Taşıt titreşim analizi
Vibration analysis of a highway vehicle
- Tez No: 39274
- Danışmanlar: DOÇ.DR. AHMET GÜNEY
- Tez Türü: Doktora
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1994
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 146
Özet
ÖZET Bu çalışmada, hazırlanan bir bilgisayar programı yardımıyla ön ve arka aks tipi kombinasyonlarına göre farklı üç taşıt modeli için taşıt titreşim analizi; seyir emniyeti, ivme, konfor, koltuk ve tekerlek-gövde bağıl yay yolu kriterleri ile yapılmıştır. Bu amaçla önce yol pürüzlülüğü tanımlanmış ve yoldan gelen uyanlar iki izli yol teorisi ile ele alınmıştır. Burada yol pürüzlülüğü rastlantısal bir fonksiyondur. Herbir tekerleğe yoldan dikey uyarılar geldiği gibi, yolun çapraz eğiminden de kanber uyarılan gelmekte, arka aks belli bir zaman sonra ön aksı takip etmektedir. Sol ve sağ tekerlek dikey ve kanber uyarıları için kombine uyarılar tarif edilmiştir. Bu şekilde bir aks için 4 uyan fonksiyonu vardır ve belli bir a kadar faz farkıyla arka aks ta aynı 4 uyarıya maruz kalmaktadır. Bu uyanların etkiledikleri taşıt titreşim modeli üç boyutlu bir model olarak kurulmuştur. Üç taşıt modeli için hareket denklemleri çıkarılmış, bağımsız aks özellikleri açıklanmıştır. Herbir uyarıya ve aranan büyüklüklere ait büyütme fonksiyonları hesaplanmış ve çizilmiştir. Ön ve arka sol dinamik ve yatay dinamik tekerlek kuvvetleri, koltuk, gövde ön ve arka sol tekerlek üstü ivmeleri, taşıt y ve z ekseni etrafında dönme hareketi ivmeleri, gövde ön ve arka yan ivmeleri, gövde burulma açısı, koltuk, sol ön ve arka tekerlek-gövde bağıl yay yolu mesafesi efektif değerleri ile taşıt titreşim konfor kriteri olarak alman konfor sayıları hesaplanmıştır. Muhtelif parametrelerin taşıt titreşimlerine etkilerinin ne mertebede oldukları ve ihmal edilip edilemiyecekleri ortaya konmuştur. Yol pürüzlülüğü spektrum yoğunluğu, yol dalgalılığı, taşıt hızı, sabit ve frekansa bağlı lastik sönümü, ön ve arka aksta bulunan U formundaki bir denge çubuğu ve gövde burulma sertliğinin taşıt seyir emniyeti ile konforuna etkisi irdelenerek literatürde bu konudaki bir boşluk giderilmeye çalışılmıştır.0
Özet (Çeviri)
VIBRATION ANALYSIS OF A HIGHWAY VEHICLE This thesis called Vibration Analysis of A Highway Vehicle consists of sîx chapters, namely; Introduction, Description of Road Surface Roughness, Mathematical Model and Formulation, Dynamic Wheel Load Variations, Method of Solution for Differential Equations, Effective Values and Comfort Numbers and Evaluation of Results. The first chapter includes the description of the problem, evaluation criteria for the analysis and the literatüre survey related to the vehicle vibrations. The aim of this study is to make a three dimensional vibration analysis of a motor vehicle that has different front and rear axle systems. The evaluation criterias for this study are as follows; Front and rear left \vheel dynamic load variations ( PdinVl, PdinHı)- Front and rear left wheel lateral load variations (SdinVl, SdinHl). Seat accelerations (23). Front and rear left body accelerations över the front and rear left wheel (^2Vı> ^2Hı)- Yavv motion accelerations of the vehicle body (£2). Pitch motion accelerations of the vehicle body ((f>2)- Front and rear body lateral accelerations (y2V, y2H).. Body torsional motions (Vav'Van)- Seat, front and rear wheel suspension space requirement (2^, z^, z^m)- The assumptions made for this study are as follows; The vehicle is on a straight road and has a constant speed. The front and rear axles of the vehicle model have the same track width.. The spring and damping elements are linear.. Vehicle body mass is considered to be two parts, öne being front, the other rear mass and they are connected to each other with torsional spring and damping elements. The correlation functions between. two tracks depend on the track width. The wider the track width, the less the correlations.-VIBRATION ANALYSIS OF A fflGHWAY VEHICLE This thesis called Vibration Analysis of A Highway Vehicle consists of six chapters, namely; Introduction, Description of Road Surface Roughness, Mathematical Model and Formulation, Dynamic Wheel Load Variations, Method of Solution for Differential Equations, Effective Values and Comfort Numbers and Evaluation of Results. The first chapter includes the description of the problem, evaluation criteria for the analysis and the literatüre survey related to the vehicle vibrations. The aim of this study is to make a three dimensional vibration analysis of a motor vehicle that has different front and rear axle systems. The evaluation criterias for this study are as follows; Front and rear left wheel dynamic load variations (PdinVır PdinHı)- Front and rear left wheel lateral load variations (SdjnVl, SdinHJ. Seat accelerations (zj). Front and rear left body accelerations över the front and rear left wheel (^2Vı> ^2Hı)' Yaw motion accelerations of the vehicle body (£2). Pitch motion accelerations of the vehicle body ((p2)- Front and rear body lateral accelerations (y2V, y2H). Body torsional motions (VavVaH)- Seat, front and rear wheel suspension space requirement (z^L, z?