A Note on the Shear Influence on Belt Drive Mechanics

Abstract Belt drives work often with short center distances and very different wrap arcs so that high adherence characteristics are required at the belt-pulley contact. In addition, the belt flexural stiffness reduces the contact width, but this decrease may be compensated in part by the belt softening due to the shear compliance.

Elia Ovazza, Professor of TMM in Palermo Around the End of the 19th Century

In this paper, the figure of Elia Ovazza, professor of TMM in Palermo around the end of the 19th century, is presented, along with his valuable legacy in regard to his activities in teaching, research, design and technology transfer. Short biographical notes outline his foremost life events and an illustrated survey explains his contributions.

Preventing the oil film instability in rotor-dynamics

Horizontal rotor systems on lubricated journal bearings may incur instability risks depending on the load and the angular speed. The instability is associated with the asymmetry of the stiffness matrix of the bearings around the equilibrium position, in like manner as the internal hysteretic instability somehow, where some beneficial effect is indeed obtainable by an anisotropic configuration of the support stiffness. Hence, the idea of the present analysis is to check if similar advantages are also obtainable towards the oil film instability. The instability thresholds are calculated by usual methods, such as the Routh criterion or the direct search for the system eigenvalues. The results …

Stability analysis of rotor whirl under nonlinear internal friction by a general averaging approach

The two main sources of internal friction in a rotor-shaft system are the shaft structural hysteresis and the possible shrink-fit release of the assembly. The internal friction tends to destabilize the over-critical rotor running, but a remedy against this effect may be provided by a proper combination of some external damping in the supports and an anisotropic arrangement of the support stiffness, or at most by the support damping alone, depending on the system geometry. The present analysis reported here considers a general asymmetric rotor-shaft system, where the rotor is perfectly rigid and is constrained by viscous–flexible supports having different stiffnesses on two orthogonal plane…

Helical Shift Mechanics of Rubber V-Belt Variators

A very common configuration of V-belt variators for motorcycles considers the correction of the belt tensioning depending on the resistant torque by means of suitable helical-shaped tracks allowing the driven half-pulleys to close/open. The theoretical model for belt-pulley coupling is rather complex for this configuration, where one half-pulley may run in advance and the other one behind with respect to the belt, and requires the repeated numerical solution of a strongly nonlinear differential system by a sort of shooting technique, until all the operating conditions are fulfilled (angular contact extent, torque, and axial force). After solving the full equations, the present study develop…

Damping of rotor conical whirl by asymmetric dry friction suspension

Abstract A new technique for the rotor whirl damping in rotating machinery, based on the elastic suspension of the journal boxes and the use of dry friction surfaces normal to the shaft axis between their supports and the frame, is here analysed theoretically for several cases of rotor systems characterized by mass and constraint asymmetry, where gyroscopic effects are to be expected and conical whirl motions may grow up. The critical flexural speeds can be easily cut off by an adhesive state of the supports and the whirl amplitude can be minimized as well throughout the remaining sliding range. Confining the operative angular speed of the rotor in the range of adhesive contact between the …

Transient Mechanics of V-Belt Variators

A Numerical Approach to Finite Journal Bearings Lubricated With Ferrofluid

Several cases of cylindrical bearings lubricated with ferrofluid are examined by means of a finite-difference numerical procedure. The subregion of cavitation is determined by imposing mass conservation across the “rupture” and “reformation” boundaries of the complete film. The examined cases refer to bearings confined by sealing rings formed by the lubricant itself, for which there is no need of external supply. In each case the most significant parameters are calculated and it is possible to see that the use of these bearings is favorable when speeds are low, clearances large, and loads light, because in such conditions the magnetic effects are comparable with the pure hydrodynamic ones a…

Coupling Mechanics of Antikythera Gearwheels

This paper discusses the gear coupling mechanics of the ancient Antikythera mechanism, among whose distinctive characteristics was the triangular shaping of the teeth. The engagement of the tooth pairs is analyzed in detail, estimating the temporal variation of the speed ratio due to the back and forth shifting of the relative instant center. The admissibility of the theoretical contact points is carefully checked, and the magnitude of the successive tooth collisions is calculated together with the energy losses arising from the particular nature of the coupling. Some interesting results are that only one tooth pair turns out to be active at each time instant and the real path may belong on…

