why the forces are produced. The dominant forces acting an a vehicle to control performance are developed by the tires against the road. Thus it becomes necessary to develop an intimate under standing of the behaviour of tires, characterized by the forces and moments generated over the broad range of conditions over which they operate studying tire performance without a thorough understanding of its significance to the vehicle is unsatisfying, as is the inverse. Understanding vehicle dynamics can be accomplished at two levels- the empirical and the analytical. The empirical understanding derives from trial and error by which one learns which factors influence vehicle performance, in which way, and under what conditions. -VII- The empirical method, however, can often lead to failure. Without a mechanistic understanding of how changes in vehicle design or properties affect performance, extrapolating past experience to new conditions may involve unknown factors which may produce a new result, defying the prevailing rules of thumb. For this reason (and because they are methodical by nature), engineers favor the analytical approach. The analytical approach attempts to describe the mechanics of interest based on the known laws of physics so that on analytical model can be established. In the simpler cases these models can be represented by algebraic or differential equations that relate forces or mutions of interest to control inputs and vehicle or tire properties. These equations then allow to evaluate the role of each vehicle property in the phenomenon of interest. The existance of the model thereby provides a means to identify the important factors, the way in which they operate, and under what conditions. The model provides a predictive capability as well, so that changes necessary to reach a given performance goal can be identified. It might be noted at this point that analytical methods also are not foolproof because they usually only approximate reality. As many have experienced, the assumtions that must be made to obtain manageable models may often prove fatal to an application of the analysis, and on occasion engineers have been found to be wrong. Therefore, it is very important for the engineer to understand the assumptions that have been made in modeling any aspect of dynamics to avoid these errors. In the past, many of shortcomings of analytical methods were a consequence of the mathematical limitations in solving problems. Before the advent of computers, analysis was only considered succesful if the "problem" could be reduced to a closed form solution. That is, only if the mathematical expression could be manipulated to a form which allowed the analyst to extract relationships between the variables of interest. To a large extent this limited the functionality of the analytical approach to solution of problems in vehicle dynamics. The existence of large numbers of components, systems, subsystems, and nonlinearities in vehicles made comprehensive modeling virtually impossible, and the only utility obtained came from rather simplistic models of certain mechanical systems, Tough useful, the simplicity of the models often constituted deficiencies that handicapped the engineering approach in vehicle development. Today with the computational power available in dekstop and mainframe computers, a major shortcoming of the analytical method has been overcome. It is now possible to assemble models (equations) for the behaviour of individual components of a vehicle that can be integrated in to comprehensive models of the overall vehicle, allowing simulation and evalution of its behaviour before being rendered in hardware. Such models can calculate performance that could not be solved for in the past. In cases where the engineer is uncertain of the importance of specific properties, those properties can be included in the model and their importance assessed by evaluating their influence on simulated behavior. This provides the engineer with a powerful new tool as a means to test our understanding of a -Will- complex system and investigate means of improving performance. In the end we are forced to confront all the variables that may influence the performans of interest, and recognize everything that is important. The subject of "vehicle dynamics"is concerned with the movements of vehicles -automobiles, trucks, buses and special purpose vehicles- on a road surface. The movements of interest are acceleration and braking, ride and turning. Dynamic behavior is determined by the forces imposed on the vehicle from the tires, gravity, and aerodynamics. The vehicle and its components are studied to determine what forces will be produced by each of these sources at a particular maneuver and trim condition, and how the vehicle will respond to these forces. For that purpose it is essential to establish a rigorous approach to modeling the system and the conventions that will be used to describe motions. A motor vehicle is made up of many components distributed within its exterior envelope. Yet for many of the more elemantary analyses applied to it, all components move together. For acceleration, braking, and most turning analyses, one mass is sufficient. For ride analysis it is often necessary to treat the wheels as separate lumped mass. For single mass representation the vehicle is treated as a mass concentrated at its center of gravity (CG) as shown below. SAE Vehicle Axis system. The point mass at the CG with appropriate rotational moments of inertia, is dynamically equivalent to the vehicle itself for all motions in which it is reasonable to assume the vehicle to be rigid. On-board, the vehicle