Base Circle Research Articles

Macrogeometric Measurement of Camshafts of Internal Combustion Engines

Abstract In this work, cam profiles of a camshaft are measured by a roundness measurement machine. First, the measured cam profiles are transformed into their actual sizes, based on the measurement of the bearing locations. The 8 cams of the camshaft are of two types. From the 4–4 cam profiles of each type an approximate profile is created by fitting them to one another using their base circles as reference, and calculating the center of gravity of the cumulative points of these fitted profiles corresponding to an arc segment.

Chatter stability analysis for non-circular high-speed grinding process with dynamic force modelling

To avoid instability and resulting chatter during the non-circular grinding process, it is necessary to elucidate the potential occurrence of periodic chatter behavior when high-speed grinding loses stability and to define the stability boundary of the grinding system. Building upon an analysis of the geometric kinematic characteristics of non-circular profiled components, a dynamic grinding force model for non-circular high-speed grinding was derived by considering both the delay effect and the elastic yielding mechanism between the grinding wheel and workpiece. Then, A multi-factor coupled dynamic model of non-circular grinding was established. By employing a multi-scale approach, bifurcation analysis and classification of the instability process in the grinding system were conducted, using a typical non-circular profiled shaft component, such as a camshaft, for theoretical analysis and experimental validation. The research determined the stability boundary of the high-speed grinding process for non-circular profile components, validated the possibility of the existence of a conditionally stable chatter region in the non-circular high-speed grinding process, and identified differences in grinding chatter characteristics among different segments of the cam profile, with a greater propensity for chatter at the juncture of the cam fall and base circle.

Optimization of geometrical parameters of positive guide vane for multi-stage pump as turbine based on orthogonal test

Abstract Multi-stage pumps as turbines (PAT) are commonly employed in the petrochemical, coal chemical, and other process industries to recover liquid residual pressure energy. This study focused on improving the performance of multi-stage PAT, specifically targeting the slope of the power-flow(P-Q) curve and hydraulic efficiency at the rated flow point. A two-stage PAT was selected as the research object for this study. According to the relationship between the power and the geometrical parameters of the positive guide vane derived based on the basic equation of the multi-stage PAT, four parameters of the positive guide vane were selected as the test factors for the orthogonal experimental study. A four-factor, three-level orthogonal table of type L9(34) was established. Using Fluent software and the RNG k-ε turbulence model to carry out numerical calculations of constant flow, the results showed that: for the slope of the P-Q curve, the influence of geometric parameter factors of the positive guide vane are in the order of the throat area, the outlet placement angle, the positive guide vanes number, and the base circle diameter; and for the hydraulic efficiency, the influence of geometric parameter factors of the positive guide vane are in the order of the throat area, the positive guide vanes number, the outlet placement angle, and the base circle diameter of the positive guide vane. At the rated flow point, the P-Q curve of the optimized solution decreased by 0.24, resulting in a flatter curve and a 0.3% increase in hydraulic efficiency. There was little change in the vicinity at the rated flow point. The best efficiency point of the optimized scheme is biased toward the high flow rate, the efficiency is increased by 1.85%, and the best efficiency zone is wider. Therefore, selecting appropriate positive guide vane geometry parameters can flatten the P-Q curve, improve internal flow, and enhance hydraulic efficiency.

Analysis of involute-curve geometry using position gradients: Application to gear-tooth profile

This paper examines using non-rational polynomials to approximate the involute-curve geometry, which is fundamental in the design of gear systems. The parametric form of the involute curve in terms of an involute-angle parameter is first presented. To be able to compare the analytical geometry results and numerical results obtained using the finite-element (FE) method for describing the geometry, the relationship between the involute-angle parameter and the FE spatial coordinate is defined. A new relationship between the involute-curve arc length and the coordinate used in the FE parameterization is also developed. To this end, the involute-curve equation is used to determine the involute-angle parameter at the intersection with circles with arbitrary radii including the gear pitch, addendum, and base circles. The parameter relationship allows defining the nodal position-gradient vectors defined by differentiation with respect to the FE spatial coordinate from involute-curve tangent vector. Two procedures for determining the left involute curve from the right involute curve of the gear tooth are described. In the first procedure, a coordinate transformation based on Rodrigues transformation with axis of rotation defined by the tooth-center line is used; while in the second procedure, the analytical expression of the left involute curve is defined using the gear-tooth thickness at the base circle. A general procedure for determining the position gradients for a given geometry obtained from analytical curves or using imaging techniques is introduced. Such a procedure can be used in case of worn gear teeth that cannot be described by simple functions. A planar rectangular element based on the absolute nodal coordinate formulation (ANCF) is used to approximate the gear-tooth geometry. While the involute geometry cannot be described exactly using non-rational polynomials, the analysis and results of this investigation demonstrate that the FE solution leads to accurate geometry results, demonstrating the potential of using the position gradients in future strength-calculation studies.