A Two-Dimensional Approach to Rubber V-Belt Mechanics

A new two-dimensional approach to the mechanics of rubber V-belt CVT's takes into account the change, along the belt sides, of the sliding velocity on the pulley walls, together with the cross section rotation due to the shear forces. The results show significant differences with the one-dimensional thin belt model and point out the gradual increase or decrease of the belt curvature in the entrance and exit regions of the contact arc, which implies the negligibility of the belt arching in the free spans. Some experimental tests on the global variables of a rubber belt CVT indicate a very fine acceptability of the theoretical model.

SHEAR COMPLIANCE AND SELF WEIGHT EFFECTS ON TRACTION BELT MECHANICS

The transverse elastic deflection of a traction belt along the free span depends mainly on the flexural stiffness, but may be significantly influenced by the distributed weight and the shear compliance, which affect together the width of the arc of contact. In particular, the shear compliance yields a virtual decrease of the flexural stiffness, flattens the free span and increases the wound regions, to the advantage of the transmissible torque. Moreover, the tensioning of a given belt may be somewhat larger, in comparison with the ideal circular-straight path with the same centre distance, because of the increased length of the deflected belt trajectory due to gravity. The present paper ad…

Analysis of the Ratio Shift Transient in V-Belt Variators

Analysis of the static and dynamic behaviour of a magnetic liquid seal

A rotating shaft seal, using ferrofluid between biconical truncated magnetic poles, is analysed both in static and dynamic conditions. After solving Laplace's equation and allowing an approximate expression for the magnetic potential, the magnetic forces acting on the working fluid are obtained. It is thus possible to determine the baric field existing in static conditions and the highest tolerable pressure jump. In the case of dynamic working the flow is schematized by two interior regions, where the azimuthal velocity prevails, and four boundary layers on the walls, where meridional transport of fluid takes place. Assuming laminar motion, by means of a perturbation procedure it is possibl…

Swerve correction of heavy-duty articulated lorries

The trailers of heavy-duty articulated lorries are usually linked to the tractors by auxiliary dollies to improve the manoeuvrability along curved paths. Connecting the dolly to the tractor by a four-bar linkage, some performance improvement may be achieved in comparison with the conventional single pin. The correct path along a road curve may be obtained exerting control moments on the horizontal plane by means of differential braking of the wheels. The results of the analysis show that the forward-converging and the crossing bar quadrilaterals are mostly yaw-stable, whereas the farther backward-converging bars prove to be inherently unstable.

Dynamical behaviour of pneumatic artificial muscles

The mechanical response of pneumatic artificial muscles is analyzed in transient and periodic conditions, assuming the inextensibility of the sheathing fibres and considering the influence of the texture geometry, of the dissipation due to the mutual sliding between the braids and of the stress field inside the bladder thickness, where the constituent elastomer is regarded as a two-parameter Mooney–Rivlin material. The polytropic exponent of the thermodynamic air evolution inside the muscle during the charging and discharging phases may be properly chosen depending on the working frequency. The muscle end shape is taken into account profiling the meridian section by a simple m-degree parabo…

Rotor whirl damping by dry friction suspension systems

An efficient and automatic attenuation technique for the whirling motion of rotating machinery can be achieved by supporting the journal boxes elastically and providing them with suitable rubbing surfaces subject to dry friction normal to the shaft axis. The critical flexural speeds are easily cut off and the whirl amplitude is minimized throughout the frequency range. Confining the usual operative angular speed of the rotor in the range of adhesive contact between the dry friction surfaces, there is no significant increase of power dissipation or heat production as a whole due to this type of suspension system, whose task is just to suppress the resonant peaks when passing the critical spe…

Non-Linear Hysteretic Instability in Rotating Machinery

A Simple Model for the Axial Thrust in V-Belt Drives

Simple formulas can relate axial thrust and torque of rubber V-belt drives, taking into consideration the radial penetration of the belt.

