Anoop Chawla

Coupled bending, longitudinal and torsional vibrations of a cracked rotor

Abstract The coupling between longitudinal, lateral and torsional vibrations is studied together for a rotating cracked shaft. These coupling mechanisms have been studied here with a response-dependent non-linear breathing crack model. Most of the earlier work on coupled vibrations due to crack has been either on stationary shaft or on rotating shaft with open crack model. The stiffness matrix of a Timoshenko beam element is modified to account for the effect of a crack and all the six degrees of freedom per node are considered. Coupled torsional–longitudinal vibrations for a cracked rotor that has not been reported earlier and coupled torsional–bending vibrations with a breathing crack model have been studied. An attempt has been made to reveal crack specific signatures by using additional external excitations. Since all the couplings are accounted, the excitation in one mode leads to an interaction between all the modes. This, coupled with the rotational effect of a cracked rotor and the non-linearities due to a breathing crack model introduces sum and difference frequencies in the response of cracked rotor. The co-existence of frequencies of other modes in the frequency spectra of a particular mode and the presence of sum and difference frequencies around the excitation frequencies and its harmonics could be useful indicators for crack diagnosis.

Transient response and breathing behaviour of a cracked Jeffcott rotor

Abstract In this paper, a cracked Jeffcott rotor is analyzed as it passes through its critical speed and subharmonic resonances. Three different crack models are studied, namely, a breathing crack model, a switching crack model and an open crack model. The breathing crack model which closely imitates the breathing behaviour of a real crack in a rotor is studied in detail as the rotor is accelerated or decelerated past the critical speed. It is shown that the breathing behaviour and the peak response are strongly influenced by the unbalance orientation angle relative to the crack direction. The effect of acceleration rate, crack depth and damping on the breathing behaviour is analysed in this study. The effects of these parameters on breathing behaviour have not been reported earlier. Due to the accurate breathing model considered in this study, the breathing behaviour obtained is closer to reality compared to that reported in previous studies. For most values of unbalance orientation angle the breathing crack model predicts a larger response compared to the switching crack model which was used earlier in literature. The presence of higher harmonics in the response causes subharmonic resonances during coasting-up of the accelerating rotor. At these subharmonic resonances, amplitudes of the higher harmonic components have been found to be stronger in the horizontal direction than in the vertical direction. It has also been observed that during passage through these subharmonic resonances the orientation of rotor orbit changes quite noticeably. Subsequently, the peak response variation as well as orbit orientation changes have been studied experimentally. The experimental findings validate most of the analytical results. It has been experimentally observed that for an unbalance phase in the range of 67.5–135°, decelerating slotted rotor gives higher response compared to accelerating rotor. The peak response variation is typical in case of slotted and cracked rotor that can be helpful in distinguishing asymmetric rotor from cracked rotor. The orbit orientation changes during passage through subharmonic resonances are also clearly seen in experimental investigation on cracked rotors, which can prove to be a convenient tool in crack diagnosis. The experimental observations also support the analytical results of stronger horizontal component of higher harmonics near the subharmonic resonances.

Experimental investigations of the response of a cracked rotor to periodic axial excitation

In this paper, the coupling of lateral and longitudinal vibrations due to the presence of transverse surface crack in a rotor is explored. A crack in a rotor is known to introduce coupling between lateral and longitudinal vibrations. Steady state unbalance response of a cracked rotor with a single centrally situated crack subjected to periodic axial impulses is investigated experimentally. The cracked rotor is excited axially using an electrodynamic exciter at a frequency equal to its bending natural frequency in both non-rotating and rotating conditions. The resulting time domain and frequency domain signals of the cracked rotor are studied. Spectral response of the cracked rotor with and without axial excitation is found to be distinctively different. When excited axially, it shows prominent presence of rotor bending natural frequency. However for an uncracked rotor, the response is similar with or without axial excitation. It is thus proposed that the response of the rotor to axial impulse excitation could be used for more reliable diagnosis of rotor cracks.

Prediction of crushing behaviour of honeycomb structures

A finite element methodology has been developed for predicting the behaviour of honeycomb structures. Dynamic analysis of hexagonal aluminium honeycomb structures is carried out using PAM-CRASH TM , an explicit FE analysis code, and the result are verified against experimental data. Relationship between the crushing behaviour of honeycomb and simulation parameters has been established. The simulation results are also compared with theoretically predicted values.