Analysis investigation of the influence of sub-surface shear stress distribution of spur gear

Spur gears endure contact fatigue loads that can lead to surface damage on the gear teeth. Contact fatigue typically arises from dedendum during engineering and experiments, primarily caused by maximum sub-surface shear stress. This study presents a contact model incorporating profile-shift to examine sub-surface shear stress in relation to the occurrence of tooth root pits. Accurate calculations are performed to determine the distribution of sub-surface stress and meshing duration, considering various modification coefficients. The geometric cause affecting the shear stress near the tooth root is found. A deviation coefficient from base circle is proposed to analyze the influence of modification coefficient and pressure angle, which can be used in design reference. The investigation comprehensively explores the effects of profile-shift and pressure angle of spur gears on stress distribution.

Pendulum type magnetically coupled rotary piezoelectric energy harvester

This research proposes a rotary motion-based non-contact pendulum piezoelectric energy harvester (P-PEH). The working region of the piezoelectric vibrator can be maintained in a magnetically coupled system at all times by means of a motion conversion mechanism. The combination of the motion conversion mechanism and the magnetic coupling system not only reduces the loss of the piezoelectric material, but also improves the output performance of the piezoelectric vibrator. The paper investigates the effects of the excitation distance L, the radius of the base circle R, and the number of excitation magnets N on the output performance of the P-PEH. When the input speed of 600 rpm, L = 10 mm, R = 21 mm, and N = 1, the peak-to-peak voltage (Vpp ) is 58.75 V. At this parameter, the output power of the device with an external 20 kΩ load is 0.0187 W. The viability of P-PEH was finally demonstrated through several application testing. P-PEH can easily light up 63 LEDs while its output energy can keep the temperature and humidity sensor in use. In summary, P-PEH can effectively collect external rotational energy for power storage and supply, and supply electricity to wireless sensor networks and microelectronic devices with further studies.

A Spherical Cap Model of Epidural Hematomas.

Background Epidural hematomas (EDHs), which have a characteristic biconvex shape, are a type of post-traumatic intracranial mass. EDHs and other types of intracranial hematomas are often diagnosed with computed tomography (CT). The volumes of EDHs are important in treatment decisions and prognosis. Their volumes are usually estimated on CT using the "ABC" method, which is based on the ellipsoid shape rather than their biconvex shape. Objective To simulate the biconvex shape, we modeled the geometry of EDHs with two spherical caps. We aim to provide simpler estimation of EDH volumes in clinical settings, and eventually recommend a threshold for surgical evacuation. Methods Applying the relationship between the sphere radius, spherical cap height, and base circle radius, we derived formulas for the shape of an EDH, relating its largest diameter and location to the other two diameters. We also estimated EDH volumes using the spherical cap volume and conventional ABC formulas and then constructed a lookup table accordingly. Results Validation of the model was performed using 14 CT image sets from previously reported patients with EDHs. Our geometric model demonstrated accurate predictions. Themodel also allows reducing the number of parameters to be measured in the ABC method from three to one, the hematoma length, showcasing its potential as a reliable tool for clinical decision-making. Based on our model, an EDH longer than 7 cm would occupy more than 30 mL of the intracranial volume. Conclusion The proposed model offers a streamlined approach to estimating EDH volumes, reducing the complexity of parameters required for clinical assessments. We recommend a length of 7 cm as a threshold for surgical evacuation of EDHs. This acceleration in decision-making is crucial for managing critically injured patients with traumatic brain injuries. Further validation across diverse patient populations will enhance the generalizability and utility of this geometric modeling approach in clinical settings.

The SASA dictionary and its sources: Statistical method of analysis and its application in the presentation of lexical corpus material

The sources of the Dictionary of Serbo-Croatian Literary and Vernacular Language, vol. 1-21 (the SASA Dictionary or Dictionary of the Serbian Academy) are analyzed applying the method of statistical analysis. Its main aim was to provide a clear idea of the frequency of relevant and particularly relevant sources in the text of the dictionary as a whole (while also pointing to the problems and hindrances that occur in the digital search of sources). This type of analysis was conducted using the volumes 2, 10 and 17 (released in 1962, 1978, and 2006, respectively). The analysis and total ratio of frequency in the volumes under examination demonstrates that the sources can be divided into: a. The basic circle (top 10 dictionary sources); b. Broader circle (top 100 sources); c. The broadest circle (top 500 sources). The analysis also yielded the fact that basic sources comprise more important dictionaries as well as collections of vernacular words, so that the circle of sources spreads further including some other more relevant collections of words, prominent authors, significant periodicals, and so on. The analysis as projection basically identified the sources upon which the SASA Dictionary is actually based. Beyond this varied and broad circle lie sources that more rarely, or hardly ever occur, as a testimony to the existence or usage of certain lexical items in the corpus material of the Dictionary of the Serbian Academy. The said indicators point the way to the further process of digitization of the SASA Dictionary and its corpus material.

