Intrinsic Internal Friction Research Articles

Friction-induced nonlinear dynamics in a spline-rotor system: Numerical and experimental studies

Excessive vibrations induced by intrinsic internal friction in spline joints critically impact the reliability and safety of high-speed rotating machinery. To address this concern, this paper presents experimental and numerical research on a flexible rotor system subjected to frictional contact within the spline joint. Experiments are conducted on a scaled rotor test rig designed to emulate the tail rotor drive shaft of helicopters, aiming to explore vibration behaviors under various operating conditions. A reduced-order mathematical model based on the test rig, considering the multi-interface friction of the spline joint and deformation coordination with a flexible coupling, is formulated. The numerical study, which incorporates both stability analysis and transient nonlinear dynamics, is then presented to quantitatively evaluate the occurrence conditions and excitation mechanisms leading to friction-induced instabilities. A parameter study is further conducted to elucidate the roles of various parameters in shaping self-excited vibration behaviors. The results reveal that the cross-coupling of frictional forces within the spline joint acts as the driving force of instabilities at supercritical speeds, with the resulting self-excited responses dominated by the frequency of the first critical speed. The study also highlights the necessity of integrating experimental and numerical analysis to better predict and understand the self-excited vibration phenomena in the spline-shaft systems.

Effect of alloying elements (Nb, Ag) on the damping performance of Cu–Al–Mn shape memory alloys

This study investigates the damping properties of Cu–Al–Mn shape memory alloys (SMAs) with various chemical compositions and the effects of the addition of quaternary alloying elements Ag and Nb on the microstructure, martensitic transformation behavior, and damping capacity of SMAs. Compared to other Cu–12Al–xMn (x = 4–7 wt%) SMAs, Cu–12Al–5Mn has a more significant inherent and intrinsic internal friction (IFPT + IFI) peak above room temperature. The addition of Ag or Nb to Cu–12Al–5Mn reduced the grain size, thereby increasing the hardness of the alloys; however, the damping capacity and temperature of the IFPT + IFI peak decreased simultaneously. The addition of Ag to Cu–12Al–5Mn significantly reduced the damping capacity (IFPT+IFI peak) because of the notable decrease in the amount of transformed martensite. Moreover, the addition of Nb to Cu–12Al–5Mn caused the AlNb3 phase to precipitate, limiting the mobility of the martensite variant interfaces and slightly decreasing the damping capacity (IFPT + IFI peak). Among the Ag- and Nb-doped Cu–12Al–5Mn SMAs, Cu–12Al–5Mn–1 Nb showed not only a significantly higher hardness but also a higher IFPT + IFI peak, with tan δ exceeding 0.01 at approximately 50 °C.

Occurrence of the R-phase with increased stability induced by low temperature precipitate-free aging in a Ni50.9Ti49.1 alloy

The R-phase transformation presents low thermal hysteresis, high stability against thermal cycling and ultrahigh internal friction (IF). However, a clear explanation for the occurrence of the R-phase after low temperature aging and systematic characterization of the condition are still lacking. In this study, the evolution of the phase transformation behaviors and IF values after aging at 250 °C for different times are investigated in a Ni50.9Ti49.1 alloy. Direct experimental evidence for the microstructure evolution of the B2 phase and the corresponding R-phase is provided utilizing in-situ transmission electron microscopy (TEM) techniques, together with geometric phase analysis (GPA). The reason for the occurrence of a nanodomain-structured R-phase after low temperature precipitate-free aging and the mechanism of ultrahigh intrinsic IF are illustrated. The results show that Ni segregation indicated by the localized strain fields is responsible for the formation of the R-phase after low temperature aging. Longer aging time causes larger element heterogeneity in the matrix, as a result, a wider existing temperature window for the R-phase. The ultrahigh intrinsic IF plateaus (IFInt = 0.120 ∼ 0.183) found in NiTi shape memory alloys (SMAs) are predominantly determined by the volume fraction of nanodomain boundaries. These findings provide basic insights into the R-phase formation mechanism and provide a simple way to adjust ultrahigh IF performance suitable for different application scenarios.

Achieved improvement of damping capacity in Ti Ni shape memory alloy through He-ion irradiation

TiNi shape memory alloys have been widely used to eliminate noise and mechanical vibrations. However, narrow working temperatures and low damping performance limit its applications. Here, a high damping capacity with the relaxational internal friction close to 0.0524 at 5 Hz and the intrinsic internal friction close to 0.04512 are detected after He ion irradiation. The internal friction value greater than 0.02 in a wide working temperature range of 200 K is reported. Further analyses indicate the critical role of He ion irradiation in increase of damping property. We demonstrate that the high broad internal friction could be derived from the interaction between He/H atoms and martensite twinning interface, and the change in twinning type (111¯) type I twinning to (001) compound twinning in the irradiated layer. The He ion irradiation strategy disclosed in the current work is expected to be a promising way to design high damping alloys.

