Correction of laser Doppler vibrometry measurements affected by steering mirror vibration

The laser Doppler vibrometer (LDV) is now well-established as an effective non-contact alternative to traditional contacting vibration transducers. LDVs are technically well suited to general application but they offer special benefits in a variety of challenging measurement scenarios. A limitation in this respect is sensitivity to vibration of the instrument itself or of any steering optics used to orient the probe laser beam. Making use of a general vectorial framework for modelling the measured velocity, this paper will present a mathematical treatment of the velocity measured in the scenario where the laser beam direction is manipulated by a vibrating mirror. It will be shown that, by knowing the steering mirror vibration, it is possible to completely correct for the perturbation of the measured signal. A complementary experimental investigation is described. The LDV, the target and the mirror were relatively carefully aligned with respect to one another enabling three alternative angles of 90°, 60° and 30° between the instrument and the target vibration direction. The vibrating target and the steering mirror assemblies were each instrumented with an accelerometer; the target measurement being the reference or “true” measurement while the mirror measurement is used to perform the required correction to the LDV measurement. Simultaneous measurements were taken with either the target or the mirror vibrating at “high” and “low” broadband levels; the LDV is shown to over-estimate in the mirror vibration only cases by over 22000 and 11000% respectively. Post-processing steps are presented which enabled the measurement to be corrected by circa 35dB

Restoring high accuracy to laser Doppler vibrometry measurements affected by vibration of beam steering optics

Laser Doppler vibrometers are now well-established as an effective non-contact alternative to traditional contacting transducers. Wide-ranging applications include those where beam steering optics are required to reach locations that are difficult to access but no attention has yet been given to measurement sensitivity to the vibration of those optics. In this paper, a thorough mathematical treatment of this sensitivity to steering optic vibration and its correction is set out. A very practical scheme requiring a single correction measurement, from the back-surface of the mirror at the incidence point and aligned with the mirror normal, delivers an error reduction typically in excess of 30 dB. After validation in the laboratory, the scheme is then applied to a genuinely challenging measurement scenario on a single cylinder racing motorcycle. Correction is theoretically perfect for translational mirror vibrations but angular mirror vibrations require an adapted scheme using a triplet of accelerometers arranged around a circular path on the mirror back-surface and this is set out theoretically

A practical guide to laser Doppler vibrometry measurements directly from rotating surfaces

Commercially available Laser Doppler vibrometers are typically configured with a single beam to measure radial and axial vibrations or with parallel beams to measure pitch, yaw and torsional vibrations. Provided sufficient light intensity can be collected, axial and torsional vibration measurements are relatively straightforward. Radial and pitch / yaw vibration measurements are less straightforward and rotor surface roughness or treatment is critically important. Unless rotor surfaces can be considered “polished-circular”, post-processing is necessary to remove a significant cross-sensitivity to motion orthogonal to that which it is intended to measure. This paper serves as a practical guide through the optimum configurations to be used on rotors to measure all components of vibration, including subtleties associated with beam diameter and vibration amplitude on polished rotors

Rotor vibration measurements using laser Doppler vibrometry: essential post-processing for resolution of radial and pitch/yaw vibrations

Background: Laser Doppler vibrometry is now a well established technique enabling noncontact vibration measurements in the most challenging of environments. Rotor vibration measurements are often highlighted as a major application of Laser Vibrometers due to their non-contact operation and inherent immunity to shaft run-out. Method of Approach: In such measurements, resolution of the individual axial and torsional vibration components is possible via particular arrangement of the laser beam(s). Resolution of the radial or pitch / yaw vibration components, however, can only be achieved by essential post-processing of the data from simultaneous orthogonal measurements. Results: This paper describes the principle and rigorous examination of a novel, dedicated resolution algorithm enabling, for the first time, real-time post-processing of the outputs from standard commercial instruments. Conclusions: The system performed well, even in the presence of noise and other typical measurement errors, and was implemented successfully in an engine vibration study

Vibration measurements using continuous scanning laser Doppler vibrometry : theoretical velocity sensitivity analysis with applications