Numerical analysis on the deformation of scroll teeth of variable base circle radius scroll expander

For research on the effect of different working loads on the deformation of variable base circle radius scroll expander scroll teeth, a multi-field-coupled calculation method is proposed to reveal the deformation law of scroll teeth under different working loads. In this paper, the equations of the variable base radius profile are derived using the normal isometric method to establish a three-dimensional model of the variable base radius scroll expander. The CFD dynamic mesh technique is used to simulate the working process of a variable base radius scroll expander to obtain the flow field variation in the inner part of the working chamber. The results of the simulation are applied to the scroll teeth by interpolation to analyze the deformation of the scroll under single-field loading and multi-field coupling, to obtain the deformation law of the scroll teeth. The results of the study show that the deformation of the scroll teeth does not decrease linearly with the involute spreading angle from the head to the tail of the teeth due to the uneven temperature distribution of the scroll expander. The thermal stress of the temperature load impacts the deformation trend and amount of the scroll tooth, whereas the gas force load just modifies the amount of scroll tooth deformation and has a lower effect on the scroll tooth's deformation trend. Under different loads, the same deformation and different deformation on the scroll teeth can interact with each other to reduce the scroll tooth deformation to a certain extent.

Influence of Dynamic and Static Interference on the Internal Flow and Vibration and Noise Characteristics of Marine Centrifugal Pump

To improve the overall performance of marine centrifugal pumps (MCPs), their vibration and noise performances were optimized using the hydraulic design of the volute casing parameters considering a constant hydraulic performance at a specific speed of 66.7. Numerical simulations of the full flow field, vibration, and noise were conducted for each of five volute base circle diameters. The impact of dynamic and static disturbances on the flow and vibration and noise characteristics were investigated. These results provide some theoretical and technical support for the design and application of MCPs. The flow pattern inside the volute becomes more uniform as the D3 increases, but the pressure pulsation decreases. The total vibration levels of the inlet flange, outlet flange, and pump base decreased by 8.3%, 7.9%, and 12.3% respectively. The sound pressure of the flow noise at each characteristic frequency showed a different degree of decreasing trend.

Analysis of Vibration Characteristics of Planetary Gearbox with Broken Sun Gear Based on Phenomenological Model

To investigate the vibration properties in healthy and fault conditions of planetary gearboxes, a phenomenological model is constructed to present the vibration spectrum structure. First, the effects of the base deflection of the gear fillet and the flexibility between the root circle and the base circle on the time-varying meshing stiffness are considered in order to construct an equivalent model of time-varying mesh stiffness and broken tooth faults, exploring the law of variation for meshing stiffness when differently sized faults occur on the sun gear. Then, considering both the effect of the vibration transfer path and the meshing impacts, we establish phenomenological models of planetary gears under healthy and fault conditions. By comparing and analyzing the phenomenological model based on the cosine function to verify the effectiveness of the proposed model. The experimental results show that the error of the proposed model is 1.38% lower than that of the traditional phenomenological model, and the proposed model can accurately analyze the frequency, amplitude, and sideband characteristics of the vibration signals of sun gear with different degrees of broken tooth, which can be used for the local fault diagnosis of planetary gearboxes.

Double-Tongue Worm Shell Structure on Plastic Centrifugal Pump Performance Study

Aiming at the problem of high vibration and high wear of centrifugal pump tongue, this paper proposes a double-tongue volute structure. Under the condition of ensuring the reliability of CFD results, the influence of various combinations of tongue and volute base circle on the turbulent kinetic energy of centrifugal pump and the radial force of impeller is explored. The traditional single-tongue volute centrifugal pump is compared with various characteristic indexes, and the unsteady numerical calculation is carried out based on different working conditions. It is concluded that the double-tongue volute structure can improve the pressure fluctuation at the monitoring points near the tongue. The results show that the double-tongue volute structure can improve the static pressure gradient and velocity gradient of the middle section of the centrifugal pump and reduce the maximum turbulent kinetic energy value at the tongue under small flow conditions. When the working condition is 1.0 Q, the radial force of the impeller of the C-type double-tongue volute reaches the minimum value of 3.03 N, which can effectively balance part of the radial force.

