Geometrik yol düzgünsüzlükleri
The Description of road roughness
- Tez No: 21865
- Danışmanlar: DOÇ. DR. ALİ GÖKTAN
- Tez Türü: Yüksek Lisans
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Konfor, Taşıtlar, Yol pürüzlülüğü, Comfort, Vehicles, Road roughness
- Yıl: 1992
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Taşıt araştırmalarında en önemli yer işgal eden titreşimler aşikar olarak taşıtın üzerinden geçtiği yol pürüzlülüğünden kaynaklanır. Araştırma-Geliştirme çalışmalarından birisi olan“konfor iyileştirilmesi”, yüzeyden gelen titreşimler tarafından uyarılan yay, asılı kütle ve sönüm elemanlarının optimizasyonu ile gerçeklik kazanır. Bu sebeple taşıtların bir çok titreşim problemi yol üzerindeki iki paralel iz boyunca ölçülen yükseklikler için“direkt veya oto spectrum yoğunluk fonksiyonları”ve bu izler arasındaki“çapraz spektrum yoğunluk fonksiyonları”nın bilinmesini gerektirir. Yol pürüzlülüğünün tamamen gelişigüzel yükseklik lere haiz olduğu kabul edilerek analitik çözüm,“sto- kastik süreç”yardımıyla gerçekleştirilebilir. Bunun için iki paralel iz boyunca zaman dilimi (time domain) içerisinde bulunan“oto korelasyon”ve“çapraz korelasyon”f onsiyonlarının Fourier dönüşümü vasıtasıy la frekans dilimi (frequency domain ) içerisinde yer alan“direkt spektrum ve çapraz spektrum yoğunluk ”fonksiyonlarına dönüştürülmesi ve bunların fonksiyonu olan“ koherans ”fonksiyonunun elde edilmesi gereklidir. Bu çalışmada rastgele süreçlerle beraber bunların temelinde yatan olasılık ve dağılım teorileri kısaca tanıtılarak ve yüzey pürüzlügü tanımının detaylarına girilerek hesap yöntemleri tartışılacak ve her iki iz boyunca ölçümlerin zor olduğu durumlarda tek iz yardımıyla belirli kısıtlamala altında genelleme yapılmasına izin veren isotropi ve homojenlik kavramları üzerinde durulacaktır. -VIII
Özet (Çeviri)
SUMMARY THE DESCRIPTION OF ROAD ROUGHNESS With the problem of the comfort criteria of vehicle traversing on a road, engineers have become aware of a new aspect of vibrations. In order to determine the vehicle response function to excitation due to the road irregularities, it is necessary to examine the road roughness by treating the irregularities as a realizations of Random Process. As mentioned above, road surfaces appear amenable to representation as a realization of random process, provided that the effects of such occasional large irregularities are removed from the analysis. In the special case of stationary random excitations with a Gaussian distribution and zero-mean value, it is only necessary to compute the second order istatistics or in effect, spectral densities from the TIME-HISTORY of excitations. So, spectral discriptions of a road together with a knowledge of treversal velocity and of dynamics properties of the vehicle will provide the response characteristics of the vehicle, as will be explained later. In practical cases, the irregularities of the road surfaces can be treated as a realizations of an ensemble of similar surfaces and can be described by a probabilistic description of the ensemble, which is accoplished with statistical averaging. Any surface may be considered as shown in Figure 1. -* u Figure l.HeightCz} of surface measured on u-v plane -IXThe function z(u,v) may then be considered to be a single realization of the ensemble <z(u,v)>. for any single point Cu,v ) the expectation ECu,v ) may be obtained averaging zCu,v > over the ensemble: E Cu,v ) = < zCu,v )> 11 11 Where <> indicates ensemble averaging. In the same way, for any pair of points Cu^.v^) and Cu,v )the correlation function R Cu,v : u,v ) may be 11 1122' obtained by averaging the product zCu,v }.zCu,v ) over the ensemble. RCu,v : u, v )= <zCu,v ).z(u,v )> 1122 11 22 On account of great difficulties in data processing and measurement, We shall restrict our attention to surfaces whose distributions are Gaussian and whose mean are zero everywhere. In general, a random process is considered as a special process whose expected value is independent of u, v and zero throughtout the analysis and whose correlation function RCu,v :u,v ) depends only on the differences 1122 ^ J 6 =Cu -u 3, 6 =Cv -v ) not on the individual values of 121 121 u,v,u,v. Such processes are called homegenous process. Thus, equation of correlation becomes RC6,6 >= < z(u,v).z( u+&, v+6 )> 12 12 Here, it must be noted that RC6,6 > remains unchanged if the signs of 6 and S are both changed together. In