Variations in vehicle noise, vibration and harshness (NVH) response from one vehicle to the next can have significant impact on an automotive company’s profile and profitability. The warranty claims due to excessive NVH response end up costing the manufacturers a large sum of money each year. In addition, the OEM will suffer a larger financial loss due to the poor perception of quality and customer dissatisfaction with their products due to the unacceptable NVH response. Therefore, measures must be taken to ensure less warranty claims and higher levels of customer satisfaction. This research focuses on aspects of design variations that are costly or difficult to be avoided in the design process such as variations with rubber parts and variations due to rotating components. Vibrations induced at the tire/wheel assembly due to variations in the radial and tangential forces and radial runout are responsible for the driverelt vibrations that can lead to a large number of warranty claims. The purpose of this research is to improve the process of determining and analyzing vibration sources in the tire/wheel assembly in order to benefit the automotive manufacturer during the development and manufacturing phases. This research identifies the relationship between non-uniformity forces of the tire/wheel assemblies and the driverelt vibrations during typical highway driving speeds. The contribution from each assembly location is analyzed and sensitivities are determined. A Monte Carlo process is used to predict numerous non-uniformity properties that are statistically representative of the assembly properties that can be expected at the manufacturing plant. The Monte Carlo produced non-uniformity properties are combined with the sensitivities to predict driverelt vibrations that can be expected from vehicles leaving the manufacturing plant. This process provides the tools to determine an acceptable level of non-uniformities based on targets for interior vibration levels or determine if the vehicle sensitivities to non-uniformities need to be improved.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

The goal of this thesis is on improving the understanding of mechanical and tribological mechanisms in microelectronic wire bonding. In particular, it focusses on the development and application of quantitative models of ultrasonic (US) friction and interfacial wear in wire bonding. Another objective of the thesis is to develop a low-stress Cu ball bonding process that minimizes damage to the microchip. These are accomplished through experimental measurements of in situ US tangential force by piezoresistive microsensors integrated next to the bonding zone using standard complementary metal oxide semiconductor (CMOS) technology. The processes investigated are thermosonic (TS) Au ball bonding on Al pads (Au-Al process), TS Cu ball bonding on Al pads (Cu-Al process), and US Al wedge-wedge bonding on Al pads (Al-Al process). TS ball bonding processes are optimized with one Au and two Cu wire types, obtaining average shear strength (SS) of more than 120 MPa. Ball bonds made with Cu wire show at least 15% higher SS than those made with Au wire. However, 30% higher US force induced to the bonding pad is measured for the Cu process using the microsensor, which increases the risk of underpad damage. The US force can be reduced by: (i) using a Cu wire type that produces softer deformed ball results in a measured US force reduction of 5%; and (ii) reducing the US level to 0.9 times the conventionally optimized level, the US force can be reduced by 9%. It is shown that using a softer Cu deformed ball and a reduced US level reduces the extra stress observed with Cu wire compared to Au wire by 42%. To study the combined effect of bond force (BF) and US in Cu ball bonding, the US parameter is optimized for eight levels of BF. For ball bonds made with conventionally optimized BF and US settings, the SS is ≈ 140 MPa. The amount of Al pad splash extruding out of bonded ball interface (for conventionally optimized BF and US settings) is between 10–12 µm. It can be reduced to 3–7 µm if accepting a SS reduction to 50–70 MPa. For excessive US settings, elliptical shaped Cu bonded balls are observed, with the major axis perpendicular to the US direction. By using a lower value of BF combined with a reduced US level, the US force can be reduced by 30% while achieving an average SS of at least 120 MPa. These process settings also aid in reducing the amount of splash by 4.3 µm. The US force measurement is like a signature of the bond as it allows for detailed insight into the tribological mechanisms during the bonding process. The relative amount of the third harmonic of US force in the Cu-Al process is found to be five times smaller than in the Au-Al process. In contrast, in the Al-Al process, a large second harmonic content is observed, describing a non-symmetric deviation of the force signal waveform from the sinusoidal shape. This deviation might be due to the reduced geometrical symmetry of the wedge tool. The analysis of harmonics of the US force indicates that although slightly different from each other, stick-slip friction is an important mechanism in all these wire bonding variants. A friction power theory is used to derive the US friction power during Au-Al, Cu-Al, and Al-Al processes. Auxiliary measurements include the current delivered to the US transducer, the vibration amplitude of the bonding tool tip in free-air, and the US tangential force acting on the