Disc Assessment Research Articles

Limit angular speed analysis of porous functionally graded rotating disk under thermo-mechanical loading

PurposeIn this work, the effect of porosity volume fraction, porosity types, material grading index, variable disk profiles and aspect ratio on disk performance was studied by performing limit elastic speed analysis of functionally graded porous rotating disks (PFGM) under thermo-mechanical loading.Design/methodology/approachThe composition change was varied by employing the power law function. The thermo-mechanical properties of PFGM such as Young's modulus and yield strength were estimated using modified rule of mixture, for density and coefficient of thermal expansion rule of mixture was used. The even and uneven distribution of porosity in a disk was taken as uniform, symmetrical, inner maximum and outer maximum. The problem was then solved with the help of the variational principle and Galerkin's error minimization theory.FindingsThe research reveals that the grading parameter, disk geometry and porosity distribution have a significant impact on the limit elastic speed in comparison to the aspect ratio.Practical implicationsThe study determines a range of operable speeds for porous and non-porous disk profiles that the industry can utilize to estimate structural performance.Originality/valueA finite element investigation was conducted to validate the findings of the present study. Limit elastic analysis of porous FG disks under thermo-mechanical loading has not been studied before.

Simulation studies on combined effect of variable geometry, rotation and temperature gradient on critical speed of gas turbine disc

PurposeThe present findings report a significant influence of disc profile and thickness on the order of excitation leading to critical speed condition. Certain transverse modes of vibration of the disc have been obtained to be more susceptible to get excited while recording the lowest critical speeds.Design/methodology/approachNumerical simulation using finite-element method has been adopted due to the complicated geometry, complex loadings and intricate analytical formulation. A comprehensive analysis of exclusive as well as combination of thermal and centrifugal loads has been taken up to determine the intensity and characteristics of the individual/combined effects.FindingsThe typical gas turbine disc profile has been analyzed to predict the critical speed under the factual working condition of an aero-engine. FEM analysis of uniform and variable thickness discs have been carried out under stationary, rotating and rotating-thermal considerations while emphasizing the effect of disc profile and thickness. Centrifugal stresses developed due to rotational effect result in unceasing stiffening of the discs with higher stiffening for a greater number of nodal diameters. On the other hand, a role reversal of thermal effect from stiffening to softening is figured out with increasing numbers of nodal diameters. However, the discs are subjected to an overall stiffening effect on account of the combined centrifugal and thermal loading, with the effect decreasing with an increase in disc thickness. Under the combined loading, the order of excitation leading to critical speed condition is dependent on disc profile and thickness. Moreover, the vibrational modes (0,1) and (0,2) are identified as more prominent adverse modes corresponding to lowest critical speeds.Practical implicationsThe present findings are expected to serve as guidelines during the design phase of gas turbine discs of aeroengine applications.Originality/valueThe present work deliberates on the simulation and analysis of gas turbine disc specific to aeroengine application. The real-life disc geometry has been analyzed with due consideration of major factual operating conditions to identify the critical speed. The identification of various critical speed using numerical analysis can help to reduce the number of experimental tests required for certification.

A Study on the Synthesis of 2D Profiles for Cycloidal Discs Used in Cycloidal Reducers

Abstract This paper proposes a simple approach on the synthesis of the 2D profiles for the rotors of cycloidal reducers. A 2D rotor (or cycloidal disc) profile (as a complex closed curve) can be defined (as an alternative to the strictly mathematical definition) as the internal bordered envelope of the family of 2D profiles of the stator (or ring gear) obtained with the stator movable (for at least a completely rotation) around the fixed rotor (or planetary gear) by respecting the gearing conditions inside a cycloidal reducer. The more 2D profiles of the stator are used the more accurate definition of 2D rotor profile is obtained. The finding of x, and y-coordinates of the points involved in the description of this 2D rotor profile is by far the most complicated problem to solve in the manufacturing of this type of reducer, the behavior and performances of the cycloidal reducer drastically depends by the accuracy of this profile. The results of this study can be easy applied in practice.