the nature such processes are not periodic but an our studies, they can be assumed that they will be periodic when taking the measurement distance infinite. The correlation function can be easily computed by integrating z values when integrants approach infinity. The correlation equations mentioned above are called Cross-correlation functions which give the relationship between two racks. Putting respectively 6=0 and 6 = 0 gives auto-correlation functions which give the features -X-of respective tracks. By now, the correlation function which is described in Time-Domain are examined but we, in fact, concern with spectral decomposition. Spectral decomposition enable the periodic time functions to sparate into the harmonic functions of different amplitude's and frequencies. In case of non-periodic time records, these functions can be converted into their harmonics by employing FOURIER INTEGRAL. Thus, Cross-correlation and Auto-correlation functions can be described by spectral density which are in Frequency Domain and very useful in mean square estimation and determining response function of the vehicle. A two dimensional spectral density Sty,y 5 for the random surfaces may be defined by appropriate Fourier transformation of a two dimensional correlation function are given by + oo -i2rrC?'.6 + j“.6 ) Sir. r >= JS RCĞ,6 ).e * 1 2 2 dö.dö i2_coi2 12 Where Y and f wave numbers Cin cycles per unit lenght ) Reversely, + a=> İ2.n(.y -S + y.6 y RCÖ,6 >= SX S (.r >r >e * i 2 2 dr.dy 12-00*1*2 ' 1 * 2 These two relationships produce a Fourier transformation pair. These two-dimensional Fourier transformations are very complicated and require very long computational time. When track width is taken constant C v = 2b ), assuming RtlCu) = E<lCu5.1Cu +<&)> R (u) = E<r(u).r(u +6)> r r R, (u) = E<lCu>.rCu +6)> I r R Cu) = E-CrCu^.lCu +6)> r I -XI-direct and cross spectral densities become jco -2i^6 S, C?0 = S R, C6). e d6.»«s -21^6 S,, tr> = S R,, <6”>. e d6 S CjO ="/ R C6). e r r.no rr -2iy<5 d<5 Where lCu) = z(u,o) and rCu) = zCu,2b) may be track width C Figure 2). Here 2b *z Figure 2. Representation of two track- Besides the cross spectral density defined in frequency domain, another useful notion in description of road roughness is coherence function which indicate inner -dependence between two tracks. 2 Coherence function ft is given by S 6 'rtJLJlr S.S r r I I Assuming that cross-spectral density function are even function of wave number, coherence function becomes 62 = lr S.S rr 11 All these processes mentioned above can be realized only in case of being able to measure height differences XII-between right and left tracks. In practical cases there are some difficulties in measuring the road elevations. Therefore very acceptable consideration in description of road roughness are developed. This consideration besides homogenity, is isotropic road assumption which enables to describe the cross-spectral density from the direert spectral density along any single track. A homogenous Gaussian random surfaces are said to be isotropic when the correlation function is independent of the direction of the vector sperating the two points. Because of the homogenity > auto correlation function derived along any single track must be idendical to that taken along the paralel one. This implies that R C<5> = R,, (6) r-r 11 and corresponding spectral relationship S (y ) = S,, Cyy = s C^> rr' 11 » ' From Figure 3, isotropy requires RiCcostp, Ccos<p >= RCC) = R C J 6 + 2 ' 4b > -* u Figure 3. Representation of the vector sperating So the cross-spectral density function can be easily derived from the direct spectral density function along any single track. On account of this consideration, the coherence function becomes gCjO = s Cr> The possibility of describing the complete road surface by a single spectral density suggest the feasibility of approximating to that spectral density by a single analytical form. A general road description useful in examining the comfort characteristics of any -XIII-vehicle travelling on the road can be approximated by -w scfy = sir > <¦ - > Y -w sc r> < - > 2 >y s y o Where Siy ) is the roughness coefficient C value of the spectral density of discontinuity frequency y ). The measurement for typical road surfaces can be classified into various groups as illustrated on Table 1. in the Section 6. -XIV-
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