bonding pad. For bonds made with typical process parameters, several characteristic values used in the friction power model such as the ultrasonic compliance of the bonding system and the profile of the relative interfacial sliding amplitude are determined. The maximum interfacial friction power during Al-Al process is at least 11.5 mW (3.9 W/mm²), which is only about 4.8% of the total electrical power delivered to the US transducer. The total sliding friction energy delivered to the Al-Al wedge bond is 60.4 mJ (20.4 J/mm²). For the Au-Al and Cu-Al processes, the US friction power is derived with an improved, more accurate method to derive the US compliance. The method uses a multi-step bonding process. In the first two steps, the US current is set to levels that are low enough to prevent sliding. Sliding and bonding take place during the third step, when the current is ramped up to the optimum value. The US compliance values are derived from the first two steps. The average maximum interfacial friction power is 10.3 mW (10.8 W/mm²) and 16.9 mW (18.7 W/mm²) for the Au-Al and Cu-Al processes, respectively. The total sliding friction energy delivered to the bond is 48.5 mJ (50.3 J/mm²) and 49.4 mJ (54.8 J/mm²) for the Au-Al and Cu-Al processes, respectively. Finally, the sliding wear theory is used to derive the amount of interfacial wear during Au-Al and Cu-Al processes. The method uses the US force and the derived interfacial sliding amplitude as the main inputs. The estimated total average depth of interfacial wear in Au-Al and Cu-Al processes is 416 nm and 895 nm, respectively. However, the error of estimation of wear in both the Au-Al and the Cu-Al processes is ≈ 50%, making this method less accurate than the friction power and energy results. Given the error in the determination of compliance in the Al-Al process, the error in the estimation of wear in the Al-Al process might have been even larger; hence the wear results pertaining to the Al-Al process are not discussed in this study.

The goal of this thesis is on improving the understanding of mechanical and tribological mechanisms in microelectronic wire bonding. In particular, it focusses on the development and application of quantitative models of ultrasonic (US) friction and interfacial wear in wire bonding. Another objective of the thesis is to develop a low-stress Cu ball bonding process that minimizes damage to the microchip. These are accomplished through experimental measurements of in situ US tangential force by piezoresistive microsensors integrated next to the bonding zone using standard complementary metal oxide semiconductor (CMOS) technology. The processes investigated are thermosonic (TS) Au ball bonding on Al pads (Au-Al process), TS Cu ball bonding on Al pads (Cu-Al process), and US Al wedge-wedge bonding on Al pads (Al-Al process). TS ball bonding processes are optimized with one Au and two Cu wire types, obtaining average shear strength (SS) of more than 120 MPa. Ball bonds made with Cu wire show at least 15% higher SS than those made with Au wire. However, 30% higher US force induced to the bonding pad is measured for the Cu process using the microsensor, which increases the risk of underpad damage. The US force can be reduced by: (i) using a Cu wire type that produces softer deformed ball results in a measured US force reduction of 5%; and (ii) reducing the US level to 0.9 times the conventionally optimized level, the US force can be reduced by 9%. It is shown that using a softer Cu deformed ball and a reduced US level reduces the extra stress observed with Cu wire compared to Au wire by 42%. To study the combined effect of bond force (BF) and US in Cu ball bonding, the US parameter is optimized for eight levels of BF. For ball bonds made with conventionally optimized BF and US settings, the SS is ≈ 140 MPa. The amount of Al pad splash extruding out of bonded ball interface (for conventionally optimized BF and US settings) is between 10–12 µm. It can be reduced to 3–7 µm if accepting a SS reduction to 50–70 MPa. For excessive US settings, elliptical shaped Cu bonded balls are observed, with the major axis perpendicular to the US direction. By using a lower value of BF combined with a reduced US level, the US force can be reduced by 30% while achieving an average SS of at least 120 MPa. These process settings also aid in reducing the amount of splash by 4.3 µm. The US force measurement is like a signature of the bond as it allows for detailed insight into the tribological mechanisms during the bonding process. The relative amount of the third harmonic of US force in the Cu-Al process is found to be five times smaller than in the Au-Al process. In contrast, in the Al-Al process, a large second harmonic content is observed, describing a non-symmetric deviation of the force signal waveform from the sinusoidal shape. This deviation might be due to the reduced geometrical symmetry of the wedge tool. The analysis of harmonics of the US force indicates that although slightly different from each other, stick-slip friction is an important mechanism in all these wire bonding variants. A friction power theory is used to derive the US friction power during Au-Al, Cu-Al, and Al-Al processes. Auxiliary measurements include the current delivered to the US transducer, the vibration amplitude of the bonding tool tip in free-air, and the US tangential force acting on the bonding pad. For bonds made with typical process parameters, several characteristic values used in the friction