^ Z2HL). The assumptions made for this study are as follovvs; The vehicle is on a straight road and has a constant speed.. The front and rear axles of the vehicle model have the same track width. The spring and damping elements are linear. Vehicle body mass is considered to be two parts, öne being front, the other rear mass and they are connected to each other with torsional spring and damping elements. The correlation functions between two tracks depend on the track width. The vvider the track width, the less the correlations.0If a three dimensional road shows the same characteristics having the same power spectrum, mean value and distribution, this is called isotropic road. According to isotropic road assumption, left and right tracks have the same power spectrum, but different road irregularities. *ta> ta = *hn hr = *hMhr The reason to descrîbe the combined road inputs is that it is not practical to compute öne track spectrum using the other. in the second chapter, road roughness and power spectrum density have been described as random functions and stochastic process. The road inputs are handled as two tracks and four inputs. The vehicle is subject to the vertical and canber road inputs and the rear axle follows the front axle after a certain time At. The combined road inputs have been given for the left and right wheel vertical and canber road excitations. in this study, depending on the front and rear axle combinations - free ör rigid axle- three 3-D vehicle models have been established. These models are; -Rigid front and rear axle vehicle vibration model (I). -Free front and rear axle vehicle vibration model (II). -Free front and rigid rear axle vehicle vibration model (III). A quarter vehicle model is adequate for arriving at a fundamental understanding of many of the issues. Hovvever, a full vehicle model is essential to reach more precise results and to find out whole vehicle vibrations because of the interactions that exist betvveen the vertical, pitch, roll and yaw motions of a vehicle. The differential equations of the vehicle vibration systems have been set up depending on the vehicle models. 13. differential equations for vehicle model I, 14 differential equations for II and 15 differential equations for vehicle model III. Before setting up the free axle vehicle model differential equations, free axle motion characteristics have been explained in detail due to complexity of the system. Short arm axle model has been taken into consideration as free axle model and in this model, it's possible to simulate the other free axles by changing the roll center height. it is intended to simulate Mc Pherson axle by taking the roll center height to be approximately O ground surface. in the fourth chapter, the dynamic and lateral dynamic wheel load variations and transformation functions of each excitation have been explained in detail.The fifth chapter is related to the solution method of the differential equations belong to the vehicle models I, II, III and the transformation matrbces are also mcluded in this chapter. The differential equations are divided into two groups which are symmetric and anti symmetric. The developed basic and general equation with respect to transformation functions of the evaluation criteria is given below; ~ReU~| TReTz -ImTz] fRez'l TReTh -ImThl rReh'1 u ==+ _ImUj [imTz ReTz J [imz'J [ImTh ReTh J'[lrah' J The calculation method of the effective values of the evaluation criteria such as wheel loads, accelerations, suspension space requirements and comfort value numbers are explained in this chapter. in this study, not only the accelerations have been taken into consideration as comfort evaluation criteria but also human sensitivity depending on frequency and comfort value numbers for seat, foot, hand, pitch and roll motions of the vehicle. Also total comfort value is given. The sbrth chapter is öne of the most important chapters, and deals with the following evaluation criteria: transformation functions, effectivity values, the effect of vehicle speed, road power spectrum density in QQ basic road frequency, vvaving exponent factor w, pneumatic tyres damping constant, anti roll bar, and vehicle body torsional stiffness on the vehicle vibrations. in the established vehicle models, anti symmetric excitations caused roll motions do not affect the vertical motions of the body center of gravity and symmetric excitations caused vertical symmetric motions do not affect the roll motions of the vehicle. That's why, vertical body accelerations över the left wheel coming from symmetric combined excitations (h^, KJ.), are proportional to body center vertical accelerations. And vertical accelerations of the body över the left wheel due to (h4, KA) are proportional to body roll accelerations. The same goes for symmetric and anti symmetric canber combined road excitations. z* Zî^ ^2 - -^J"^L ' ~~ hs hsKS K£ZfcLSV2Z*LS\j/2.5. --- hA2hAKA2 KA Only the transformation functions of the free front and rigid rear axle vehicle vibration systems have been included into the thesis in order not to be repetitive similar transformation functions. The effect of vehicle body torsional stiffness Ct to the vehicle vibrations has been shown in the transformation functions. it is possible to see the effect of the vehicle vibration model on the vibrations. in this context, Ct=0 represents 2-D vehicle model and Ct?tO represents 3-D model. As can be seen in figures in chapter 6, the vehicle body torsional stiffness does not effect the symmetric transformation functions and effective values. Its effect is only on the anti symmetric transformation functions and effective values. The dam'ping constant of the pneumatic tyres is included into the computations as O, 150 N s/m and frequency dependent. Damping constant is accepted to be 10 % of spring stiffness of the tyre and to be dependent on frequency. Including the damping constant of the pneumatic tyre into the differential equations as 10 % of its stiffness decreases dynamic wheel load and body accelerations by l %. The other important element in the