Predictions of friction and temperature at marine cam-tappet interface based on mixed lubrication analysis with real surface roughness

The working conditions of cam-tappet pairs in marine diesel engines are directly influenced by the engine output power, the operational speed, the temperature, as well as the components surface micro-morphology, etc., which cause the cam-tappet pairs work in the mixed lubrication state, thus the interfacial friction, pressure and temperature rise are vital to engine performance, efficiency, and durability. An interfacial friction–temperature prediction model for the cam-tappet pairs, considering the effects of transient working conditions and the real surface roughness, is developed in the present study, based on the theories of the transient mixed EHL and the heat transfer under the condition of a fast moving heat source. The numerical results of surface temperature rise are compared with those from the Blok formula, and a good agreement is found. The obtained results show that the presence of 3D roughness may lead to a decrease in the lubricant film thickness, and the surface temperature rise of tappet may exceed 700 K, which is close to the material scuffing temperature, causing the surface failure due to scuffing and wear. If increasing the cam speed and base circle radius within certain range, it may lead to the increment of film thickness and reduction of surface temperature rise, thus the lubrication effectiveness is increased. In addition, using cast aluminum bronze may significantly reduce the surface temperature rise and improve the interfacial characteristics.

Dynamic characteristics of the rack and pinion lift mechanism of the combined command cabin

This paper presents a novel approach to accurately simulate the dynamic characteristics of a rack and pinion lifting mechanism while accounting for the coupling effect of meshing tooth pair stiffness and grease characteristics in real-world environments. A structure-grease coupling meshing stiffness model is established based on the deformation coordination conditions of the tooth pair meshing. The model incorporates the effect of the grease stiffness term on the time-varying meshing stiffness of the rack and pinion. By analyzing the dynamic characteristics of the combined command cabin lifting mechanism using this model, we find that the total meshing stiffness of the gear teeth is lower when the transient thermoelastic flow effect of the grease is considered. Furthermore, the total stiffness value decreases as the normal meshing force at the meshing point decreases. This research reveals that the worst lubrication conditions are typically found on the gear wheel teeth near the base circle, where the grease film temperature rise is highest, the grease film pressure is highest, and the grease film thickness is thinnest.

Measurement and evaluation of time-varying meshing stiffness of faulty gears under different types

When operating under complex conditions, gear failure is inevitable, and gears are often accompanied by multiple failures. In view of this phenomenon, this paper establishes a pitting crack coupling failure model and sets four different fault levels, from healthy to severe. Time-varying meshing stiffness (TVMS) decreases with the occurrence of faults, such that it could be employed as a gauge to assess the level of failure. Firstly, considering that the base circle and the tooth root circle do not coincide, the improved potential energy method is used to solve the TVMS under different fault degrees. Secondly, the effects of crack depth, angle, pitting radius, depth and number on meshing stiffness are studied. Then, the result of the potential energy method is verified by the finite element method, and the consequence shows that the difference between the two is within 5%, which indicates the effectiveness of the proposed model. Finally, when the crack degree is certain, the influence of pitting evolution on the meshing stiffness of the coupling model is studied.

Parameter based definition of eccentric cycloid gearings

Current challenges for today’s industry are an increase in gear ratio in one stage, an increase in load capacity as well as an increase in efficiency compared to standard gears. The standard tooth profile for cylindrical gears is an involute. This tooth profile has certain limits for external gearings regarding its geometry, e.g., undercutting and a small radius of curvature near the base circle. Special gearings overcome these limits and offer an enormous potential in gear design through their adapted profile geometries. New manufacturing possibilities for gears, such as additive manufacturing or 5‑axis milling, mean that special gears can also be produced economically.In comparison to involute gears the description of non-involute gears is often not standardized and parameters describing the geometry are not commonly defined. Thus, it is not possible to adequately determine the corresponding properties. One of these special tooth profiles is the eccentric cycloid gearing (EC gearing), in which a circular profile rolls with a profile of a trochoid equidistant. This flank geometry can provide advantages over the standard involute in certain applications.This study introduces a geometric description of the EC gearing, which is based on a defined set of parameters. Besides the geometrical parameters, parameters describing the characteristics of the gearing are proposed in accordance with the description of involute gears. This parametric description of the EC gearing enables an analytical determination of the flank, the contact geometry and load-free characteristics. With the parametric description shown and the variation of the geometry possible with it, gearings suitable for practical applications can be generated.

