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UDC 631.1.658
EFFICIENCY OF AGRICULTURAL MACHINERY BRAKING SYSTEMS.
MEASUREMENT ERRORS AND UNCERTAINTIES
Tukhtabayev Mirzokhid Akhmadjanovich NamMQI, PhD, dotsent, [email protected]
Tukhliev Gayratali Akhmadalievich NamMQI, PhD, dotsent, [email protected]
Abstract. In article estimated uncertainty measurements of standard on braking distance that as a result of acceptable measurement errors traverse speed of wheel technique is considered. Article contains the analysis of one of the main indicators of an estimation of brake effectiveness of the agricultural machinery, taken for standard. The most important indicator of brake effectiveness of agricultural machinery is the braking distance which standard values calculates on formulas which, per se, are indirect measurement method of a braking distance where measurand is the speed of V0 and so random error of its measurement causes to dispersion of rated measurements of a brake distance. To set a limit GOST 12.2.002.3-91 of an acceptable relative measurement error of speed ±0,03 (±3 to %) and it defines limits of an interval of concentration within which there could be calculated values of a braking distance which with the sufficient basis can be accepted to standard. Thereof a half interval with known probability is an indicator of measurement uncertainty and by the name «expanded uncertainty» U is on the international compulsory characteristics of measuring results. Resulted in calculated value tables of a braking distance conclusions are drawn: the standard of braking distance of self-propelled agricultural machines not less than for 25 % is more than to tractors. The relative error of indirect measurement of standard braking distance to be in limits of 4,5-5,3 % at tractors and 4,4-5,3 % at agricultural machines that defines an acceptable relative error of its measure instruments no more than 1 %. As value of expanded uncertainty follows, to accept values of an absolute measurement error of a path that conforms to confidence probability to 99,7 %.
Аннотация. В статье рассмотрена оценка неопределенности измерений норматива тормозного пути вследствие допустимых погрешностей измерения скорости движения колесной техники. Статья содержит анализ одного из основных показателей оценки эффективности тормозных систем сельхозтехники, принимаемого за норматив. Важнейшим показателем эффективности тормозных систем сельхозтехники является тормозной путь, нормативные значения которого рассчитываются по формулам, которые, по сути, являются косвенными методами измерения тормозного пути, где измеряемой величиной является скорость V0 и поэтому случайная погрешность её измерения вызывает рассеяние расчетных измерений тормозного пути. ГОСТ 12.2.002.3-91 устанавливает пределы допустимой относительной погрешности измерения скорости ±0,03 (±3 %) и это определяет границы интервала рассеяния, в пределах которого могут находиться расчетные значения тормозного пути, которые с достаточным основанием могут приниматься за норматив. Половина этого интервала с известной вероятностью является показателем неопределенности измерений и под названием «расширенная неопределенность» U является по международной обязательной характеристикой результатов измерений. Из приведенной таблицы расчетных значений тормозного пути сделаны выводы: норматив тормозного пути самоходных сельскохозяйственных машин не менее чем на 25 % больше, чем у тракторов. Относительная погрешность косвенного измерения норматива тормозного пути находиться в пределах 4,5-5,3 % у тракторов и 4,4-5,3 % у сельскохозяйственных
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AVTOMOBIL VA QISHLOQXO'JALIKMASHINALARI машин, что определяет допустимую относительную погрешность средств его измерений не более 1 %. В качестве значения расширенной неопределенности следует, принимать значения абсолютной погрешности измерения пути, что соответствует доверительной вероятности 99,7 %.
Annotasiya. Maqolada g'ildirakli transport vositalarining tezligini o'lchashda ruxsat etilgan xatolar tufayli tormoz masofasi standartining o'lchov noaniqligini baholash muhokama qilinadi. Maqolada standart sifatida qabul qilingan qishloq xo'jaligi texnikasining tormoz tizimlarining samaradorligini baholashning asosiy ko'rsatkichlaridan biri tahlili mavjud. Qishloq xo'jaligi mashinalarining tormoz tizimlari samaradorligining eng muhim ko'rsatkichi tormoz masofasi bo'lib, uning standart qiymatlari formulalar yordamida hisoblanadi, ular aslida tormoz masofasini o'lchashning bilvosita usullari bo'lib, o'lchangan qiymat V0 tezligi va shuning uchun uni o'lchashdagi tasodifiy xato hisoblangan tormoz masofasi o'lchovlarining tarqalishini keltirib chiqaradi. GOST 12.2.002.3-91 tezlikni o'lchashning ruxsat etilgan nisbiy xatosi chegaralarini belgilaydi ±0,03 (±3%) va bu tormoz masofasining hisoblangan qiymatlari joylashishi mumkin bo'lgan dispersiya oralig'ining chegaralarini belgilaydi, bu standart sifatida oqilona qabul qilinishi kerak. Ma'lum bo'lgan ehtimollik bilan bu intervalning yarmi o'lchov noaniqligining ko'rsatkichidir va "kengaytirilgan noaniqlik" nomi ostida U o'lchov natijalarining xalqaro miqyosda majburiy xarakteristikasi hisoblanadi. Hisoblangan tormoz masofasi qiymatlarining berilgan jadvalidan xulosalar chiqariladi: o'ziyurar qishloq xo'jaligi mashinalari uchun tormoz masofasi standard traktorlarga qaraganda kamida 25% ko'proq. Tormoz masofasi standartini bilvosita o'lchashning nisbiy xatosi traktorlar uchun 4,5-5,3% va qishloq xo'jaligi mashinalari uchun 4,4-5,3% oralig'ida bo'lib, bu uning o'lchash vositalarining 1% dan ko'p bo'lmagan ruxsat etilgan nisbiy xatosini aniqlaydi. Kengaytirilgan noaniqlik qiymati sifatida 99,7% ishonch ehtimoliga to'g'ri keladigan yo'lni o'lchashning mutlaq xatosi qiymatlarini olish kerak.