power model such as the ultrasonic compliance of the bonding system and the profile of the relative interfacial sliding amplitude are determined. The maximum interfacial friction power during Al-Al process is at least 11.5 mW (3.9 W/mm²), which is only about 4.8% of the total electrical power delivered to the US transducer. The total sliding friction energy delivered to the Al-Al wedge bond is 60.4 mJ (20.4 J/mm²). For the Au-Al and Cu-Al processes, the US friction power is derived with an improved, more accurate method to derive the US compliance. The method uses a multi-step bonding process. In the first two steps, the US current is set to levels that are low enough to prevent sliding. Sliding and bonding take place during the third step, when the current is ramped up to the optimum value. The US compliance values are derived from the first two steps. The average maximum interfacial friction power is 10.3 mW (10.8 W/mm²) and 16.9 mW (18.7 W/mm²) for the Au-Al and Cu-Al processes, respectively. The total sliding friction energy delivered to the bond is 48.5 mJ (50.3 J/mm²) and 49.4 mJ (54.8 J/mm²) for the Au-Al and Cu-Al processes, respectively. Finally, the sliding wear theory is used to derive the amount of interfacial wear during Au-Al and Cu-Al processes. The method uses the US force and the derived interfacial sliding amplitude as the main inputs. The estimated total average depth of interfacial wear in Au-Al and Cu-Al processes is 416 nm and 895 nm, respectively. However, the error of estimation of wear in both the Au-Al and the Cu-Al processes is ≈ 50%, making this method less accurate than the friction power and energy results. Given the error in the determination of compliance in the Al-Al process, the error in the estimation of wear in the Al-Al process might have been even larger; hence the wear results pertaining to the Al-Al process are not discussed in this study.

Made available in DSpace on 2016-03-15T19:36:56Z (GMT). No. of bitstreams: 1 Ricardo Mazziero Quartarolo.pdf: 8600660 bytes, checksum: 6058bd2a64c8a23a963ef69194501521 (MD5) Previous issue date: 2015-11-30 / Increasing the energy efficiency of internal combustion engines manufactured for light vehicles is a growing demand from society due to the importance of the transport sector in relation to emissions of greenhouse gases. In a move led by the developed countries of Europe, regulatory agencies have been imposing aggressive emission reduction targets for new cars. The reduction of the mechanical losses caused by friction between engine components through the development of new technologies and materials is mandatory for the most industries involved in the manufacture of engines. The piston rings are responsible for much of the losses due to their adverse operating conditions within the combustion chamber. The interaction between the rings and the cylinder is decisive in determining beyond the mechanical friction losses, wear of the assembly, oil consumption and power. The improvement of mechanical properties of piston rings by heat treatment is an important alternative to reduce friction. The reduction of tangential force is especially important in the rings of the second channel, although they are known as scraper rings, in practice its main function is to stabilize the piston and prevent compression ring floating and consequently the flow of combustion gases into the crankcase. Results suggest that bainitic microstructure, obtained by austempering of the piston rings made from gray cast iron enables the reduction of their tangential force. This reduction has a positive relationship with the engine operating temperature exposure time as found in simulations carried out at constant temperature and logarithmic timescale. / O aumento da eficiência energética dos motores de combustão interna utilizados por automóveis leves é uma demanda crescente da sociedade, devido à representatividade do setor de transporte em relação às emissões dos gases do efeito estufa. Em um movimento liderado pelos países desenvolvidos da Europa, as agências reguladoras vêm impondo metas agressivas de redução de emissões para automóveis novos. A redução das perdas mecânicas geradas pelo atrito entre os componentes do motor através do desenvolvimento de novas tecnologias e materiais é mandatório entre a maior parte das indústrias envolvidas na fabricação de motores. Os anéis de pistão são responsáveis por grande parte dessas perdas, devido às suas condições de operação adversas dentro da câmara de combustão. A interação entre os anéis e o cilindro é decisiva para determinar além das perdas mecânicas por atrito, o desgaste do conjunto, consumo de óleo e potência. A modificação das propriedades mecânicas dos anéis de pistão através de tratamento térmico é uma alternativa importante para reduzir o atrito. Esse efeito é especialmente importante nos anéis de segunda canaleta, que apesar de serem considerados anéis raspadores, na prática tem como principal função estabilizar o conjunto e evitar a flutuação do anel de compressão e consequentemente a passagem de gases de combustão para o cárter. Os resultados sugerem que a microestrutura bainítica, obtida através da austêmpera dos anéis de pistão fabricados a partir de ferro fundido cinzento possibilita a redução da força tangencial, sendo que essa redução apresenta uma relação positiva com o tempo de exposição à temperatura de trabalho do motor conforme constatado em simulações realizadas à temperatura constante e escala logarítmica de tempo.

