Modélisation du comportement mécanique des engrenages en plastique renforcé

Polymer gears present several advantages: they can be used without lubricant, their meshing is silencer, resistance to corrosion is better, weight is reduced. However they have a poor heat resistance and are limited to rotation transmission. In order to improve the gears performance, glass fibre reinforcement is being increasingly used, where their lower cost and higher strength, compared to unreinforced polyamide, offer a potential increase in gear performance. Mechanical behaviour of polymers materials is very complex; it depends on time, history of displacement, temperature and for several polymers, on humidity. Moreover, an addition of fibres can make the material properties heterogeneous and anisotropic. The particular case of Polyamide 6 + 30% glass fibres which is the most common fibre reinforced plastic is studied in this work. In the first part of this work, a mould was developed to better control the material choice and moulding conditions. Using tomographic observations, investigations were done to better understand the relation between moulding conditions, gears geometry and fibres orientation. Based on these observations and with the help of mechanical characterisation, a linear rheological generalized-Kelvin model was developed to simulate the viscoelastic behavior of the polymer material. In a second part, this model taking into account temperature, humidity and rotation speed is integrated in quasi-static load sharing computation developed by the LaMCoS laboratory. In the load sharing calculus, the displacements are obtained on a large meshing covering the entire surface of the tooth. This relation integrates the viscoelastic displacement, the fibre orientation and the geometrical influence coefficients. The method permits to obtain results such as the loaded transmission error, the instantaneous meshing stiffness, the load sharing and the root tooth stress at different temperature, humidity and rotation speeds within a reasonable computation time. Investigation have shown interesting results regarding the historic of displacements which represents up to 15% of the total displacement at the tip radius, the localization of the maximal tooth root stress, which is the same than metal gears, or the influence of the thermal expansion toward transmission error. On another hand, we have highlighted the low difference between a realistic description of the fibre orientation and an homogeneous anisotropic one. The last step concerns the validation of the numerical. The measurements are carried out on a test bench developed at the LaMCoS laboratory. It provides two experimental results: the temperature of the gear during operation, and the load transmission error using optical encoders to measure the angular positions of the pinion and the gear. This one is global enough to validate the three steps of the model: geometry, kinematics and load sharing.Les engrenages en matériau polymère présentent de nombreux avantages par rapport aux aciers. Ils sont plus légers, résistants à la corrosion, fonctionne sans lubrifiant et leurs coûts de revient est moindre grâce au moulage par injection. Ils sont de plus en plus utilisés dans des domaines variés, mais se limitent à la transmission de mouvement. L’ajout de fibre de verre courte permet d’augmenter leur tenue mécanique et de diversifier leur domaine d’utilisation à des transmissions de petite à moyenne puissance. Le polyamide (Nylon) renforcé de fibres de verre est le composite le plus couramment utilisé dans le domaine des engrenages. Néanmoins, son comportement viscoélastique ainsi que la présence de fibres introduit une difficulté supplémentaire dans la modélisation. En outre, le comportement viscoélastique dépend de la température et pour le Polyamide, de l’humidité. Par conséquent, la viscoélasticité impacte directement la répartition des charges, l’erreur de transmission sous charge, la raideur d’engrènement. Dans cette thèse, une méthode numérique originale modélisant le comportement mécanique des engrenages en Polyamide 6 renforcé de fibre de verre est proposée. L’approche utilise le modèle rhéologique linéaire de Kelvin généralisé pour simuler le comportement viscoélastique du matériau et prendre en compte la température, l’humidité ainsi que le taux de fibre et leur anisotropie. Ensuite ce modèle rhéologique est intégré dans le modèle quasi-statique du partage des charges développé par le LaMCoS. Ce processus de calcul permet d’obtenir les résultats essentiels pour les engrenages (répartition des charges, pressions de contact, erreur de transmission sous charge, raideur d’engrènement) avec un temps de calcul assez court. Afin de de valider les modèles numériques développés, un banc d’essai a été mis en place, permettant la mesure de l'erreur de transmission et la visualisation de la température de l’engrenage pendant son fonctionnement

Through-Process Modelling for Accurate Prediction of Long Term Anisotropic Mechanics in Fibre Reinforced Thermoplastics.