Creating a Supportive Clinical Learning Environment for Physiotherapy Students: A Feasibility Study to Enhance Collaboration Between Students and Educators Using the ‘Everything DiSC’

Aim: To investigate if an intervention aimed at creating a supportive clinical learning environment (through shared debriefing of behaviour styles for physiotherapy students and their educators) can i) improve the clinical skills outcomes (grades) and ii) enhance the perceived quality of clinical education experiences for students and educators compared to placements without this intervention. Method: This quasi-experimental, non-equivalent groups, mixed methods study was conducted across two Australian universities and two public health sector settings. For the intervention group, Everything DiSC profiles and comparison reports were utilised to indicate differences and similarities in behaviour traits and this information was shared with students and clinical educators attending a 5-week placement. Written strategies were provided to enhance collaboration. For the comparison group, physiotherapy students attending usual clinical placements. Outcomes: Assessment of Physiotherapy Practice (APP) grades, Clinical Learning Environment Inventory (CLEI), Maastricht Teaching Evaluation, perspectives of clinical educators (obtained through focus groups). Results: At the completion of the 5-week placement, no significant differences between groups were found in APP grades, CLEI, or Maastricht scores. Focus groups (n=2) with clinical educators (n=12) revealed mostly positive perspectives on the utility of DiSC in the clinical education setting. Conclusion: Whilst sharing DiSC profiles and comparison reports between physiotherapy students and their clinical educators did not demonstrate significant benefits for students in terms of grades, positive outcomes regarding the collaboration between physiotherapy clinical educators and their students were reported by clinical educators.

Debiasing the Minimum-mass Extrasolar Nebula: On the Diversity of Solid Disk Profiles

A foundational idea in the theory of in situ planet formation is the “minimum-mass extrasolar nebula” (MMEN), a surface density profile (Σ) of disk solids that is necessary to form the planets in their present locations. While most previous studies have fit a single power law to all exoplanets in an observed ensemble, it is unclear whether most exoplanetary systems form from a universal disk template. We use an advanced statistical model for the underlying architectures of multiplanet systems to reconstruct the MMEN. The simulated physical and Kepler-observed catalogs allow us to directly assess the role of detection biases, and in particular the effect of nontransiting or otherwise undetected planets, in altering the inferred MMEN. We find that fitting a power law of the form to each multiplanet system results in a broad distribution of disk profiles; g cm−2 and encompass the 16th–84th percentiles of the marginal distributions in an underlying population, where is the normalization at a 0 = 0.3 au. Around half of the inner planet-forming disks have minimum solid masses of ≳ 40M ⊕ within 1 au. While transit observations do not tend to bias the median β, they can lead to both significantly over- and underestimated and thus broaden the inferred distribution of disk masses. Nevertheless, detection biases cannot account for the full variance in the observed disk profiles; there is no universal MMEN if all planets formed in situ. The great diversity of solid disk profiles suggests that a substantial fraction (≳23%) of planetary systems experienced a history of migration.

Cotton gravity and 84 galaxy rotation curves

Recently, as a generalization of general relativity, a gravity theory has been proposed in which gravitational field equations are described by the Cotton tensor. That theory allows an additional contribution to the gravitational potential of a point mass that rises linearly with radius as $\Phi = -GM/r + \gamma r/2$, where $G$ is the Newton constant. The coefficients $M$ and $\gamma$ are the constants of integration and should be determined individually for each physical system. When applied to galaxies, the coefficient $\gamma$, which has the dimension of acceleration, should be determined for each galaxy. This is the same as having to determine the mass $M$ for each galaxy. If $\gamma$ is small enough, the linear potential term is negligible at short distances, but can become significant at large distances. In fact, it may contribute to the extragalactic systems. In this paper, we derive the effective field equation for Cotton gravity applicable to extragalactic systems. We then use the effective field equation to numerically compute the gravitational potential of a sample of 84 rotating galaxies. The 84 galaxies span a wide range, from stellar disk-dominated spirals to gas-dominated dwarf galaxies. We do not assume the radial density profile of the stellar disk, bulge, or gas; we use only the observed data. We find that the rotation curves of 84 galaxies can be explained by the observed distribution of baryons. This is due to the flexibility of Cotton gravity to allow the integration constant $\gamma$ for each galaxy. In the context of Cotton gravity, "dark matter" is in some sense automatically included as a curvature of spacetime. Consequently, even galaxies that have been assumed to be dominated by dark matter do not need dark matter.

