Methodological Approach in the Simulation of the Robustness Boundaries of Tribosystems under the Conditions of Boundary Lubrication
Abstract
In the presented work, a methodical approach was developed for determining rational operation modes of tribosystems, taking into account their design. This approach makes it possible in the designing stage, according to the predicted operating modes, to calculate the limits and margins of stable work in operation. The definition of the robustness of the tribosystem and the criteria for assessing the robustness are formulated based on the theory of stability of technical systems. It is shown that such a methodical approach allows for determining the modes of the rational operation of the designed structures without damaging the friction surfaces. Experimental studies have proven that not all designs of tribosystems lose stability due to the appearance of friction surface burrs. There are designs where the loss of stability occurs upon the appearance of accelerated wear. The developed criteria take into account two options for the loss of stability. An experimental verification of the modes of loss of stability of tribosystems was performed by the appearance of a burr or the beginning of accelerated wear with the calculated values of the robustness criteria. The obtained results allow us to conclude that the modeling error is within 8.3–18.7%, which is a satisfactory result in the study of friction and wear processes. Robustness criteria is based on the coefficient of friction RRf and wear rate RRI, and must be used when designing new constructions of tribosystems. Theoretical calculations of such criteria and the dependence of their change on changing the predicted operating modes will allow for justifying rational operating modes within their stability.
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Citation: Al-Quraan, T.M.A.; Alfaqs, F.; Alrefo, I.F.S.; Vojtov, V.; Voitov, A.; Kravtsov, A.; Miroshnyk, O.; Kondratiev, A.; Kuˇcera, P.; Píštˇek, V. Methodological Approach in the Simulation of the Robustness Boundaries of Tribosystems under the Conditions of Boundary Lubrication. Lubricants 2023,11, 17. https://doi.org/10.3390/ lubricants11010017 Received: 9 November 2022 Revised: 30 December 2022 Accepted: 2 January 2023 Published: 4 January 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). lubricants Article Methodological Approach in the Simulation of the Robustness Boundaries of Tribosystems under the Conditions of Boundary Lubrication Tareq M. A. Al-Quraan 1,* , Fadi Alfaqs 2, Ibrahim F. S. Alrefo 1, Viktor Vojtov 3, Anton Voitov 3, Andrey Kravtsov 3, Oleksandr Miroshnyk 4, Andrii Kondratiev 5, Pavel Kuˇcera 6and Václav Píštˇek 6,* 1Department of Technical Sciences, Ma’an College, Al-Balqa Applied University, Al-Salt 19117, Jordan 2Department Mechanical Engineering, Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan 3Department of Transport Technologies and Logistics, State Biotechnological University, 61052 Kharkiv, Ukraine 4Department of Electricity Supply and Energy Management, State Biotechnological University, 61052 Kharkiv, Ukraine 5 Department of Materials Science and Engineering of Composite Structures, O.M. Beketov National University of Urban Economy in Kharkiv, Marshal Bazhanov Str. 17, 61002 Kharkiv, Ukraine 6Institute of Automotive Engineering, Brno University of Technology, Technická2896/2, 616-69 Brno, Czech Republic *Correspondence: [email protected] (T.M.A.A.-Q.); [email protected] (V.P.); Tel.: +420-541-142-271 (V.P.) Abstract: In the presented work, a methodical approach was developed for determining rational operation modes of tribosystems, taking into account their design. This approach makes it possible in the designing stage, according to the predicted operating modes, to calculate the limits and margins of stable work in operation. The definition of the robustness of the tribosystem and the criteria for assessing the robustness are formulated based on the theory of stability of technical systems. It is shown that such a methodical approach allows for determining the modes of the rational operation of the designed structures without damaging the friction surfaces. Experimental studies have proven that not all designs of tribosystems lose stability due to the appearance of friction surface burrs. There are designs where the loss of stability occurs upon the appearance of accelerated wear. The developed criteria take into account two options for the loss of stability. An experimental verification of the modes of loss of stability of tribosystems was performed by the appearance of a burr or the beginning of accelerated wear with the calculated values of the robustness criteria. The obtained results allow us to conclude that the modeling error is within 8.3–18.7%, which is a satisfactory result in the study of friction and wear processes. Robustness criteria is based on the coefficient of friction RR f and wear rate RR I , and must be used when designing new constructions of tribosystems. Theoretical calculations of such criteria and the dependence of their change on changing the predicted operating modes will allow for justifying rational operating modes within their stability. Keywords: tribosystem; limit lubrication mode; burr of friction surfaces; accelerated wear; stability of technical