Study on Migratory Behavior of Aggregate in Asphalt Mixture Based on the Intelligent Acquisition System of Aggregate Attitude Data

In order to provide a new method to study the migration behavior of coarse aggregates in the compaction process of asphalt mixtures, the “Intelligent Aggregate Attitude Acquisition System (IAS)” is developed based on 3D printing technology and wireless intelligent sensing technology, and the “Intelligent Attitude Aggregate (IAA)” is prepared as the acquisition terminal. The Superpave Gyratory Compaction (SGC) test and the Internet of Things (IOT) wireless sensor technology are combined to collect and analyze the attitude data of an SMA-20 asphalt mixture built in IAA at different compaction stages, and the migration behavior of coarse aggregate in the compaction process is quantitatively characterized. The result shows that the IAA is suitable as a “tracking aggregate” to study the aggregate transfer behavior in asphalt mixtures. The IAA in the upper layer tends to move vertically downward, while the particles in the lower layer tend to move horizontally and spatial rotation in the process of rotating compaction. With the increase in asphalt content, the lubrication effect between aggregate particles is obvious, and the friction resistance of aggregate particles decreases when it is embedded downward. Affected by shear force in the process of rotary compaction, the aggregate particles are easier to overcome friction and cause large horizontal migration and spatial rotation. With the increase in compaction temperature, the viscosity of asphalt binder decreases, and the contact friction between aggregate particles decreases. The asphalt content has a significant effect on the displacement in the horizontal plane Dxoy of the aggregate. The asphalt content and compaction temperature have significant effects on the spatial rotation angle Φ of aggregate, but the asphalt content has a greater impact on it.

Fatigue strength of disk cutting tool of robotic equipment

The spatial rotation of the robotic unit cutting disk model is considered. The connection between the stresses in the disk and the kinematics of spherical motion is established. A criterion for the fatigue strength of a disk of robotic equipment is proposed. Keywords circular saw, disc, rotation frequency, inertial forces. [email protected]

SU(2) × SU(2) Algebras and the Lorentz Group O(3,3)

The Lie algebra of the Lorentz group O(3,3) admits two types of SU(2) × SU(2) subalgebras: a standard form based on spatial rotation generators and a second form based on temporal rotation generators. The units of measurement for the conserved quantity due to invariance under temporal rotations are investigated and found to be the same units of measure as the Planck constant. The breaking of time reversal symmetry is considered and found to affect the chiral properties of a temporal SU(2) × SU(2) algebra. Finally, the symmetry between algebras is explored and pairs of algebras are found to be related by SU(2) × U(1) symmetry, while a group of three algebras are related by SO(4) symmetry.

Properties of Spatial-Rotation Transformations of Fractional Derivatives

The transformation properties of the fractional derivatives under spatial rotation in two-dimensional space and for both the Riemann-Liouville and Caputo definitions are investigated and derived in their general form. In particular, the transformation properties of the fractional derivatives acting on scalar fields are studied and discussed. The study of the transformation properties of fractional derivatives is an essential step for the formulation of fractional calculus in multi-dimensional space. The inclusion of fractional calculus in the Lagrangian and Hamiltonian dynamical formulation relies on such transformation. Specific examples on the transformation of the fractional derivatives of scalar fields are discussed.