Comparison of Theoretical Disc and Point Source Profiles with Actual-Melt Source Profile in Conduction Welding

Prediction of fusion zone in numerical modelling of welds using a modified heat transfer model requires experimental results for validation. Primarily, the modified heat transfer models are developed from the point and disc source heat models which can be assumed to be a semi-circle or spherical shape. In this study, a simple relationship between melt areas, the depth of penetration and weld width was proposed for point and disc source profiles to represent the actual weld profile. The results obtained for focused and defocused laser beams indicate that the actual weld profile is closer to a point source than the disc source. The transition between the conduction and keyhole regimes was achieved when the actual weld depth of penetration is below that of the point source.

Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods

In the present paper, the transfer matrix method (TMM) is to be employed for the first time in the open literature for the elastic analysis of variable-thickness disks made of functionally graded (FG) two orthotropic materials. Those materials are assumed to be continuously radially functionally graded (FG) based on the Voigt rule of mixture with two models. An exponential disk profile with two parameters is considered. Effects of the different boundary conditions (free-free, fixed-free, and fixed-fixed) and inhomogeneity indexes on the elastic response of the disk rotating at a constant angular speed are also examined. Additionally, direct numerical solutions of the problem with the complementary functions method (CFM) are presented in tabular forms together with the transfer matrix method solutions in which CFM was used as an assistant tool. It was observed that both location and amplitude of the maximum equivalent stress are affected by the grading models chosen. Such differences become more obvious for small values of the inhomogeneity indexes. The maximum relative error may reach 18% for the two material grading models in fixed-free disks. Consequently, Model-I may be recommended for just the inhomogeneity indexes equal to or greater than 0.5.

A Dynamical Model of the M101/NGC 5474 Encounter

We present the first dynamical simulation that recreates the major properties of the archetypal nearby spiral galaxy M101. Our model describes a grazing but relatively close (∼14 kpc) passage of the companion galaxy NGC 5474 through M101's outer disk approximately 200 Myr ago. The passage is retrograde for both disks, yielding a relatively strong gravitational response while suppressing the formation of long tidal tails. The simulation reproduces M101's overall lopsidedness, as well as the extended NE Plume and the sharp western edge of the galaxy’s disk. The post-starburst populations observed in M101's NE Plume are likely a result of star formation triggered at the point of contact where the galaxies collided. Over time, this material will mix azimuthally, leaving behind diffuse, kinematically coherent stellar streams in M101's outer disk. At late times after the encounter, the density profile of M101's disk shows a broken “upbending” profile similar to those seen in spiral galaxies in denser environments, further demonstrating the connection between interactions and long-term structural changes in galaxy disks.

Superradiance in massive vector fields with spatially varying mass

Superradiance is a process by which massive bosonic particles can extract energy from spinning black holes, leading to the build up of a condensate if the particle has a Compton wavelength comparable to the black hole's Schwarzschild radius. One interesting possibility is that superradiance may occur for photons in a diffuse plasma, where they gain a small effective mass. Studies of the spin-0 case have indicated that such a build up is suppressed by a spatially varying effective mass, supposed to mimic the photons' interaction with a physically realistic plasma density profile. We carry out relativistic simulations of a massive Proca field evolving on a Kerr background, with modifications to account for the spatially varying effective mass. This allows us to treat the spin-1 case directly relevant to photons, and to study the effect of thinner disk profiles in the plasma. We find similar qualitative results to the scalar case, and so support the conclusions of that work: either a constant asymptotic mass or a shell-like plasma structure is required for superradiant growth to occur. We study thin disks and find a leakage of the bosonic condensate that suppresses its growth, concluding that thick disks are more likely to support the instability.

