End Of Collision Research Articles

A Contact Force Model Considering Meshing and Collision States for Dynamic Analysis in Helical Gear System

The current research on gear system dynamics mainly utilizes linear spring damping model to calculate the contact force between gears. However, this linear model cannot correctly describe the energy transfer process of collision that often occurs in gear system. Focus on the contact-impact events, this paper proposes an improved gear contact force model for dynamic analysis in helical gear transmission system. In this model, a new factor associated with hysteresis damping is developed for contact-impact state, whereas the traditional linear damping factor is utilized for normal meshing state. For determining the selection strategy of these two damping factors, the fundamental contact mechanics of contact-impact event affected by supporting forces are analyzed. During this analysis, an effect factor is proposed for evaluating the influence of supporting forces on collision. Meanwhile, a new restitution of coefficient is deduced for calculating hysteresis damping factor, which suitable for both separation and non-separation states at the end of collision. In addition, the time-varying meshing stiffness (TVMS) is obtained based on the potential energy approach and the slice theory. Finally, a dynamic analysis of a helical gear system is carried out to better understand the contact force model proposed in this paper. The analysis results show that the contribution of supporting forces to the dynamic response of contact-impact event within gear pair is important. The supporting forces and dissipative energy are the main reasons for gear system to enter a steady contact state from repeated contact-impact state. This research proposes an improved contact force model which distinguishes meshing and collision states in gear system.

The Zhireken porphyry Mo ore-magmatic system (eastern Transbaikalia): U–Pb age, sources, and geodynamic setting

Two intrusive complexes are recognized in the Zhireken deposit: Amanan and ore-bearing porphyry. According to the ages obtained by U–Pb zircon dating (Amanan complex—162.6 ± 1.4 Ma, granites and monzonite-porphyry of the ore-bearing complex—159.0 ± 1.6 and 157.5 ± 2.9 Ma), the Amanan complex formed at the end of collision, and the ore-bearing porphyry complex, during the change of the geodynamic regime by the postcollisional (rift) one. The rocks of two complexes have high contents of LILE and LREE and low contents of HFSE and HREE. The (87Sr/86Sr)0ratio in the gabbro and granites of the Amanan complex is 0.70501 and 0.70534, respectively, and that in the rocks of the porphyry complex is within 0.70451–0.70633. The Amanan gabbro, gabbro-diorites, and granites are characterized by εNd(T) = –1.4, –1.8, and –10.3, respectively, and the rocks of the ore-bearing complex, by εNd(T) = –3.7 to +1.0. The model TNd(DM) age of the Amanan granites is 1.5 Ga, and that of the granites and porphyry of the ore-bearing complex is 1.0–0.8 Ga. The Pb isotope ratios in the rocks of the Amanan and porphyry complexes are: 206Pb/204Pb = 18.086–18.136 and 18.199–18.442, 207Pb/204Pb = 15.487–15.499 and 15.506–15.545, and 208Pb/204Pb = 38.046–38.256 and 38.230–38.456. The results of geological, geochemical, and isotope studies admit that magmas were generated from juvenile and ancient crusts. Melts probably ascended from a depth of no less than 55 km during the melting of crust thickened as a result of tectonic deformations (in the upper horizons) and during the basic-magma supply (in the lower horizons). Juvenile mafic crust is considered to be the major source of fluid components and metals. Favorable conditions for the ore generation in the magmatic system during the formation of the porphyry complex arose at the previous stage, during the formation of the Amanan complex, which we regard as a preparatory stage in the evolution of the long-living ore-magmatic system.© 2015, V.S. Sobolev IGM, Siberian Branch of the RAS. Published by Elsevier B.V. All rights reserved.