The aim of this thesis was to investigate roller ski characteristics; classical and freestyle roller skis’ rolling resistance coefficients (μR) and classical style roller skis’ static friction coefficients (μS), and to study the influence of different μR and μS on cross-country skiers’ performance and both physiological and biomechanical indices. The aim was also to study differences in skiing economy and efficiency between recreational skiers, female and male junior and senior elite cross-country skiers.The experiments showed that during a time period of 30 minutes of rolling on a treadmill (warm-up), μR decreased significantly (p<0.05) to about 60-65 % and 70-75 % of its initial value for freestyle and classical roller skis respectively. Also, there was a significant influence of normal force on μR, while different velocities and inclinations of the treadmill only resulted in small changes in μR.The study of the influence on physiological variables of a ~50 % change in μR showed that during submaximal steady rate exercise, external power, oxygen uptake, heart rate and blood lactate were significantly changed, while there were non-significant or only small changes to cycle rate, cycle length and ratings of perceived exertion. Incremental maximal tests showed that time to exhaustion was significantly changed and this occurred without a change in maximal power, maximal oxygen uptake, maximal heart rate and blood lactate, and that the influence on ratings of perceived exertion was non-significant or small.The study of classical style roller skis μS showed values that were five to eight times more than the values of μS reported from on-snow skiing with grip-waxed cross-country skis.The subsequent physiological and biomechanical experiments with different μS showed a significantly lower skiing economy (~14 % higher v̇O2), higher heart rate, lower propulsive forces coming from the legs and shorter time to exhaustion (~30 %) when using a different type of roller ski with a μS similar to on-snow skiing, while there was no difference between tests when using different pairs of roller skis with a (similar) higher μS.The part of the thesis which focused on skiing economy and efficiency as a function of skill, age and gender, showed that the elite cross-country skiers had better skiing economy and higher gross efficiency (5-18 %) compared with the recreational skiers, and the senior elite had better economy and higher efficiency (4-5 %) than their junior counterparts, while no differences could be found between the genders. / Syftet med denna avhandling var att undersöka fristils- och klassiska rullskidors rullmotståndskoefficienter (μR) och klassiska rullskidors statiska friktionskoefficienter (μS) samt effekter av olika μR och μS på längdskidåkares prestation vid rullskidåkning på rullande band. Syftet var även att undersöka s.k. åkekonomi och mekanisk verkningsgrad mellan motionärer och kvinnliga och manliga junior- och seniorlängdskidåkare på elitnivå.Experimenten visade att under en period av 30 minuters kontinuerligt rullande, på rullande band, så sjönk μR signifikant (p<0.05) till 60-65 % och 70-75 % av initiala värden, för fristils- respektive klassiska rullskidor. Undersökandet av olika normalkrafter, hastigheter och lutningars påverkan på μR resulterade i en signifikant, negativ korrelation för μR som funktion av normalkraft, medan olika hastigheter och lutningar endast medförde små förändringar av μR.Studien som undersökte fysiologiska effekter av olika μR visade, vid submaximala konstanta arbetsbelastningar, att yttre effekt, syreupptagning, hjärtfrekvens och blodlaktat förändrades signifikant vid ~50 % förändring av μR. Försökspersonernas frekvens och sträcka per frekvens samt skattning av upplevd ansträngning resulterade dock i mestadels icke signifikanta eller små förändringar. Protokollen med successivt ökande arbetsbelastning (maxtest) resulterade i signifikant förändrad tid till utmattning, vid ~50 % förändring av μR. Detta inträffade utan signifikant skillnad i maximal syreupptagning, hjärtfrekvens och blodlaktat, vilket även mestadels gällde för skattning av upplevd ansträngning.Experimenten som undersökte klassiska rullskidors μS visade att dessa erhöll värden som är fem till åtta gånger högre än vad som rapporterats från studier av μS på snö med fästvallade skidor.Den efterföljande studien som undersökte fysiologiska och biomekaniska influenser av olika μS visade, vid submaximala konstanta arbetsbelastningar, att åkekonomin försämrades (~14 % högre syreförbrukning), hjärtfrekvensen ökade, den framåtdrivande kraften från benen på rullskidorna minskade samt att det blev kortare tid till utmattning (~30 %), vid maxtest, när skidåkarna använde rullskidor med en μS i likhet med vad som rapporterats för skidåkning på snö. För arbetsförsöken med olika rullskidor av olika fabrikat med en högre, och likartad, μS förelåg ingen skillnad i de undersökta variablerna.Studien som undersökte åkekonomi och mekanisk verkningsgrad som funktion av prestationsnivå, ålder och kön, visade att elitskidåkarna hade bättre åkekonomi och verkningsgrad (5-18 %) i jämförelse med motionärerna, att seniorerna hade bättre åkekonomi och verkningsgrad (4-5 %) än juniorerna och att ingen skillnad kunde konstateras mellan könen.