motions are defined with reference to a right-hand orthogonal coordinate system (the vehicle fixed coordinate system) which originates at the CG and travels with the vehicle. By SAE convention the coordinates are: ?IX- x- Forward and onthe longitudinal plane ut symmetry y- Lateral out the right side of the vehicle z- Downward with respect to the vehicle p- Roll velocity about the x axis q- Pitch velocity about the y axis r- Yaw velocity about the z axis Vehicle motion is usually described by the velocities (forward, lateral, vertical, roll, pitch and yaw) with respect to the vehicle fixed coordinate system, where the velocities are referenced to the earth fixed coordinate system. Vehicle attitude and trajectory through the course of a maneuver are defined with respect to a right hand orthogonal axis system fixed on the earth. It is normally selected to coincide with the vehicle fixed coordinate system at the point where the maneuver is started. The coordinates are shown below. X A Vehicle in an Earth Fixed Coordinate System X- y- 2- «. V- B- Forward travel Travel to the right Vertical travel Heading angle (angle between x and X in the ground plane) Course angle (angle between the vehicle's velocity vector and X axis) Sideslip angle (angle between x axis and and the vehicle velocity vector) The fundamental law from which most vehicle dynamics analyses begin in the second law formulated by Sir Isaac Newton (1642-1727). The law applies to both translational and rotational systems. -X- The sum of the external forces acting on a body in a given direction is equal to the product of its mass and the acceleration in that direction (assuming the mass is fixed). These forces called as translational systems and they are calculated as below: F = m. a x x where: F = Forces in the x direction x m = Mass of the body a = Acceleration in the x direction The sum of the torques acting on a body about a given axis is equal to the product of its rotational moment of inertia and the rotational acceleration about that axis. These forces are called as rotational systems and they are calculated as below: T = 1.* X XX x where T 'x = Torques about the x-axis I = Moment of inertia about the x-axis xx « - Acceleration about the x axis, ^x Newton's Second Law is applied by visualing a boundary around the body of interest, the appropriate forces and/or moments are. substituted at each point of contact with the outside world, along with any gravitational forces. Newton's Second Law can be written for each of the three independent directions. Determining the axle loadings on a vehicle under arbitrary conditions is a first simple application of Newton's Second Law. It is an important first step in analysis of acceleration and braking performance because the axle loads determine the tractive effort obtainable at each axle, affecting the acceleration, gradeability, maximum speed, and drawbar effort. Consider the vehicle below, in which most of the significant forces on the vehicle are shown. -XI- Arbitrary Furces acting on a vehicle Ul is the weight of the vehicle acting at its CG with a magnitude equal to its mass times the accaleration of gravity. On a grade it may have two components, a cosine component which is perpendicular to the road surface and a sine companent parallel to the road. If the vehicle is accelerating along the x*oad, it is convenient to represent the effect by an equivalent inertial force known as a "d'Alembert Force" denoted by A. W/g. a acting at the center of gravity opposite to the directrun of the acceleration. 7\ represents effects of the rotational mass and is between 1,1 and 1,6. The tires will experience a force normal to the road, denoted by Wh and W., representing the dynamic weights carried on the front and rear wheels. Tractive forces F.. k and F..., or rolling resistance forces WR m and WR. may act in the ground plane in the tire contact patch. W, is the aerodynamic force acting on the body of the vehicle. It may be represented as acting at a point above the ground indicated by the height, h or by a longitudinal force of the same magnitude in the ground plane with an associated moment (the aerodynamic pitching moment) equivalent to W. times h_. -XII- W and w are vertical and longitudinal forces acting ç,x ç,z at the hitch pointwhen the vehicle is towing a trailer. The reason of the force acting on a vehicle and vehicle and vehicle vibrations is road surface roughness. Certain aspects such as life time of the road, driving, safety, comfort, energy consumption and life time of vehicles are all influenced by the road surface roughness. Shock and vibration from the road have an effect on the ride quality, damage to the suspension and the bady, etc. Therefore, road profile measurement is a very important step preceding vehicle development. Measuring of the sectional road profile in the direction of the vehicle's run is a particular necessity. This sectional road profile herein is abbreviated to road profile or profile. In this thesis, the effects of road surface roughness, in other words the variations of road surface level, on vehicles and on the road itself due to the produced vibrations are investigated. Only the roughness in the longitudinal direction is considered and the lateral direction roughnesses are ignored. Measured characteristic parameters describing the surface profile have been stated and particularly the measurement techniques providing information for the calculation of vehicle vibrations have been investigated. The measurement methods of road profiles are developing. The best result is abtained by the method using four laser displacement sensors and an optical speed.

