Murat Inalpolat

Dynamic Modelling of Planetary Gears of Automatic Transmissions

Abstract In this paper, a generalized dynamic model for multi-stage planetary gear trains of automotive automatic transmissions is proposed. The planetary gear train is formed by N number of planetary gear sets of different types (single-planet, double-planet, or complex-compound), connected to each other in any given kinematic configuration. In addition, each planetary stage can have any number of parallel planet branches. A generalized power flow formulation and a gear mesh load distribution model are used to determine the stiffnesses, displacement excitations, and fundamental frequencies at the gear mesh interfaces. The natural modes are computed by solving the corresponding eigenvalue problem. The forced vibration response to gear mesh excitations is obtained by applying the modal summation technique. At the end, the model is applied to a three-stage planetary gear train representative of an automotive automatic transmission application to demonstrate the influence of coupling stiffnesses and the kinematic configurations on the natural modes and the dynamic response.

Structural health monitoring of wind turbine blades using acoustic microphone array

This article proposes a non-contacting measurement technique based on acoustic monitoring to detect cracks or damage within a structure by observing sound radiation using a single microphone or a beamforming array. The technique works by mounting an audio speaker inside a hollow structure, such as a wind turbine blade, and observing the sound radiated from the blade to identify damage. The primary hypothesis for this structural damage detection technique is that the structural damage (cracks, edge splits, holes, etc.) on the surface results in changes in the sound radiation characteristics of the structure. Preliminary measurements to validate the methodology were carried out on a section of a wind turbine blade containing different sized holes and cracks. An acoustic microphone array with 62 microphones was used to measure the sound radiated from the structure when an audio speaker generating random noise was placed inside a cavity emulating a wind turbine blade. A phased array beamforming technique and CLEAN-based subtraction of point spread function from a reference were employed to locate the different damage types on the test structures. The same experiment was repeated using a commercially available 48-channel acoustic ring array to compare the test results. It was shown that both the acoustic beamforming and the CLEAN-based subtraction of point spread function from reference techniques can identify the damage in the test structures with sufficiently high fidelity.

Analysis of near field sound radiation from a resonant unbaffled plate using simplified analytical models

Near field radiation behavior of an unbaffled square plate with free edges, which is excited by a harmonic force at its midpoint, is analytically, computationally and experimentally studied. Emphasis is on the applicability of simplified analytical models to predict the near field sound pressures and spatially-averaged surface and acoustic intensities. First, the plate is computationally discretized into equal segments that are replaced by simple, phase-correlated discrete acoustic sources. Piston radiator models (with and without mutual radiation impedance terms) as well as pulsating sphere models are employed to exhibit the contribution of mutual impedance terms. The near field pressure and spatially-averaged intensity radiated from phase-correlated discrete sources are calculated based on the premise that their individual phases are obtained from the plate (surface) vibration measurements. The importance of mutual impedance terms on the near field radiation is highlighted. Second, the two-microphone acoustic intensity and the surface intensity techniques are employed to determine the spatially-averaged intensity spectra, like analytical models. Results are examined on both narrow and 1/3 octave band bases up to 1600 Hz covering radiation from several plate vibration modes. Finally, an indirect boundary element model is used to predict spatially-averaged intensity spectra, as well as to simulate the two-microphone method given surface vibration data. All predictions are compared with analogous measurements. Discrepancies between theory and experiments (and even between two intensity measurements) are discussed along with possible sources of error.

An acoustic-array based structural health monitoring technique for wind turbine blades

This paper proposes a non-contact measurement technique for health monitoring of wind turbine blades using acoustic beamforming techniques. The technique works by mounting an audio speaker inside a wind turbine blade and observing the sound radiated from the blade to identify damage within the structure. The main hypothesis for the structural damage detection is that the structural damage (cracks, edge splits, holes etc.) on the surface of a composite wind turbine blade results in changes in the sound radiation characteristics of the structure. Preliminary measurements were carried out on two separate test specimens, namely a composite box and a section of a wind turbine blade to validate the methodology. The rectangular shaped composite box and the turbine blade contained holes with different dimensions and line cracks. An acoustic microphone array with 62 microphones was used to measure the sound radiation from both structures when the speaker was located inside the box and also inside the blade segment. A phased array beamforming technique and CLEAN-based subtraction of point spread function from a reference (CLSPR) were employed to locate the different damage types on both the composite box and the wind turbine blade. The same experiment was repeated by using a commercially available 48-channel acoustic ring array to compare the test results. It was shown that both the acoustic beamforming and the CLSPR techniques can be used to identify the damage in the test structures with sufficiently high fidelity.