The suspension of the motor vehicle is one of the most important elements of the flexible mounted and inflexible mounted masses of the vehicle bodywork, and most attention is paid to its exploration and improvement. Analysis of models of equivalent oscillation systems of motor vehicles testifies that the evaluation of motor vehicle oscillations and modelling of its motion modes is still very topical and requires further research. Suspension models of motor vehicles offered in publications regard only the influence of road irregularities, and the modernisation of these models is directed towards the improvement of passengers’ comfort. However not much research has been done on the influence of oscillations of flexible mounted and inflexible mounted masses of the bodyworks of vehicles in the process of braking; also there is not much investigation of the post-accident identification of the vehicle’s movement mode corresponding to the deformations of the suspension and the longitudinal pitch of the bodywork. Research of oscillations in the conditions of emergency braking is primarily important for the work in two practical directions: 1) improvement of calculation methods of motor vehicle’s response to external impact in the conditions of real operation; 2) further improvement of research methods on the road, and analysis of fait accompli road accidents related to oscillations in the emergency braking. Methodology defining the oscillations occurring in the braking may be applied... [to full text]

The suspension of the motor vehicle is one of the most important elements of the flexible mounted and inflexible mounted masses of the vehicle bodywork, and most attention is paid to its exploration and improvement. Analysis of models of equivalent oscillation systems of motor vehicles testifies that the evaluation of motor vehicle oscillations and modelling of its motion modes is still very topical and requires further research. Suspension models of motor vehicles offered in publications regard only the influence of road irregularities, and the modernisation of these models is directed towards the improvement of passengers’ comfort. However not much research has been done on the influence of oscillations of flexible mounted and inflexible mounted masses of the bodyworks of vehicles in the process of braking; also there is not much investigation of the post-accident identification of the vehicle’s movement mode corresponding to the deformations of the suspension and the longitudinal pitch of the bodywork. Research of oscillations in the conditions of emergency braking is primarily important for the work in two practical directions: 1) improvement of calculation methods of motor vehicle’s response to external impact in the conditions of real operation; 2) further improvement of research methods on the road, and analysis of fait accompli road accidents related to oscillations in the emergency braking. Methodology defining the oscillations occurring in the braking may be applied... [to full text]

Réduire l’énergie générée par le frottement et dissipée dans les systèmes mécaniques réels est un des challenges actuels en tribologie. Ce point représente une importance toute particulière dans le domaine des transports terrestres. En réponse à cette nécessité, les constructeurs automobiles se concentrent sur la réduction de la consommation d'énergie en sélectionnant des lubrifiants et des matériaux appropriés d'une part et les systèmes mécaniques performants d'autre part. Grâce à leurs propriétés physiques et tribologiques en termes de réduction de la friction et de l'usure, les couches minces de DLC (Diamond-like Carbon) sont considérées comme l'une des solutions. Le comportement tribologique de couches minces de ta-C (carbone amorphe très dur dépourvu d’hydrogène) et de a-C:H (carbone amorphe hydrogéné) est ici exploré. D’autre part, des “lubrifiants verts“ et des additifs participant aussi à la réduction du frottement et de l'usure sont testés. Ces essais sont effectués dans différentes conditions en utilisant une nouvelle méthodologie expérimentale. Le tribomètre dynamique oscillant développé au LTDS possède la capacité de quantifier avec une très grande précision et sans recourir à une quelconque mesure de force, des niveaux de frottement faibles (dans la gamme 10 – 5 à 10 – 2), et permet en plus d’identifier différentes contributions du frottement. Dans un premier temps, une loi de frottement linéaire a été utilisée afin d’évaluer deux contributions de frottement. La première, μ0 est le coefficient transitoire de frottement quand la vitesse s’annule au changement de direction (du type frottement de Coulomb). La seconde, μ1, est une contribution dépendante de la vitesse de glissement. Ensuite, une étude numérique a été réalisée en appliquant une loi de