Researching vehicle dynamics is a v/ery important step to provide vehicle development. Vehicle dynamics examines the forces acting on a hihg-speed motor vehicle. Vehicle dynamics in its broadest sense encompasses all forms of conveyans-ships. airplanes, railroad trains, as well as rubber-tired vehicle. The principles involved in the dynamics of these many types of vehicles are divers and extensive. İn this thesis, vehicle dynamics is explained in basic terms, the forces acting on a high-speed motor and rubber tired vehicle are introduced, the forces where the tires contact the road and movement resistance are calculatedand movement diagram is drawn. After that, the vibrations of venicies are examined. The effects of the road surface roughness are explained and methods of road profile measuring systems are introduced. İt has often been said that the primary forces by which a high-Speed motor vehicle is controlled are developed in four patches- each the size of a man's hand-where the tires contact the road. This is indeed the case. A knowledge of the the forces and moments generated by pneumatic (rubber) tires at the ground is essential to understanding highway vehicle dynamics. Inasmuch as the performance of a vehicle-the motions accomplished in accelerating, braking and ride- is a response to forces imposed, much of the study of vehicle dynamics must involve the study of how and why the forces are produced. The dominant forces acting an a vehicle to control performance are developed by the tires against the road. Thus it becomes necessary to develop an intimate under standing of the behaviour of tires, characterized by the forces and moments generated over the broad range of conditions over which they operate studying tire performance without a thorough understanding of its significance to the vehicle is unsatisfying, as is the inverse. Understanding vehicle dynamics can be accomplished at two levels- the empirical and the analytical. The empirical understanding derives from trial and error by which one learns which factors influence vehicle performance, in which way, and under what conditions. -VII- The empirical method, however, can often lead to failure. Without a mechanistic understanding of how changes in vehicle design or properties affect performance, extrapolating past experience to new conditions may involve unknown factors which may produce a new result, defying the prevailing rules of thumb. For this reason (and because they are methodical by nature), engineers favor the analytical approach. The analytical approach attempts to describe the mechanics of interest based on the known laws of physics so that on analytical model can be established. In the simpler cases these models can be represented by algebraic or differential equations that relate forces or mutions of interest to control inputs and vehicle or tire properties. These equations then allow to evaluate the role of each vehicle property in the phenomenon of interest. The existance of the model thereby provides a means to identify the important factors, the way in which they operate, and under what conditions. The model provides a predictive capability as well, so that changes necessary to reach a given performance goal can be identified. It might be noted at this point that analytical methods also are not foolproof because they usually only approximate reality. As many have experienced, the assumtions that must be made to obtain manageable models may often prove fatal to an application of the analysis, and on occasion engineers have been found to be wrong. Therefore, it is very important for the engineer to understand the assumptions that have been made in modeling any aspect of dynamics to avoid these errors. In the past, many of shortcomings of analytical methods were a consequence of the mathematical limitations in solving problems. Before the advent of computers, analysis was only considered succesful if the "problem" could be reduced to a closed form solution. That is, only if the mathematical expression could be manipulated to a form which allowed the analyst to extract relationships between the variables of interest. To a large extent this limited the functionality of the analytical approach to solution of problems in vehicle dynamics. The existence of large numbers of components, systems, subsystems, and nonlinearities in vehicles made comprehensive modeling virtually impossible, and the only utility obtained came from rather simplistic models of certain mechanical systems, Tough useful, the simplicity of the models often constituted deficiencies that handicapped the engineering approach in vehicle development. Today with the computational power available in dekstop and mainframe computers, a major shortcoming of the analytical method has been overcome. It is now possible to assemble models (equations) for the behaviour of individual components of a vehicle that can be integrated in to comprehensive models of the overall vehicle, allowing simulation and evalution of its behaviour before being rendered in hardware. Such models can calculate performance that could not be solved for in the past. In cases where the engineer is uncertain of the importance of specific properties, those properties can be included in the model and their importance assessed by evaluating their influence on simulated behavior. This provides the engineer with a powerful new tool as a means to test our understanding of a -Will- complex system and investigate means of improving performance. In the end we are forced to confront all the variables that may influence the performans of interest, and recognize everything that is important. The subject of "vehicle dynamics"is concerned with the movements of vehicles -automobiles, trucks, buses and special purpose vehicles- on a road surface. The movements of interest are acceleration and braking, ride and turning. Dynamic behavior is determined by the forces imposed on the vehicle from the tires, gravity, and aerodynamics. The vehicle and its components are studied to determine what forces will be produced by each of these sources at a particular maneuver and trim condition, and how the vehicle will respond to these forces. For that purpose it is essential to establish a rigorous approach to modeling the system and the conventions that will be used to describe motions. A motor vehicle is made up of many components distributed within its exterior envelope. Yet