Об одном способе формирования коник

In the articles of the Geometry and Graphics magazine devoted to the properties of the Dupin cyclide, the construction of a conic – ellipse, hyperbola and parabola – using the properties of the cyclide was considered. At the same time, the center of the transformation was located on a straight line connecting the centers of the two base circles, and its location on such a straight line was negotiated separately and was located as the center of homology. To construct a parabola, it was necessary to take a straight line instead of the second circle, and the center of the transformation – the center of homology – had to be located at the intersection point of a straight line passing through the center of the first circle perpendicular to the second circle-a straight line with the first circle. Two different parabolas were obtained as a result of the transformation. In this paper, it is proved that if we take the center of correspondence that does not belong to a circle, we get other second–order curves - ellipses and hyperbolas. The construction of an ellipse is geometrically proved. To do this, the center of correspondence must lie on a straight line connecting the centers of the circles, but outside the actual circle. Several examples are considered. If the center of correspondence is inside the circle, we will have a hyperbola. Thus, having initially given only one con-figuration from a straight line and a circle, it is possible to obtain all conics: ellipses, parabolas, and hyperbolas, passing into one another. The proposed scheme for constructing conics can be used for computer drawing of all conics, which is more convenient than with the available options sewn into today's graphical drawing systems.

Multi-objective optimization design in a centrifugal pump volute based on an RBF neural network and genetic algorithm

The hydraulic and acoustic performance of centrifugal pumps are interrelated and contradictory in hydraulic structure design. An optimization design method of a volute based on a radial basis function (RBF) neural network and genetic algorithm (GA) is proposed to solve this problem. The efficiency and total sound pressure level of the centrifugal pump are used as the optimization objectives. The diameter of the base circle, the width of the base circle, the installation angle of the volute tongue, and the height of the volute diffuser tube are used as the optimization variables. Latin hypercube sampling (LHS) is used to establish the sample space, the RBF neural network is used to build the agent model between the optimization variables and objectives, and the GA is used to multi-objective optimization. For the Pareto solution set obtained, two extremal individuals and initial individuals are selected for comparative analysis of hydraulic and acoustic performance under different working conditions. The result demonstrates that under the rated working condition, compared with the initial individual, the efficiency of the optimal individual of efficiency increases by 3.79%; the internal noise of the optimal individual of sound pressure level decreases by 5.5%, and the external noise decreases by 2.3%.

Adjustment for profile deviations of gear involute artefacts

Gear involute artefact (GIA) is a kind of measurement standard for calibrating the gear involute measuring instrument. To reduce the profile form deviations and the difference of the profile slope deviations between the opposite flanks (left and right flank) of GIA, the effect of installation eccentricity on the profile deviations is analysed, and an adjustment method for profile deviations of GIA by the eccentric installation is proposed. The difference of profile slope deviations between the opposite flanks of GIA with designed base circle radius r b = 100 mm changes from 0.31 μm to 0.1 μm after the adjustment through the eccentricity of the mandrel. The difference of profile slope deviations between the opposite flanks of GIA with designed base circle radius r b = 60cos20° mm changes from 0.77 μm to 0.12 μm after the adjustment through a kind of rotary stroke bearing with eccentricity, meanwhile, the profile form deviations are reduced from 0.53 μm to 0.34 μm (right flank) and 0.89 μm to 0.46 μm (left flank). This adjustment method could improve the used accuracy of GIA without improving the machining accuracy of the involute and changing the measurement process of the measurement standard of GIA.

Mechanical analysis of finned special-shaped tubes in bending-torsional coupling deformation

Because of the excellent thermal conductivity and increased strength, finned special-shaped tube (FSST) is frequently utilized in a variety of industrial applications. However, duo to the complex section structure of FSST, the elastic–plastic evolution of the FSST section is more complex than that of circular and rectangular tubes, when FSST is subjected to various coupling effects of bending moment and torque. Moreover, until now, no literature has studied the bending-torsional-coupled deformation of FSST. In this study, based on the power-law stress–strain curve model and the Henky-Ilyushin equations, an analytical model that can precisely characterize the bending-torsional-coupled deformation of the FSST section is established by using the stress method. According to the boundary conditions divided by the geometric characteristics of FSST, the stress and strain distribution, elastic–plastic evolution, and the coupling relationship between the base circle and fins under different bending radii and unit torsion angles are discussed in detail. Besides, the relationship between bending radius and unit torsion angle and bending moment and torque on the section is presented based on the concept of section moment superposition. Finally, the rationality and accuracy of the proposed analytical model are verified by simplified finite element model (FEM), FEM, and practical tests.