systems; robustness; modelling; robustness criteria; modelling error; modes of operation 1. Introduction The stable operation of tribosystems in the entire load–speed range of operation is the most important characteristic that the reliability indicators of machines and mechanisms depend on. The range of the stable operation of tribosystems is predicted at the stage of the construction development of new machines and is based on the experimental data of previous designs or experimental data of laboratory bench tests. The most promising direction is mathematical modelling of the limits of the stable operation (robustness) of tribosystems, which will allow for significantly reducing material Lubricants 2023,11, 17. https://doi.org/10.3390/lubricants11010017 https://www.mdpi.com/journal/lubricants
Lubricants 2023,11, 17 2 of 16 resources during the construction of new equipment. The development of such models is based on the theoretical foundations of the stability of technical systems, developed by O.M. Lyapunov, who created the modern theory of the stability of motion of mechanical systems determined by a finite number of parameters. The concept of the stability of tribosystems is the most important qualitative assessment of their dynamic properties and depends on constructive, technological, and operational factors. Through the stability of the operation of tribosystem, it is possible to restore the original mode of operation after the removal of an external influence. In addition, an important parameter is the limit of the loss of the stable operation of the tribosystem, i.e., the amount of load and the sliding speed when burr or accelerated wear occurs [1,2]. According to this, three types of tribosystems were formulated in [1]. 1. Stable tribosystems, which, after being brought out of equilibrium by any external disturbance (change in load or sliding speed, or the short-term cessation of lubricant supply), after the removal of this disturbance, return to the original stable state, i.e., the established operating mode. 2. Neutral tribosystems, which, after removing the disturbance, switch to a state of stable operation in a new mode, which is different from the original one. 3. Unstable tribosystems, which, as they are brought out of equilibrium by any external disturbance, do not return to the original stable state after the removal of this disturbance, but switch to the mode of accelerated wear or to burr, i.e., cease operation. It should be noted that majority of studies are devoted to the failure of tribosystems due to the burring (seizing) of friction surfaces. However, there are options for terminating the operation of tribosystems due to the appearance of accelerated wear. The task of determining the limits of the stable operation (robustness) of tribosystems, considering the design, manufacturing technology, and the load–speed range of operation, is an urgent task. This task is solved in the stage of designing new structures of tribocouplers, which allows for increasing their resource and reliability in operation. This article deals only with sliding friction processes. An analysis of recent publications on the use of mathematical models for predicting the reliability and service life of tribosystems at the stage of development and design allows us to conclude that entropy analysis is promising in the study of energy dissipation during friction [ 3 – 6 ]. For example, in [ 4 ], a mathematical model for predicting the reliability of rolling bearings is developed on the basis of the hierarchical Bayesian method of maximum entropy. Theoretical developments that show the relationship of wear with the thermodynamic concept of entropy are presented in [ 5 – 7 ]. This approach allowed the authors of the work to study the effect of consistent grease on the resources of tribosystems. On the basis of the provisions of the thermodynamics of open systems in [ 8 – 10 ], equations for the conservation of mass and energy are proposed, which allow for simulating various modes of energy dissipation in a tribosystem, considering the friction surface. These equations can be considered as a tool for modelling various modes of energy dissipation in the dynamic contact of friction surfaces with the development of practical recommendations for the design of new structures. For simulating the work of tribosystems and predicting the resource, the authors of [ 11 – 13 ] used the achievements of artificial intelligence, particularly artificial neural networks. The authors showed that the use of this approach allowed for modelling and forecasting the wear and reliability of tribosystems during exploitation. The authors of [ 10 – 14 ] paid attention to the importance of considering the friction surface in mathematical models. For example, the importance of considering the roughness of the friction surface in the models is noted in [ 14 ], the values of the actual contact area are noted in [ 15 , 16 ], the change in the roughness of friction surfaces during running-in or running-out in is noted [ 17 ], and the distribution of actual pressures and stresses over the contact surface is noted in [ 18 , 19 ]. According to the results of the authors, consideration of the listed factors will increase the accuracy of modelling and predicting the resources during the operation of tribosystems.