711 ボールエンドミル加工における切削抵抗予測法の高制度化 : 逃げ面を考慮した工具干渉終了点の算出

711 ボールエンドミル加工における切削抵抗予測法の高制度化 : 逃げ面を考慮した工具干渉終了点の算出

Geochronology on Cenozoic volcanic rocks of a profile Linzhou Basin, Tibet, China and their geological implications

Geochronology on Cenozoic volcanic rocks of a profile Linzhou Basin, Tibet, China and their geological implications

Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes

The distinct element method (DEM) has proven to be reliable and effective in characterizing the behavior of particles in granular flow simulations. However, in the past, the influence of different force–displacement models on the accuracy of the simulated collision process has not been well investigated. In this work, three contact force models are applied to the elementary case of an elastic collision of a sphere with a flat wall. The results are compared, on a macroscopic scale, with the data provided by the experiments of Kharaz et al. (Powder Technol. 120 (2001) 281) and, on a microscopic scale, with the approximated analytical solution derived by Maw et al. (Wear 38 (1976) 101. The force–displacement models considered are: a linear model, based on a Hooke-type relation; a non-linear model, based on the Hertz theory (J. Reine Angew. Math. 92 (1882) 156) for the normal direction and the no-slip solution of the theory developed by Mindlin and Deresiewicz (Trans. ASME. Ser. E, J. Appl. Mech. 20 (1953) 327) for the tangential direction; a non-linear model with hysteresis, based on the complete theory of Hertz and Mindlin and Deresiewicz for elastic frictional collisions. All the models are presented in fully displacement-driven formulation in order to allow a direct inclusion in DEM-based codes. The results show that, regarding the values of the velocities at the end of collision, no significant improvements can be attained using complex models. Instead, the linear model gives even better results than the no-slip model and often it is equivalent to the complete Mindlin and Deresiewicz model. Also in the microscopic scale, the time evolution of the tangential forces, velocities and displacements predicted by the linear model shows better agreement with the theoretical solution than the no-slip solution. However, this only happens if the parameters of the linear model are precisely evaluated. The examination of the evolution of the forces, velocities and displacements during the collision emphasizes the importance of correct accounting for non-linearity in the contact model and micro-slip effects. It also demonstrates how these phenomena need to be considered into the model in order to perform deeper analyses on granular material in motion and, in general, for systems sensitive to the actual force or displacement. For these cases, more accurate models such as the complete Mindlin and Deresiewicz model should be addressed.

High-pressure blueschists and eclogites in Hong'an: a framework for addressing the evolution of high- and ultrahigh-pressure rocks in central China

The Hong'an region in the Qinling–Dabie collisional zone in eastern China hosts a series of metamorphic rocks exposing a south-to-north distribution from blueschist/blueschist–greenschist, amphibolite, eclogite (kyanite free) and kyanite–eclogite to coesite–eclogite facies rocks that represent progressively deeper levels of the Mesozoic subduction–collision complex. The Hong'an area is interesting for three reasons: (1) it escaped the thermal and structural overprint imparted on much of the Dabie Mountains during Early Cretaceous intrusion of voluminous granites and granodiorites; (2) the high-pressure (HP) Hong'an eclogites are widely distributed, often preserve prograde crystallization histories and can be directly linked in time and space to the blueschist/blueschist–greenschist rocks exposed to the south; (3) the blueschist/blueschist–greenschist facies rocks are generally better exposed than their equivalents in the southeastern Dabie Mountains and offer some opportunity for simultaneous structural and metamorphic analysis. The Hong'an area HP rocks offer perhaps the closest approximation to a preserved snapshot of Mesozoic pressure–temperature ( P– T) conditions attending early subduction–exhumation in the region, and are thus essential to generating a coherent picture of the dynamics attending both metamorphism and exposure of the coeval ultrahigh-pressure (UHP) rocks. The purpose of this contribution is twofold: (1) to document previously unpublished metamorphic and structural data characterizing these HP sequences and their relative continuity in Hong'an; (2) to incorporate these data with recent geochronologic, structural and paleomagnetic information in the context of protracted, late Paleozoic through Mesozoic subduction, collision and exhumation. Metamorphism and exhumation of some of the southern Hong'an HP sequences appear to have occurred concomitant with oceanic subduction immediately to the west, and thus may have preceded widespread continental subduction/collision. Moreover, all of the HP–UHP sequences in the region were exhumed before the end of collision between the Sino-Korean and Yangtze cratons at ca. 160 Ma. Exhumation of HP–UHP rocks both before and during continental plate collision is neither novel for central China nor for other HP–UHP zones, but is important to take into account when reconstructing the evolution of such orogens.

