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METHODS AND MEANS OF THE ESTIMATION OF INDICATORS OF RELIABILITY OF MECHANICAL AND ELECTROMECHANICAL ELEMENTS OF DEVICES AND
SYSTEMS
V. Zhadnov •
Moscow State Institute of Electronics and Mathematics (Technical University), Moscow, Russia
e-mail: jadnov@mitme.ru
ABSTRACT
Features of the application of standards for evaluation (predict) the reliability of mechanical and electromechanical devices and systems are considered. The main characteristics of the models of operational failure rate of mechanical components and provides recommendations for their use are given. The use of software tools that implement the methods for calculating reliability, can cause significant difficulties with the reliability of initial data.
1. INTRODUCTION
Handbook "Reliability ERP" is the main source for the calculation of reliability indices of elements of sensors, devices and systems at the present time in Russia. The handbook is an official document of the Ministry of Defence of Russian Federation in accordance with standard (RDV 319.01.20-98 1998). Mathematical models of the operational failure rate electro-radio-products (ERP) and the numerical values of the coefficients are given in it. The survey provides data not only for performance reliability of electronic devices, such as integrated circuits, semiconductor devices, etc., and of electromechanical components (such as electrical machines of small capacity) and the purely mechanical components (connections, circuit boards, etc.).
Since the range of such elements is limited, so in practical calculations the reliability of the elements that are missing in the Handbook "Reliability ERP", not included and considers them an "absolutely reliable". However, this approach can lead (and leads) to a significant overestimation of the reliability of systems (Markin et al. 2010), primarily of test containing primary transducers (sensors). Evaluation of reliability of such systems requires taking into account not only the reliability of the electronic devices, but also a wide class of mechanical components (connections, details, etc.).
2. MODELS RELIABILITY OF MECHANICAL COMPONENTS
Mathematical models of operational failure rates are given in article (Shavykin & Petruhin 2006) for the following classes of mechanical connections, components, assemblies and equipment manufactured in Russia:
• Non-demountable fasteners
• Threaded fasteners
• Demountable fasteners
• Nodes of transmission of motion
• Bearings
• Seals and Gaskets
• Bellows and tubular springs
• Impeller flow sensors
• Membrane
• Pressure Gauges
• Vacuum gauges with tubular springs
• Springs, couplings, watch mechanisms All these models are as follows:
i
k=Ao n« i=i
where: Xs = operational failure rates of seals; Xo = base failure rate of seals; ai = multiplying factors which considers the effect on the base failure rate; I = number of multiplying factors.
In addition to mathematical models (formulas) in article (Shavykin & Petruhin 2006) also shows a table containing the numerical values of their coefficients. The possibility of using these models due to the fact that they are full copies of the "Procedure..." (Shavykin et al. 1998) in terms of mechanical parts, which at present applies to ROSATOM.
As an example we will consider class "Seals and Gaskets". For this class in article (Shaykin & Petrukhin 2006) the following mathematical model of operational failure rate is resulted:
X3 = k-«i•«„ (1)
where: XЭ = operational failure rate of seals; X0 = base failure rate of seals; a1 = multiplying factor which considers the effect of service conditions and etc. on the base failure rate; am = multiplying factor which considers the effect of type of a material on the base failure rate.
In turn, the multiplying factor a1 pays off on model:
«1 = k11 • k12 • k13 ■ k14 ■ k15, (2)
where: k11 = multiplying factor which considers the effect of service conditions, vibrating loadings and amortization on the base failure rate; k12 = multiplying factor which considers the effect of service conditions, shock loadings and amortization on the base failure rate; k13 = multiplying factor which considers the effect of type of a climate, presence of the conditioner, heating and premise hermetic sealing on the base failure rate; k14 = multiplying factor which considers the effect of a kind of equipment and quality of service on the base failure rate; k15 = multiplying factor which considers the effect of a kind of equipment and quality of manufacturing on the base failure rate.
Numerical values multiplying factors k11-k15 are given in tables. Due to the limited size of the article yourself a table full list here are not going to give only their fragments (see Table 1-4).
Table 1. Values of multiplying factors kn and ki2
Operating conditions kM (vibration) k]2 (strikes)
not amortized amortised not amortized amortised
Lab, instrument-making enterprises, assembly plants 1,0 1,0 1,0 1,0
Marine conditions 3,0 1,0 1,2 1,0
... ... ■ mm ■ ■■ ...