Lubricants 2023,11, 17 3 of 16 The authors of [ 20 , 21 ] note that mathematical models of the functioning of tribosystems are tools for designing new friction units. The work presents a methodical approach and models that consider the design of the friction unit, which increases the accuracy of forecasting. The authors of [ 22 , 23 ] aimed their work at considering the stability and efficiency of tribosystems. The models created by the authors were built on the basis of stochastic models of surface roughness. It was shown that the tribological behavior in contact depended on the properties of the friction surfaces and the spectrum of loads. Moreover, edge effects at the boundaries of the contact area affected the pressure distribution and membrane thickness, which should be taken into account while modelling. The authors of [ 24 – 26 ] noted that when developing mathematical models for the functioning of tribosystems, it is necessary to consider wear during the running-in period. Because of the intense deformation of microprotrusions, the running-in mode allows for the formation of an equilibrium roughness of friction surfaces and a change in the structure of thin surface layers, which are analyzed in [ 24 ]. Optimal running-in conditions will help increase the service life and reliability of tribosystems. The analyses of publications determining the boundaries of the stable operation of tribosystems shows that these are the operating modes when the scuffing or seizing of friction surfaces occurs with the transfer of material from one triboelement to another. The difficulty in predicting the failure of tribosystems is a fundamental problem of tribology, which is noted in [ 27 ]. The article presents an analysis of various factors (residual stresses, surface free energy, and surface topography) that lead to the initial phase of the process of burr. The studies presented in [ 28 ] are aimed at a better understanding of the occurrence of burr. The authors affirm that the parametric assessment of the state of the friction surface is of crucial importance in the technology of preventing burrs. The durability limits of the tribosystem and the transition from stable to unstable operating conditions, namely seizing, were studied in [ 29 ]. The purpose of the research was to determine the boundaries of the stable operation of tribosystems and to use the obtained results while designing tribosystems. The authors of [ 30 ] studied the influence of random overloads on the occurrence of burrs in tribosystems. The results of the research were the determination of the boundary of the exit of the tribosystem to the burr. The mechanism of occurrence of burrs, based on adiabatic shear instability, was experimentally evaluated in [ 31 ]. The authors of the work related the mechanism of burr formation to the density of dislocations in the surface layer. The equations for modeling the burr of friction surfaces, which were obtained on the basis of adiabatic shear instability, are presented in [ 32 ]. With the help of equations, it is proposed to model the mechanism of loss of strength from the surface layer of the material during adiabatic shear. The main factor in the loss of strength is the work of friction. On the basis of this mechanism, a quantitative criterion for predicting reliability has been developed, where burr formation is the result of competition between thermal strength loss and strain hardening during adiabatic shear. The mechanism of burr formation in friction nodes was the subject of tribological studies in [ 33 ]. According to the authors, the approach to this problem requires taking into account a large number of working parameters for predicting burr. This work proposes using the parameter (pressure × velocity × time) instead of the frequently used parameter (pressure × velocity). According to the authors, such an approach will allow for taking into account the duration or frequency of loads during the operation of friction nodes. These parameters can significantly affect the stability of the properties of the lubricating membrane, especially in the context of the formation of an elastohydrodynamic membrane or boundary layer. The results of the gear tests on a test bench with changes in the torque, sliding speed, oil bath temperature, gear geometry, and viscosity of the base lubricant are presented in [ 34 ]. The developed model takes into account normal pressure and tangential stresses at several points along the line of the clutch of the gear. Gear seizure results are analyzed using two
Lubricants 2023,11, 17 4 of 16 different approaches: one takes into account the general parameters of the gear, including the clutch line, and the other, based on the local parameters of the roughness of the friction surfaces, is determined using the mixed lubrication model. An analysis of the roughness level was used to explain the causes of burr formation. A method for predicting the appearance of burr on friction surfaces, using the analysis of the dynamics of the transient process, is proposed in [ 35 ]. Quasi-static and nonlinear dynamic models take into account the increase in temperature during the transition process when the load changes during operation. The model allows for determining the thickness of the lubricating membrane on the friction surface and for determining the limit of the burr when the load changes. The processes of the stability of tribosystems when oscillations occur in frictional contact were studied in [ 36 , 37 ]. For example, strict criteria for the