Keywords: uncertainty, standard, confidence level, dispersion value, expanded uncertainty, admissible error, braking distance, traverse speed.
Ключевые слова: неопределенность, норматив, доверительный уровень, рассеяние значений, расширенная неопределенности, допустимая погрешность, тормозной путь, скорость движения.
Introduction. Road tests of the efficiency of the brake systems of tractors, self-propelled agricultural machines and tractor trains are in the sphere of labor safety standards and are mandatory for certification of equipment [1-6]. The most important indicator of the efficiency of the brake systems of wheeled vehicles is the braking distance B, the standard values of which are calculated using the formula [7]:
V2
SS=ASV0 + 00
26Js
where: Ss - standard value (standard) of braking distance, m; V0 - speed at the start of braking, km/h;
As - coefficient characterizing the response time of the braking system; js - coefficient characterizing the standard deceleration during braking. Standard values of the coefficients for all types of tractors are the same as for all types of self-propelled agricultural machinery. Tests of the braking systems of tractors and self-propelled agricultural machinery are carried out under steady-state driving conditions at the maximum design speed [8], and the standard braking distance is calculated using the following formulas [7]: a) for tractors
V 2
Ss =0,15 • V0 + ; (2)
s 0 116
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b) for self-propelled agricultural machinery
V2
Ss=0,18 • V0 + V. (3)
s 0 90
For tractor trains (a tractor with one or more trailers), there is no standard braking distance and it is considered reliable for braking systems to ensure stopping and holding on a slope of -12% [7].
The formula for determining the standard braking distance is, in fact, an indirect method of its measurement, where the measured value is only the speed and therefore the error in its measurement causes dispersion, i.e. uncertainty of the calculated values.
GOST [8] establishes the limits of permissible error in measuring speed, in the form of a relative error of ±0.03 (±3%) and this allows us to determine the boundaries of the range within which the calculated values of the braking distance may be located, which with sufficient reason can be taken as the standard. Since the values of the errors in measuring speed have signs of ±, then the calculated values of the standard within the range will be symmetrically located around the average value.
Modern requirements for the presentation of measurement results necessitate the determination of the expanded uncertainty, i.e. half the range of possible values with the specified confidence level. When testing equipment for safety, the confidence level (reliability) is assumed to be high, and even greater than one, and therefore the expanded uncertainty can be equated with high reliability to the values of absolute maximum errors in measuring the braking distance with a reliability of 99.7.
All this corresponds to the term expanded uncertainty [9], and the limits of the range of dispersion of the calculated values allow us to determine the expanded uncertainty of the values of the braking distance standard and, as is customary in applied metrology, the limit values of the absolute and relative errors of indirect measurement of the braking distance, calculated using the above formulas (2) and (3).
The table shows the calculated values characterizing the dispersion of the values of the braking distance standard and the error of the indirect measurement taken as the standard.
Table
Dispersion of braking distance standards for agricultural machinery
Types of agricultural machinery Initial braking speed Vcp, (km/h) Scattering of standard values Sn at V0=Vcp (1 ± 0.03), m Error of indirect measurement of braking distance calculated using formulas (2) and (3)
Lower bound Upper bound Average value Absolute, (±m) Relative, (±%)
Tractors 15 4,0 4,38 4,19 0,19 4,5
20 6,15 6,75 6,45 0,3 4,6
30 11,7 12,9 12,3 0,6 4,9
40 18,8 20,8 19,8 1,0 » 5,0
50 27,5 30,6 29,0 1,55 5,3
Self-propelled agricultura l machines 15 4,97 5,43 5,2 0,23 4,4
20 7,67 8,42 8,0 0,37 4,6
30 14,6 16,2 15,4 0,8 5,2
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40 23,7 26,3 25,0 1,3 5,2
50 34,9 38,8 36,8 1,95 5,3
Results and Analysis
The following can be seen from the table:
At the same driving speeds, the standard braking distance of self-propelled agricultural machines is at least 25% greater than that of tractors.
The error in speed measurement significantly affects the dispersion of the values of the standard braking distance, so the values of the relative error of indirect measurement of the braking distance taken as the standard are 4.5-5.3%.
The process of testing to assess the effectiveness of braking systems comes down to measuring the actual values of the braking distance, the results of which should not exceed its standard [10-13]. Therefore, the error of the means of measuring the braking distance should, according to modern requirements, be five times less than the error of indirect measurement taken as the standard, i.e. no more than 1%.
Conclusions. The values of the relative error of the result of calculating the braking distance standard, as an indirect measurement of it, are within the range of 4.5 -5.3%. The error of the means of measuring the braking distance should be no more than 1%. The values of the absolute error of measuring the braking distance with a confidence level of 99.7 correspond to the value of the expanded uncertainty.
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Scientific Journal Of Mechanics And Technology ISSN 2181-158Х, Volume 5, Issue 3, Special Issue 2024 AVTOMOBIL VA QISHLOQXO'JALIKMASHINALARI
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