It is readily accepted that a Laser Vibrometer measures target velocity in the direction of the incident laser beam but this measured velocity must be considered in terms of the various target velocity components. This paper begins with a review of the theoretical description of the velocity sensed by a single laser beam incident in an arbitrary direction on a rotating target undergoing arbitrary vibration. The measured velocity is presented as the sum of six terms, each the product of a combination of geometric parameters, relating to the laser beam orientation, and a combination of motion parameters – the “vibration sets”. This totally general velocity sensitivity model can be applied to any measurement configuration on any target. The model is also sufficiently versatile to incorporate time dependent beam orientation and this is described in this paper, with reference to continuous scanning Laser Doppler Vibrometry. For continuous scanning applications, the velocity sensitivity model is shown formulated in two useful ways. The first is in terms of the laser beam orientation angles, developing the original model to include time dependency in the angles, whilst the second is an entirely new development in which the model is written in terms of the mirror scan angles, since it is these which the operator would seek to control in practice. In the original derivation, the illuminated section of the rotating target was assumed to be of rigid cross-section but, since continuous scanning measurements are employed on targets with flexible cross-sections, such as beams, panels and thin or bladed discs, the theory is developed in this paper for the first time to include provision for such flexibility

Establishing correction solutions for Scanning Laser Doppler Vibrometer measurements affected by sensor head vibration

Scanning Laser Doppler Vibrometer (SLDV) measurements are affected by sensor head vibrations as if they are vibrations of the target surface itself. This paper presents practical correction schemes to solve this important problem. The study begins with a theoretical analysis, for arbitrary vibration and any scanning configuration, which shows that the only measurement required is of the vibration velocity at the incident point on the final steering mirror in the direction of the outgoing laser beam and this underpins the two correction options investigated. Correction sensor location is critical; the first scheme uses an accelerometer pair located on the SLDV front panel, either side of the emitted laser beam, while the second uses a single accelerometer located along the optical axis behind the final steering mirror. Initial experiments with a vibrating sensor head and stationary target confirmed the sensitivity to sensor head vibration together with the effectiveness of the correction schemes which reduced overall error by 17 dB (accelerometer pair) and 27 dB (single accelerometer). In extensive further tests with both sensor head and target vibration, conducted across a range of scan angles, the correction schemes reduced error by typically 14 dB (accelerometer pair) and 20 dB (single accelerometer). RMS phase error was also up to 30% lower for the single accelerometer option, confirming it as the preferred option. The theory suggests a geometrical weighting of the correction measurements and this provides a small additional improvement. Since the direction of the outgoing laser beam and its incident point on the final steering mirror both change as the mirrors scan the laser beam, the use of fixed axis correction transducers mounted in fixed locations makes the correction imperfect. The associated errors are estimated and expected to be generally small, and the theoretical basis...Comment: 39 pages, 3 tables, 8 figure

The development of a methodology to determine the relationship in grip size and pressure to racket head speed in a tennis forehand stroke

AbstractThis study developed a methodology to examine the effects of grip size and grip firmness on the kinematic contribution of angular velocity (KCAV) to the generation of racket head speed during a topspin tennis forehand. The KCAV is subdivided into kinematic contribution of joint angular velocity and kinematic contribution of the body segments in the upper trunk translational and angular velocities. Two Babolat Pure Storm GT rackets, with grip sizes 2 and 4 respectively, were used with Tekscan 9811E pressure sensors applied to the handles to examine pressure distribution during the stroke. Upper body kinematic data taken from the racket arm and trunk were obtained by means of a Vicon motion capture system. One elite male tennis player was recruited. Fifty topspin forehand strokes per grip at two nominal grip pressures were performed in a laboratory environment with balls being tossed towards the player and struck on the bounce towards a target on a net in as consistent a way as practically achievable.Processing of the results showed that the firm grip condition led to a significant (p<0.001) increase in average racket head speed compared to a normal grip condition. The normal gripping condition resulted in a significant (p<0.001) increase in average racket head speed for grip size 2 compared to grip size 4. A trend in negative linear relationships was found between upper trunk and shoulder joint in KCAV across conditions. Using the smaller grip also led to a trend in negative linear relationship between shoulder joint and wrist joint in KCAV across grip conditions. Grip pressure for grip size 2 showed the same pattern across gripping conditions. From 50-75% of completion in forward swing, the pressure difference due to grip firmness decreased. This feasibility study managed to quantify the KCAV while performing a topspin forehand, with respect to changing of grip size and grip pressure in an elite male tennis player for the first time