The equipment of rolling mills, forging hammers, presses 10,0 3,0 15,0 5,0
Table 2. Values of multiplying factor kp
Heated room Not heated room
Climate air conditioning sealed not sealed not
scaled sealed
Cold 1,0 1,0 1,2 1,2 2,0
Moderate, middle band 1,0 1,0 1,2 1,0 1,3
... ... ...
marine subtropical 1,1 - - 1,5 2,0
Table 3. Values of multiplying factors ki4 and ki5
Equipment A'u (service) Au (production)
Household 5,0 2,0
Management of individual units 1,0 1,0
... ... ...
Process control 0,8 0,5
Table 4. Values of i Material nultiplying factor am Temperature
20 °C 40 "C 60 °c 80 °C loo uc
Organic fibrous 1,0 1,5 2,0 4,0 8,0
Rubber 1,0 1,2 1,5 2,5 4,0
... ... ... ...
Fluoroplastic 1,0 1,0 1,0 1,0 1,2
Even a simple analysis of Tables 1-4 shows that the model (1) is of little use to solve practical problems of reliability. Indeed, the failure rate of the seals does not depend on their size, nor on the quantitative characteristics of the physical and mechanical properties of materials, etc.
For example, in the standard (TU 38 005 1166-98 1998) is defined more than 50 brands of rubber compounds with different physic-chemical properties and the calculation of the model (1) for all of them give the same failure rate (see Table 5)!
Fragment of the table the standard (TU 38 005 1166-98 1998) are as follows (see Table 5).
Table 5. Characteristics of rubber compounds
Mark rubber compound Operating conditions The main purpose of Relative tensile strength, n/m Elonga tion at break, % n/m Hardn ess, Shore unit
environment T, °C MPa kgs/sm2
«-14 HTA Air -45...+ 100 Molded rubber and rubber parts and immobile joints operating under a static strain 10,8 110 160 72-92
Oil AMT-10 60...+ 100
Ethanol -60...+70
/M 4-1 HTA Air -45...+ 100 Molded Rubber and rubber parts and immobile joints operating under a static strain 11,8 120 150 78-85
Ethanol -60...+70
... ... ... ... ... ... ...
//P/7-1354 HTA Air -70. ..+250 Shaped syringe electrical parts operating in the unstressed state, Amortisseur, Molded and non-sealing parts (rings, gaskets, etc.) for fixed joints 5,4 55 280 54-66
Air with high ozone -76...+125
The electric Held -60...+250
Lubrication HHHM HH-279 -60...+150
In other words, if the resulting failure rate calculations seals (or any other elements) will be high, the number of possible ways to enhance their security in the use of model (1) is limited, and, consequently, the possibility of implementation of relevant activities is unlikely or will require a large material costs.
And the "Procedure..." (Shavykin et al. 1998), and the standard TU 38 005 1166-98 were published in the same year. But the data presented in "Procedure." (Shavykin et al. 1998) almost entirely with the data of the Recommendation (RM 25 446-87 1987). From this it follows that the conduct of the calculation is based on data from 20-years old ago.
From this point of view of greater interest are the models listed in the American standard (NSWC-98/LE1 1998), developed by experts Naval Surface Warfare Center, or rather, its latest edition (NSWC-06/LE10 2006).
The standard includes mathematical models of operational failure rate for the following classes of mechanical equipment: Seals and Gaskets Springs Solenoids Contactors Valve assemblies, Bearings
Gears and Splines Actuators Pumps Fluid Filters Brakes and Clutches Compressors Electric Motors Accumulators, Reservoirs Threaded Fasteners mecanical Couplings Slider cranks mechanisms Sensors and Transducers. Shafts
Belt and chain drivers Fluid conductors
To give an idea of the mathematical models of operational failure rates present a model for the class "Seals and Gaskets":
1=1 ■ C ■ C ■ C ■ C ■ C ■ C ■ C ■ C (3)
/lSE SE,B ^P ^Q DL H F W ^ T N i VJ/
where: XSE = failure rate of seals in failures/million hours; XSE,B = base failure rate of seals, 2,4 failures/million hours; CP = multiplying factor which considers the effect of pressure on the base failure rate; Cq = multiplying factor which considers the effect of allowable leakage on the base failure rate; CDL = multiplying factor which considers the effect of seal size on the base failure rate; CH = multiplying factor which considers the effect of contact stress and seal hardness on the base failure rate; CF = multiplying factor which considers the effect of seat smoothness on the base failure rate; Cv = multiplying factor which considers the effect of fluid viscosity on the base failure rate; CT = multiplying factor which considers the effect of temperature on the base failure rate; CT = multiplying factor which considers the effect of contaminants on the base failure rate.