Impact of indexing errors on spur gear dynamics

A transverse-torsional dynamic model of a spur gear pair is employed to investigate the influence of gear tooth indexing errors on the dynamic response. This model includes periodically-time varying gear mesh stiffness and nonlinearities caused by tooth separations in resonance regions. With measured long-period quasi-static transmission error time traces as the primary excitation, the model predicts frequency-domain dynamic mesh force and dynamic transmission error spectra. The quasi-static transmission error time traces are measured using unity-ratio spur gear pairs having certain intentional indexing errors. The dynamic responses due to both deterministic and random teeth indexing errors are predicted.

A Design Framework to Improve the Dynamic Characteristics of Double Planet Planetary Gearsets

Double planet planetary gear sets have significantly more design options than their single planetary counterparts as the addition of the second planet set allows for greater flexibility in sizing and synthesizing transmission kinematic chains. Generally, the primary design constraints for these systems are based on transmitted load, speed ratio, and availability of space. However, once these specifications are met, few attempts are made to optimize the design any further as manual design techniques fail to assess all performance related aspects of the system. In this paper, a methodology to improve existing double planetary gear sets through adjustment of limited set of feasible design constraints is proposed. The improvement will be achieved through modifying the values of gear tooth profile shift, tooth thickness, and planet gear center distances. Design of experiments (DOE) approach is implemented to generate a finite set of models that accurately represent the entire design space. In order to investigate if the proposed alternative designs are an improvement from the baseline system, a finite element tool is used to model all of the potential configurations. The parameters that are used for the fundamental measurement of system performance in this study are bearing forces, gear mesh forces and transmission error spectra.

A Computational Model to Investigate the Influence of Spacing Errors on Spur Gear Pair Dynamics

In this paper, a computational model is developed to investigate the influence of tooth spacing errors on the dynamics of spur gear pairs. This finite element based computational model implicitly includes periodically-time varying gear mesh stiffness and nonlinearities caused by tooth separations in resonance regions. The model can simulate the long period transmission error induced dynamic response from a spur gear with different spacing error patterns and predicts both time domain histories and frequency-domain spectra of dynamic mesh force and dynamic transmission error. The dynamic responses due to both deterministic and random teeth spacing errors are predicted and compared to the previously generated results from a lumped parameter model capable of utilizing experimentally measured transmission error as the realistic excitation mechanism. This study also enables creation of an extensive database of dynamic response spectra of gear pairs under the influence of spacing errors that will later be utilized for investigating the diagnostics of gear pairs.

An experimental investigation into the insertion loss from subscale acoustic enclosures with geometric imperfections

Enclosures with different geometries constitute the internal sections of various engineering applications including cabins of passenger cars, fuselages of aircraft wings, and internal compartments of wind turbine blades. Acoustic insertion loss from and to these enclosures affect certain objective and subjective acoustic measures along with the ability to detect damage. This presentation describes a thoroughly executed test plan that identifies the effect of geometric imperfections, such as holes, edge splits, and cracks with different severity levels and locations, on the insertion loss from a subscale acoustic enclosure. A composite rectangular prism enclosure, located inside an anechoic chamber, was internally ensonified using a loudspeaker, and an externally located condenser microphone was used to measure the insertion loss under different conditions. One of the faces of the enclosure possessed various size and location imperfections simulating damage. Insertion loss deviations introduced through the...

Development of an Acoustic Sensing Based SHM Technique for Wind Turbine Blades

Wind turbine blades are exposed to continuously-varying aerodynamic forces, gravitational loads, lightning strikes, and weather conditions that lead the blade damage such as leading and trailing edge splits, cracks and holes. In this study, actively-controlled acoustic sources were utilized in order to excite the blade’s cavity structure from internal. The blade damage manifests itself in changes to the acoustic cavity frequency response functions and to the blade acoustic transmission loss. Proposed research examines the use of wireless sensing approach for detecting surface damage of the blades, while they are rotating when wind turbine is operational. A subscale wind turbine was built and used for carrying out preliminary experimental studies. Sensing system and strategy was benchmarked both using computational (FEM) model of the blades as well as the experimental results in the lab.

A Dynamic Model for Double-Planet Planetary Gearsets

In this study, a two-dimensional, steady-state, discrete dynamic model of a double-planet planetary gearset is proposed. The dynamic model is generalized such that it can consist of number of planet branches and can operate under any operating conditions (load and speed). The contact between each external to external and external to internal gear pair is modeled to obtain stiffnesses and mesh displacement excitations using a generalized load distribution model. The natural modes are computed by solving the corresponding eigenvalue problem. The forced vibration response to gear mesh excitations is obtained by applying the modal summation technique. The model is capable of predicting gear mesh dynamic load and dynamic transmission error spectra for each gear mesh, dynamic bearing load spectra for each bearing as well as gear body dynamic displacements. Forced vibration response of an example system that consists of three double-planet branches is studied to demonstrate the influence of some of the key design parameters.Copyright