Who they are versus what they want: How dominance, influence, steadiness, and compliance profiles can aid in developing employability

This paper draws attention to a behavior-based assessment instrument that is frequently utilized in industry settings but less utilized in the academic classroom. The authors argue that this instrument, the dominance, influence, steadiness, and compliance (DISC) profile, can be useful in training and developing soft skills desired by employers. They also examine the effects of gender and work experience on the various DISC patterns to better understand how this instrument may be useful for coaching and mentoring in those academic and organizational contexts. In this study, DISC pattern data were gathered from 1547 undergraduate and graduate students across multiple universities in the USA. A multivariate analysis of variance was performed on the data and the results show males scoring higher on Dominance and females scoring higher on Steadiness, as predicted. Females scored higher on Compliance, contrary to predictions. Graduate students scored higher on Dominance and undergraduates scored higher in Steadiness, as hypothesized. Undergraduates also scored higher on Influence than did graduate students. Such differences in DISC profiles suggest that, as a behavior-based instrument, DISC may be helpful for students in understanding their behavioral tendencies as well as identifying workplace behaviors needed to bridge the gap between the soft skills employers want and the competencies students possess.

Shadows and optical appearance of a power-Yang-Mills black hole surrounded by different accretion disk profiles

In the present work, we investigate the image of a power-Yang-Mills black hole and its luminosity under distinctive accretion models. Meanwhile, a special emphasis is put on the different image characteristics of the distant observer when the related physical quantity of the black hole varies. Concretely, after showing the power Yang-Mills black hole's relevance with the Event Horizon Telescope data, we unveil the impact of the power parameter $\ensuremath{\gamma}$ on the photon trajectories, the observed intensity, and consequently on the image formation of such black hole. Furthermore, we establish that for the thin disk accretion model that the shadow, lens ring, and photon ring appear near the black hole following some parameter impact ranges. We also show that due to the extreme demagnetization, the remote observer cannot obtain the observation flux provided by the photon ring. Hence, the intensity of observation is provided by the direct image from accretion, and the lens ring also contributes, but only a small part. In addition, different emission profiles of the accretion will also directly affect the observed specific intensity. Such investigations have been realized within a variety of $\ensuremath{\gamma}$'s values. Later, the spherical infalling accretion model is considered and discussed within the $\ensuremath{\gamma}$ variation and by paying attention to the conformally invariant case associated with $\ensuremath{\gamma}=\frac{3}{4}$. Lastly, one concludes that the black hole presents a larger intensity as the power parameter $\ensuremath{\gamma}$ increases. In a word, observational appearances of the power Yang-Mills black hole surrounded by various accretions present some nice features that can be used to distinguish black holes from different gravity theories.

Dynamical Implantation of Blue Binaries in the Cold Classical Kuiper Belt

Abstract Colors and binarity provide important constraints on the Kuiper Belt formation. The cold classical objects at radial distance r = 42–47 au from the Sun are predominantly very red (spectral slope s > 17%) and often exist as equal-size binaries (∼30% observed binary fraction). This has been taken as evidence for the in situ formation of cold classicals. Interestingly, a small fraction (∼10%) of cold classicals is less red with s < 17%, and these “blue” bodies are often found in wide binaries. Here we study the dynamical implantation of blue binaries from r < 42 au. We find that they can be implanted into the cold classical belt from a wide range of initial radial distances, but the survival of the widest blue binaries—2001 QW322 and 2003 UN284—implies formation at r > 30 au. This would be consistent with the hypothesized less-red to very-red transition at 30 < r < 40 au. For any reasonable choice of parameters (Neptune’s migration history, initial disk profile, etc.), however, our model predicts a predominance of blue singles, rather than blue binaries, which contradicts existing observations. We suggest that wide blue binaries formed in situ at r = 42–47 au and their color reflects early formation in a protoplanetary gas disk. The predominantly VR colors of cold classicals may be related to the production of methanol and other hydrocarbons during the late stages of the disk, when the temperature at 45 au dropped to ≃20 K and carbon monoxide was hydrogenated.