stable operation of tribosystems in various modes of frictional sliding and the occurrence of vibrations were presented in [ 36 ]. The stability of the tribosystem, with the help of a complex analysis of the oscillating elements of the tribosystem and their influence on the process was investigated in [37]. Studies on the burrs of the gear were presented in [ 38 , 39 ]. The flash point on the actual contact patches was explored in [ 38 ]. The optimization of the design of the gearbox according to the criterion of power loss due to friction in the gears was described in [39]. The analysis of works devoted to the determination of the limits of the stable operation of tribosystems allowed us to conclude that when developing and justifying such criteria, it is necessary to take into account the constructive, technological, and operational factors of tribosystems. In the works listed above, the geometric dimensions of tribocouplers, physical and mechanical properties of combined materials of triboelements, the tribological properties of the lubricating medium, and theroughness of friction surfaces are not sufficiently taken into account. Accounting for the mentioned factors will allow us to extend the obtained criteria to a wide class of tribosystems and make such an analysis systematic. 2. Materials and Methods The purpose of this study is to develop a methodical approach for determining the robustness of tribosystems in conditions of extreme lubrication, modelling changes in the robustness of tribosystems at the stage of constructive development, and experimental verification of the modelling error. To substantiate the methodical approach in the research, we will use the equation of the dynamics of tribosystem functioning, which is given in [1]. The friction unit is modeled as a series and parallel connection of dynamic links from which the equivalent transfer function of the friction unit is obtained. On the basis of the equivalent transfer function, a differential equation for the process of operation of the friction unit is written. The differential equation of the third order is written in operator form, as follows: (T1T2T3)p3+(T1T2+T1T3+T2T3)p2+(T1+T2+T3+K2K3T1)p+K2K3+1=(K1K2T3)p+K1K2, (1) where pis the differentiation operator, which is equivalent to writing d/dt; T1,T2,T3are the time constants in the dimension of seconds (s); K1,K2,K3are the gain coefficients, which are dimensionless quantities. In [ 1 ], it was proven that time constant T 1 characterizes the change in the structure of the materials of the surface layers during run-in. It is defined by the following expression: T1=trun 3, (2) where trun ia the tribosystem run-in time in the dimension of seconds.
Lubricants 2023,11, 17 5 of 16 Time constant T 2 has a physical sense of the time, during which the temperature is equalized by the volumes of triboelement materials when the load and sliding speed change. It is defined by the following expression: T2=254 ·Vrun arun ·dacs ·nacs , (3) where V run is the stated volume of materials of the moving and stationary triboelements of the tribosystem, in the dimension of m 3 , and is determined by Expressions (2) and (3), which are given in [40], taking into account the total volume of the material of the friction node; a run is the given coefficient of the thermal conductivity of the materials of the moving a r and stationary a s triboelements, in the dimension of m 2 /s, and is calculated according to Expression (6), which is given in [40]; d acs is the diameter of the actual contact spot, in the dimension of m, and it is calculated according to the expression given in [41]; n acs is the number of contact spots on the friction surface, and is calculated according to the expression given in [41]. Time constant T 3 characterizes the time until the friction and wear parameters stabilize in the new operating mode of the tribosystem. Time constant T3has different expressions to the model wear rates T3(I)and friction coefficient T3(f): T3(I)=428000 ·Vde f . εrun ·d3 acs ·nacs , (4) T3(f)=1068000 ·Vde f . εrun ·d3 acs ·nacs , (5) where V def is the given volume of deformable surface layers, measured in m 3 , and is determined by the expression given in [40], using Formulas (15) and (16); . εrun is the indicated value of the rate of deformation of the surface layers of the materials of the movable and immovable triboelements, in the dimension of c−1, which is calculated according to the formulas given in [30], using Formulas (8)–(10). The coefficient K 1 includes the degree of external influence on the tribosystem, considering the design features, which was proven in [40]: K1=Qmax Q0, (6) where Q 0 and Q max are the initial value of the Q-factor of the tribosystem and the value of the Q-factor that was formed during the run-in. They are determined by the formulas given in [41]. Coefficient K 2 characterizes the sensitivity of the tribosystem to changes in the external conditions: K2=5500 ·WTR ·Kf Qmax •arun , (7) where W TR is the speed of dissipation in the tribosystem, measured in J/s, which is calculated according to the equations given in [1], using Formula (8); K f is the shape coefficient of the tribosystem, in the dimension of m −1 , and includes the friction areas and the volumes located under the friction areas of the moving and stationary triboelements. It is calculated according to the equation given in [41]. Coefficient K 3 characterizes the ability of the tribosystem to change the structure of the surface layers of the triboelement materials during transient processes: K3=170 ·RS2 TS(max)·arun . εrun , (8)
