Pure rolling motion of hyperquadrics in pseudo-Euclidean spaces

<p style='text-indent:20px;'>This paper is devoted to rolling motions of one manifold over another of equal dimension, subject to the nonholonomic constraints of no-slip and no-twist, assuming that these motions occur inside a pseudo-Euclidean space. We first introduce a definition of rolling map adjusted to this situation, which generalizes the classical definition of Sharpe [<xref ref-type="bibr" rid="b26">26</xref>] for submanifolds of an Euclidean space. We also prove some important properties of these rolling maps. After presenting the general framework, we analyse the particular rolling of hyperquadrics embedded in pseudo-Euclidean spaces. The central topic is the rolling of a pseudo-hyperbolic space over the affine space associated with its tangent space at a point. We derive the kinematic equations, as well as the corresponding explicit solutions for two specific cases, and prove the existence of a rolling map along any curve in that rolling space. Rolling of a pseudo-hyperbolic space on another and rolling of pseudo-spheres are equally treated. Finally, for the central theme, we write the kinematic equations as a control system evolving on a certain Lie group and prove its controllability. The choice of the controls corresponds to the choice of a rolling curve.</p>

Design of vehicle using Ackermann steering with IoT concept

Electric vehicles are becoming more demanding these days. In this project the possibility of using Ackerman steering with electric drive servomotor is explained. Scalability is the advantage of using this mechanism which can be adopted for four-wheel vehicle system as well. The objective of this project is to do design a system using Ackerman steering which determines the maximum and minimum angle of the turning of the wheels. It also avoids the front tire slippage and activates pure rolling. Ackermann steering geometry is a geometric arrangement of linkages in the steering of a car or other vehicle designed to solve the problem of wheels on the inside and outside of a turn needing to trace out circles of different radii. The geometrical solution to this is for all wheels to have their axles arranged as radii of circles with a common centre point. As the rear wheels are fixed, this centre point must be on a line extended from the rear axle. Intersecting the axes of the front wheels on this line as well requires that the inside front wheel be turned, when steering, through a greater angle than the outside wheel. The microcontroller used in this project is ATMega16 andlmax232 is used for the serial data transmission.

Algebraic Method for Exact Synthesis of 1-DOF Linkages With Arbitrarily Prescribed Constant Velocity Ratios

This paper addresses the synthesis of 1-DOF linkages that can exactly transmit angular motion between coplanar axes (i.e. parallel axes or intersectant axes) with arbitrarily prescribed constant velocity ratios. According to motion polynomials over dual quaternions and pure rolling models between two circles, an algebraic approach is presented to precisely synthesize new 1-DOF linkages with arbitrarily prescribed constant velocity ratios. The approach includes four steps: (a) formulate a characteristic curve occurred by the pure rolling, (b) compute the motion polynomial of the minimal degree that can generate the curve, (c) deal with the factorization of the motion polynomial to construct an open chain, (d) convert the open chain to a 1-DOF linkage. Using this approach, several 1-DOF planar, spherical, and spatial linkages for angular motion transmission between parallel axes or intersectant ones are constructed by designating various velocity ratios. Taking the planar and spherical linkages with a constant 1:2 velocity ratio as examples, kinematics analysis is implemented to prove their motion characteristics. The result shows that the generated linkages indeed can transmit angular motion between two coplanar axes with constant velocity ratios. Meanwhile, 3D-printed prototypes of these linkages also demonstrate such a conclusion. This work provides a framework for synthesizing linkages that have great application potential to transmit motion in robotic systems that require low inertia to achieve reciprocating motion with high speed and accuracy.

Professor Duncan Dowson, a source of inspiration

The current paper highlights the contribution of the Dowson and Higginson work to numerical line contact elastohydrodynamic lubrication film thickness prediction and the Hamrock and Dowson contribution to the film thickness prediction in elliptical contacts. This paper shows that, even by today’s standards, both the numerical pressure and film thickness results and the curve-fitted film thickness predictions are very accurate. As for the elliptical results, the authors show that the original predictions remain surprisingly accurate for moderately elliptical contact. For very long elliptical contacts, their prediction does not tend to a line contact asymptote. This paper then concludes that the predicted pressure spikes by Dowson, Higginson, and Hamrock are correct in shape and amplitude, at least near pure rolling conditions.

Tribological Behavior of Ionic Liquid with Nanoparticles

This research aims to formulate a new lubricant containing oxide nanoparticles for enhancing anti-wear ability and reducing friction. Different concentrations of copper oxide (CuO) and zinc oxide (ZnO) nanoparticles were separately added to an ionic liquid, methyltrioctylammonium bis(trifluoromethylsulfonyl)imide [N1888] [NTf2], to formulate the tested lubricants. The tribological properties of the lubricants were tested by performing ball-on-disc wear tests on a tribotester (MTM, PCS Instruments). The results show that both the CuO and ZnO nanoparticles can increase the friction reduction ability of the ionic liquid when used as a neat lubricant. The anti-wear characteristic of the ionic liquid is increased by adding ZnO nanoparticles but decreased by adding CuO nanoparticles. The best tribological performance observed for the concentration of 0.2 wt% ZnO, with the wear scar diameter is reduced by 32% compared to the pure ionic liquid. The results of SEM/EDX analysis on the worm morphologies show different lubrication mechanisms of the nanoparticles in the [N1888] [NTf2], which are tribo-sintering for CuO nanoparticles, and third body with pure rolling effect for ZnO nanoparticles.