Influence of Rotor Suspension Anisotropy on Oil Film Instability

A crucial problem of turbomachinery is the oil film instability on increasing the angular speed, which is correlated with the asymmetry of the bearing stiffness matrix and resembles the hysteretic instability somehow. As a beneficial effect is exerted on the latter by the anisotropy of the support stiffness, some favorable effects have been recently found by the author also for the former, whence a systematic analysis has been undertaken. The instability thresholds may be detected by the usual conventional methods, but a detailed analysis may be carried out by closed-form procedures in the hypothesis of symmetry of the rotor-shaft-support system, which condition approaches the real working …

On the Frequency Behaviour, Stability and Isolation Properties of Dry Friction Oscillators

This paper proposes a new approach to the frequency responses of one-degree-of-freedom oscillators subject to periodic excitations in presence of mixed dry-viscous friction. The idea is to get free from the analysis of one fixed system by letting the physical parameters cover their own whole ranges and investigating the various behavioural aspects of wide classes of oscillators. The existence, uniqueness and stability of the steady-state solutions are analysed in detail, assuming different coefficients of static and sliding friction. The possible arising of motions characterized by anti-periodic asymmetry or multi-stick oscillations is enlightened and maps of the system behaviour are presen…

A Note on the Shear Influence on Drive Belt Mechanics

Belt drives work often with short center distances and very different wrap arcs so that high adherence characteristics are required at the belt-pulley contact. In addition, the belt flexural stiffness reduces the contact width, but this decrease may be compensated in part by the belt softening due to the shear compliance.

A nonlinear dynamical approach to the path correction of multi-steering articulated vehicles

When designing articulated tractor-trailer systems, engineers should take care to contrast some undesired phenomena associated with the lateral dynamics: the path off-tracking, namely the trajector...

On the Birth and Growth of Pendulum Clocks in the Early Modern Era

Measuring the passage of time has intrigued humankind throughout the centuries. Ancient times witnessed the appearance and development of clepsydras and water clocks, whose place was subsequently taken by mechanical clocks in the Middle Ages. It is really surprising how the general architecture of mechanical clocks has remained almost unchanged in practice up to the present time. Yet the foremost mechanical developments in clock-making date from the 17th century, when the discovery of the laws of pendular isochronism by Galilei and Huygens permitted a higher degree of accuracy in the measuring of time.

On the beneficial effect of rotor suspension anisotropy on viscous-dry hysteretic instability

The destabilizing influence of the internal friction on the supercritical rotor whirl can be efficiently counterbalanced by other external dissipative sources and/or anisotropic suspension systems. The theoretical approach may take the internal dissipation into consideration either by dry or viscous models. Nevertheless, several numerical results and a new perturbation technique of the averaging type prove that similar rotor motions and stability limits are achievable by both models, whence the linear viscous assumption appears preferable. Thus, the internal hysteretic force may be expressed by the product of an equivalent viscous coefficient and the rotor centre velocity relative to a refe…

On the gear mechanics before the cycloid and involute profiling

After the extraordinary development of the machinery in the Hellenistic antiquity, the gear technique was transmitted to the Middle Ages through the Byzantine and Islamic culture and then to the Modern Era. The tooth profile was very crude, often trapezoidal or even rectangular and the gear behavior differed substantially from the modern involute profile. The kinematics of trapezoid profiles is here analyzed in detail, focusing on the temporal variation of the speed ratio due to the back and forth shifting of the relative instant center. Considering an isolated tooth pair, an approach phase is firstly observable, where the tip of the driven profile is pushed by the driver flank and then, af…

On the flexural vibrations of sandwich plates

A simplified approach to sandwich plate free vibrations, based on the superposition method, can provide approximations to the lowest modes for various boundary conditions, showing a characteristic influence of the bending-shear stiffness ratio.

V-Belt Winding along Archimedean Spirals During the Variator Speed Ratio Shift

Starting from a previous model for the shift mechanics of rubber belt variators, this lecture elaborates practical design formulas for the torque and the axial thrust making use of the very close resemblance of the belt path to a linear spiral of Archimedes along a large part of the arc of contact. In addition, as an alternative to the modern calculus tools, it is shown how the drive variables can be equally calculated applying some propositions of Archimedes’ classical treatise πeρί ‘eλίκων (On Spirals).