Deformational history of the central Brooks Range, Alaska: Results from fission‐track and 40Ar/39Ar analyses

The Brooks Range is the northernmost orogenic belt in Alaska. From south to north it consists of a thin belt of oceanic basalt and chert, followed by two belts of high‐pressure/low‐temperature metamorphic rocks (the schist and central belts), a basement‐cored anticlinorium (the Doonerak Window), a fold and thrust belt, and a foreland basin (the Colville Basin). We have used apatite and zircon fission‐track (FT) and 40Ar/39Ar white mica analyses of a N‐S transect of the central Brooks Range to study the cooling history. These data are used with a balanced cross section to constrain the timing of deformational events in northern Alaska. The oldest cooling ages from this study were clusters of ∼185 Ma and ∼135 Ma zircon FT ages from the fold and thrust belt. Based on the similarity of the 185 Ma ages with the age of crystallization of the western Brooks Range ophiolites [Wirth et al., 1993], we suggest that the Brooks Range orogeny in northern Alaska had begun prior to this time. Cooling rates in the fold and thrust belt were very slow from 185 to 135 Ma, suggesting little or no deformation was occurring. Apatite and zircon FT analyses from the fold and thrust belt indicate that a substantial amount of cooling (caused by uplift and erosion) occurred from 135 to 95 Ma. We suggest that an increase in the rate of cooling at ∼135 Ma was caused by contractional deformation associated with renewed subduction with the opening of the Canada Basin. The 40Ar/39Ar white mica cooling ages of 130 to 120 Ma from the schist belt rocks of the southern Brooks Range indicate that peak metamorphism must have occurred prior to 130 Ma. An 40Ar/39Ar muscovite age of 113 Ma from the southernmost Brooks Range is interpreted to be the age of movement on normal faults juxtaposing lower‐grade phyllite belt rocks against schist belt rocks. At the same time, rapid deposition of Brooks Range‐derived sedimentary sequences began to the north, in the Colville foreland basin, and to the south, in the Yukon‐Koyukuk basin. Unstrained high‐level granitic plutons, which intruded the Yukon‐Koyukuk basin and Ruby terrane from 107 to 95 Ma, indicate the end of collision with the Yukon‐Koyukuk arc. By 95 Ma, cooling rates in the Brooks Range had slowed and little or no deformation was occurring. At 60 Ma, a major episode of rapid cooling occurred throughout northern Alaska, when the active plate margin in Alaska was more than 500 km to the south. In the Colville Basin, cooling was caused by thrust faulting and folding, and hence erosion, within the Albian‐age and younger sedimentary rocks. Within the interior of the Brooks Range, a large‐scale basement‐involved anticlinorium (the Doonerak Window) became active at this time. At 25 Ma, another episode of rapid cooling occurred within the Doonerak Window region. Both of these events may be related to shallow subduction of the Kula plate from the southern Alaskan plate margin.

Sedimentary record of subduction to forearc transition in the rotated Eocene basin of western Oregon

Systematic changes in compositions of Eocene sandstones in the southern part of the Oregon Coast Range constrain proposed models of tectonic accretion and rotation of this crustal fragment. Three basic petrofacies of lithic, arkosic, and volcanolithic composition can be defined sequentially from the base to the top of the section. The lithic petrofacies was deposited prior to rotation and was derived from the nearby Klamath Mountains during collision of the subjacent seamount terrane. The transition to arkosic composition coincided with the end of collision and the initiation of forearc basin subsidence. The arkosic sands contain muscovite and potassium feldspar derived from a continental-plutonic source area; their presence in the forearc sequence suggests that the Coast Range block lay farther to the east and closer to interior parts of the Mesozoic batholith belt prior to tectonic rotation. Volcanolithic sandstones were deposited after rotation of the Coast Range had begun, and they mark the beginning of volcanic activity in the adjacent Cascade arc.