Ackermann Principle and its Implementation in Modern Cars

The Ackermann principle was developed when it became possible to separately control the four wheels of a moving object in the process of turning. In this case, two tasks arose. The first task was to control the wheels to ensure their pure rolling when the object is turned. The solution of this problem was in the Ackermann principle. The second task was to implement this principle in a specific mechanism. The paper analyzes the mechanisms common in modern cars in order to assess their compliance with the Ackermann principle. The method of analysis was in generating and modeling a finite-difference equation describing the process of transferring the movement of the steering wheel to the movement required to turn the wheels.

Analytical Study of Dry Whip Phenomena During Rotor-Stator Rub

Rotor-Stator Rub is a rare but catastrophic phenomenon and in most cases leads to failure of Gas Turbine Engines. Asynchronous rub namely Partial Rub and Dry whip are two of the most common observed rub related phenomena. Dry whip leads to pure backward whirl and instability. This paper studies the dry whirl analytically to determine the boundaries of instability and establish expressions for nonlinear vibrations in case of dry whip. First, Nonlinear Natural Frequency has been defined for a rotor-stator rub system and expression for natural motion of the system has been formulated. Next, Pure rolling of rotor on stator has been used as a condition to approximate the nonlinear system to find out the dependence of dry whip frequency on the parameters such as stiffness, damping ratio, coefficient of friction and spin speed of the rotor. Moreover, a validation of the obtained frequencies and amplitudes obtained analytically has been performed through the simulation of rotor stator rub system using RK-4 integration technique. Furthermore, this study offers insight into the frequencies that are present in the Radial motion of the rotor and its source of origin. The radial displacement of the rotor has harmonics which are the result of interaction between the rotor speed and the backward whirl frequency causing dry whip.

Experimental Study of the Lubrication Mechanism of Micro-Spherical Solid Particles between Flat Surfaces

In this study, a novel apparatus was designed and constructed to perform micro-sliding friction experiments while simultaneously observing the motion of micro-sized spheres using a visual inspection technique. The apparatus comprises a precision elevation stage that is used to elevate a flat mica disk, with the microspheres on top of it, to bring it into contact with a stationary surface and apply low loads on the contact. During micro-sliding experiments, it was found that the velocity of the center of the microsphere was half the velocity of the mica disk; in addition, friction force measurements revealed a very low coefficient of friction (about 0.03), indicating the rolling motion of the microspheres. The main outcome of our study was the verification of the hypothesis that spherical particles can be used to avoid direct contact among flat surfaces and can also introduce rolling motion within the system. The pure rolling motion of the microspheres sandwiched between a stationary and a moving flat surface supports the idea of adding rigid spherical particles to oil lubricants to further reduce friction and wear in the system by performing as micro and nanoscale ball bearings.

Research on the centre distance separability of parallel shaft line gear pair

For gear pairs with centre-distance separability, transmission ratios are not affected by centre distance error. Based on space curve meshing theory, the centre distance separability of a line gear pair was studied. A novel line gear pair called the separable and pure rolling parallel shaft line gear pair (SPRPSLG) was proposed, which has centre-distance separability characteristics and pure rolling transmission. The basic design theory of the SPRPSLG pair was established. A design method of the SPRPSLG pair with an eccentric arc tooth profile was given. An SPRPSLG pair example was designed and manufactured using the form milling method. Kinematic experiments and meshing efficiency experiments were conducted. Gear contact spot testing and gear contact simulation analysis were carried out. The SPRPSLG pair was shown to have centre distance separability, which provides a further theoretical basis for the popularization and application of line gears.

Lubrication state identification of the line contact tribo-pair under a pure rolling condition with ultrasonic method

A line contact tribo-pair is a key mechanism unit in rolling bearings, which is often characterized by ultra-high contact pressure and ultra-thin oil film. Elastohydrodynamic lubrication is often adopted to characterize the lubrication state of such a tribo-pair. As a primary parameter for elastohydrodynamic lubrication, the oil film thickness is often evaluated with simplified theoretical models or complicated measurements. So far, a comprehensive verification of the lubrication states in a real line-contact tribo-pair, however, is rarely reported. Focusing on the roller/ring tribo-pair of a wet-lubricated rolling bearing under pure rolling conditions, this study investigates the lubrication states by integrating multiple theories. Five regions including isoviscous hydrodynamic, piezoviscous hydrodynamic, elastohydrodynamic lubrication, mixture lubrication, and boundary lubrication regions can be identified using the framework. Then, validation experiments are carried out on a line contact tribo-pair test rig under the same operating conditions applied in the theoretical analysis. The oil film thickness is measured by the ultrasonic method. The analysis results demonstrate that only two regions, the elastohydrodynamic lubrication and mixture lubrication regions, can be identified using the experimental data. The identified elastohydrodynamic lubrication and mixture lubrication regions are consistent with theoretical analysis; and the Blok equation and elastohydrodynamic lubrication theory are suggested to calculate the oil film thickness in the elastohydrodynamic lubrication and mixture lubrication regions, respectively. Moreover, the oil film thickness calculated by the Dowson equation is larger than that based on the elastohydrodynamic lubrication theory due to a different viscous pressure equation.