Joint Influence of Transverse Compression and Shear-Flexural Stiffness on Rubber V-Belt Mechanics

The elasto-mechanical behavior of a rubber V-belt in the neighborhood of the seating and unseating regions of the pulley is affected by the transverse belt compliance, which produces a gradual radial penetration into the groove and by the shear-flexural deformation, which arches the belt line along the free strand away from the ideal straight path. These effects are always analyzed separately in the literature, but are in close correlation with each other. This lecture describes the matching between the free strand and the wrap region, showing a remarkable reduction of the belt arching and of the contact losses, with respect to the conventional theory.

Einstein, Planck and Vera Rubin: Relevant Encounters Between the Cosmological and the Quantum Worlds

In Cosmology and in Fundamental Physics there is a crucial question like: where the elusive substance that we call Dark Matter is hidden in the Universe and what is it made of? that, even after 40 years from the Vera Rubin seminal discovery [1] does not have a proper answer. Actually, the more we have investigated, the more this issue has become strongly entangled with aspects that go beyond the established Quantum Physics, the Standard Model of Elementary particles and the General Relativity and related to processes like the Inflation, the accelerated expansion of the Universe and High Energy Phenomena around compact objects. Even Quantum Gravity and very exotic Dark Matter particle candid…

Nonlinear analysis of cylindrical and conical hysteretic whirl motions in rotor-dynamics

Abstract The internal friction of a rotor–shaft-support system is mainly due to the shaft structural hysteresis and to some possible shrink-fit release of the assembly. The experimentation points out the destabilizing effect of the internal friction in the over-critical rotor running. Nevertheless, this detrimental influence may be efficiently counterbalanced by other external dissipative sources located in the supports or by a proper anisotropic configuration of the support stiffness. The present analysis considers a rotor–shaft system which is symmetric with respect to the mid-span and is constrained by viscous-flexible supports with different stiffness on two orthogonal planes. The cylin…

Motion and force analysis of slow-speed multi-trailer systems

Comparing with the tractor-trailer systems for the road haulage, which must cope with some typical undesired trends, such as high-speed instability, over- or under-steering and off-tracking, the multi-trailer systems for the transport of luggage in the airports or in the railway stations, or for the transfer of goods in the warehouses, run at quite low speeds, but must manage to steer clear of the many obstacles encountered along their path. This type of vehicle is not subject to tire cornering phenomena, because the speed is just low and the wheels are generally stiff. Hence, the vehicle movement is in practice ruled by the non-holonomic rolling constraint of the wheels and by the steerin…

Surge instability in a distributed parameter radial compression system

Turbocompressor surge in a line with a long suction duct and plenum chamber is analysed using a distributed parameter propagation model which accounts for dynamic damping. The results, though obtained with simplifying assumptions, show very good agreement with experimental data.

Notes on Elia Ovazza, professor of TMM in Palermo since the end of 19-th century

In this lecture the figure of Elia Ovazza, professor of TMM in Palermo since the end of 19-th century, is presented with a valuable legacy as referring to his activity in teaching, research, design and technology transfer with short biographical notes

BCD-9 OPERATIVE VARIATOR CHARACTERIZATION FOR CVT IMPROVEMENT(BELT AND CHAIN DRIVES)

Shift Mechanics of Metal V-Belt CVT

KRYLOV-BOGOLIUBOV APPROACH TO NON-LINEAR HYSTERETIC INSTABILITY IN ROTORDYNAMICS

The internal friction due to the shaft hysteresis or the shrink fitting release exerts a destabilizing effect on the overcritical rotor whirl, but may be counteracted by other external dissipative sources and/or by proper anisotropy of the support stiffness. The internal friction effect may be treated by either dry or viscous models, obtaining similar results in the hypothesis of small dissipation levels, provided that proper equivalence criteria are defined between the two approaches. The equivalence is here stated by imposing the same energy dissipation over a large number of shaft revolutions. Approximate closed-form autonomous solutions for a symmetric rotor arrangement subject to Coulo…

Approximate Closed-Form Solutions for the Shift Mechanics of Rubber Belt Variators

