Experimental Nonlinear Dynamics of a Highly Flexible Spinning Beam Using a 3-D Motion Analysis System

Qian, Xin; Du, Xi‐Wen; Pai, P. Frank

doi:10.2514/6.2010-2892

Cited by 5 publications

(5 citation statements)

References 4 publications

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“…After each camera's seven parameters (i.e. x c , y c , z c , f, T 11 , T 12 , and φ) are estimated using the L-frame calibration and equations ( 6)-( 8) and (10), their values can be refined by processing data from dynamic measurements by moving the three-marker T-wand within a user-defined capture volume for a certain time length (e.g., 60 s), as shown in figure 4. Because the image coordinates (v i , w i ), i = 1, 2, 3, of the three markers at many different time instants are known from the CMOS sensor, it follows from figure 4…”

Section: Refinement Of Estimation and Correction Of Optical Distortionmentioning

confidence: 99%

“…If not, the x c , y c , z c , f, [T ] determined from equations ( 8), ( 6) and (7) and the (ṽ i , wi ) calculated from equation ( 12) are inaccurate, and then the distortion model derived from equations ( 17) and ( 18) cannot be accurate. After the model parameters K 1 , K 2 , K 3 , P 1 and P 2 are obtained, one can use this improved lens distortion model to repeat the whole signal processing steps shown in equations ( 6)-( 8) and (10) to have more accurate estimations of x c , y c , z c , f, T 11 , T 12 and φ for each camera.…”

Section: Refinement Of Estimation and Correction Of Optical Distortionmentioning

confidence: 99%

“…Figure 7(a) shows a forward whirling slender shaft driven by a dc motor at a spinning speed = 8.69 Hz at the root [10]. The shaft had a length L = 846.88 mm, a diameter d = 1.397 mm, a mass density m = 12.065 g m −1 , Young's modulus E = 203 GPa and Poisson's ratio ν = 0.32.…”

Section: Vertical Spinning Shaftmentioning

confidence: 99%

“…For vibration testing of structures, such large spherical markers are not appropriate because they are not directly adhered to structural surfaces and they cause serious unknown aerodynamic effects. Although these motion analysis systems are convenient for noncontact measurement of large deformations of mechanical systems, because of low accuracy and usage of spherical markers, their use for vibration testing of structures requires users to have certain understanding about how such systems work in order to have appropriate experimental set-ups and obtain repeatable/accurate measurements [6][7][8][9][10]. Unfortunately, the details of measurement theories and signal processing techniques are commercial secrets, and companies producing camera-based motion analysis systems do not release them to their customers.…”

Section: Introductionmentioning

confidence: 99%

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Camera-based noncontact metrology for static/dynamic testing of flexible multibody systems

Pai

Ramanathan

et al. 2010

Meas. Sci. Technol.

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Presented here is a camera-based noncontact measurement theory for static/dynamic testing of flexible multibody systems that undergo large rigid, elastic and/or plastic deformations. The procedure and equations for accurate estimation of system parameters (i.e. the location and focal length of each camera and the transformation matrix relating its image and object coordinate systems) using an L-frame with four retroreflective markers are described in detail. Moreover, a method for refinement of estimated system parameters and establishment of a lens distortion model for correcting optical distortions using a T-wand with three markers is described. Dynamically deformed geometries of a multibody system are assumed to be obtained by tracing the three-dimensional instantaneous coordinates of markers adhered to the system's outside surfaces, and cameras and triangulation techniques are used for capturing marker images and identifying markers' coordinates. Furthermore, an EAGLE-500 motion analysis system is used to demonstrate measurements of static/dynamic deformations of six different flexible multibody systems. All numerical simulations and experimental results show that the use of camera-based motion analysis systems is feasible and accurate enough for static/dynamic experiments on flexible multibody systems, especially those that cannot be measured using conventional contact sensors.

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Section: Refinement Of Estimation and Correction Of Optical Distortionmentioning

confidence: 99%

Section: Refinement Of Estimation and Correction Of Optical Distortionmentioning

confidence: 99%

Section: Vertical Spinning Shaftmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Camera-based noncontact metrology for static/dynamic testing of flexible multibody systems

Pai

Ramanathan

et al. 2010

Meas. Sci. Technol.

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show abstract

“…Experimental investigations on a cantilevered spinning shaft have been reported. Qian et al (2010) conducted a non-contact dynamic testing of a highly flexible spinning vertical shaft.…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis for coupled flexural-torsional spinning beams with unsymmetrical cross sections

Wang

Jiang

2017

jtam

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The structural modeling and dynamic properties of a spinning beam with an unsymmetrical cross section are studied. Due to the eccentricity and spinning, transverse deflections along the two principal directions and the torsional motion about the longitudinal axis are coupled. The structural model of the beam is established based on the Hamilton principle and by incorporating the torsional inertia. Moreover, because of its significant influence on characteristics for the non-circular cross-sectional beam, the warping effect is considered in the formulation. The proposed model is effectively validated in two cases: the spinning beam with a symmetric cross section and the cantilevered beam with an unsymmetrical cross section. Then the effects of the spinning speed on natural frequencies and mode shapes are investigated. Numerical results reveal that the critical speed is altered with respect to noncoincidence of the centroid and the shear center. For the beams with strong warping rigidities, the warping effect cannot be neglected due to significant influence on natural frequencies.

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Coupled flexural–torsional vibration of spinning smart beams with asymmetric cross sections

Wang

Jiang

2015

Finite Elements in Analysis and Design

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Experimental Nonlinear Dynamics of a Highly Flexible Spinning Beam Using a 3-D Motion Analysis System

Cited by 5 publications

References 4 publications

Camera-based noncontact metrology for static/dynamic testing of flexible multibody systems

Camera-based noncontact metrology for static/dynamic testing of flexible multibody systems

Modeling and analysis for coupled flexural-torsional spinning beams with unsymmetrical cross sections

Coupled flexural–torsional vibration of spinning smart beams with asymmetric cross sections

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