Material modelling and limit angular speed analysis of porous trigonometric functionally graded rotating disk

ABSTRACT In the current study, limit elastic angular speed analysis of porous trigonometric functionally graded porous rotating disks was investigated. The approach used was variational principle, and the solution was achieved using Galerkin’s error minimisation theory. This study aims to analyse the effect of trigonometric grading, aspect ratio, porosity volume fraction and porosity types on disk performance. Four different porosity types which are uniform, symmetric, inner maximum and the outer minimum was considered. The disk profile was taken as uniform, tapered and exponential type. The study yielded a decrease in limit speed as the aspect ratio increases. The porosity volume fraction was found to be a more significant parameter than the aspect ratio. A comparison of limit speeds for porous and non-porous disks was presented and the most significant porosity model type has been identified. With a change in disk profile from uniform thickness disk to exponential varying profile, the performance of rotating disk can be improved to a large extent.

Acceleration and cooling of the corona during X-ray flares from the Seyfert galaxy I Zw 1

ABSTRACTWe report on X-ray flares that were observed from the active galactic nucleus I Zwicky 1 (I Zw 1) in 2020 January by the NuSTAR and XMM-Newton observatories. The X-ray spectrum is well-described by a model comprised of the continuum emission from the corona and its reflection from the accretion disc around a rapidly spinning (a > 0.94) black hole. In order to model the broadband spectrum, it is necessary to account for the variation in ionization across the disc. Analysis of the X-ray spectrum in time periods before, during and after the flares reveals the underlying changes to the corona associated with the flaring. During the flares, the reflection fraction drops significantly, consistent with the acceleration of the corona away from the accretion disc. We find the first evidence that during the X-ray flares, the temperature drops from $140_{-20}^{+100}$ keV before to $45_{-9}^{+40}$ keV during the flares. The profile of the iron K line reveals the emissivity profile of the accretion disc, showing it to be illuminated by a compact corona extending no more than $7_{-2}^{+4}$ rg over the disc before the flares, but with tentative evidence that the corona expands as it is accelerated during the flares. Once the flares subsided, the corona had collapsed to a radius of $6_{-2}^{+2}$ rg. The rapid time-scale of the flares suggests that they arise within the black hole magnetosphere rather than in the accretion disc, and the variation of the corona is consistent with the continuum arising from the Comptonization of seed photons from the disc.

The impact of the presence of water ice on the analysis of debris disk observations

Context. The analysis of debris disk observations is often based on the assumption of a dust phase composed of compact spherical grains consisting of astronomical silicate. Instead, observations indicate the existence of water ice in debris disks. Aims. We quantify the impact of water ice as a potential grain constituent in debris disks on the disk parameter values estimated from photometric and spatially resolved observations in the mid- and far-infrared. Methods. We simulated photometric measurements and radial profiles of debris disks containing water ice and analyzed them by applying a disk model purely consisting of astronomical silicate. Subsequently, we quantified the deviations between the derived and the true parameter values. As stars in central positions we discuss a β Pic sibling and main-sequence stars with spectral types ranging from A0 to K5. To simulate observable quantities we employed selected observational scenarios regarding the choice of wavelengths and instrument characteristics. Results. For the β Pic stellar model and ice fractions ≥50% the derived inner disk radius is biased by ice sublimation toward higher values. However, the derived slope of the radial density profile is mostly unaffected. Along with an increasing ice fraction, the slope of the grain size distribution is overestimated by up to a median factor of ~1.2 for an ice fraction of 90%. At the same time, the total disk mass is underestimated by a factor of ~0.4. The reliability of the derived minimum grain size strongly depends on the spectral type of the central star. For an A0-type star the minimum grain size can be underestimated by a factor of ~0.2, while for solar-like stars it is overestimated by up to a factor of ~4–5. Neglecting radial profile measurements and using solely photometric measurements, the factor of overestimation increases for solar-like stars up to ~7–14.