The mechanical behavior of V-belt variators during the speed ratio shift is different from the steady operation as a gross radial motion of the belt is superimposed to the circumferential motion. The theoretical analysis involves equilibrium equations similar to the steady case, but requires a re-formulation of the mass conservation condition making use of the Reynolds transport theorem. The mathematical model of the belt-pulley coupling implies the repeated numerical solution of a strongly non-linear differential system. Nevertheless, an attentive observation of the numerical diagrams suggests simple and useful closed-form approximations for the four possible working modes of any pulley, o…

Approach to rotor-shaft hysteretic whirl using Krylov-Bogoliubov techniques

The internal friction associated with the shaft hysteresis or with the possible release of some shrink-fit coupling exerts a destabilizing effect on the over-critical rotor running, but may be efficiently counteracted by other external dissipative sources or by a proper anisotropic configuration of the support stiffness. The present analysis considers a symmetric rotor-shaft system on viscous-flexible supports with different stiffness on two orthogonal planes containing the bearing axis. The internal friction of the shaft is described either by a linear hysteretic model or by a nonlinear Coulombian force contrasting the rotor motion relative to the shaft ends. The nonlinear equations of mo…

On the sway stability improvement of car–caravan systems by articulated connections

The present analysis is addressed to some promising connection arrangements between the towing vehicles and the towed trailers, where the two units are linked by four-bar isosceles trapeziums in place of the conventional pintle hitch. Two types of instability, of the divergent type or the oscillating type, may be analysed by the Routh–Hurwitz criterion or by the direct analysis of the characteristic equation. The constant term of this equation vanishes at the divergent instability threshold (zero of a real root), whereas the equation splits into two lower degree algebraic ‘sub-equations’ when the oscillating instability arises (pair of pure imaginary roots). A large field of geometrical con…

Optimization of vehicle-trailer connection systems

The three main requirements of a vehicle-trailer connection system are: en route stability, over- or under-steering restraint, minimum off-tracking along curved path. Linking the two units by four-bar trapeziums, wider stability margins may be attained in comparison with the conventional pintle-hitch for both instability types, divergent or oscillating. The stability maps are traced applying the Hurwitz method or the direct analysis of the characteristic equation at the instability threshold. Several types of four-bar linkages may be quickly tested, with the drawbars converging towards the trailer or the towing unit. The latter configuration appears preferable in terms of self-stability and…

A Qualitative-Quantitative Approach to V-Belt Mechanics

A simplified formulation is adopted for the theoretical problem of tension distribution and radial penetration of a V-belt along the pulley groove. The trajectory portrait of the second order differential system describing the belt behavior is carefully analyzed and asymptotic approximations for the tension solutions are derived which are well suited for design purposes.

BCD-01 JOINT INFLUENCE OF TRANSVERSE COMPRESSION AND SHEAR-FLEXURAL STIFFNESS ON RUBBER V-BELT MECHANICS(BELT AND CHAIN DRIVES)

Inarcamento delle cinghie di trasmissione nei rami liberi. Influenza sul pre-tensionamento e sulla potenza limite

Hysteretic whirl stabilization in rotor-shaft-bearing systems on dry friction suspension

SUMMARY. The undesired whirl of rotating machines can be reduced by elastic journal box suspension systems equipped with dry friction dampers. The critical speeds can be cut off by the adhesion of the friction surfaces and the whirl amplitude can be restrained throughout the remaining sliding range by a proper choice of the suspension-to-shaft stiffness ratio and of the support-to-rotor mass ratio. The dry friction forces counteract also efficiently the well known destabilising effect of the shaft hysteresis in the supercritical range. This lecture deals firstly with the natural precession speeds, investigates the steady response to unbalance and defines the ranges of adhesive or sliding co…

A theoretical approach to pneumatic muscle mechanics

The mechanical response of pneumatic artificial muscles is analyzed assuming the inextensibility of the sheathing braids and taking into account the stress field inside the rubber bladder, which is regarded as a Mooney-Rivlin hyperelastic material. The end effects are simulated by heuristically profiling the meridian section. After estimating the constitutive parameters by traction tests on rubber specimens, the theoretical results are compared with experiments and a satisfactory accordance may be detected.

