Power Loss Predictions in High-Speed Rolling Element Bearings Using Thermal Networks

In high-speed rolling element bearings (REB), the lubricant is used to separate the mating surfaces but also to cool down the parts while the system is in operation. In the context of optimizing oil circuits, a clear understanding of the lubricant cooling mechanisms is therefore required in order to reach a compromise between a good cooling capacity and the constraints on mass, size, and power. In this article, a model is presented that makes it possible to predict temperature distributions in high-speed thrust ball bearings. It is found that the prediction or measurement of global power loss cannot discriminate between several combinations of traction and drag forces. On the other hand, the predicted temperature distributions appear as very sensitive to the relative importance given to hydrodynamic rolling tractions or drag losses. Based on these findings, a methodology is suggested in order to define the most realistic power loss models to be used in high-speed REB simulations.     

Development of an analytical model to estimate the churning losses in high-speed axial piston pumps

The axial piston pumps in aerospace applications are often characterized by high-speed rotation to achieve great power density. However, their internal rotating parts are fully immersed in the casing oil during operation, leading to considerable churning losses (more than 10% of total power losses) at high rotational speeds. The churning losses deserve much attention at the design stage of high-speed axial piston pumps, but accurate analytical models are not available to estimate the drag torque associated with the churning losses. In this paper, we derive the analytical expressions of the drag torque acting on the key rotating parts immersed in oil, including the cylinder block and the multiple pistons in a circular array. The calculated drag torque agrees well with the experimental data over a wide range of rotational speeds from 1500 to 12000 r/min. The presented analytical model provides practical guidelines for reducing the churning losses in high-speed axial piston pumps or motors.     

基于流体动力学的斜齿轮副搅油功率损失分析

在高速工况下,搅油损失在总功率损失中占很大比重,研究齿轮搅油功率损失对于提高传动效率具有重要意义。提出一种基于流体动力学的能够计算斜齿轮副搅油功率损失的计算模型,该模型采用将斜齿轮沿接触线划分为若干个薄直齿轮的方法计算斜齿轮副的搅油损失;将齿轮副搅油功率损失分为周面搅油功率损失、端面搅油功率损失以及啮合区挤压功率损失三部分,分析浸油深度、转速、螺旋角、齿宽、模数对搅油损失的影响以及各部分搅油损失占总搅油损失的比重。结果表明：搅油损失随着浸油深度、转速、螺旋角、齿宽、模数的增大而增大,其中转速、齿宽和模数对搅油损失的影响较大,浸油深度和螺旋角对搅油损失的影响较小;啮合区挤压功率损失在整个搅油功率损失中占最大比重。     

Fluid Flow Analysis for Friction Torque around Rolling Element in Ball Bearings

Ball bearings (e.g., deep-groove, angular-contact, and roller bearings) support loads in a rotor system and provide lubrication between the shaft and housing. The deep-groove ball bearings used in a turbopump do not differ significantly from angular-contact ball bearings or the bearings found in other applications. Deep-groove ball bearings consist of rolling elements, an inner raceway, an outer raceway, and a retainer to guide the rolling elements. In ball bearings, the resistive (churning or drag) forces and torques acting on the rolling elements and raceways are affected by the fluid flow rate and direction, as well as the rotational speed. These churning and drag forces and torques affect the internal dissipation or power losses into the bearing, which become very significant for high-speed applications. This study numerically investigated the characteristics of the flow conditions for deep-groove ball bearings, with a particular focus on the friction distribution on the rolling elements. A simple analytical model of the fluid flow inside a ball bearing was developed using a computational analysis, and the flow characteristics at high rotational speeds are presented.     

Numerical Investigations on Drag Coefficient of Balls in Rolling Element Bearing

In high-speed rolling element bearings the drag force generated by the motion of the balls in an air–oil mixture is frequently taken into account using the results for a sphere in an infinite medium. This approach is surprising because important interaction between the flows around the balls may occur. The drag coefficient value should be then adjusted to the configuration that is observed in a rolling element bearing (REB). In this article, a computational fluid dynamics code is applied to simulate three configurations: one single sphere, two spheres in tandem, and a set of spheres that are aligned along the air flow. It can be seen that both the flow pattern around one sphere and its drag coefficient are modified when placing another sphere in its vicinity. Furthermore, in REB configuration the drag coefficient value is far from the one observed when the obstacle is isolated and mainly depends on the space between the obstacles.     