Even simple comparison of models (2) and (3) shows that models of standard (NSWC-06/LE10 2006) more exact, than resulted in article (Shavykin & Petruhin 2006). Besides, factors of these models also represent functions of the geometrical sizes, physic mechanical properties of materials, etc. For example, the formula for calculating the factor CH is shown below:
r M/C Y3
Ch =
(4)
0,55
v J
2. ^____,__,_______ n__/-2
where: M = Meyer hardness, lbs/in ; C = contact pressure, lbs/in .
It is obvious that application of models of standard (NSWC-06/LE10 2006) essentially increases labor input of "manual" calculations in comparison with article (Shavykin & Petruhin
2006). Therefore along with formulas for calculation of factors in it corresponding monograms (Figure 1 see) are resulted.
Figure 1. NSWC-06/LE10: Dependence of multiplying factor Ch on relation M/C.
These monograms may be helpful in justifying the choice of measures aimed at improving the reliability, because give a clear idea of the effect of each option on the magnitude of the coefficients and, consequently, the operational failure rate in general. However, these monograms rather to the tradition of information in handbooks on reliability than a means to facilitate the calculations, since with a large number of elements the complexity of calculations, even for simple models of article (Shavykin & Petruhin 2006) increases significantly.
Another feature of the standard (NSWC-06/LE10 2006) is that some elements are considered as a system. For example, the calculation of the failure rate of the electric motor is carried out according to the model:
AM — Abe + AJWJ + ABS + Aas + AST + Agr , (5)
where: XM = total failure rate of motor system, failures/million hours; XBE = failure rate of bearings, failures/million hours; XWI = failure rate of electric motor windings, failures/million hours; XBS = failure rate of brushes, failures/million hours; XAS = failure rate of the armature shaft, failures/million hours; XST = failure rate of the stator housing, failures/million hours; Xgr = failure rate of gears, failures/million hours.
As follows from (5), the calculation of the electric motor, you must first calculate the failure rate of the bearings and gears.
2. SOFTWARE FOR THE CALCULATION OF RELIABILITY
To automate the calculation of reliability of mechanical connections, parts, components and devices on models of article (Shavykin & Petruhin 2006) can be used system ASONIKA-K-ME, which is part of the software complex ASONIKA-K (Zhadnov et al. 2011). The main form of the interface of the user of system is resulted on Figure 2.
Figure 2. System ASONIKA-K-ME: the Interface of the user.
To automate the calculation of reliability of mechanical equipment on the models standard (NSWC-06/LE10 2006) developers provide a computer program MechReal (see Figure 3).
t<* Amrr+>) Add Tech «tic
M .1
3 I'WM
M •<*« PrcidUrf-ta 1 CMW» 1
Evw
6M> Code 1 Ph»tciF«ik»»fi«» 3«» l'nkilan
UtHl
1
V*1
Figure 3. Program MechReal: the Interface of the user.
It is natural that models of this standard are included and into structure of software (modules of Reliability Prediction) well-known manufacturers, such as PTC Corporate Headquarters (Relex visual studio), ReliaSoft Corporation (Lambda predict), ALD Ltd. (RAM Commander), Etc. (Stroganov et al. 2007). And, many are constructed of them in such a manner that allow to consider in one calculation as electronic devices, and mechanical elements, unlike system ASONIKA-K-ME and programs MechReal.
On Figure 4 is shown the interface of the user of program Lambda Predict of company ReliaSoft Corporation.
But practical application of these programs causes considerable difficulties that is connected not only (and not so much) with the English-speaking interface (Figure 3, 4 see), how many with search of the initial information. Therefore in standard (NSWC-06/LE10 2006) tables with "typical" values of parameters are resulted.
For example, a fragment of the table "typical" values of is maximum-admissible working temperatures (TR) of materials of Seal is shown below (see Table 6).
