Stress Solitary Waves Generated by a Second-Order Polynomial Constitutive Equation

In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton's second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves

Correlation of Copper Interaction, Copper-Driven Aggregation, and Copper-Driven H2O2 Formation with Aβ40 Conformation

The neurotoxicity of Aβ is associated with the formation of free radical by interacting with redox active metals such as Cu2+. However, the relationship between ion-interaction, ion-driven free radical formation, and Aβ conformation remains to be further elucidated. In the present study, we investigated the correlation of Cu2+ interaction and Cu2+-driven free radical formation with Aβ40 conformation. The Cu2+-binding affinity for Aβ40 in random coiled form is 3-fold higher than that in stable helical form. Unexpectedly but interestingly, we demonstrate in the first time that the stable helical form of Aβ40 can induce the formation of H2O2 by interacting with Cu2+. On the other hand, the H2O2 generation is repressed at Aβ/Cu2+ molar ratio ≥1 when Aβ40 adopts random coiled structure. Taken together, our result demonstrates that Aβ40 adopted a helical structure that may play a key factor for the formation of free radical with Cu2+ ions

Model of Inverse Envelope Cutter with Ring-Involute Tooth

[[abstract]]The design of a conical cutter is important in the manufacture of concave and convex gears. An inverse method is presented for determining the mathematical model of a rack cutter. The obtained rack cutter was used to generate concave and convex gears. The method proposed in this paper addressed design problems in the rack cutter that were used to generate a new type of concave and convex gears. Based on the two-parameter family of surfaces and direct envelope method, the conical cutter was used as the generating tool for the proposed gear type, and a mathematical model of gears with ring-involute teeth was developed according to gear theory. The contour of von-Mises stress distribution of the gear and the pinion of the proposed mathematical model is presented. Using CNC manufacturing technology, a gear with ring-involute teeth was manufactured by a conical cutter. Based on the inverse envelope concept, the mathematical model of the developed gear tooth was used to determine the geometrical and mathematical models of the rack cutter with ring-involute teeth. To illustrate the effectiveness of the method, a numerical example is presented to demonstrate the geometric model of a gear with a gear ratio of 3:2

Geometry and Simulation of the Generation of Cylindrical Gears by an Imaginary Disc Cutter

[[abstract]]This paper proposed a method of representing the geometry of an imaginary disc cutter in parameter form. The undercutting condition of the imaginary disc cutter is studied, and the mathematical model of the generated gears is developed by the undercutting condition of the cutter. Through a mathematical model of the generation process, the vector equations of generated gears are established. According to the proposed method, a planetary gear mechanism and a pair of gear pump with smaller numbers of teeth are illustrated. A cutting simulation process is presented for machining the proposed gear pairs. Stress analysis for the proposed gear mechanism is performed. Finally, the proposed method is applied to determine singular points of the proposed disc cutter

A Study of an Elbow Mechanism Generated by a Conical Cutter

[[abstract]]This paper presents a method for determining the mathematical model of an elbow mechanism with a convex tooth and a concave tooth. Based on this method, the mathematical model presents the meshing principles of a conical cutter meshed with a tooth that is either convex or concave. Using the developed mathematical models and the tooth contact analysis, kinematic errors are investigated according to the obtained geometric modelling of the designed gear meshing when assembly errors are present. The influence of misalignment on kinematic errors has been investigated. The goal of the current study is to investigate von-Mises stress for three teeth contact pairs. A structural load is assumed to act on a gear of the proposed mechanism. The von-Mises of the proposed gear is determined. The conical cutter used in the design and manufacture of the convex and concave gear is shown. For example, the proposed mechanism with a transmission ratio of 3:2 was determined with the aid of the proposed mathematical model. Using rapid prototyping and manufacturing technology, an elbow mechanism with a convex gear, a concave gear and a frame was designed. The RP primitives provide an actual full-size physical model that can be analysed and used for further development. Results from these mathematical models are applicable to the design of an elbow mechanism

Applying Two-Parameter Envelope Theory to Determining Spherical Cam Profile with Cylinderical Followers