Lubricants 2023,11, 17 6 of 16 where RS TS(max) is the maximum value of the rheological properties of the combined materials in the tribosystem after running-in, measured in dimension m −1 , and is calculated according to the equations given in [42]. Formulas (7) and (8) are obtained for the specific design of the friction unit. The design is taken into account by using the shape factor, K f . The shape factor takes into account the magnitude of the friction areas and the volumes of material that are placed under the working areas of friction. Values of 5500 and 170 were introduced to improve the accuracy of the simulation. When changing the structure of the friction unit, it is necessary to adjust the values of these coefficients. To analyze the stability of the technical systems, several special methods have been developed, which are called stability criteria in the theory of automatic regulation. Stability criteria are divided into two varieties—algebraic and frequency. Algebraic criteria are analytical and frequency criteria are grapho analytical [ 43 – 45 ]. At the same time, all criteria are based on the theory of the stability of technical systems developed by Lyapunov [46–49]. The algebraic criterion, Hurwitz’s criterion [ 50 – 52 ], is the most common criterion and is used to determine the stability of technical systems when the characteristic equation is known. As the characteristic equation acts the left part of the differential equation in operator form (1). Let us write down the characteristic equation, making a substitution and equating it to zero: A0p3+A1p2+A2p+A3=0, (9) where A0=T1·T2·T3, (10) A1=T1·T2+T1·T3+T2·T3, (11) A2=T1+T2+T3+K2K3T1, (12) A3=K2·K3+1, (13) According to Hurwitz’s algebraic stability criterion, a technical system is stable when all coefficients A i of the characteristic Equation (9) are more than zero. This is a necessary condition for stability: A0>0; A1>0; A2>0; A3>0, (14) A sufficient condition for stability is that all determinants from the coefficients A i of the characteristics in Equation (9) are more than zero. If at least one of the determinants is equal to zero, then the system is on the verge of loss of stability. If at least one of the determinants is negative, then the system is unstable. In the tribosystem, burr or accelerated wear occur. According to the rules, let us write down all of the determinants for the characteristic Equation (9): ∆1=A1>0, (15) ∆2= A1A3 A0A2 =A1·A2−A0·A3>0, (16) ∆3= A1A30 A0A20 0A1A3 = A1A3 A0A2 A3>0=(A1·A2−A0·A3)·A3>0, (17) Let us write down the value of the determinant∆3in the following form: ∆3=(A1·A2−A0·A3)·A3>0, (18) Expression (18) is a necessary and sufficient condition for the stable functioning of the tribosystem according to the Hurwitz criterion. Using this expression, you can determine
Lubricants 2023,11, 17 7 of 16 the range of stable operation for the tribosystem, namely the range of robustness. The more the value of ∆3 , measured in dimension s 3 , the more the margin of robustness for the tribosystem. When the value ∆3 = 0, the tribosystem works on the verge of loss of stability, with negative values for ∆3 , and there is burr or accelerated wear and the tribosystem has “lost stability”. To compare tribosystems and build a rating on the margin of stable operation, it is necessary to obtain a dimensionless parameter—a criterion that depends on constructive, technological, and operational factors. The most acceptable, in our opinion, is the analysis of the expression of the stability of technical systems based on the Hurwitz algebraic criterion, using formula (18). Based on the formulated approach, let us write down, in a general form, the evaluation criterion for the margin of stable operation of the tribosystem—the robustness criterion: RR =A1·A2 A0·A3 >1, (19) where RR is criterion of tribosystem robustness, with a dimensionless value. The physical meaning for determining the robustness of the technical systems is given in [53]. An analysis of Equation (1) shows that processes of friction and wear in the tribosystem, especially the running-in processes, depend on the first derivative of the input effect on the tribosystem, i.e., on the load speed. The load speed of the tribosystem can be considered by the coefficient of the change in the load speed, which is proportional to the right-hand side of the differential Equation (1): kd≈(K1K2T3)dWi dtl +K1K2, (20) where the amount of load (external influence during experimental studies) on the tribosystem is determined by the following expression: Wi=N·vsl, (21) where Nis the load on the tribosystem, N; vsl is the sliding speed, m/s; tlis the load change time, s. With the help of laboratory experimental studies carried out on various designs of tribosystems with different amounts of load on the tribosystem and different rates of load change, an expression for calculating the coefficient of change of the load speed was obtained. Determining the robustness of the tribosystem using the friction coefficient parameter is completed as follows: kd(f)=0.62ln(K1·K2·T3(f) tl ). (22) Evaluating the operation of the tribosystem by the wear rate parameter is completed as follows: kd(I)=0.95ln(K1·K2·T3(I) tl ). (23) Including the expressions of the coefficient of change in the load speed (22) and (23), which were obtained according to the results of experimental studies, equations for determining the robustness of tribosystems (19), including expressions (10)–(13), will be presented in the following form.