数控机床主动力系统载荷能量损耗系数的计算获取方法

机床量大面广,能量消耗巨大并且能量效率低、能量效率规律复杂,因此机床能量效率的研究和应用正在全球迅速兴起。机床主动力系统载荷能量损耗,是机床最复杂的部分,一般占到机床切削能量的10%~20%,其具体多少决定于载荷损耗系数。针对机床主动力系统载荷损耗系数在线获取非常困难,以及现有获取方法存在切削仪器昂贵、测量过程复杂以及许多机床无法安装等不足,提出一种根据数控机床主动力系统载荷能量损耗数学模型而建立的载荷损耗系数计算获取方法。上述数学模型由三部分组成:基于主电动机的变频器额定功率、额定功率损耗和散热器额定功率等基础参数的变频器功率损耗近似计算模型;基于主电动机额定功率、基频、空载功率和基频下的效率等基础参数的主电动机功率损耗模型;基于机床机械传动系统中每种传动副的数量和载荷效率等基础参数的机械传动系统载荷损耗模型。实际计算时只需获取基础参数和测量机床主动力系统空载功率,便可计算出机床主动力系统的载荷能量损耗系数。基于上述计算方法,计算获取了数控加工中心PL700主动力系统的载荷能量损耗系数。实验结果证实了该方法的准确性和实用性。该方法可广泛用于数控机床的切削功率获取、数控机床能量效率评价和工件能量效率预测及优化等研究和应用中,具有多方面的应用前景。     

水平轴风力机的转矩性能及叶尖损失对其的影响

分析了叶尖损失机理,根据PRANDTL 和GLAUERT叶尖损失修正因子及叶素-动量理论,推导出考虑叶尖损失的叶片弦长公式,然后沿叶片展向积分,推导出与风力机尖速比和翼型升阻比关联的风力机转矩系数解析表达式,并得到风力机在任何稳定运行状态转矩系数的最高参数值,可作为风力机转矩系数的设计参考值。研究表明,叶尖损失对弦长的影响集中在叶尖部位,当升阻比为无穷大且尖速比从常见范围10变化到4时,叶尖损失导致转矩性能损失约4%~10%,且损失的数值随升阻比的变化极小。     

齿轮啮合过程摩擦功耗研究

A novel method for frictional power losses of a gear meshing was presented according to the basic theory of power and energy of the system. It was provided that the relative sliding of two disks existed during the disks rotating, frictional power losses will be caused by the frictional torque for each disk. Based on the above principle, the model for the friction power loss of the gears meshing was built. The frictional coefficient plays important role to the frictional power loss of gears and the time-varying coefficient was analyzed. Based on the system frictional power loss of the gears, the time-varying frictional power loss was calculated. The results indicate that the power loss in the double tooth meshing plays significantly role in the whole power losses. Finally, the results obtained from the new method were compared to the test results by Velex and it is shown that the model of frictional power loss is feasible.     

MODELING A SOLID BOUNDARY AS A FLUID OF INFINITE VISCOSITY

0 IamODUCTIONFollowing the experimental data reported by Li.Pman['j on the existence of boundary layers over aflat plate, some interesting facts are observed:(l )There is a viscous sublayer developed near the wall which has practically zero fluid velocity inthe vicinity Of the wall(refer to Fig. I a). This sublayer may be calculated by substituting V = 0. 05, aridthe boundary layer is calculated by taking V = 3.5 where V = y (U/Zus )"' is a non-dimensionalsimilarity transformation funct…     

Miniature drag sphere velocity probe

The development and testing of a miniature drag sphere velocity probe is described. Impetus for its development arose from a need to investigate the flow structure and turbulence beneath breaking surface water waves, i.e., a requirement for a fast-response small velocity probe which is useable in oscillatory flows. However, the presence of both drag (velocity) and inertial (acceleration) forces limits the measurable fluctuations to those having scales at least an order of magnitude larger than the sphere diameter, while the sphere diameter is itself limited by the requirement that the drag coefficient be independent of velocity. The resulting probe, with a sphere diameter of 0.43 cm, while not free of temperature drifts, pressure sensitivity, and cross-channel talk, yields encouraging results.     

Experimental study of drag coefficient of multistrand wires using single normal hot-wire anemometer probe

In a vertical wind tunnel, used for testing of aircraft and helicopters spin and simulation of skydiving, a protective net made of multistrand wires is installed below the flight chamber to prevent the fall of the test models or skydivers to the ground. The drag due to the protective net is significant, which results in pressure drop and subsequent increase in the required power to attain a desired speed in the tunnel. This paper presents the results of an experimental study of drag coefficient of multistrand wires, using (i) a single normal hot-wire anemometer probe (HWA), (ii) a pitot tube, which measures the total pressure downstream of the multistrand wires. Initially, the non-dimensional distance, X/D, at which HWA measurements can be used to determine the drag coefficient of the multistrand wires with acceptable accuracy, was obtained by considering flow velocity profile and turbulence intensity, downstream of a cylindrical rod of diameter D. The distance was determined to be X/D>30, where X is the distance along the test section downstream of the cylindrical rod. Results of pitot tube and HWA measurements are in good agreement. These results show that at Reynolds number, Re=2000, drag coefficient of the multistrand wires is greater than the cylindrical rod by approximately 16%. However, the difference in the drag coefficients decreases with increase in Re; the two values approaching each other and attaining an almost equal value at Re=10,000.     

