New Exact Solutions with a Linear Velocity Field for the Gas Dynamics Equations for Two Types of State Equations

In this paper, exact solutions with a linear velocity field are sought for the gas dynamics equations in the case of the special state equation and the state equation of a monatomic gas. These state equations extend the transformation group admitted by the system to 12 and 14 parameters, respectively. Invariant submodels of rank one are constructed from two three-dimensional subalgebras of the corresponding Lie algebras, and exact solutions with a linear velocity field with inhomogeneous deformation are obtained. On the one hand of the special state equation, the submodel describes an isochoric vortex motion of particles, isobaric along each world line and restricted by a moving plane. The motions of particles occur along parabolas and along rays in parallel planes. The spherical volume of particles turns into an ellipsoid at finite moments of time, and as time tends to infinity, the particles end up on an infinite strip of finite width. On the other hand of the state equation of a monatomic gas, the submodel describes vortex compaction to the origin and the subsequent expansion of gas particles in half-spaces. The motion of any allocated volume of gas retains a spherical shape. It is shown that for any positive moment of time, it is possible to choose the radius of a spherical volume such that the characteristic conoid beginning from its center never reaches particles outside this volume. As a result of the generalization of the solutions with a linear velocity field, exact solutions of a wider class are obtained without conditions of invariance of density and pressure with respect to the selected three-dimensional subalgebras.

DESIGN AND EXPERIMENT OF CENTRIFUGAL COLLISION TEST DEVICE FOR MILLET AND SWEET BUCKWHEAT GRAIN

This critical collision damage force of millet and sweet buckwheat grain and the shelling force of shelled granular materials are important basic data for research of threshing and shelling technology and equipment. In order to master the linear velocity and collision force of grain with different moisture content when collision damage occurs, a centrifugal collision test device is designed. Based on the dynamic and kinematic analysis of grain in the centrifugal rotary table, the collision force between grain and steel plate was measured by PVDF piezoelectric pressure sensor and data acquisition system. The results showed that: under the same moisture content, the higher the rotational speed, the higher the grain crushing rate; at the same rotational speed, with the increase of moisture content, the crushing rate first decreased and then increased. When the moisture content of Jingu-21 and Yuqiao-4 is 19.7% and 17.8%, respectively, the grain crushing rate was the lowest. In terms of the anti-collision ability of grain, the optimum moisture content of threshing is between 19.7% and 21% for millet. For sweet buckwheat, the optimum moisture content of threshing is 17.8% ~19%, while the optimum moisture content of shelling by centrifugal sheller is about 11%. The faster the rotational speed of centrifugal rotary table is, the greater the linear speed of grain is, and the greater the collision force is. When the linear velocity of grain was 8.32 m/s and 11.30 m/s respectively, the millet grain moisture content was 11.1% and 20.9% respectively, damage began to appear, and the corresponding collision force was about 5.51 N and 10.6 N, respectively. When the linear velocity of grain was 8.32 m/s and 11.30m/s respectively, and the moisture content was 11.1% and 22.8% of the sweet buckwheat grain respectively, damage began to appear, the corresponding collision force was about 8.92 N and 12.79 N, respectively. When the rotating speed of rotary table was 910 r/min, the linear speed of grain was 27.05 m/s, the crushing rate of millet and sweet buckwheat grain in harvest period were 56.30% and 63.76%, respectively, and the crushing rate of millet and buckwheat grain with 11.1% moisture content were 86.27% and 89.4%, respectively. The research results can provide theoretical basis for design and optimization of millet and sweet buckwheat combine harvester, threshing device and shelling device.