Variational approach to the mechanics of metal V-belt systems

The mechanical behaviour of metal V-belt drives is strongly dependent on the elastic properties of both the belt and the pulley, which influence the belt penetration into the groove and the sliding on the pulley wall. The distribution of tension and penetration is quite different from the rubber belts, which may be dealt with in the assumption of perfectly rigid pulleys. The restoring effect of the centrifugal forces of the plate elements has also to be taken into account. The present analysis considers the combination of all those effects, choosing a three parameter deformation function to describe the plate bending and applying the principle of virtual work for the calculation of the unkn…

The Rotary Aero-Engine from 1908 to 1918

The rotary aero engine is a special type of air-cooled radial engine, where the cylinders are arranged like the spokes of a wheel and turn around the crankshaft. The propeller is connected to the cylinders, while the crankshaft is fixed to the frame. The rotary aero engine, developed in 1908, set new standards of power and light weight within the aircraft industry. It was adopted by many pioneer aviators and widely used to set records of endurance, speed and height. Many aero engine manufacturers produced different models and variants of this type of engine, which was extensively used until the end of the First World War. The latest evolution of the rotary engine was the counter-rotary arra…

A Note on the Mechanics of Ancient Gear Systems

This paper deals with the mechanical behavior of the gearwheels of the antiquity, which were generally characterized by triangular shaping of the teeth. The engagement of the conjugate profiles is analyzed in detail, calculating the temporal variation of the speed ratio due to the back and forth shifting of the relative instant center. The admissibility of the points of the theoretical contact path is carefully checked, estimating also the magnitude of the successive tooth collisions and ascertaining the energy losses arising from the particular nature of the coupling. Some very interesting results are that only one couple of teeth turns out to be active at each time instant and that the re…

Mechanical Behaviour of Two-Degree-of-Freedom Oscillators in Presence of Dry Friction

On the birth and growth of pendulum clocks in the Early on the History Modern Era

Measuring the passage of time has intrigued humankind throughout the centuries. Ancient times witnessed the appearance and development of clepsydras and water clocks, whose place was subsequently taken by mechanical clocks in the Middle Ages. It is really surprising how the general architecture of mechanical clocks has remained almost unchanged in practice up to the present time. Yet the foremost mechanical developments in clock-making date from the 17th century, when the discovery of the laws of pendular isochronism by Galilei and Huygens permitted a higher degree of accuracy in the measuring of time.

Three-mode pneumatic management of marine U-tank systems

Abstract This paper deals with a new pneumatic control strategy for the roll damping enhancement of marine U-tank stabilizers. The proposed technique consists in a three-mode operation, where the control is active only within a limited resonant range around the ship natural frequency, whereas the control valves are kept closed in the remaining frequency range. Moreover the connection valve between the two air chambers is either closed or partially opened for the low or high frequencies, respectively. The pressurized air for the active control is fed by a turbo-blower set aboard and operates accelerating the motion of the water mass in the U-duct. The theoretical analysis is conducted in the…

The Rotary Aero Engine from 1908 to 1918

The rotary aero engine is a special type of air-cooled radial engine, where the cylinders are arranged like the spokes of a wheel and turn around the crankshaft. The propeller is connected to the cylinders, while the crankshaft is fixed to the frame. The rotary aero engine, developed in 1908, set new standards of power and light weight within the aircraft industry. It was adopted by many pioneer aviators and widely used to set records of endurance, speed and height. Many aero engine manufacturers produced different models and variants of this type of engine, which was extensively used until the end of the First World War. The latest evolution of the rotary engine was the counter-rotary arra…

Correction of Long Vehicle Off Tracking by Multiple Axle Steering

When planning the road vehicles for the transport of passengers or goods, engineers should take care to contrast some undesirable phenomena in the lateral dynamics, such as high-speed instability or off tracking. While the former is less troubling in the slow heavy vehicles, the latter is a serious problem due to the risk of invading the neighbouring lanes. The use of multi-wheel steering may completely cancel this drawback and, pursuing an optimized correlation among the steering angles, a functional inter-dependence based on the cubic “witch of Agnesi” is found to be very promising. Simple control systems with electromechanical or electronic components may be easily implemented for the mu…

On the isochronism of Galilei's horologium

Measuring the passage of time has always fascinated the humankind throughout the centuries. It is amazing how the general architecture of clocks has remained almost unchanged in practice to date from the Middle Ages. However, the foremost mechanical developments in clock-making date from the seventeenth century, when the discovery of the isochronism laws of pendular motion by Galilei and Huygens permitted a higher degree of accuracy in the time measure.