PERFORMANCE PREDICTION MODELS FOR TURNING WITH ROUNDED CORNER PLANE FACED LATHE TOOLS. I. THEORETICAL DEVELOPMENT

In this paper the need for reliable quantitative machining performance information for efficient and effective use of machining operations is discussed, as are the recent developments of predictive models for forces and power in practical machining operations based on the 'unified mechanics of cutting approach'. This investigation is aimed at extending this mechanics of cutting approach to turning with rounded corner plane faced lathe tools. Three predictive models for the forces, power and chip flow angle based on the 'unified mechanics of cutting approach1 have been developed while the surface roughness models have been based on the feed marks generated on the machined surface allowing for the precise tool corner profile. The first force model is based on the modified mechanics of cutting analyses for single edge tools while the two alternative models are based on the generalised mechanics of cutting analyses for single edge and multi-edge form tools for the turning cut as a whole. The predictive force models incorporate the effects of the major tool geometrical variables including the corner radius, the cutting conditions as well as the effect of TiN coating. This first paper will outline the development of the models while the proposed models will be numerically tested and experimentally verified qualitatively and quantitatively in the subsequent parts of this investigation.     

Numerical investigation of fluid flow past a square cylinder using upstream,downstream and dual splitter plates

A two-dimensional numerical study is carried out to analyze the drag reduction and vortex shedding suppression behind a square cylinder in presence of splitter plate arranged in upstream, downstream and both upstream and downstream location at low Reynolds number (Re = 160). Computations are performed using a Single relaxation time lattice Boltzmann method (SRT-LBM). Firstly, the code is validated for flow past a single square cylinder. The obtained results are compared to those available in literature and found to be in good agreement. Numerical simulations are performed in the ranges of 1 ≤ L ≤ 4 and 0 ≤ g ≤ 7, where L and g are the length of splitter plate and gap spacing between the splitter plate and main square cylinder, respectively. The effect of these parameters on the vortex shedding frequency, time-trace analysis of drag and lift coefficients, power spectra analysis of lift coefficient, vorticity contours visualization and force exerted on the cylinder are quantified together with the observed flow patterns around the main cylinder and within the gap spacings. The observed results are also compared with a single square cylinder without splitter plate. We found that at some combinations of L and g, the mean drag coefficient and Strouhal number reach either its maximum or minimum value. It is found that the drag is reduced up to 62.2 %, 13.3 % and 70.2 % for upstream, downstream and dual splitter plates, respectively as compared to a single square cylinder (without splitter plate). In addition, in this paper we also discussed the applications of SRT-LBM for suppression of vortex shedding and reduction of the drag coefficients.     

带有圆锥齿轮的复合行星传动功率流与传动效率分析

对带有圆锥齿轮的复合行星传动进行运动分析,在此基础上采用虚功率理论分析该复合行星传动在不考虑啮合功率损失和考虑啮合功率损失时的功率流,在定义速比与转矩比的情况下,获得复合行星传动效率表达式,进一步研究速比、转矩比和啮合功率损失系数及几何参数比对复合行星传动效率的影响规律,并开展相关试验验证。理论分析表明：在复合行星传动啮合功率损失系数和几何参数比被确定的情况下,复合行星传动效率随着转矩比的增大而增大,但随着速比的增大呈先减小后增大趋势;在复合行星传动速比和转矩比及几何参数比被确定的情况下,各齿轮副的啮合功率损失系数对复合行星传动效率的影响存在差异;在复合行星传动速比和转矩比及各齿轮副的啮合功率损失系数被确定的情况下,复合行星传动效率随着几何参数比的增大而增大。传动效率试验表明：选用高精度等级的锥齿轮、增大复合行星传动机构的转矩比及其行星轮的节圆半径可提高复合行星传动机构的传动效率。     

A novel approach to the estimation and application of the wear coefficient of metal-on-metal hip implants

A novel approach is proposed to estimate and model the wear of metal-on-metal hip implants. The approach is based on two distinct wear coefficients for the head and cup, derived from separate measurements on the two components. This is in contrast to the usual assumption that a single wear coefficient (k) is valid for both bodies. Actually, the head and cup do not wear equally; thus, assuming equal wear leads to predictive errors. Additionally, in most papers, k is chosen considering only implant materials while neglecting geometry and testing conditions. It is suggested that experimental procedures designed for hip implants should measure the head and cup volume losses separately and that wear maps should be provided to validate numerical models.     