Fibre reinforced thermoplastic (FRTP) materials offer great potential for, among others, weight and cost reduction in a wide range of applications. In this paper, consequences of fiber orientation-induced anisotropy (due to injection molding process) in the development of FRTP parts as well as predictive engineering techniques for part performance evaluation are discussed. A coupled simulation methodology will be used to predict the processing-microstructure-properties relation in FRTP parts, thereby enabling the ability to include fiber orientation-induced anisotropy. In parallel, long term fatigue data was collected on increasingly complex geometries for the purpose of model validation

Fiber reinforced plastic gear mechanical behavior modeling

Les engrenages en matériau polymère présentent de nombreux avantages par rapport aux aciers. Ils sont plus légers, résistants à la corrosion, fonctionne sans lubrifiant et leurs coûts de revient est moindre grâce au moulage par injection. Ils sont de plus en plus utilisés dans des domaines variés, mais se limitent à la transmission de mouvement. L’ajout de fibre de verre courte permet d’augmenter leur tenue mécanique et de diversifier leur domaine d’utilisation à des transmissions de petite à moyenne puissance. Le polyamide (Nylon) renforcé de fibres de verre est le composite le plus couramment utilisé dans le domaine des engrenages. Néanmoins, son comportement viscoélastique ainsi que la présence de fibres introduit une difficulté supplémentaire dans la modélisation. En outre, le comportement viscoélastique dépend de la température et pour le Polyamide, de l’humidité. Par conséquent, la viscoélasticité impacte directement la répartition des charges, l’erreur de transmission sous charge, la raideur d’engrènement. Dans cette thèse, une méthode numérique originale modélisant le comportement mécanique des engrenages en Polyamide 6 renforcé de fibre de verre est proposée. L’approche utilise le modèle rhéologique linéaire de Kelvin généralisé pour simuler le comportement viscoélastique du matériau et prendre en compte la température, l’humidité ainsi que le taux de fibre et leur anisotropie. Ensuite ce modèle rhéologique est intégré dans le modèle quasi-statique du partage des charges développé par le LaMCoS. Ce processus de calcul permet d’obtenir les résultats essentiels pour les engrenages (répartition des charges, pressions de contact, erreur de transmission sous charge, raideur d’engrènement) avec un temps de calcul assez court. Afin de de valider les modèles numériques développés, un banc d’essai a été mis en place, permettant la mesure de l'erreur de transmission et la visualisation de la température de l’engrenage pendant son fonctionnement.Polymer gears present several advantages: they can be used without lubricant, their meshing is silencer, resistance to corrosion is better, weight is reduced. However they have a poor heat resistance and are limited to rotation transmission. In order to improve the gears performance, glass fibre reinforcement is being increasingly used, where their lower cost and higher strength, compared to unreinforced polyamide, offer a potential increase in gear performance. Mechanical behaviour of polymers materials is very complex; it depends on time, history of displacement, temperature and for several polymers, on humidity. Moreover, an addition of fibres can make the material properties heterogeneous and anisotropic. The particular case of Polyamide 6 + 30% glass fibres which is the most common fibre reinforced plastic is studied in this work. In the first part of this work, a mould was developed to better control the material choice and moulding conditions. Using tomographic observations, investigations were done to better understand the relation between moulding conditions, gears geometry and fibres orientation. Based on these observations and with the help of mechanical characterisation, a linear rheological generalized-Kelvin model was developed to simulate the viscoelastic behavior of the polymer material. In a second part, this model taking into account temperature, humidity and rotation speed is integrated in quasi-static load sharing computation developed by the LaMCoS laboratory. In the load sharing calculus, the displacements are obtained on a large meshing covering the entire surface of the tooth. This relation integrates the viscoelastic displacement, the fibre orientation and the geometrical influence coefficients. The method permits to obtain results such as the loaded transmission error, the instantaneous meshing stiffness, the load sharing and the root tooth stress at different temperature, humidity and rotation speeds within a reasonable computation time. Investigation have shown interesting results regarding the historic of displacements which represents up to 15% of the total displacement at the tip radius, the localization of the maximal tooth root stress, which is the same than metal gears, or the influence of the thermal expansion toward transmission error. On another hand, we have highlighted the low difference between a realistic description of the fibre orientation and an homogeneous anisotropic one. The last step concerns the validation of the numerical. The measurements are carried out on a test bench developed at the LaMCoS laboratory. It provides two experimental results: the temperature of the gear during operation, and the load transmission error using optical encoders to measure the angular positions of the pinion and the gear. This one is global enough to validate the three steps of the model: geometry, kinematics and load sharing

A Low Phase Noise and Wide-Bandwidth BiCMOS SiGe:C 0.25µm Digital Frequency Divider For An On-Chip Phase-Noise Measurement Circuit

