Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis

Deformation of the flexspline is the basis of analyzing tooth trajectory and designing tooth profile. Considering the tooth influence on the position of equivalent neutral layer, a piecewise method for calculating the deformation of flexspline assembled with a cam wave generator is presented in this paper. Firstly, a mechanic model of a ring of uniform thickness in contact with a rigid cam is established. The displacements of the ring inside and outside an unknown wrapping angle are determined by the geometric constraints of the cam profile and the equilibrium relationship, respectively. Meanwhile, the wrapping angle is solved according to the boundary conditions. The assembly forces are derived to investigate the circumferential elongation and strain. Then, considering the tooth effects on the neutral layer of flexspline, the tooth is positioned on the equivalent neutral layer, which is the non-elongation layer within one gear pitch but offset from the geometric mid-layer. The equivalent neutral layer is positioned by the empirical formula of the offset ratio, which is summarized by the orthogonal simulation on finite element models of racks. Finally, finite element models of a ring-shaped and a cup-shaped flexspline assembled with elliptical cam are established to verify the effectiveness and accuracy of the piecewise method. The results show that, compared with the geometric method, the tooth positioning deviation calculated by the piecewise method can be reduced by about 70% with a more accurate deformation description from the geometric condition and mechanic condition inside and outside the wrapping angle.

Influence of the electromagnetic field pressure on the free bending of the straight side

Bending is the operation of forming or changing the angles between the parts of the workpiece or giving it a curved shape and in the mean time is the most difficult and timeconsuming operation of the technological process of manufacturing parts from profiles. Aircraft bending parts of the following nomenclature are obtained as profiles: frames, ribs, stringers, linings and brackets. Profile parts are responsible for their intended purpose; therefore, high requirements are placed on the accuracy of their dimensions and the preservation of the crosssection shape. The process of bending profiles has its own characteristics, which are due to the shape of the profile section; the first feature is the presence of vertical shelves, significantly loaded and deformed due to large distances from the neutral axis of the bent section, the second is the mismatch of the bending plane with the main axes of inertia of the section, which causes oblique bending and twisting of the part. When analyzing the bending process of extruded profiles, it should be borne in mind that the neutral layer of the workpiece coincides with the line that passes through the centers of gravity of the sections. When using the hypothesis of planar sections of the plot of deformations and stresses in the stretched and compressed zones do not have a mutually reflected form. It is very important how the profile is oriented in the bending plane. Different orientation of the profile, even the simplest cross-section (for example, angular), gives a qualitatively different picture of the deformed state.

Investigation on Deformation of the Flex-Gear and Optimization Design of Compound Curve Cam Wave Generator with Spiral

The deformation shape and mechanical property of flex-gear greatly affect the meshing accuracy and service life of harmonic drive, and the stress wave generator plays a decisive role in the deformation shape and mechanical properties of the flexible gear. The investigation on deformation of the flex-gear around the major axis is developed with comparative analysis with three kinds of traditional and commonly used wave generators. Based on the influence of the deformation around the major axis on meshing accuracy and service life, the eccentric arc cam wave generator improved by transition curve for controlling the deformation shape and reducing the deformation stress is developed. Considering the achievable flexibility of spiral with smooth curvature change rate, the contour of the compound curve cam wave generator with arc and spiral is proposed. The deformation of the flex-gear under the influence of this compound curve cam and the standard elliptic cam is further comparative analyzed. The conclusion shows that this compound curve cam can indeed reduce the deformation stress in the meshing area by increasing the meshing width, and correct deformation shape can also be gained by shape control on the whole circumference of the flex-gear’s neutral layer.

A strain gradient strategy to quantifying longitudinal compression behavior in slender fibrous assembly structures

Slender fibrous assembled structures can easily buckle under longitudinal compressive load. The limitation in characterizing the longitudinal compression behavior poses a significant challenge to the mechanics optimization of such structures. To address this challenge, we use one-dimensional yarns as a model system, and the yarns are deformed in bending to form a strain gradient, from tension to compression, along the radial direction of the yarns. The compression modulus as a function of compression strain is calculated based on bi-moduli elastic theory. The evolution of the fiber arrangement and the position of the neutral layer in the yarn is interpreted along with the change of compression modulus. Also, the local stress distribution in the bent yarn was determined by finite element simulation, and it is remarked that the bending property of yarns is sensitive to the compression modulus. The present study offers insights on the modeling and simulation of fabrics and garments in drape and bending deformation. Results from such investigations can provide effective guidance for the mechanical and structural design of textiles and textile-based composites.

Resist-Free Directed Self-Assembly Chemo-Epitaxy Approach for Line/Space Patterning

This work reports a novel, simple, and resist-free chemo-epitaxy process permitting the directed self-assembly (DSA) of lamella polystyrene-block-polymethylmethacrylate (PS-b-PMMA) block copolymers (BCPs) on a 300 mm wafer. 193i lithography is used to manufacture topographical guiding silicon oxide line/space patterns. The critical dimension (CD) of the silicon oxide line obtained can be easily trimmed by means of wet or dry etching: it allows a good control of the CD that permits finely tuning the guideline and the background dimensions. The chemical pattern that permits the DSA of the BCP is formed by a polystyrene (PS) guide and brush layers obtained with the grafting of the neutral layer polystyrene-random-polymethylmethacrylate (PS-r-PMMA). Moreover, data regarding the line edge roughness (LER) and line width roughness (LWR) are discussed with reference to the literature and to the stringent requirements of semiconductor technology.

Spring-Back Prediction of the Bi-Layered Metallic Tube under CNC Bending Considering Neutral Layer Shifting Extraction

Bi-layered metallic bending tubes are widely used in extreme environments. The spring-back prediction theory for precise forming of such tube configuration is lacking. The layered coupling causes complex section internal force and new boundary conditions. This work proposed a theoretical prediction model of bimetallic tubes’ spring-back under computer numerically controlled (CNC) bending. This model calculated the spring-back angle by importing two new parameters—the composite elastic modulus (Ec) and the composite strain neutral layer (Dε). To investigate Dε, the neutral layer shifting extraction method was proposed to get the shifting value from finite element simulations. Simulations and full-scale bending experiments were carried out to verify the reliability of this prediction model. The theoretical results are closer to the experimental results than the finite element (FE) results and the theoretical results neglecting neutral layer shifting. The change of spring-back angle with the interlaminar friction coefficient was investigated. The results indicated that the normal mechanical bonding bimetallic tube with an interlaminar friction coefficient below 0.3 can reduce spring-back.