for many of the more elemantary analyses applied to it, all components move together. For acceleration, braking, and most turning analyses, one mass is sufficient. For ride analysis it is often necessary to treat the wheels as separate lumped mass. For single mass representation the vehicle is treated as a mass concentrated at its center of gravity (CG) as shown below. SAE Vehicle Axis system. The point mass at the CG with appropriate rotational moments of inertia, is dynamically equivalent to the vehicle itself for all motions in which it is reasonable to assume the vehicle to be rigid. On-board, the vehicle motions are defined with reference to a right-hand orthogonal coordinate system (the vehicle fixed coordinate system) which originates at the CG and travels with the vehicle. By SAE convention the coordinates are: ?IX- x- Forward and onthe longitudinal plane ut symmetry y- Lateral out the right side of the vehicle z- Downward with respect to the vehicle p- Roll velocity about the x axis q- Pitch velocity about the y axis r- Yaw velocity about the z axis Vehicle motion is usually described by the velocities (forward, lateral, vertical, roll, pitch and yaw) with respect to the vehicle fixed coordinate system, where the velocities are referenced to the earth fixed coordinate system. Vehicle attitude and trajectory through the course of a maneuver are defined with respect to a right hand orthogonal axis system fixed on the earth. It is normally selected to coincide with the vehicle fixed coordinate system at the point where the maneuver is started. The coordinates are shown below. X A Vehicle in an Earth Fixed Coordinate System X- y- 2- «. V- B- Forward travel Travel to the right Vertical travel Heading angle (angle between x and X in the ground plane) Course angle (angle between the vehicle's velocity vector and X axis) Sideslip angle (angle between x axis and and the vehicle velocity vector) The fundamental law from which most vehicle dynamics analyses begin in the second law formulated by Sir Isaac Newton (1642-1727). The law applies to both translational and rotational systems. -X- The sum of the external forces acting on a body in a given direction is equal to the product of its mass and the acceleration in that direction (assuming the mass is fixed). These forces called as translational systems and they are calculated as below: F = m. a x x where: F = Forces in the x direction x m = Mass of the body a = Acceleration in the x direction The sum of the torques acting on a body about a given axis is equal to the product of its rotational moment of inertia and the rotational acceleration about that axis. These forces are called as rotational systems and they are calculated as below: T = 1.* X XX x where T 'x = Torques about the x-axis I = Moment of inertia about the x-axis xx « - Acceleration about the x axis, ^x Newton's Second Law is applied by visualing a boundary around the body of interest, the appropriate forces and/or moments are. substituted at each point of contact with the outside world, along with any gravitational forces. Newton's Second Law can be written for each of the three independent directions. Determining the axle loadings on a vehicle under arbitrary conditions is a first simple application of Newton's Second Law. It is an important first step in analysis of acceleration and braking performance because the axle loads determine the tractive effort obtainable at each axle, affecting the acceleration, gradeability, maximum speed, and drawbar effort. Consider the vehicle below, in which most of the significant forces on the vehicle are shown. -XI- Arbitrary Furces acting on a vehicle Ul is the weight of the vehicle acting at its CG with a magnitude equal to its mass times the accaleration of gravity. On a grade it may have two components, a cosine component which is perpendicular to the road surface and a sine companent parallel to the road. If the vehicle is accelerating along the x*oad, it is convenient to represent the effect by an equivalent inertial force known as a "d'Alembert Force" denoted by A. W/g. a acting at the center of gravity opposite to the directrun of the acceleration. 7\ represents effects of the rotational mass and is between 1,1 and 1,6. The tires will experience a force normal to the road, denoted by Wh and W., representing the dynamic weights carried on the front and rear wheels. Tractive forces F.. k and F..., or rolling resistance forces WR m and WR. may act in the ground plane in the tire contact patch. W, is the aerodynamic force acting on the body of the vehicle. It may be represented as acting at a point above the ground indicated by the height, h or by a longitudinal force of the same magnitude in the ground plane with an associated moment (the aerodynamic pitching moment) equivalent to W. times h_. -XII- W and w are vertical and longitudinal forces acting ç,x ç,z at the hitch pointwhen the vehicle is towing a trailer. The reason of the force acting on a vehicle and vehicle and vehicle vibrations is road surface roughness. Certain aspects such as life time of the road, driving, safety, comfort, energy consumption and life time of vehicles are all influenced by the road surface roughness. Shock and vibration from the road have an effect on the ride quality, damage to the suspension and the bady, etc. Therefore, road profile measurement is a very important step preceding vehicle development. Measuring of the sectional road profile in the direction of the vehicle's run is a particular necessity. This sectional road profile herein is abbreviated to road profile or profile. In this thesis, the effects of road surface roughness, in other words the variations of road surface level, on vehicles and on the road itself due to the produced vibrations are investigated. Only the roughness in the longitudinal direction is considered and the lateral direction roughnesses are ignored. Measured characteristic parameters describing the surface profile have been stated and particularly the measurement techniques providing information for the calculation of vehicle vibrations have been investigated. The measurement methods of road profiles are developing. The best result is abtained by the method using four laser displacement sensors and an optical speed.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1995

##### Anahtar kelimeler

Otomotiv endüstrisi,
Taşıtlar,
Titreşim,
Automotive industry,
Vehicles,
Vibration