Effect of Co additions on the damping properties of Cu–Al–Ni shape memory alloys

This study investigates the effect of Co additions on the damping properties of Cu-13.5Al–4Ni-xCo and Cu-14.0Al–4Ni-xCo (x = 0–2 wt%) shape memory alloys (SMAs). The Cu-14.0Al–4Ni SMA exhibits a higher inherent and intrinsic internal friction (IFPT + IFI) peak than the Cu-13.5Al–4Ni SMA, but its (IFPT + IFI) peak temperature is below 0 °C. Adding Co into the Cu-14.0Al–4Ni SMA can effectively increase the (IFPT + IFI) peak temperature and reduce the grain size of the alloys. The grain size of the Cu-14.0Al–4Ni-xCo SMAs decreases from approximately 300 μm to below 50 μm when the Co content increases from 0 to 2 wt%. The (IFPT + IFI) peak temperature for the Cu-14.0Al–4Ni-xCo SMAs increases from −0.1 °C to 77.7 °C when the Co content increases from 0 to 1 wt%, but their tan δ values decrease from 0.0402 to 0.0090 simultaneously. The Cu-14.0Al–4Ni–2Co SMA does not exhibit an observable (IFPT + IFI) peak. The tan δ values of the (IFPT + IFI) peaks decrease with increasing Co content because the movements of the parent/martensite phase interfaces and twin boundaries are impeded by the increased amounts of grain boundaries and γ2 phase precipitates. Among these Cu–Al–Ni–Co SMAs, the Cu-14.0Al–4Ni-0.5Co SMA is more suitable for high-damping applications as it possesses an (IFPT + IFI) peak with tan δ close to 0.02 at approximately 50 °C.

Damping Characteristics of Inherent and Intrinsic Internal Friction of Cu-Zn-Al Shape Memory Alloys

Damping properties of the inherent and intrinsic internal friction peaks (IFPT + IFI) of Cu-xZn-11Al (x = 7.0, 7.5, 8.0, 8.5, and 9.0 wt. %) shape memory alloys (SMAs) were investigated by using dynamic mechanical analysis. The Cu-7.5Zn-11Al, Cu-8.0Zn-11Al, and Cu-8.5Zn-11Al SMAs with ( IF PT + IF I ) β 3 ( L 2 1 ) → γ 3 ′ ( 2 H ) peaks exhibit higher damping capacity than the Cu-7.0Zn-11Al SMA with a ( IF PT + IF I ) β 3 ( L 2 1 ) → γ 3 ′ ( 2 H ) peak, because the γ 3 ′ martensite phase possesses a 2H type structure with abundant movable twin boundaries, while the β 3 ′ phase possesses an 18R structure with stacking faults. The Cu-9.0Zn-11Al SMA also possesses a ( IF PT + IF I ) β 3 ( L 2 1 ) → γ 3 ′ ( 2 H ) peak but exhibits low damping capacity because the formation of γ phase precipitates inhibits martensitic transformation. The Cu-8.0Zn-11Al SMA was found to be a promising candidate for practical high-damping applications because of its high (IFPT + IFI) peak with tan δ > 0.05 around room temperature.

Effect of carbon on the damping capacity and mechanical properties of thermally trained Fe-Mn based high damping alloys

The effect of C on the damping and mechanical properties of thermally trained Fe-17wt%Mn-X wt%C (0<X<0.06) high-damping alloys was analyzed by the impulse internal friction technique and uniaxial tensile tests. The alloys were subjected to a combination of thermo-mechanical processing and thermal cycling which resulted in a C content independent phase fraction and grain size of ɛ-martensite and γ-austenite. The ɛ↔γ phase transformation and the anti-ferromagnetic transition in the γ-phase were observed in the temperature-dependent damping and modulus measurements, respectively. While C had no influence on the intrinsic internal friction of the γ-phase, small amounts of C significantly reduced the damping associated with the motion of ɛ-γ interface boundaries and the widening of stacking faults by the movement of partial dislocations. The C content at which these relaxation processes were suppressed, i.e. approximately 0.03wt%C, coincided with the onset of dynamic strain aging as inferred from the appearance of serrations on the flow curves.

