A 2-DOF Large Stroke Flexure Based Positioning Mechanism

2012 ◽  
Author(s):  
K. G. P. Folkersma ◽  
S. E. Boer ◽  
D. M. Brouwer ◽  
J. L. Herder ◽  
H. M. J. R. Soemers
Keyword(s):  
Natural Frequency ◽  
Experimental Test ◽  
Degrees Of Freedom ◽  
Vibration Mode ◽  
Internal Stresses ◽  
Two Degrees Of Freedom ◽  
Test Setup ◽  
Flexure Hinges ◽  
Exact Constraint

Flexure based stages are particularly important for vacuum applications because they combine low hysteresis, no wear and no contamination with a high supporting stiffness. However, flexure hinges inherently lose stiffness in supporting directions when deflected. Therefore the workspace to footprint ratio is limited. In this article we present the design and modeling of a two degrees of freedom cross flexure based stage that combines a large workspace to footprint ratio with high vibration mode frequencies. Because the mechanism is an assembly of optimized components, the stage is designed according to the exact constraint principle to avoid build-up of internal stresses due to misalignment. FEM results have been validated by measurements on an experimental test setup. The test setup has a workspace-area to footprint ratio of 1/32. The lowest measured natural frequency with locked actuators over a 60 × 60mm workspace was 80Hz.

scholarly journals ANALYTICAL MODELING OF PLANETARY GEAR AND SENSITIVITY OF NATURAL FREQUENCIES

2013 ◽  
pp. 35-40
Author(s):  
MAJID MEHRABI ◽  
DR. V.P. SINGH
Keyword(s):  
Natural Frequency ◽  
Degrees Of Freedom ◽  
Analytical Modeling ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Planetary Gear ◽  
Vibration Modes ◽  
Planetary Gears ◽  
System Parameters ◽  
Inertia Parameters

This work develops an analytical model of planetary gears and uses it to investigate their natural frequencies and vibration modes. The model admits three planar degrees of freedom for each of the sun, ring, carrier and planets. Vibration modes are classified into rotational, translational and planet modes. The natural frequency sensitivities to system parameters are investigated for tuned (cyclically symmetric) planetary gears. Parameters under consideration include support and mesh stiffnesses, component masses, and moments of inertia. Using the well-defined vibration mode properties of tuned planetary gears, the eigen sensitivities are calculated and expressed in simple exact formulae. These formulae connect natural frequency sensitivity with the modal strain or kinetic energy and provide efficient means to determine the sensitivity to all stiffness and inertia parameters by inspection of the modal energy distribution.

Damping Measurement of Bending Vibration in Alpine Skis: An Improvement of Standard ISO 6267

2006 ◽  
Vol 5-6 ◽  
pp. 199-206 ◽  
Author(s):  
Giulio Fanti ◽  
R. Basso ◽  
V. Montauti
Keyword(s):  
Natural Frequency ◽  
Experimental Test ◽  
Vibration Mode ◽  
Damping Ratio ◽  
Time History ◽  
Measuring Method ◽  
Bending Vibration ◽  
Natural Modes ◽  
The Fourier Transform

The ISO 6267 standard defines a damping measuring method in terms of the half-time of the vibration of clamped alpine skis that is mainly related to the first vibration mode only. By means of the experimental test done in laboratory, it is shown that this method is not able to completely characterize the damping of the skis that depends on the vibration mode considered. For example in the case a ski sample, damping ratio varies from 0.45%±0.05% of the first mode to 2.1%±0.1% of the fourth one. The experimental test done on ski tracks by means of piezo-accelerometers placed on the skis running at speed of 12.5 m/s showed that the skis vibrate according to a combination of at least the first 4 vibration modes and that the snow better excites frequencies greater than the first one. As the excitation frequencies on the skis during the descent are much higher than the first natural frequency of the ski, it appears not correct to hypothesize that only the damping coefficient relative to the first natural frequency is representative of the ski vibrations. To improve the UNI ISO 6267 standard, a new method based on the Fourier Transform filtering to separate the time history into the vibration components is proposed for the characterization of the ski damping that is variable with its natural modes.

scholarly journals Exact Constraint Design of a Two-Degree of Freedom Flexure-Based Mechanism1