CFD analysis of effects on fluid flow resistance of metallic wavy structures

Microscale wrinkles can be utilized to enhance the characteristics of products. For example, a shark skin having riblet surface can move faster underwater, minimizing fluid flow resistance. We introduce a novel approach to fabricate microscale metallic wrinkles using a soft lithography and electroforming process; we also evaluated the effects of wrinkles by computational fluid dynamics (CFD) analyses. For the generation of metallic wrinkles, a UV-curable resin, NOA68T was used to fabricate a master wrinkling pattern by mechanism of compressive forces on a skin of the weakly polymerized resin layer. The master pattern was molded and replicated as metallic wrinkles on a surface via soft lithography and electroforming processes. To understand the advantages of a wavy surface on reduction of flow resistance, we carried out two- and three-dimensional (2D and 3D) CFD analyses. The drag coefficient of a wrinkled 2D square model was decreased about 17.1 %, and a 3D real wrinkle model showed 4.9 to 7.3 % reduction of it compared to without wrinkle models. We believe that it is possible to reduce the fluid flow resistance using wavy surfaces that can easily be generated selectively or wholly on an arbitrary surface.

     

不同波长瞬态侧风对汽车气动性能影响分析

利用大涡模拟对某轿车受到的瞬态侧风进行研究,并采用自定义函数（UDF）控制边界的方法实现了正弦侧风在时间及空间上的瞬态变化,分析了三种不同波长的正弦侧风对气动力系数的影响,并将结果与风洞实验及稳态模拟的结果进行对比。结果表明：受到瞬态变化的正弦侧风时,气动力系数呈周期性变化,但气动阻力系数的变化频率是气动侧力及横摆气动力矩系数变化频率的两倍;瞬态正弦侧风波长减小时,气动阻力系数的变化范围逐渐减小;在瞬态侧风作用下,A柱对汽车的气动性能产生了重要影响。     

基于非光滑表面与涡流干扰的车身气动减阻方法

探讨了将表面非光滑形态结构减阻思想与流场主动控制相结合的车身气动减阻方法。将凹坑型非光滑表面布置在MIRA直背式模型的尾部,并在非光滑形态模型的基础上,在凹坑阵中加装喷射速度可变的涡流发生器来控制模型的尾部气流,改善尾涡结构。通过对光滑、非光滑、非光滑加涡流喷射三种模型的三维流场数值模拟,得到不同尾部形态模型的气流速度、压力以及湍动能等参数,对比不同风速下不同模型气动阻力系数的差异以及不同喷射速度下的减阻效果,分析模型尾部流场参数的变化,阐述了非光滑形态车身气动减阻机理以及涡流喷射扰动效应。研究结果表明：通过对非光滑形态被动减阻与涡流喷射主动减阻的优化组合,能有效地减少不同风速下直背式MIRA模型的气动阻力。     

Constraint-force-based approach of modelling compliant mechanisms: Principle and application

Numerous works have been conducted on modelling basic compliant elements such as wire beams, and closed-form analytical models of most basic compliant elements have been well developed. However, the modelling of complex compliant mechanisms is still a challenging work. This paper proposes a constraint-force-based (CFB) modelling approach to model compliant mechanisms with a particular emphasis on modelling complex compliant mechanisms. The proposed CFB modelling approach can be regarded as an improved free-body- diagram (FBD) based modelling approach, and can be extended to a development of the screw-theory-based design approach. A compliant mechanism can be decomposed into rigid stages and compliant modules. A compliant module can offer elastic forces due to its deformation. Such elastic forces are regarded as variable constraint forces in the CFB modelling approach. Additionally, the CFB modelling approach defines external forces applied on a compliant mechanism as constant constraint forces. If a compliant mechanism is at static equilibrium, all the rigid stages are also at static equilibrium under the influence of the variable and constant constraint forces. Therefore, the constraint force equilibrium equations for all the rigid stages can be obtained, and the analytical model of the compliant mechanism can be derived based on the constraint force equilibrium equations. The CFB modelling approach can model a compliant mechanism linearly and nonlinearly, can obtain displacements of any points of the rigid stages, and allows external forces to be exerted on any positions of the rigid stages. Compared with the FBD based modelling approach, the CFB modelling approach does not need to identify the possible deformed configuration of a complex compliant mechanism to obtain the geometric compatibility conditions and the force equilibrium equations. Additionally, the mathematical expressions in the CFB approach have an easily understood physical meaning. Using the CFB modelling approach, the variable constraint forces of three compliant modules, a wire beam, a four-beam compliant module and an eight-beam compliant module, have been derived in this paper. Based on these variable constraint forces, the linear and non-linear models of a decoupled XYZ compliant parallel mechanism are derived, and verified by FEA simulations and experimental tests.