The effect of tensile deformation on the damping capacity of NiTi shape memory alloy

The vibration damping capacity of a near-equiatomic NiTi shape memory alloy was characterized as a function of tensile deformation by utilizing dynamic mechanical analysis. The intrinsic internal friction (IF) values of the martensite phase (Qint,m−1) decreased with increasing deformation levels up to 10%, attributed to a decrease in the density of martensite variant and twin boundaries. Deformation increased the temperature of the transformation peak during the first reverse transformation of thermal cycling. A two-stage behavior was observed in terms of the IF values of the transformation peak. IF reached a peak value at 4%, dropped at 5% and monotonically increased again up to 10% deformation. Thermal cycling partially restored Qint,m−1 levels and shifted the transformation peak close to its undeformed IF and temperature values during the second reverse transformation.

Influence of Heat Treatment on Internal Friction Spectrum in NiTiCu Shape Memory Alloy

Internal friction (IF) and storage modulus evolution during the martensitic transformation were measured using the DMA technique in order to compare the effect of heat treatment on the behavior of IF in Ti44.6Ni5Cu (%at.) shape memory alloy. Two kinds of experiment were performed: IF measurements as a function of temperature and IF measurements at a fixed temperature to obtain the static term of the intrinsic internal friction. The results are compared with those obtained from DSC measurements. IF results show a clear dependence on the temperature of the heat treatment with distinctive regions that could be attributed to microstructural changes.

Influence of chemical composition on the damping characteristics of Cu–Al–Ni shape memory alloys

Cu– XAl–4Ni shape memory alloys (SMAs) are capable of martensitic transformation across a wide temperature range through the precise adjustment of their chemical composition from X = 13.0 to 14.5. In addition, the variations in chemical composition significantly influence the internal friction characteristics of Cu– XAl–4Ni SMAs. Cu– XAl–4Ni SMAs with a higher content of Al exhibit lower internal friction peaks due to decreases in the amount of transformed martensite and the formation of γ 2 phase precipitates. The damping capacity of the inherent and intrinsic internal friction for Cu–13.5Al–4Ni SMA is extremely low due to the fact that the transformed β ′ 1 ( 18 R ) martensite has only an ordered 9R structure with stacking faults. The Cu–14.0Al–4Ni SMA exhibits a relative increase in the inherent and intrinsic damping capacity because the transformed γ ′ 1 ( 2 H ) martensite exhibits twinning with abundant moveable twin boundaries.

Internal friction of R-phase and B19′ martensite in equiatomic TiNi shape memory alloy under isothermal conditions

The intrinsic internal friction IF I of R-phase and B19′ martensite are composed of static internal friction IF S and dynamic internal friction IF D. The tan δ values of I F S R and I F S B 1 9 ′ are both proportional to σ 0/ υ 1/2 and are related to the stress-assisted motions of twin boundaries. The tan δ values of I F S R are higher than those of I F S B 1 9 ′ is owing to the softer storage modulus E 0 in R-phase. The tan δ values of I F D B 1 9 ′ are linearly proportional to T ˙ / υ 1 / 2 . The occurrence of relaxation peak at ≈−60 °C is found to come from the I F S B 1 9 ′ , instead of the I F D B 1 9 ′ .

Internal friction and loss tangent of nonlinear viscoelastic materials: different concepts, different results

This paper aims to give some insight into measurements of the nonlinear processes involved in the dynamical response of viscoelastic materials. The main goal is to point out that these nonlinear effects can be observed with forced oscillating torsion pendulums, but by measuring the complete hysteretic loop, instead of just looking at the phase lag angle. The response of a nonlinear rheological model constructed with a standard anelastic element in series with a nonlinear dashpot is considered. The characteristic parameters of this model are according to previous empirical results reported in the literature. This system is dynamically driven as if it were in a forced torsion pendulum, which is almost the optimal device for the analysis of amplitude dependent internal friction at low frequencies. The intrinsic internal friction is calculated from the ratio between the dissipated energy per cycle and the maximum stored energy for the nonlinear rheological model. The simulation of the internal friction that could be measured with a torsion pendulum for the rheological model is then determined from the intrinsic internal friction after considering the non-homogeneous strain distribution. The intrinsic internal friction and the simulated internal friction data are compared with the tangent of the phase angle by which the strain lags behind the stress in order to show that the differences are important enough to be measured. In summary, the nonlinear response could potentially be measured with commercial equipment, but usually is not, because only the phase lag angle is considered. Automatic measurements of both the temporal evolution of stress and strain in a cycle will lead to the determination of the real value of the internal friction of nonlinear systems from the hysteretic σ– ε loop.