vehicle dynamic systems is anti roll bars in either u ör z form. The main functions of the u form anti roll bar are to improve the turning and roll motion capability of the vehicle. in this study, the effect of the anti roll bars to the vehicle safety and comfort has been evaluated for the free front and rear axle vehicle model. Anti roll bar is considered in vehicle inodels in three variations: only in front; only in rear; and both in front and rear axles. The torsional stiffness values of the anti roll bar have been increased from 3000 to 15000 Nm/rad to see the effects on the vehicle vibrations. The results can be seen in the figures in chapter 6.6. According to these figures, anti roll bar decreases the dynamic wheel load variations and slightly increases the vehicle discomfort. But the effect is only trivial. in the last part of the sbcth chapter, the effect of the vehicle body torsional stiffness to the vibrations including body torsional damping constant are evaluated with a slight torsional damping. The body torsional stiffness constant Ct is taken to be, O, 25000, 50000 Nm/rad and approximately °°. The effective values, that is evaluation criteria have been found out for the Ct values. If Ct =0, there is no correlation between front and rear body axle systems. If Ct = «>, there is a full correlation between front and rear body-axle systems. The increase in the body torsional stiffness Ct, decreases both the dynamic wheel loads and accelerations. Actually, it affects the dynamic wheel loads and accelerations caused by anti symmetric excitations. The decreases in the vehicle vibration values lead to better comfort numbers. Ct does not affect the seat spring and suspension space distance. Finally, the following conclusions and recommendations have been reached. - As it has been stated, the free axle vehicles present better values compared to rigid axle vehicles in terms of dynamic wheel loads as an evaluation criteria for vehicle safety and road life time. But this disadvantage of rigid axle can be compensated by choosing the optimum spring and damping constants. - The lateral dynamic wheel loads of the rigid axle vehicle are higher than free axle vehicles due to the impossibility of choosing the roll center height near to the ground surface. For reasons caused by steering wheel vibrations, rigid axle is not preferred in front axle of the vehicles. - In order to find out the basic vibration characteristics, the simple vehicle vibration models such as quarter and semi vehicle models can be adequate, but, in order to reach more realistic and precise results, the vehicle models should be 3-D. The big difference between 2-D and 3-D models can be seen in tables of chapter 6.2. Here, Q = 0 represents 2-D and Ct = «> is used for 3-D vehicle models. - Power Spectrum Density in basic road frequency causes a linear increase in the lateral wheel loads. This increase in the dynamic wheel loads does not change linearly and depends on the level of increase in the Power Spectrum Density of the basic road frequency. - The change in the waving factor exponent w results in a linear increase in the dynamic and lateral dynamic wheel loads. - If the vehicle speed is gradually increased, the dynamic wheel loads proportionally increase and the lateral dynamic wheel loads decrease. These results are due to the increasing characteristics of the lateral wheel damping constant and decreasing characteristics of the Power Spectrum Density of camber excitations with the increasing speed. - Although not at an important level, anti roll bar decreases the dynamic wheel loads and does not affect the lateral dynamic wheel loads. (xiii)- The increase in the vehicle body torsional stiffness decreases the dynamic and lateral dynamic wheel loads. For that reason, body torsional stiffness has to be chosen as rigid as possible. - Seat spring and suspension space increases with Power Spectrum Density in Qq basic road frequency, waving factor w and vehicle speed. Pneumatic tyre damping constant, anti roll bar and body torsional stiffness do not affect the seat spring and suspension space. - The increase in Power Spectrum Density in basic road frequency decreases the vehicle comfort. But, as the waving factor w increases, seat accelerations decrease. Hand, foot, roll, pitch accelerations and total comfort values stay approximately the same. - If the vehicle speed is increased, the seat accelerations increase. The increase in vehicle speed has a slight effect on hand, roll and pitch accelerations. - To include in the calculations, a pneumatic tyre damping constant equal to 10 % of tyre stiffness, enhances more or less 1% of the vehicle comfort. - Anti roll bar does not have an important effect on the total vehicle comfort. - The increase in the vehicle body torsional stiffness does not affect the body yaw motion accelerations, but increases body front and rear lateral accelerations. - The change in the vehicle body torsional stiffness does not affect the dynamic wheel loads caused by symmetric road excitations. - In order to get better comfort values, the body torsional stiffness has to be increased as high as possible. - In modelling the vehicle vibration system and road roughness, even small parameters have to be considered in order to reach more realistic and accurate results. The data used in this study are given in appendix A. Mass M, spring C, damping K matrix and transformation and excitation and excitation transformation matrixes resulting from the chapters 3, 4, 5 are given in appendix B. (xv)
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