Studies with a small gamelan gong

A gamelan is an ensemble of ethnic musical instruments from parts of Indonesia where it is central to musical art and commands huge respect. It is also found in some neighboring countries. While it involves many different types of instruments its backbone consists of metalophones and gongs. show a vertical cross-section through the centre of a typical small gamelan gong placed on a horizontal surface. It consists of a central dome A on top of a flat plate which is terminated by a shoulder BC and then a deep inward sloping rim CD. The vertical line AE is the axis of symmetry. These gongs are rung by being stuck on the central dome with a mallet. Large gongs are suspended vertically by strings. Smaller ones are mounted horizontally from underneath on parallel strings. Since a “perfect” gong has complete axial symmetry one can conclude that its normal modes have nodal patterns consisting of m equally spaced “diameters” and n circles parallel to the rim’s edge. Modes with m = 0 are axisymmetric singlets while those with m > 0 occur in degenerate pairs with the diameters of one bisecting those of its partner. Modes can be designated by (m, n) with the addition of a subscript outside the brackets if it is desired to distinguish between a doublet’s components. In practice gamelan gongs are cast, sometimes rather roughly, and so have geometrical and metallurgical imperfections which break the basic axial symmetry. Consequently the doublets split and distortions appear in some nodal patterns. In the present work we are concerned with a small steel gong of 20.7cm diameter originating from Sarawak

Understanding the dynamic behaviour of a tennis racket under play conditions

The 'feel' of tennis rackets is of increasing importance to manufacturers seeking product differentiation in a context where further performance enhancements are prevented by a combination of mechanical limits and regulations imposed to protect the integrity of the sport. Vibrations excited during a shot contribute greatly to the perception of 'feel'. Previous studies have been reported but none has covered the full set of mode families or the frequency range in this study. In-plane vibrations associated with the routine use of topspin shots in modern tennis have not been documented so far in the literature. To consider modal behaviour, multiple measurements during play conditions are required but this is practically impossible. This paper proposes an alternative approach and successfully relates a comprehensive modal analysis on a freely suspended racket to vibration measurements under play conditions. This is achieved through an intermediate stage comprising a necessarily more limited modal analysis on a hand-gripped racket and use of the mass modification modal analysis tool. This stage confirmed the prevailing view that hand-gripping can be considered as a mass modification distributed along the handle of the freely suspended racket but the associated mass was much lower than that of an actual hand and the hand also increased the damping ratio of frame modes significantly. Furthermore, in frame vibration measurements during forehand groundstrokes, a greater reduction in bending mode frequencies was observed, consistent with a mass-loading of around 25 % of the actual hand as a consequence of the tighter grip. In these play tests, the first two bending modes, the first torsional mode, the first eight stringbed modes, the first three hoop modes and the third in-plane bending mode were identified, with the stringbed modes being particularly prominent. © 2013 Society for Experimental Mechanics

The use of rapid prototyping in the design of a customised ankle brace structure for ACL injury risk reduction.

Rapid prototyping, or additive manufacturing, is becoming more useful in creating functional prototypes, especially when customisation is required. This paper explores the use of three-dimensional (3D) printing in designing a customised ankle brace structure for anterior cruciate ligament (ACL) injury risk reduction. A new process is proposed to obtain ankle flexion angles and the corresponding foot surface strain associated with high ACL injury risks through motion analysis. This data is used in the design of the customised ankle brace structure and printed using rapid prototyping. One customised ankle brace structure was printed and tested to demonstrate this proposed framework. The ankle flexion range of motion (ROM) was significantly reduced in the high-risk ankle positions with the ankle brace structure. Rapid prototyping could thus be used to design customised ankle brace structures and this is useful in reducing fabrication time and complexity of customisation. © 2013 Taylor & Francis