Contactless mode-selective resonance ultrasound spectroscopy: Electromagnetic acoustic resonance

A noncontacting resonant-ultrasound-spectroscopy (RUS) method for measuring elastic constants and internal friction of conducting materials is described, and applied to monocrystalline copper. This method is called electromagnetic acoustic resonance (EMAR). Contactless acoustic coupling is achieved by energy transduction between the electromagnetic field and the ultrasonic vibrations. A solenoidal coil and static magnetic field induce Lorentz forces on specimen surfaces without using a coupling agent. By changing the field direction, a particular set of vibration modes can be selectively excited and detected, an advantage in identifying the vibration modes of the observed resonance peaks. Contactless coupling allows the measure of intrinsic internal friction free from energy loss associated with contact coupling. The elastic constants and internal friction measured by EMAR are compared with those by the usual RUS method for a rectangular-parallelepiped copper monocrystal. Both methods yielded the same elastic constants despite fewer resonant peaks in the EMAR case. The two methods gave essentially the same shear-mode internal friction, but the RUS method gave higher volume-mode internal friction.

Elastic constants and internal friction of an SiC-fiber-reinforced Ti-alloy-matrix crossply composite: measurement and theory

The complete elastic-constant tensor C ij and the corresponding internal friction Q −1 ij for a crossply composite are measured. It consists of silicon-carbide fibers in a Ti–6Al–4V matrix; it contained 35 vol.% fibers. With tetragonal symmetry, this composite possesses six independent C ij and Q −1 ij . Principally, two measurement methods were used: noncontacting and point-contact resonance-ultrasound spectroscopy. Specimens were rectangular parallelepipeds measuring a few to several millimeters. By changing the magnetic-field direction, which is needed for the Lorentz-force coupling, a particular macroscopic-vibration-mode group among the eight groups for free vibration of a rectangular parallelepiped could be independently excited and detected. This provides a big advantage in identifying the vibration modes of the observed resonance peaks, whose frequencies yield the C ij by solving an inverse problem. Contactless coupling allowed the measurement of intrinsic internal friction, avoiding the energy loss associated with contact coupling. The internal-friction tensor was determined by a free-decay method. Theoretical calculations were made using an extended Mori–Tanaka mean-field theory and good theory–measurement agreement was found.

A method to deconvolute amplitude-dependent internal-friction data: Theory and experiment

Abstract A numerical deconvolution method is presented which, by accounting for the specimen geometry and the experimental deformation mode imposed, allows conversion of measured internal-friction (MIF) data into amplitude-dependent intrinsic internal-friction (IIF) values. The only requirement of the procedure is the assumption usually made that the IIF can be unequivocally described using some properly chosen scalar strain parameter. The method, which consists of adjusting an implicit empirical function to the experimental values, is implemented here to treat the case of parallelepiped specimens of arbitrary width-to-thickness ratio deforming in torsion. The method is tested by applying it to actual data of MIF obtained from torsion experiments performed on circular and rectangular beams of the same material. The agreement between the IIF against strain curves that result after deconvoluting the MIF curves associated with the different specimen geometries supports the validity of the method.

Intrinsic internal friction in solids measured by torsion pendulums

A mechanical theory is developed for composite torsion pendulums emphasising the interaction between components. The interaction is eliminated to obtain the intrinsic internal friction in solids. A definition of internal friction is given in a general form as a function of frequency and the moment of inertia. Two equivalent formulations of internal friction, which are related to each other through a simple relation, are obtained by the use of the definition. A torsion pendulum in forced oscillation is considered to clarify the significance of the formulation.

Analytical expressions of intrinsic internal friction based on damping data under inhomogeneous strains

Abstract The effect of a strain distribution in a vibrating specimen on the amplitude-dependent damping is analysed for several kinds of measurements. An analytical procedure is given for converting damping data measured as a function of the maximum strain amplitude under inhomogeneous strains to intrinsic internal friction expressed as a function of the homogeneous strain amplitude. On the basis of the analysis by Povolo and Gibala, correct mathematical expressions of internal friction are derived for longitudinal, flexural and torsional modes of free resonant vibrations. The formulae obtained are applied to an experimental curve of damping which increases according to a power of the maximum strain amplitude.

Internal friction and modulus defect of materials subjected to inhomogeneous stresses

Abstract A general method is given for calculating the intrinsic or true internal friction and modulus defect from data for specimens subjected to inhomogeneous applied stresses in the amplitude-dependent range. The method is applied to the cases of longitudinal and torsional vibrations. Some experimental data are analysed to demonstrate the importance of using such procedures in examining amplitude-dependent results.

Elastic relaxation model for seismic wave attenuation in the earth

Love wave amplitude data are satisfied by an Earth model in which the intrinsic internal friction ( Q −1) at each depth is taken to be due to a single thermally activated relaxation mechanism. In this model the intrinsic Q −1 is completely specified by a simple function of frequency, temperature, and pressure. This model is in better agreement with observed behavior of solids than previous models and requires fewer arbitrary parameters to satisfy seismic data.