Research on the Possibility of Lowering the Manufacturing Accuracy of Cycloid Transmission Wheels with Intermediate Rolling Elements and a Free Cage

Purpose: In the present work, different combinations of fits and accuracies, in relation to the profiles of mating parts, have been analysed in order to assess the degree of the engagement of transmissions that contain intermediate rolling elements. The aim of this work is to determine which fits have decreased accuracy, but nevertheless provide a minimum manufacturing clearance for the transmission engagement in order to reduce the cost of parts production. Methods and materials: Considering the normal probabilistic distribution law in relation to the obtained dimensions of the manufacturing equipment, a combination of fits were selected using the incomplete interchangeability method, taking into account the peculiarities of the cycloid engagement in transmissions with intermediate rolling elements (IRE). Results: Having studied various combinations of fits of parts that are engaged in transmissions with intermediate rolling elements and a free cage (IREFC), a combination of fits for a “ring, rolling-element cam” were determined, in which a technological clearance of 3 µm is formed in the engagement. At the same time, cycloid disk profiles are manufactured according to the 9th tolerance grade, which reduces the laboriousness and cost of the production. Discussion. When reducing the manufacturing accuracy of cycloid disks, it is possible to obtain both very ample clearances and significant negative allowances. For example, having manufactured a ring with the H9 fit, rolling elements with h6 and a cam with js9, the maximum manufacturing clearance can reach 0.086 mm, while the clearance limits vary from 0.025 mm to 0.061 mm. Additionally, if mating parts are manufactured using a combination of K9-h6-js9 fits, a negative allowance varying from 0.014 mm to 0.026 mm will emerge in the engagement. Both described cases are unacceptable because both ample clearances and large negative allowances will negatively influence the working capacity of the mechanism. However, it is possible to select a combination of fits using the 9th tolerance grade of the basic parts, by which the parts will contact in the range from a small negative allowance of 1 µm to a clearance of 3–4 µm. Furthermore, if this is considered, taking into account the machine settings, it is possible to obtain parts according to the 9th accuracy tolerance grade and, at the same time, provide a clearance in the engagement that is almost equal to zero. Moreover, such a combination of fits is relevant for any transmission with IRE. This is a positive result because it reduces the laboriousness when manufacturing parts and, at the same time, provides high accuracy of the mechanism. Conclusions: It has been established that when lowering the accuracy of manufacturing transmission parts with IRE, both clearances and negative allowances may occur in the engagement, depending on the combination of fits. At the same time, it is possible to select such a combination of fits, by which the parts manufactured according to the 9th tolerance grade, will provide almost zero clearance of the engagement of the transmission. In this way, it is possible to reduce the cost of manufacturing the parts for gears with intermediate rolling elements and, at the same time, maintain a high accuracy of the transmission mechanism.

Development of an End-Toothed Disc-Based Quick-Change Fixture for Ultra-Precision Diamond Cutting

With its standardized and unified interface, the quick-change fixture is an important part for maintaining high efficiency without compensation of precision in the metal-turning process because it can conveniently realize high-precision repeated clamping and multi-station conversion without complex positioning and adjustment steps. However, the existing quick-change fixture products and related research cannot fully meet the needs of repeatability and applicability raised from ultra-precision, single-point diamond turning with ultra-high accuracy and ultra-small depth of cut. In this paper, we develop a quick-change fixture for ultra-precision diamond turning, in which the end-toothed disc acts as the positioning element. Specifically, the main parameters of two key components of the end-toothed disc and slotted disc spring are calculated analytically to ensure the positioning accuracy of the designed fixture used in the rotation condition, which is further ensured by controlling the machining tolerance of the tooth profile of the end-toothed disc. Additionally, finite element simulations are performed to investigate the static and modal states of the quick-change fixture, which demonstrate a maximum deformation of about 0.9 μm and a minimum natural frequency of 5655.9 Hz for the designed fixture. Two high-precision sensors are used to detect the radial jump and end run-out values after repeated clamping actions, which are employed to verify the repetitive positioning accuracy of the fixture. Subsequent finite-element simulation of the clamping of small-diameter copper bar, as well as the diamond turning experiment, jointly demonstrate that the designed fixture can achieve a precision of 1 μm. Current work provides an effective quick-change fixture to reduce the deformation of a weak-stiffness workpiece caused by clamping deformation in ultra-precision diamond cutting.