Figure 4. Program Lambda Predict: the Interface of the user. Table 6. Typical values of is maximum-admissible working temperatures of materials of seal
Comparing the first columns of Table 4 and 6 it is easy to notice that search of values is carried out not to concrete marks of materials, and to the more general classification signs. Since these tables are standard (NSWC-06/LE10 2006) and placed in modules "Prediction of Reliability", as stated above, it is clear that, despite the adequacy of the model, calculations with the this data source will be little different from the calculations on model article (Shavykin and Petrukhin, 2006) for accuracy
Therefore for maintenance of accuracy of calculations creation of the database containing all necessary help given (characteristics of materials, maximum-permissible operating modes etc.) is necessary. For the decision of this problem in structure of a help part of a database of the system ASONIKA-K-SCh such database has been added. On Figure 5 as an example the model of the data for a class "Bearings", created in Sybase PowerDesigner is resulted.
Feature of the developed base is that are stored in it not only numerical values, but also codes of mathematical models (formulas) on which calculation is carried out. In addition, the database stores brand materials and their characteristics are necessary for the calculation of the coefficients of models standard (NSWC-06/LE10 2006). For work with this database the system has been modified ASONIKA-K-SCh.
Feature of the developed database is that are stored in it not only numerical values, but also codes of mathematical models (formulas) on which calculation is carried out. In addition, the database stores brand materials and their characteristics are necessary for the calculation of the coefficients of models standard (NSWC-06/LE10 2006). For work with this database has been modified the system ASONIKA-K-SCh. On Figure 6 is shown the interface of the user of system which allows to carry out calculations of the products containing electronic devices and mechanical elements.
In addition, in the system ASONIKA-K-SCh were added to the model, listed in article (Shavykin and Petrukhin, 2006). Thus, the new version of system ASONIKA-K-SCh allows the do calculation of mechanical elements on models of standard (NSWC-06/LE10 2006) and article (Shavykin and Petrukhin, 2006).
Figure 5. Class "Bearings": model of the data.
Figure 6. System ASONIKA-K-SCh: the Interface of the user.
3. CONCLUSION
In the conclusion it is necessary to note the following. Even creation of a database doesn't remove all problems with the initial information for calculations. In the model standard (NSWC-06/LE10 2006) enter the variable parameters, depending on the application (allowable leakage, size of gasket, the pressure on the gasket, etc.). Already in itself calculation of these parameters is not a trivial problem and, despite an abundance of software of modeling physical process (mechanical, hydraulic, etc.), that under force only to professionals in area of mechanics, resistance of materials, etc.
In other words, calculation of reliability of such products can be hardly spent one expert. However program realization of system ASONIKA-K-SCh in technology "client-server" allows to carry out calculation of one product from different workstations (i.e. to involve in calculations so much experts, how many it is necessary) that will help to remove the specified problem partly.
REFERENCES
1. Markin A.V., Polesskey S.N., Zhadnov V.V. (2010). Methods of the estimation of mechanics elements reliability and electro mechanics of electronic means at early design stages. "Reliability" magazine, Vol. 33, No 2, pp. 63-70. (In Russian).
2. Handbook "Reliability ERP". The Ministry of Defence of the Russian Federation, Moscow. (In Russian).
3. RDV 319.01.20-98. Position about a "Handbook "Reliability of ERP". (In Russian).
4. Shavykin N.A., Petruhin B.P. (2006). Estimation of indicators of non-failure operation of mechanical elements of production of instrument making. "Sensors & systems" magazine, No 6, pp. 28-35. (In Russian).
5. Shavykin N.A., Petruhin B.P., Zhidomirova E.M. (1998). Procedure of an estimation of indicators of non-failure operation of means. Institute of problems of management of the Russian Academy of Sciences, Moscow. (In Russian).
6. TU 38 005 1166-98 "Mixtures of uncured rubber for aircraft". (In Russian).
7. RM 25 446-87. Instrument making products. Design procedure of indicators of non-failure operation. Recommended material. (In Russian).
8. NSWC-98/LE1. Handbook of reliability prediction procedures for mechanical equipment.
9. NSWC-06/LE10. Handbook of reliability prediction procedures for mechanical equipment.
10. Zhadnov V., Avdeev D., Kulygin. V., Polesskey S., Tihmenev A. (2011), Information technology of maintenance of reliability of difficult electronic means of the military man and special purpose. "Components & technologies" magazine, Vol. 119, No 6, pp. 168-174. (In Russian).
11. Stroganov A., Zhadnov V., Polesskey S. (2007). The review of program complexes by calculation of reliability of difficult technical systems. "Components & technologies" magazine, Vol. 70, No 5, pp. 74-81. (In Russian).