2013 ◽  
Vol 5 (4) ◽  
Author(s):  
Dannis M. Brouwer ◽  
(Ger) K. G. P. Folkersma ◽  
Steven E. Boer ◽  
Ronald G. K. M. Aarts
Keyword(s):  
Degrees Of Freedom ◽  
Vibration Mode ◽  
Singular Value ◽  
Actuation Force ◽  
Singular Value Decomposition Method ◽  
Kinematic Loops ◽  
Value Decomposition ◽  
Exact Constraint ◽  
Deterministic Behavior ◽  
Two Degree Of Freedom

We present the exact constraint design of a two degrees of freedom cross-flexure-based stage that combines a large workspace to footprint ratio with high vibration mode frequencies. To maximize unwanted vibration mode frequencies the mechanism is an assembly of optimized parts. To ensure a deterministic behavior the assembled mechanism is made exactly constrained. We analyze the kinematics of the mechanism using three methods; Grüblers criterion, opening the kinematic loops, and with a multibody singular value decomposition method. Nine release-flexures are implemented to obtain an exact constraint design. Measurements of the actuation force and natural frequency show no bifurcation, and load stiffening is minimized, even though there are various errors causing nonlinearity. Misalignment of the exact constraint designs does not lead to large stress, it does however decrease the support stiffness significantly. We conclude that designing an assembled mechanism in an exactly constrained manner leads to predictable stiffnesses and modal frequencies.

Experimental Study on Vibration Characteristics of Acoustic System in Ultrasonic Vibration Lapping

2010 ◽  
Vol 455 ◽  
pp. 313-319 ◽  
Author(s):  
Chang Juan Zhang ◽  
Chuan Shao Liu ◽  
Bo Zhao
Keyword(s):  
Experimental Study ◽  
Natural Frequency ◽  
Ultrasonic Vibration ◽  
Degrees Of Freedom ◽  
Vibration Mode ◽  
Excitation Frequency ◽  
Acoustic System ◽  
Resonant Condition ◽  
Vibration Effect ◽  
Displacement Equation

In this paper, the natural frequency and the vibration mode of the lapping tool in ultrasonic vibration lapping are analyzed, the resonance mechanism of the lapping tool is researched by establishing its mechanical model and displacement equation, and the experimental study is carried out in ultrasonic vibration lapping of engineer ceramics. The conclusions include: 1) The natural frequency of the designed lapping tool is ; 2) The acoustic system in ultrasonic vibration lapping is simplified to equivalent many-degrees of freedom system, while the damp is ignored, the lapping tool is resonant with itself-natural frequency, the joint of the horn and the lapping tool is a displacement node, and the whole system is in resonant condition. 3）While the experimental condition is no-load and ultrasonic, the vibration frequency of the lapping tool is 21.3125 , which is further closed to the calculated natural frequency, at that time the amplitude of the lapping tool is maximal and the system is in resonant condition. Moreover, while the resonance frequency of the horn and the lapping tool is different, the good vibration effect of the lapping tool can be obtained by adjusting the excitation frequency of generator.

scholarly journals Decoupling Optimization Design of Under-Chassis Equipment Suspension System in High-Speed Trains

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Zhanghui Xia ◽  
Dao Gong ◽  
Jinsong Zhou ◽  
Wenjing Sun ◽  
Yu Sun
Keyword(s):  
Natural Frequency ◽  
High Speed ◽  
Optimization Design ◽  
Degrees Of Freedom ◽  
Vibration Mode ◽  
Ride Comfort ◽  
Vibration Damping ◽  
Dynamic Vibration Absorber ◽  
Damping Effect ◽  
High Speed Trains

The vibrations of high-speed trains may strongly affect the safety and ride comfort of passengers, which issue requires the damping optimization of under-chassis equipment (UCE). In this study, the natural frequency of UCE is determined via the dynamic vibration absorber theory. The performed investigation of UCE-car body system vibration behavior revealed that an eccentricity of UCE results in the coupling vibration in six degrees of freedom, which leads to significant changes in its vibration mode and frequency. Thus, the natural frequency of UCE deviates from the initially determined value, which implies that the vibration damping effect is weakened. In this study, two decoupling optimization design methods, namely, forward and inverse decoupling methods, are proposed to solve this problem. The analysis of results obtained proves the feasibility of the proposed methods, which yield favorable decoupling degrees for the UCE vibration modes and minimize the offset of the vibration mode frequency from the initial natural one. These methods are considered quite instrumental in the improvement of vibration damping effect for high-speed trains.

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