Forced Stick-Slip Oscillations of Two-Degree-of-Freedom Systems with Dry-Viscous Dissipation and Time-Dependent Static Friction

A Theoretical Approach to the Shift Mechanics of Rubber Belt Variators

This paper proposes a theoretical description of the mechanical behavior of rubber belt variators during the speed ratio shift. Comparing with the steady operation, the mass conservation of the belt is completely reformulated considering an elementary dihedral control volume between two planes through the pulley axis and balancing the inside mass variation with the total mass flux through the control surface. On the other hand, the belt equilibrium conditions are similar to the steady case, as the inertia forces due to the shifting motion are negligible with respect to the other forces. Assuming a one-dimensional belt model, it is shown that adhesive regions may appear inside the arc of con…

Full Sliding “Adhesive-Like” Contact of V-Belts

Abstract Analysis of power transmission in a belt drive consisting of e. g. two pulleys might be treated as a boundary value problem. Tight side tension FT, slack side tension FS and the wrap angle α are the three natural boundary conditions. In the literature, theories are developed where seating and unseating as well as the power transmitting part of the contact are considered. The solutions presented so far don’t fulfil the boundary conditions properly, since a certain tension ratio FT/FS is associated with a certain contact angle and not an a priori specified one. It appears that a new type of full sliding solution must be introduced to handle the boundary condition problem. During part…

Innovative Vehicle-Trailer Connection for Yaw Stability Improvement

As well known, dangerous conditions may occur for the lateral stability of the road vehicles on increasing the running velocity. While it is easy to make up for this drawback in the case of a vehicle alone, by a proper weight distribution, the unstable trend may worsen unfavourably for the vehicle-trailer configuration, imposing a very hard correction task to the driver, who has to cope with the development of two types of instability, exponentially divergent or swaying with increasing amplitude. The critical velocity depends on the geometrical and inertial characteristics of the car-trailer system, on the cornering stiffness of the tires and on the weight distribution among the axles. The …

Experimental results for a belt variator in transient conditions

An Efficient Damping Technique for the Unstable Hysteretic Rotor Whirl by Proper Suspension Systems

This paper shows as the destabilising influence of the shaft hysteresis on the supercritical rotor whirl can be efficiently counterbalanced by external dissipative sources. After calculating the steady whirling paths of the rotor and the bearing due to unbalance, the stability is checked by the Routh-Hurwitz procedure, investigating the influence of the stiffness anisotropy of the supports. A fairly interesting result is that the instability phenomena can be conveniently prevented by different suspension stiffness in the horizontal and vertical planes.

The "Mathematical Table" in the Chinese Lodge of Palermo

The end of the 18th century sees the decline of the late baroque and rococo in the decorative arts and the origin of the neoclassic essentiality. Nonetheless, the spirit of competition among the members of the European courts and of the aristocracy in erecting magnificent residences inside spectacular parks, full of astonishing pieces of furniture, is still alive and floods of money are spent without restraint. In this very period, a new curious type of dining table makes its appearance in the aristocratic dwelling houses and precisely in the hunting lodge of the Bourbon Court close to the city of Palermo in Sicily: the "Mathematical Table". This name is due to the fantasy of its designer, …

Control of hysteretic instability in rotating machinery by elastic suspension systems subject to dry and viscous friction

Abstract Most of the undesired whirling motions of rotating machines can be efficiently reduced by supporting journal boxes elastically and controlling their movement by viscous dampers or by dry friction surfaces normal to the shaft axis, which rub against the frame. In the case of dry dampers, resonance ranges of the floating support configuration can be easily cut off by planning a motionless adhesive state of the friction surfaces. On the contrary, the dry friction contact must change automatically into sliding conditions when the fixed support resonances are to be feared. Moreover, the whirl amplitude can be restrained throughout the speed range by a proper choice of the suspension-to-…

Sulla risposta in frequenza di sistemi meccanici con dissipazione non lineare