4 pagesInternational audienceA low phase noise and wide-bandwidth frequency divider has been developed in a 0.25 µm SiGe:C process. This paper discusses the BiCMOS design improvements used for ultra low phase noise applications like on-chip phase-noise measurement circuit. From a single-ended signal provided by a local oscillator LO, the wide-bandwidth frequency divider circuit generates accurate quadrature signals. For the full 1kHz-5.5 GHz input frequency range, the frequency divider achieves an output quadrature error less than ±1°. This paper presents a novel architecture designed for improving phase noise and exhibits a measured residual phase noise of -164 dBc/Hz @ 100 kHz with a 3.5 GHz input frequency

Diviseur de fréquence SiGe:C 0,25 µm, large bande et faible bruit, pour banc de mesure de bruit de phase intégré

La conception, la réalisation et la caractérisation d'un diviseur de fréquence par 2, large bande et faible bruit de phase est présentée. L'application ciblée est un banc de mesure de bruit de phase totalement intégré. Le diviseur de fréquence sert à fournir des signaux de référence en quadrature, sur la bande [1 kHz ; 5,5 GHz]. Ainsi, une erreur de quadrature inférieure à ± 1° a été mesurée sur toute la bande, avec un bruit de phase résiduel de seulement −164 dBc/Hz à 100 kHz de la porteuse de 3,5 GHz

A Baseband Ultra-Low Noise SiGe:C BiCMOS 0.25 µm Amplifier And Its Application For An On-Chip Phase-Noise Measurement Circuit

4 pagesInternational audienceThe design and realization of an ultra-low noise operational amplifier is presented. Its applications are integrated low-frequency noise measurements in electronic devices and on-chip phase-noise measurement circuit. This paper discusses the SiGe:C BiCMOS 0.25 µm design improvements used for low noise applications. The proposed three-stage operational amplifier uses parallel bipolar transistor connection as input differential pair for low noise behavior. This operational amplifier provides both low noise and high gain performances. This operational amplifier has an area of only 660x250 µm2 with an equivalent input noise floor of only 1.1 nV/√Hz at 10 kHz. The measured noise characteristics (versus total power consumption) are better than those of most operational amplifiers commonly adopted in low-frequency noise measurements. The AC gain is 83 dB and the unity gain bandwidth is 210 MHz, with a total current consumption of 18 mA at 2.5 V supply voltage

Etude numérique et expérimentale du comportement sous charge d'engrenage cylindrique en polymère

National audienc

A Low Phase Noise and Wide-Bandwidth BiCMOS SiGe:C 0.25µm Digital Frequency Divider For An On-Chip Phase-Noise Measurement Circuit

4 pagesInternational audienceA low phase noise and wide-bandwidth frequency divider has been developed in a 0.25 µm SiGe:C process. This paper discusses the BiCMOS design improvements used for ultra low phase noise applications like on-chip phase-noise measurement circuit. From a single-ended signal provided by a local oscillator LO, the wide-bandwidth frequency divider circuit generates accurate quadrature signals. For the full 1kHz-5.5 GHz input frequency range, the frequency divider achieves an output quadrature error less than ±1°. This paper presents a novel architecture designed for improving phase noise and exhibits a measured residual phase noise of -164 dBc/Hz @ 100 kHz with a 3.5 GHz input frequency

Quasi-static Load Sharing Model in the Case of Moulded Glass Fibre Reinforced Polyamide 6 Gears

International audienceThis paper presents a fast and efficient computational method to predict the mechanicalbehaviour of plastic cylindrical gears made of fibre reinforced polyamide 6. Based on this method, aninvestigation on the relation between the fibre orientation and the gear behaviour is done. Thenumerical method uses a viscoelastic model accounting for the temperature, humidity and rotationalspeed dependence of the gear. This model is developed under the assumption that the material isstressed in its linear domain. The method is performed in three steps: the first one consists of definingthe fibre orientation from simulation and experimental results. The second step characterises theviscoelastic behaviour of the material. The third step consists in calculating the load sharing with localmeshing, which integrates the viscoelastic model over the entire surface of the tooth. This modelpermits computation of the load sharing between instantaneously engaged teeth and provides resultssuch as contact pressure, tooth root stress and transmission error. Three fibre orientation models withan increasing complexity are compared. Simulation results show a limited influence of the fibreorientation on the contact pressure and tooth root stress, nevertheless difference up to 10% areobserved on the transmission error amplitude