Model-based design of motorized spindles with different bearing configurations

This paper conducts a dynamic design of motorized spindles with different configurations using an integrated dynamic electro-thermo-mechanical model. The dynamic electro-thermo-mechanical model consists of a thermo-mechanical bearing model, a shaft dynamic model and a thermal model. These sub-models interact on each other based on the bearing configuration, and general cases of bearing configurations can be modeled with the use of the pertinent mapping between shaft stiffness and bearing stiffness matrices. Based on the integrated model a design flow chart is developed and four design variables (DVs) are identified. The proposed model is validated experimentally and a design sensitivity analysis of the four DVs is then presented with a 170MD15Y20 type motorized spindle. The good agreement between the theoretical results and the experimental data indicates that the integrated model is capable of accurately predicting the multi-physics coupled dynamic behaviors of motorized spindles, and the sensitivities of the four DVs to the nature frequencies of the spindle system are obtained with different configurations

Rational points on x3+x2y2+y3=kx^{3} + x^{2} y^{2} + y^{3} = k

We study the problem of determining, given an integer $k$, the rational solutions to $C_{k} : x^{3}z + x^{2} y^{2} + y^{3}z = kz^{4}$. For $k \ne 0$, the curve $C_{k}$ has genus $3$ and there are maps from $C_{k}$ to three elliptic curves $E_{1,k}$, $E_{2,k}$, $E_{3,k}$. We explicitly determine the rational points on $C_{k}$ under the assumption that one of these elliptic curves has rank zero. We discuss the challenges involved in extending our result to handle all $k \in \mathbb{Q}$.Comment: 18 page

On the Emotional Colors and Performance Techniques in Brahms' Interlude Op.118 No.2

Johannes Brahms was the last German Austrian classical master of the romantic period. In this era of significant changes in music style, Brahms' early creative style still retained some traces of classical style. However, in his later years, he became more passionate about small genre lyrical works. I believe that these works must be the gentlest and most monologue works of Brahms' life. The interlude Op118 No.2, created in the late period of Brahms, possesses extremely clever creative techniques and extremely beautiful melodies, and is later known as the "Love Letter to Clara". The emotions and performance techniques involved are worth further exploration

Effects of elevated CO\u3csub\u3e2\u3c/sub\u3e, increased nitrogen deposition, and plant diversity on aboveground litter and root decomposition

Global change-induced litter decomposition strongly affects the carbon (C) and nitrogen (N) dynamics in grassland ecosystems. However, few studies show the interactive effects of global change factors on litter and root decomposition. We conducted a four-year grassland field experiment to examine the quality and decomposition of litter and root in a three-factorial experiment with elevated CO2, increased N deposition, and plant species richness. We found that elevated CO2 decreased the litter N content and root lignin content. N addition increased the root N content and decreased the litter lignin content. Increasing plant richness decreased the N and lignin contents in litter and root. In contrast to the quality changes, elevated CO2 had no effect on decomposition of litter and root. N addition increased the C loss of the litter by 4.8%, but did not affect C and N loss in root. Increasing plant richness affected the C and N loss in litter and root. ANCOVAs showed that tissue quality and root biomass affected the C and N loss in litter and root, and soil C and N affected the N loss of litter and root. However, changes in tissue quality, biomass, and soil as covariates did not significantly change the effects of CO2, N, and plant richness on decomposition. The structural equation model showed that elevated CO2 indirectly decreased litter N loss and increased root N loss, while N addition indirectly increased the C and N loss in litter and root, via their effects on tissue quality. Increasing plant richness increased litter C and N loss, but indirectly decreased root C and N loss. N deposition can accelerate litter and root decomposition, thus modifying the limitation of elevated CO2 on soil N availability. Biodiversity loss greatly alters litter and root decomposition, potentially driving any changes in C and N cycling. Our study clearly demonstrates a relative certainty of a predicted increase in the C loss and N release in litter and root decomposition with increased N deposition, whereas the effects of elevated CO2 and plant diversity changes on decomposition strongly differ between litter and root in grassland ecosystems

Nonlinear modelling and transient dynamics analysis of a hoist equipped with a two-stage planetary gear transmission system

A system-level nonlinear dynamic model for a two-stage planetary gear transmission system of a hoist is established with the consideration of time-varying meshing stiffness, backlash, damping, and bearing stiffness. Vibrational test results are also presented in accordance with simulation results computed from the dynamic model, and engagement-impacting dynamic simulations are achieved by adapting a dynamic explicit algorithm based on this model. Accordingly, variation in the contact state in relation to the engaging position is obtained together with vibration characteristics of the transmission system. This study provides a theoretical basis for the reduction of vibration and noise for the transmission system

Model-based dynamical properties analysis of a motorized spindle system with an adjustable preload mechanism

This paper presents a dynamical model for an especially designed motorized spindle with an adjustable preload mechanism and analyzes the effects of bearing preload on the spindle dynamical properties in both of the non-working and working states. In the model, the housing, rear bearing pedestal, shaft, drawbar and tool are taken into account using the finite element (FE) method. The effects of bearing preload are provided by this mathematical model as well as the experiments, in which the axial displacement of spindle tool, frequency response function (FRF), vibration displacement etc. are measured under all kinds of operating conditions. Various results such as bearing nonlinear stiffness, inherent modal shapes and frequencies of the system, spindle stiffness and chatter stability have been obtained under different preload. The good agreement between the calculated results and the tested data indicates that the model is capable of predicting the dynamical properties of the motorized spindle system accurately. And it is indicated that choosing an appropriate bearing preload can contribute to acquire good dynamical properties for the motorized spindle

Nonlinear bound states with prescribed angular momentum

We prove the existence of a class of orbitally stable bound state solutions to nonlinear Schr\"odinger equations with super-quadratic confinement in two and three spatial dimensions. These solutions are given by time-dependent rotations of a non-radially symmetric spatial profile which in itself is obtained via a doubly constrained energy minimization. One of the two constraints imposed is the total mass, while the other is given by the expectation value of the angular momentum around the z-axis. Our approach also allows for a new description of the set of minimizers subject to only a single mass constraint.Comment: 15 pages; some typos and small mistakes corrected; more explanations added regarding (2.1); more references added regarding remark 1.3 and lemma 3.