[[abstract]]Using the envelope theory of two-parameter family of ball surfaces, two geometric models of spherical cam can be easily obtained when the follower-motion program has been given. The results of the envelope theory are used to determine an optimal spherical cam profile with an oscillating cylindrical follower. Some investigations of geometric characteristic, such as pressure angle and cutting path, are determined using the obtained geometric model. The principle curvatures are analyzed to avoid undercutting. Finally, a numerical example is given to illustrate the application of the procedure

A Planetary Gear Train with Ring-Involute Tooth

[[abstract]]This paper proposes a planetary gear train with ring-involute tooth profile. Inherent in a planetary gear train is the conjugate problem among the sun, the planet gears and the ring gear. The sun gear and the planet gear can be obtained by applying the envelope method to a one-parameter family of a conical tooth surface. The conical tooth rack cutter was presented in a previous paper [5]. The obtained planet gear then becomes the generating surface. The double envelope method can be used to obtain the envelope to the family of generating surfaces. Subsequently the profile of a ring gear of the planetary gear trains can be easily obtained, and using the generated planet gear and applying the gear theory, the ring gear is generated. To illustrate, the planetary gear train with a gear ratio of 24:10:7 is presented. Using rapid prototyping and manufacturing technology, a sun gear, four planet gears, and a ring gear are designed. The RP primitives provide an actual full-size physical model that can be analyzed and used for further development. Results from these mathematical models are applicable to the design of a planetary gear train

A Geometric Model of a Spherical Gear with a Double Degree of Freedom

[[abstract]]This paper presents a double degree of freedom spherical gear mechanism with circular arc teeth. The developed spherical gear is very suitable for the flexible wrist of a robot. Based on the envelope theory of a two-parameter family of generating surfaces, mathematical and geometrical models of a spherical gear with circular arc teeth are proposed. In the process of machining a gear blank, the required tool path can be generated by using the obtained geometric models, the forms of which are determined easily by envelope theory. Finally, the geometric model of the spherical gear can be obtained simultaneously by Mastercam and SolidWorks software

A Mathematical Model of a cc-type Single-Screw Compressor

[[abstract]]In this paper, a method is proposed for determining a basic profile of a cc-type single-screw compressor including the gate rotor and the screw rotor. The cc-type has a cylindrical screw and two cylindrical gate rotors. Based on this method, a mathematical model of the meshing principles of a cc-type screw rotor meshed with a gate rotor, that has either straight edge teeth or conical teeth, is presented. The inverse envelope concept is used to determine the cutting-edge curve of a gate rotor. Based on this concept, the required cutter for machining a cc-type screw rotor can be obtained by the envelope of a one-parameter family. The obtained screw rotor is an envelope to the family of the gate rotor's surfaces. The obtained envelope becomes the generating surface. The inverse envelope can be used to obtain the envelope to the family of generating surfaces. Then the profile of a gate rotor cutting-edge curve can be easily obtained. The surface analysis including contact lines is shown for the design and manufacture of a screw compressor. As an example, the cc-type single-screw compressor with a compressor ratio of 11:6 was determined with the aid of the proposed mathematical model. Using rapid prototyping (RP) and manufacturing technology, a cc-type single-screw rotor with a gate rotor was designed. The RP primitives provide an actual full-size physical model that can be analysed and used for further development. Results from these mathematical models should have applications in the design of cc-type single-screw compressors

Study of a Single Screw Compressor with a Conical Teeth Gate Rotor

[[abstract]]From a geometric viewpoint, a mathematical model of a single screw compressor with a conjugate pair of meshing conical teeth gate rotor is a conjugate problem. Coordinate transformation and envelope theory are applied to determine the sets of spatial points of the contacting surfaces that define the main rotor of a single screw compressor. Envelope theory and analytical procedure are used to derive mathematical models of a gate rotor and a main rotor. Stress analysis for the single screw compressor mechanism is performed. PowerMILL software package is used to simulate the manufacture of a main rotor. A numerical example with a compressor ratio of 11:6 is presented to demonstrate the application of the mathematical models developed in mis paper