Break type and interactions from ultra-deep optical imaging of isolated galaxies

AbstractIn the standard cosmological model of galaxy evolution, mergers and interactions play a fundamental role in shaping galaxies. Galaxies that are currently isolated are thus interesting, allowing us to identify how internal or external processes impact galactic structure. However, current observational limits may be obscuring crucial information in the low-mass or low-brightness regime. We use the AMIGA catalog of isolated galaxies to explore the impact of different factors on the structure of these galaxies. In particular, we study the type of disk break based on the degree of isolation and the presence of interactions which are only detectable in the ultra-low surface brightness regime. We present the first results of an extensive observational campaign of ultra-deep optical imaging targeting a sample of 25 low-redshift (z < 0.035) isolated galaxies. The nominal surface brightness limits achieved are comparable to those to be obtained in the 10-year LSST coadds ( mag arcsec−2; 3σ ; 10” × 10”). We find that isolated galaxies have a considerably higher fraction of purely exponential disk profiles and a lower presence of up-bending breaks than field or cluster galaxies. Our extreme imaging depth allows us to detect the presence of previously unreported interactions with minor companions in some of the galaxies in our sample (∼40% of the galaxies show signs of interaction). The results of our work fit with the general framework of galactic structure in which up-bending breaks (Type III) would be produced by mergers and down-bending breaks (Type II) due to a threshold in star formation that would tend to become single exponential disk (Type I) in case of cessation or decrease of star formation.

ИСКЛЮЧЕНИЕ ЧРЕЗМЕРНОГО ПОДРЕЗА НОЖКИ ЗУБА КОСОЗУБЫХ ЦИЛИНДРИЧЕСКИХ КОЛЕС ПРОТУБЕРАНЦЕМ ЧЕРВЯЧНОЙ ФРЕЗЫ НА ОСНОВЕ ГРАФИЧЕСКИХ ОБКАТОВ

In the paper there are considered procedures for designing a transition curved tooth leg of helical cylindrical gears. A significant parameter of a transition curve is a diameter of boundary points. The boundary point diameter belongs to a bottom point of the involute profile of the teeth side surface of a gear ring. The boundary point position must be lower of the design end point of the involute profile defined by the designer of gearing. A diameter value depends upon a great number of production factors: a profile and wear of a grinding disk, setting up parameters, teeth machining modes of a gear ring, but it is impossible to ensure the specified values of the diameter of boundary points without a correct design solution in the course of the form choice of milling cutter protuberance. The solution on protuberance acceptable parameters of a gear-cutting tool is made by the designer of a cutter during graphic run-in fulfillment. In the paper there are revealed conditions under which arise mistakes in the course of graphic run-in fulfillment within the limits of one teeth pitch of a milling cutter. There are shown recommendations for the fulfillment ensuring the diameter dimension of boundary points of the transition curve specified by the designer of gearing. The data on the design parameter impact of the hob protuberance upon the continuance of cutting edge interaction are shown. There are recommendations given to prevent undercut arising caused by the fulfillment of graphic two-dimensional run-ins of cylindrical helical gears. 
 The work purpose: the elimination of tooth leg excessive undercut in helical cylindrical gears with the protuberance of a worm milling cutter at the expense of the fulfillment of graphic run-in conditions. 
 The investigation methods: the graphical modeling of a run-in process. 
 The investigation results and novelty: there are defined conditions of arising an excessive undercut in the tooth leg of helical cylindrical gears during the fulfillment of graphic run-ins of a tool rack. 
 The conclusions: for mistake prevention in the calculations of the protuberance geometrical parameters of the helical milling cutter the graphic run-in must be carried out not less than on the 1.5 pitch of the milling cutter.