Impact modelling studies for a three-wheeled scooter taxi

Three-wheeled scooter taxis (TSTs) are being used in many Asian countries and along with buses are the main mode of public transport for the urban middle class population. The TST chassis is made by the manufacturer and the body is fabricated by local body-makers. The vehicle is not subject to any crash safety specifications. This work is the first attempt to study the crash characteristics of TSTs using a crash simulation computer software (MADYMO) with the objective of developing practical guidelines to make the vehicle safer in collisions with other motorized road users and pedestrians. Impact modelling was done for the standard and modified TST occupied by a driver and one passenger at impact velocities of 10-30 km/h crashing with a pedestrian and a bus front. The results show that the passenger and the driver of the standard TST can sustain high HICs, face/head contact forces and tibia/knee contact forces in crashes with buses at velocities 20 km/h and greater. The magnitude of these parameters can be reduced slightly by small changes in the design of the interior and padding of critical surfaces. To increase the safety of the TST significantly major modifications need to be incorporated in the design of TSTs and bus fronts. Pedestrian impact simulations indicate that it may be possible to reduce the impact forces by changing the shape of the front of the TST. The results indicate that it should be possible to improve the crash safety properties of vehicles indigenously designed in Asian and African countries by the use of crash simulation models like MADYMO. This procedure is relatively inexpensive and can provide the first approximations for design of safer vehicles.

SAFER TRUCK FRONT DESIGN FOR PEDESTRIAN IMPACTS

Truck and bus frontal impacts account for a major proportion of pedestrian fatalities in many less motorized countries. To understand this phenomenon, we have collected injury data on pedestrian impacts with buses and trucks and performed computer simulations to identify critical design parameters at 15–45 km/h impact velocities for further investigation. A male dummy which was scaled to fifty percentile Indian dimensions has been used for simulations using MADYMO. Bumper height, bumper offset and grille inclination affect the pelvis and thorax forces and Head Injury Criterion values critically. Bumper width has less effect. Simulations were performed to optimize for the above–mentioned three parameters. Changes in front geometric parameters reduce injury to the upper body and head below safety limits for the existing force–displacement properties but do not affect leg injuries significantly. Hence bumpers need to be made less stiff. Injury data shows that pedestrians also sustain tibia fractures in bus/truck impacts in apparent low velocity impacts. The computer modeling does not offer adequate explanation for this phenomenon. These simulations confirm that it is theoretically possible to make truck/bus fronts safer for pedestrians in impacts up to 35 km/h.

Effect of Active Muscle Forces on Knee Injury Risks for Pedestrian Standing Posture at Low-Speed Impacts

Objectives: The objective of the present study is to investigate the effect of muscle active forces on lower extremity injuries for various impact locations and impact angles for a freely standing pedestrian. Methods: FE simulations have been performed using a validated lower extremity FE model with active muscles (A-LEMS). In all, nine impact orientations have been studied. For each impact orientation, three different pre-impact conditions of a freely standing pedestrian, representing a cadaver, and an unaware and an aware braced pedestrian, have been simulated. Stretch-based reflexive action was included in the simulations for an unaware pedestrian. Results: Strains in knee ligaments and knee joint kinematics have been compared in each impact orientation to assess the effect of muscle activation. It is observed that strain in knee ligaments is dependent on impact locations and angles and the MCL is the most vulnerable ligament. Further, due to muscle effects, except when the impact is on the knee, peak strain values in all the ligaments are lower for an unaware pedestrian than either for a cadaver or for a fully braced pedestrian. Conclusions: It is concluded that active muscle forces significantly affect the knee kinematics and consequently reduce strains in knee ligaments.

FE simulations of motorcycle—car frontal crashes, validations and observations

Abstract ISO 13232 [1] requires 7 configurations for full scale tests (FSTs) between the motorcycle (MC) and the car (also called the opposing vehicle, OV). Of these, 3 involve the impact of the MC with the front of the OV. This paper presents Finite Element (FE) based simulations of these impact configurations. It does not evaluate the efficacy of any safety devices but refers to parts of ISO 13232 for developing these simulations. This paper analyses FE based simulations of the above-mentioned impacts. The simulations have been developed using the PAM-CRASHTM solver. In this paper an attempt has been made to compare the kinematics of the simulations with those obtained from the FSTs. The simulations indicate that the MC-OV impacts are sensitive to many phenomena. The objective of this paper is to highlight some of the important aspects of MC-OV simulations. This paper has been revised from an earlier version of the paper [2].

Blade life: A comparison by cumulative damage theories

A turbine blade is modeled as a rotating pretwisted beam and subjected to aerodynamic excitation from the flow path interference. The resonant stresses are determined using a modal analysis. With the help of steady steam bending and centrifugal stresses and the dynamic stresses, life estimates are made using the linear and nonlinear cumulative damage theories and a comparison of the results is presented. Based on these results, recommendations are made on the usefulness of different theories for practical application.

Determining the strain rate dependence of cortical and cancellous bones of human tibia using a Split Hopkinson pressure bar

Mechanical properties of tibial bone at compressive strain rates of 50–200/s are obtained through a Split Hopkinson pressure bar. Cylindrical specimens of 12–15 mm diameter and 2–5 mm thickness were prepared. The Youngs moduli are calculated from linear portion of stress–strain curves. For both cortical and cancellous part of the bones, the Youngs modulus was found to increase with the increasing strain rates. Also for both cancellous and cortical bones, the Youngs modulus increases consistently with increase in densities.