Acoustic microstreaming produced by two interacting gas bubbles undergoing axisymmetric shape oscillations

An analytical theory is developed that describes acoustic microstreaming produced by two interacting bubbles. The bubbles are assumed to undergo axisymmetric oscillation modes, which can include radial oscillations, translation and shape modes. Analytical solutions are derived in terms of complex amplitudes of oscillation modes, which means that the modal amplitudes are assumed to be known and serve as input data when the velocity field of acoustic microstreaming is calculated. No restrictions are imposed on the ratio of the bubble radii to the viscous penetration depth and the distance between the bubbles. The interaction between the bubbles is considered both when the linear velocity field is calculated and when the second-order velocity field of acoustic microstreaming is calculated. Capabilities of the analytical theory are illustrated by computational examples.

Kinematics of a screw linkage

This paper proposes a kinematics methodology in twist coordinates for screw linkages. Based on the definition of a twist, both the angular velocity of a link and the linear velocity of a point on it may be explicitly represented in twist coordinates. Through integration on the twist solution numerically or analytically, we may obtain the displacements. By differential or numerical differential interpolation of the twist, we can find the accelerations of the link. The most outstanding advantage of this kinematic algorithm is that only the numerical differential interpolation of the first order is required to calculate the acceleration while only the first order integration of the twist is enough to compute the displacement. This merit makes it particularly fit for developing programmes to accomplish the kinematics analysis of a spatial linkage.

Demonstrating Tangential Velocity by a Self-Coded Robot

Tangential velocity is a concept that is often taught as a part of rotation, and is the linear velocity an object has as it turns about a fixed axis. The main goal of this research project was to examine this concept and demonstrate it on a self-coded robot. The robot was designed with two rotating motors with two wings of different lengths to be attached on top, and the motors were connected to a circuit board and coded using the programming language C to rotate with equal and constant angular velocities upon initiation. The main hypothesis is that the length of rotating wings is directly proportional to the tangential velocity of the wings. The project provides a new way of demonstrating tangential velocity in a high school physics class.

Construction of a Rotation Acquisition System using Arduino and Scada Supervisory Software

This work presents the development and implementation of a System for Acquisition of Rotations composed of an open-source Arduino electronic prototyping platform and a Supervision and Data Acquisition System (SCADA). This system obtains instantaneous values for frequency, linear velocity, and angular velocity, and the graphical representation of said instantaneous values is in real-time. Thus, the proposed system is a mediator of learning for the teaching of Circular Movement Uniform, with theoretical/practical interaction essential in classes for understanding the content.

What determines focal depth?

The interior of the Earth has smaller linear velocity than the Earth surface, but larger inertia due to gravity. This generates longer period of decelerations or accelerations in the interior producing strain with vertical and horizontal components. Faster linear velocity results in larger strain. Focal depth is the compromise of these two factors. Slender potential energy produces focal depth with hundreds of kilometers deep.

Optimizing the High-Performance Milling of Thin Aluminum Alloy Plates Using the Taguchi Method

Most aerospace parts are thin walled and made of aluminum or titanium alloy that is machined to the required shape and dimensions. Deformation is a common issue. Although the reduced cutting forces used in high-speed milling generate low residual stress, the problem of deformation cannot be completely resolved. In this work, we emphasized that choosing the correct cutting parameters and machining techniques could increase the cutting performance and surface quality and reduce the deformation of thin plates. In this study, a part made of a thin 6061 aluminum alloy plate was machined by high-speed milling (HSM), and a Taguchi L16 orthogonal array was used to optimize the following parameters: linear velocity, feed per tooth, cutting depth, cutting width, and toolpath. The impact of cutting parameters on the degree of deformation, surface roughness, as well as the cutting force on the thin plate were all investigated. The results showed that the experimental parameters for the optimal degree of deformation were A1 (linear velocity 450 mm/min), B1 (feed per tooth 0.06 mm/tooth), C1 (cutting depth 0.3 mm), D4 (cutting width 70%), and E4 (rough zigzag). Feed per tooth was the most significant control factor, with a contribution as high as 63.5%. It should also be mentioned that, according to the factor response of deformation, there was a lower value of feed per tooth and less deformation. Furthermore, the feed per tooth and the cutting depth decreased and the surface roughness increased. The cutting force rose or fell with an increase or decrease of cutting depth.