frottement quadratique afin de mieux comprendre l'aspect dynamique des réponses libres. Cela nous a permis d'étudier numériquement la décroissance d’amplitude des oscillations déterminée grâce à la méthode de moindres carrés. Nous nous intéressons aussi à l‘étude des formes de l'enveloppe de ces oscillations en relation avec le modèle de frottement. Les résultats numériques et expérimentaux pour les lois de frottement linéaire et quadratique sont ensuite comparés. En complément, nous avons mesuré la force tangentielle correspondant aux tribosystèmes testés. Finalement, nous avons étudié numériquement un système dynamique masse-ressort à un degré de liberté, modélisé par la loi de frottement LuGre. Cette loi est décrite par le phénomène d’hystérésis et l’effet de décalage de temps qui ont été détectés expérimentalement. Les résultats expérimentaux obtenus avec le tribomètre oscillant montrent qu'ils sont qualitativement comparables à ceux obtenus en configuration classique cylindre-plan, travaillant à vitesse de glissement constante. Dans tous les cas, les résultats montrent la supériorité du tribosystème ta-C/ta-C dans la réduction du frottement μ0. De plus, les résultats numériques et expérimentaux sont cohérents. Cette étude montre qu’une loi de frottement quadratique est capable de décrire correctement toutes les formes d’enveloppes obtenues expérimentalement : droite, convexe, concave et une combinaison des formes convexe et concave. / Controlling friction is a one of the most significant challenges in the field of tribology. Its major purpose is directed towards the reduction of energy in real mechanical systems, especially in the area of transportation. In response to this necessity, the automobile industries are emphasizing on minimizing the consumption of energy by selecting the appropriate lubricants and materials on one hand and mechanical system with high performance on the other hand. DLC (Diamond-like carbon) coated surfaces are considered one of the solutions thanks to their physical and tribological properties in reducing friction and wear. In this study, we have been interested in investigating the friction behavior of both amorphous hydrogenated (a-C:H) and hydrogen-free tetrahedral amorphous carbon (ta-C) DLC coatings. Furthermore, some “green lubricants” and additives are tested which play a role in reducing friction and wear. These latter tests are performed at different operating conditions using a new experimental methodology, known as the dynamic oscillating tribometer. This original tribometer, developed at the Laboratory of Tribology and System Dynamics (LTDS), is able to measure the oscillatory motion corresponding to various tribosystems having low friction. This technique has the ability to quantify with remarkable precision and without any force transducer, low friction values (in the range of 10 – 5 to 10 – 2 ) and also to evaluate different friction contributions from the displacement and velocity-time responses of a mass-springdamper oscillating system. First, a linear friction law has been used for the systems tested in order to calculate two contributions of friction. The first one, μ0 is the transient friction coefficient at zero speed and the second one (Coulomb-type fiction), μ is a velocitydependent friction coefficient. Then, a numerical study is carried out in order to better understand the dynamic aspect of the oscillatory vibratory free responses. A quadratic friction law is used to model on the mechanical system of the apparatus. This allows us to study numerically the behavior of the decreasing amplitudes of the damping responses which are determined using the Averaging method. Furthermore, we are interested in studying the various forms of these oscillations’ envelop in relation with the polynomial expansion of the friction model. Also, numerical and experimental results are compared using both the linear and quadratic friction models. In addition, a particular attention is given to the measured tangential forces corresponding to our tribosystems. Finally, we study numerically a damped mass-spring single degree-of-freedom mechanical system, induced by LuGre friction law described by both hysteresis and lag effect which have been detected experimentally. Results show that friction tests performed with the oscillating tribometer can be qualitatively compared to those obtained with a conventional tribometer. Moreover, ta-C/ta-C surfaces reveal the lowest friction μ0 when tested by both oscillating and reciprocating tribometers. Also, both numerical and experimental results are found to be of good agreement. This study shows that a quadratic friction law is able to describe correctly the envelopes observed in our experimental tests: straight, convex, concave and a combination of both convex and concave.