The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations

We complete and improve the fits to experimental $\pi\pi$ scattering amplitudes, both at low and high energies, that we performed in the previous papers of this series. We then verify that the corresponding amplitudes satisfy analyticity requirements, in the form of partial wave analyticity at low energies, forward dispersion relations (FDR) at all energies, and Roy equations below$\bar{K}K$ threshold; the first by construction, the last two, inside experimental errors. Then we repeat the fits including as constraints FDR and Roy equations. The ensuing central values of the various scattering amplitudes verify very accurately FDR and, especially, Roy equations, and change very little from what we found by just fitting data, with the exception of the D2 wave phase shift, for which one parameter moves by $1.5 \sigma$. These improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test various physical relations. We also present a list of low energy parameters and other observables. In particular, we find $a_0^{(0)}=0.223\pm0.009 M^{-1}_\pi$, $a_0^{(2)}=-0.0444\pm0.0045 M^{-1}_\pi$ and $\delta_0^{(0)}(m^2_K)-\delta_0^{(2)}(m^2_K)=50.9\pm1.2^{\rm o}$.Comment: Plain TeX. 29 figures. Version to be published in PRD, with improved P and F wave

Experimental study on circular eccentric cam-follower pairs

Experimental verifications of cam-follower contacts are very important because of the difficulties for a reliable simulation due to the continuous variation of load, speed and geometry of the lubricated contact. Some experiments have been carried out with a new apparatus, specifically designed and realised for investigation on cam-follower and gear teeth contacts, in order to test its capability to measure film thickness and contact forces. Circular eccentric cams have been used because they feature lower transient effects and comparison of the results with the theoretical/numerical ones is easier. The tests have been performed using cams with two different eccentricities and surface roughness, and two different followers, one made of steel and one made of glass. The behaviour of the cam-follower contacts at several different rotational speeds, ranging from 50 to 500 rpm, and different pre-loads have been investigated. Lubrication regimes ranged from boundary to complete, being most of the tests performed under mixed lubrication conditions. Localised wear has occurred during some tests. Data of all contact force and moment components as well as of the cam shaft driving torque have been acquired at high acquisition frequency. Some methodologies for numerical data elaboration have been identified. Optical interference images have been correctly recorded at the desired frequency. The trends of the normal and friction forces measured in the different tests are presented in the paper, as well as the evaluated trends of the friction coefficient. Some sample optical interference images are also shown. The results furnish encouraging indications about the capabilities of the experimental apparatus

Investigation on cam-follower lubricated contacts

The cam-follower contact is one of the most complex lubricated non-conformal contact due to its continuous variation of load, speed and geometry. The complexity of the phenomena occurring in the camshaft systems make experimental verifications very important. In this work, an already existing versatile experimental apparatus for investigation of non-conformal lubricated contacts, able to measure film thickness using the optical interference method and friction force trough a load cell, has been modified in order to tests cam-follower contacts. Some test have been carried out for investigating the behaviour of some fundamental components of the rig. A theoretical/numerical simulations has been performed to investigate the dynamic behaviour of the system and in order to provide some indications for the interpretation of the experimental results. Purposely developed versions of the programme have been also an important support for the design and of a new apparatus specifically addressed to the cam-follower contact and with increased potentialities capable of more detailed measurement of film thickness and contact forces. The apparatus is able to reproduce a cam-follower mechanism that uses a rocker as a link device between the cam follower set and the valve

Wear predictions for reverse total shoulder replacements

Reverse total shoulder arthroplasty (RTSA) has become the gold standard to treat rotator cuff tear arthropathy. RTSA is performed by substituting the humeral head and the glenoid cavity by a plastic cup in UHMWPE and a metallic head, respectively, in a geometrical reversed configuration with respect to the anatomical one. Major complications affect 27% of cases and mainly regard scapular notching due to cup-bone impingement and wear debris. Unfortunately, wear in shoulder prosthesis has not been largely studied as for hip and knee implants. Indeed, no wear test standards or even shoulder simulators exist, also because of a limited knowledge on shoulder/RTSA dynamics. Additionally, only a few numerical wear models for RTSA can be found in the literature, mainly focused on the comparison between anatomical and reverse solutions, and which often simulates simplified conditions, such as planar unloaded motions even neglecting fundamental aspects of wear process, i.e. cross-shearing (CS). The aim of the present study is to numerically investigate wear in RTSAs analysing the effect of: a) wear factor and wear law; a) implant geometry; b) inversion of bearing materials, i.e. plastic head + metallic cup, which should reduce the risks associated to scapular notching

Commissioning of a Novel Test Apparatus for the Identification of the Dynamic Coefficients of Large Tilting Pad Journal Bearings

This paper describes the commissioning of a novel test bench for the static and dynamic characterization of large tilting pad journal bearings, realized within a collaboration of the Department of Civil and Industrial Engineering of the University of Pisa, BHGE and AM Testing. The adopted test bench configuration has the test article (TA) floating at the mid-span of a rotor supported by two rolling bearings. The TA is statically loaded vertically upwards by a hydraulic actuator and excited dynamically by two orthogonal hydraulic actuators with multiple frequency sinusoidal forces. The test rig is capable of testing bearings with a diameter from 150 to 300 mm. It includes very complex mechanical, hydraulic, electrical and electronic components, and needs, for the whole plant, about 1 MW of electric power. The commissioning of the testing system involved several aspects and presented various issues. This work focuses on measuring systems and data acquisition of high-frequency data (forces, accelerations and relative displacements) and on data processing for the identification of the bearing dynamic coefficients. The identification procedure is based on the linearity assumption and the principle of superposition, operating in the frequency domain with the fast Fourier transforms of the applied forces and displacement signals. First results, referred to a 4-pad bearing, are in satisfactory agreement with theoretical ones