Influence of Clearance Between Plates in Metal Pushing V-Belt Dynamics

2002 ◽  
Vol 124 (3) ◽  
pp. 543-557 ◽  
Author(s):  
G. Carbone ◽  
L. Mangialardi ◽  
G. Mantriota
Keyword(s):  
Rigid Body ◽  
Power Transmission ◽  
Dynamical Behavior ◽  
Continuous Model ◽  
Steel Plates ◽  
Body Motion ◽  
Speed Ratio ◽  
Friction Forces ◽  
One Dimensional ◽  
Significant Difference

This paper proposes a one-dimensional continuous model of the steel pushing V-belt, which describes the shifting dynamics of the CVT transmission during rapid speed ratio variations. The model investigates the influence of the clearance among the steel segments on the belt dynamics. The plates and pulleys strain motion is neglected, with respect to their rigid body motion, for the evaluation of the friction forces. The power transmission is assured only if an active arc exists where the plates are pressed against each other and where compressive forces arise among the steel segments. Conversely on the idle arc the steel plates are separated and no longitudinal compressive forces exist among the metal segments. The paper shows a significant difference in dynamical behavior between the drive and the driven pulley. Moreover, differences also exist between the pitch radius increasing phases and pitch radius decreasing phases.

scholarly journals Sliding-vibrating responses of elastic structures

1988 ◽  
Vol 21 (3) ◽  
pp. 190-197
Author(s):  
Yu-An Fu
Keyword(s):  
Rigid Body ◽  
Harmonic Excitation ◽  
Body Motion ◽  
Shake Table ◽  
Reciprocating Motion ◽  
Friction Forces ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Analytical Expressions ◽  
Vibrating Response

By using simulated friction forces, analytical expressions were derived from the sliding-vibrating response of a single degree of freedom system under harmonic excitation or the "disadvantageous period reciprocating motion", taking the mass of the sliding base into consideration. Some of the general laws were studied and some new characteristics determined which had previously been ignored by assuming rigid body motion. The analysis methods adopted in this paper have been confirmed in comparison with the results of model tests on a shake table.

The Influence of Pulley Deformations on the Shifting Mechanism of Metal Belt CVT

2005 ◽  
Vol 127 (1) ◽  
pp. 103-113 ◽  
Author(s):  
G. Carbone ◽  
L. Mangialardi ◽  
G. Mantriota
Keyword(s):  
Coulomb Friction ◽  
Rate Of Change ◽  
Groove Width ◽  
Speed Ratio ◽  
Dimensional Model ◽  
Friction Forces ◽  
One Dimensional ◽  
Mode Behavior ◽  
Radial Thickness ◽  
Transversal Width

This paper is concerned with the shifting behavior of a metal belt CVT. The calculations are performed for the chain belt case by using a one-dimensional model of the belt: the radial thickness of the belt is neglected. The friction forces are modeled on the basis of the Coulomb friction hypothesis. The deformation of the belt, i.e., the variation of its transversal width, is shown to be negligible with respect to the variation of the local groove width caused by the elastic deformation of the pulleys and by the clearance in the bearings. The particular shape of the deformed pulley is described on the basis of Sattler model (1999) who showed that the variation of the groove angle and that one of the local groove width of the pulley can be easily described by simple trigonometric formulas. The paper shows that the characteristic behavior of the transmission during slow shifting maneuvers, referred to as “creep mode,” is caused by the bending of the pulleys, that is to say for rigid pulleys no “creep mode” can be observed. Moreover, the model shows that increasing the rate of change of speed ratio a transition from the “creep-mode” to the so called “slip-mode” behavior of the variator takes place, as experimentally observed.

Rigid-body motion in phosphorus chalcogenides

1971 ◽  
Vol 27 (4) ◽  
pp. 383-387 ◽  
Author(s):  
R. A. Forder
Keyword(s):  
Rigid Body ◽  
Rigid Body Motion ◽  
Thermal Parameters ◽  
Body Motion ◽  
Bond Lengths ◽  
Body Model ◽  
Significant Difference ◽  
Rigid Body Model

The thermal parameters of P4S5, P4S7, P4S10 and P4Se5 have been analysed on the basis of the rigid-body hypothesis, using both Cruickshank's and Shomaker & Trueblood's methods. For these compounds, at least with the data at present available, the fit to the rigid-body model is only moderate, and there is no significant difference in the results of the two methods. Librational corrections to bond lengths have been calculated.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

scholarly journals Viscous Flow Around a Rigid Body Performing a Time-periodic Motion

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Thomas Eiter ◽  
Mads Kyed
Keyword(s):  
Rigid Body ◽  
Sobolev Spaces ◽  
Periodic Motion ◽  
Viscous Incompressible Fluid ◽  
Body Motion ◽  
Translational Velocity ◽  
Ill Posed ◽  
Homogeneous Sobolev Spaces ◽  
The Mean ◽  
Time Periodic

AbstractThe equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.

Optical strain measurements on fast moving fiber reinforced polymer rotors using diffraction gratings

2019 ◽  
Vol 86 (3) ◽  
pp. 175-183
Author(s):  
Julian Lich ◽  
Tino Wollmann ◽  
Angelos Filippatos ◽  
Maik Gude ◽  
Robert Kuschmierz ◽  
...  
Keyword(s):  
Rigid Body ◽  
Strain Measurement ◽  
Composite Structures ◽  
Dynamical Behavior ◽  
Image Correlation ◽  
Fiber Reinforced Polymers ◽  
Strain Gauges ◽  
Objective Lens ◽  
Fiber Reinforced ◽  
Body Movements

AbstractIn-situ measurements of the deformation and of the structural dynamical behavior of moving composite structures, such as rotors made of glass fiber reinforced polymers (GFRP), are necessary in order to validate newly developed simulation models. Local methods like strain gauges and fiber Bragg gratings lack spatial resolution, while contactless optical methods like image correlation or speckle interferometry suffer from noise effects in the presence of fast rigid body movements. A novel compact sensor – based on the diffraction grating method – is introduced for spatially and temporally resolved strain measurement. The use of a line camera allows the measurement of vibrations up to several tens of kHz. With a scanning movement, strain fields at submillimeter resolution can be recorded. The use of two diffraction orders and an objective lens reduces cross sensitivities to rigid body movements on the strain measurement by two to three orders of magnitude. A validation on a GFRP probe was conducted in a quasi-static tensile test with an optical extensometer up to 14500 µϵ. Furthermore, a strain measurement on a moving rotor at surface speeds up to 75 m/s was performed and the results were compared with those of strain gauges as a gold standard. The statistical standard deviation was around 10 µϵ and independent of the rotational speed.

A planar reconfigurable linear rigid-body motion linkage with two operation modes

2014 ◽  
Vol 228 (16) ◽  
pp. 2985-2991 ◽  
Author(s):  
Guangbo Hao ◽  
Xianwen Kong ◽  
Xiuyun He
Keyword(s):  
Rigid Body ◽  
Single Mode ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Reference Guide ◽  
Revolute Joints ◽  
Operation Modes ◽  
Straight Line ◽  
Motion Stage ◽  
Motion Mode

A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques

1995 ◽  
Author(s):  
X. Tong ◽  
B. Tabarrok
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
The Body ◽  
Body Motion ◽  
Heteroclinic Orbits ◽  
Coordinate Frame ◽  
Global Motion ◽  
Stable And Unstable Manifolds ◽  
Body Subject

Abstract In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.

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