Lubricants 2023,11, 17 8 of 16 To determine the robustness of the tribosystem by the friction coefficient: RRf=T1T2+T1T3,f+T2T3,f×T1+T2+T3,f+K2K3T1 T1T2T3,fK2K3+T1T2T3,f·kd(f) >1. (24) To determine the robustness of the tribosystem by the rate of wear: RRI=((T1T2+T1T3,I+T2T3,I)×(T1+T2+T3,I+K2K3T1)) (T1T2T3,IK2K3+T1T2T3,I)·kd(I) >1. (25) It is necessary to calculate criteria for the robustness of the tribosystem RR f and RR I for each load of the operating range of tribosystems, including the analysis of the obtained values. If the value of the criterion is more than one, then the tribosystem works in a stable range. The more the value of the robustness criterion, the more the margin of sustainable work. If the value of the criterion is equal to one, the tribosystem works on the verge of loss of stability. If the value of the criterion is less than one, the tribosystem has lost stability, and burr or accelerated wear has occurred. To answer the question of which the parameter loss of stability occurred in, it is necessary to calculate two criteria: according to the coefficient of friction, formula (24) and according to the rate of wear, formula (25). The value of the criterion, which first becomes less than one, answers the question on which parameter the loss of stability occurred. Figure 1presents the theoretical dependence of the change in the robustness criterion of various structures of tribosystems according to the friction coefficient on the value of the input influence, using formula (24). Input influence on the tribosystem, W,W, is represented as the product of load, N, and sliding speed, m/s, using formula (21). Different designs of tribosystems are included by the value of the Q-factor, Qo, J/m3, [41,42]. Lubricants2023,11,178of17 𝑘0.95 𝑙𝑛⋅⋅ .(23) Includingtheexpressionsofthecoefficientofchangeintheloadspeed(22)and(23), whichwereobtainedaccordingtotheresultsofexperimentalstudies,equationsforde‐ terminingtherobustnessoftribosystems(19),includingexpressions(10)–(13),willbepre‐ sentedinthefollowingform. Todeterminetherobustnessofthetribosystembythefrictioncoefficient: 𝑅𝑅,,, ,,⋅ 1.(24) Todeterminetherobustnessofthetribosystembytherateofwear: 𝑅𝑅,,, ,,⋅ 1.(25) ItisnecessarytocalculatecriteriafortherobustnessofthetribosystemRRfandRRI foreachloadoftheoperatingrangeoftribosystems,includingtheanalysisoftheobtained values.Ifthevalueofthecriterionismorethanone,thenthetribosystemworksinastable range.Themorethevalueoftherobustnesscriterion,themorethemarginofsustainable work. Ifthevalueofthecriterionisequaltoone,thetribosystemworksonthevergeofloss ofstability.Ifthevalueofthecriterionislessthanone,thetribosystemhasloststability, andburroracceleratedwearhasoccurred. Toanswerthequestionofwhichtheparameterlossofstabilityoccurredin,itisnec‐ essarytocalculatetwocriteria:accordingtothecoefficientoffriction,formula(24)and accordingtotherateofwear,formula(25).Thevalueofthecriterion,whichfirstbecomes lessthanone,answersthequestiononwhichparameterthelossofstabilityoccurred. Figure1presentsthetheoreticaldependenceofthechangeintherobustnesscriterion ofvariousstructuresoftribosystemsaccordingtothefrictioncoefficientonthevalueof theinputinfluence,usingformula(24).Inputinfluenceonthetribosystem,W,W,isrep‐ resentedastheproductofload,N,andslidingspeed,m/s,usingformula(21).Different designsoftribosystemsareincludedbythevalueoftheQ‐factor,Qo,J/m3,[41,42]. Figure1.Dependenciesofchangesintherobustnesscriterionofvariousdesignsoftribosystems accordingtothecoefficientoffrictiononthevalueoftheinputimpact:1—steel5140+steel5140,Kf =6.25m−1,hydraulicoilHH,ISO‐L‐HL,Q0=1.12∙1010J/m3;2—steel5140+bronzeC61900,Kf=12.5 Figure 1. Dependencies of changes in the robustness criterion of various designs of tribosystems according to the coefficient of friction on the value of the input impact: 1—steel 5140 + steel 5140, K f = 6.25 m −1 , hydraulic oil HH, ISO-L-HL, Q 0 = 1.12 · 10 10 J/m 3 ; 2—steel 5140 + bronze C61900, Kf= 12.5 m−1 , motor oil SAE 40, APICC, Q 0 = 5.5 · 10 10 J/m 3 ; 3—steel 5140 + brass CW723R, Kf= 14.5 m−1; transmission oil SAE120, APIGL-4, Q0= 7.69·1010 J/m3. Experimental studies were carried out on a universal friction machine according to the «ring-ring» kinematic scheme. The design of the friction machine is presented in [41].
Lubricants 2023,11, 17 9 of 16 The friction unit is represented by movable sample 1 and fixed sample 2. The friction between the samples occurs over the area of the ends. During the tests, fixed sample 2 is pressed against movable sample 1 by load N. Friction occurs over the area of the ends. The movable sample performs a rotational movement around its axis. An acoustic emission sensor GT300 is mounted on fixed sample 2. The acoustic emission signal from the GT300 transducer with a frequency of 100–800 kHz is transmitted to a preamplifier and then to a USB oscilloscope, which acts as an A/D converter. Then, the signal in a digital code is entered into the computer to calculate the diagnostic parameters. The AE signal from the friction zone is recorded by a broadband sensor GT300 ( 100–800 kHz ), Figure 2, which is installed on a fixed triboelement, transmitted to an amplifier, then, in analog form, to a PV6501 USB oscilloscope, which performs the functions of an analog-to-digital converter and spectrum frequency analyzer at the same time. After processing in a USB oscilloscope, the digital signal enters the computer, where it is processed by special software. Lubricants2023,11,179of17 m−1,motoroilSAE40,APICC,Q0=5.5∙1010J/m3;3—steel5140+brassCW723R,Kf=14.5m−1;trans‐ missionoilSAE120,APIGL‐4,Q0=7.69∙1010J/m3. Experimentalstudieswerecarriedoutonauniversalfrictionmachineaccordingto the«ring‐ring»kinematicscheme.Thedesignofthefrictionmachineispresentedin[41]. Thefrictionunitisrepresentedbymovablesample1andfixedsample2.Thefriction betweenthesamplesoccursovertheareaoftheends.Duringthetests,fixedsample2is pressedagainstmovablesample1byloadN.Frictionoccursovertheareaoftheends. Themovablesampleperformsarotationalmovementarounditsaxis.Anacousticemis‐ sionsensorGT300ismountedonfixedsample2.Theacousticemissionsignalfromthe GT300transducerwithafrequencyof100–800kHzistransmittedtoapreamplifierand thentoaUSBoscilloscope,whichactsasanA/Dconverter.Then,thesignalinadigital codeisenteredintothecomputertocalculatethediagnosticparameters. TheAEsignalfromthefrictionzoneisrecordedbyabroadbandsensorGT300(100– 800kHz),Figure2,whichisinstalledonafixedtriboelement,transmittedtoanamplifier, then,inanalogform,toaPV6501USBoscilloscope,whichperformsthefunctionsofan analog‐to‐digitalconverterandspectrumfrequencyanalyzeratthesametime.Afterpro‐ cessinginaUSBoscilloscope,thedigitalsignalentersthecomputer,whereitisprocessed byspecialsoftware. Figure2.BlockdiagramofexperimentalequipmentforrecordingandprocessingAEsignals:1— movabletriboelement;2—fixedtriboelement;N—load. SamplesfortestingarepresentedinFigure3,wheremovablesample1ismadeof steel5140,andfixedsample2ismadeofvariousmaterials:steel5140,bronzeC61900,and brassCW723R.Thus,duringthetests,itwaspossibletoobtainvariousconstructionsof tribosystems,forexample,amovablesampleofsteel5140+fixedsampleofsteel5140; movablesamplesteel5140+fixedsamplebronzeC61900;movablesamplesteel5140+ fixedsamplebrassCW723R.Atthesametime,thefrictionareaoffixedsamples2was changed,whichmadeitpossibletoobtaindifferentcoefficientsfortheshapeofthetested tribosystems. Figure 2. Block diagram of experimental equipment for recording and processing AE signals: 1—movable triboelement; 2—fixed triboelement; N—load. Samples for testing are presented in Figure 3, where movable sample 1 is made of steel5140, and fixed sample 2 is made of various materials: steel 5140, bronze C61900, and brass CW723R. Thus, during the tests, it was possible to obtain various constructions of tribosystems, for example, a movable sample of steel 5140 + fixed sample of steel 5140; movable sample steel 5140 + fixed sample bronze C61900; movable sample steel 5140 + fixed sample brass CW723R. At the same time, the friction area of fixed samples 2 was changed, which made it possible to obtain different coefficients for the shape of the tested tribosystems. Lubricants2023,11,1710of17 Figure3.Samplesfortesting:1—movablesamplesteel5140;2—fixedsamples:steel5140,bronze C61900,brassCW723Rwithdifferentfrictionareasontheendsurfaces;3—frictionsurfacesofthe movingsample;4—frictionsurfacesofafixedsample. Duringthetests,theloadonthetribosystemincreasedatdifferentloadspeeds:1s, 10s,and20s. Thelossofstabilityoftribosystems,accordingtothecoefficientoffrictionwasdeter‐ minedbyusingthevalueofthemomentoffriction,whichwasregisteredbytherecorder ofmachine2070SMT‐1.Accordingtotheparameterofthestartofacceleratedwear,the lossofstabilitywasdeterminedbyusingoftheacousticemissionmethod.Themeasuring complexandthemethodforrecordingtheacousticemissionsignalsaregivenin[54].To recordacousticeradiationfromthefrictionzone,theacousticemissionsensorisinstalled onastationarytriboelement. Accordingtotheresultsofthreerepetitions,theaverageburrloadortheonsetof acceleratedwear,therootmeansquaredeviationofvaluesofregisteredvaluesduring experimentalstudies,formula(26);coefficientofvariationofmeasurementsofexternal influence,whentheoccasionoflossofstabilityofthetribosystemoccurs,formula(27); modellingerroraccordingtotheformula(28),weredetermined. Theroot‐mean‐squaredeviationofthevaluesoftheexternalinfluenceduringexper‐ imentalresearchisrepresentedbytheformula: 𝑆 ∑𝑊𝑊 ,(26) whereWb(i),Wb(aw)arethevaluesofexternalinfluenceonthetribosystem,formula(21),at whichthereisalossofstability(burroracceleratedwear),whichismeasuredduringthe experimentandisaveragedoverthenumberofrepetitionsn. Thecoefficientofvariationofmeasurementsofexternalinfluence,whentheoccasion oflossofstabilityofthetribosystemoccurs,isdeterminedbytheexpression: 𝑣 ⋅100%,(27) Therelativeerrorofmodellingtherobustnessoftribosystemsisdeterminedbythe expression: 𝑒 ⋅100%,(28) whereWb(exp),Wb(s)isthevalueofthemagnitudeoftheexternalinfluenceonthetribosys‐ tematwhichalossofstability(burroracceleratedwear)occurs,whichismeasureddur‐ ingtheexperimentandaccordingtotheresultsofthesimulation. 3.TheResultsoftheExperimentalResearch Theresultsofmodellingtherobustnessoftribosystemsandtheresultsoftheexper‐ imentaltestingarepresentedinTable1.Thepurposeoftheexperimentalresearchisto comparethecalculatedvaluesofthemagnitudeoftheexternalinfluenceonthetribosys‐ temWb(s),atwhichalossofstabilityoccurs(burroracceleratedwear),accordingto Figure 3. Samples for testing: 1—movable sample steel 5140; 2—fixed samples: steel 5140, bronze C61900, brass CW723R with different friction areas on the end surfaces; 3—friction surfaces of the moving sample; 4—friction surfaces of a fixed sample.
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