Involute Curve Research Articles

헬리컬기어 제조공정에 따른 특성 비교 -단조품과 기계가공품-

Although high productivity is possible, cold forged helical gears have not been widely used due to difficulty in achieving mechanical properties as well as dimensional accuracy of the product. Confidence in the gear characteristics also is very important in heavy-duty gear applications. Therefore, the properties of forged gears must be compared to the properties of conventional machined gears. The properties might be different due to the different fabrication processes. In this study, machined and forged products both before and after heat-treated have been compared by measuring the residual stress and involute curve of the tooth. Characteristics of hardness and microstructure were also compared. Additionally, tooth fracture strength was compared for the heat-treated products. Moreover, the tooth strength and the fracture pattern were compared between the machined and forged gears. The forged gear showed decreased changes in residual stress and decreased changes in dimensions when compared to the machined gear before and after heat treatment. The forged gear was over 10% better than the machined gear in tooth strength.

Variational Formulation of the Log-Aesthetic Surface and Development of Discrete Surface Filters

The log-aesthetic curves include the logarithmic (equiangular) spiral, clothoid, and involute curves. Although most of them are expressed only by an integral form of the tangent vector, it is possible to interactively generate and deform them and they are expected to be utilized for practical use of industrial and graphical design. The discrete log-aesthetic filter based on the formulation of the log-aesthetic curve has successfully been introduced not to impose strong constraints on the designer's activity, to let him/her design freely and to embed the properties of the log-aesthetic curves for complicated ones with both increasing and decreasing curvature. In this paper, in order to define the log-aesthetic surface and develop surface filters based on its formulation, at first we reformulate the log-aesthetic curve with variational principle. Then we propose several new functionals to be minimized for free-form surfaces and define the log-aesthetic surface. Furthermore we propose new discrete surface filters based on the log-aesthetic surface formulation

Parametric multi-axis tool path planning for CNC machining: the case of spur gears

Four and five axis machining strategies are difficult to standardise in the general case. General purpose CAM systems are an important tool allowing the experienced machinist to experiment with machining strategies and assess quality of the resulting tool paths. However, in the case of machine elements, such as gears, shape definition by parametric equations is most inviting for development of fit-for-purpose machining strategies and corresponding parametric tool paths without the use of CAM software. Such an approach is materialised in this paper for spur gears, drawing on discretisation of involute and trochoidal curves constituting the tooth profile, so as to satisfy scallop height constraints. The roughing stage is performed with a flat end mill, implementing slot milling along a meander type tool path. The finishing stage is performed with a bull-nose end mill, implementing peripheral milling circumferentially around the full gear profile. The algorithms were tested on a three-axis machining centre equipped with an additional 4th rotary axis to manufacture a plastic spur gear.

Control of involute curve of gear tooth using the fuzzy logic

Three dimensional coordinate metrology is a firmly established technique in industry. Scanning technology is now widely used in coordinate metrology and is increasingly used for the measurement of small features. This paper presents a new real shape approach to closest point inspection involutes curve of gear tooth by coordinate measuring machinery (CMM). This method aims to select the most likely contact point for each successive arc by applying geometrical criteria and a fuzzy logic estimator. This method is particularly, but not exclusively, suitable for the metrology of features with small radii as well as metrological discontinuities. It does not require obtaining the normal vector traditionally used for probe tip correction. Elapsed time is 144.09 s. Tests have been done on limps of machine tool speed (pinion type cutter), which is highly applied in our country.

Study on the generation of spiral bevel gears with spherical involute tooth profile by the tracing line

In this article, a new gear generating method for the spiral bevel gear with spherical involutes tooth curves was proposed. It was analysed that the tooth flank with cone-spiral involute surface could be formed by the space trajectory of a straight line. The straight line was named as a tracing line. In the method, three motions were demanded; those were the rotary motion of the workpiece, the rectilinear motion of the end of the tracing line along the dedendum, and the rotary motion of the tracing line in the plane. The motion equations were derived. The plate milling cutter with face cutting edges could be used to machine the spiral bevel gears and the chord line of the face circle worked as the tracing line. By the method, the spiral bevel gears without principle errors whose tooth flanks are exact spherical involute curves that could be achieved.

Control Operation and Analysis of the Spur Gears Profile

The theoretic profile of cylindrical gear can be described with an involute curve detected in the front section. The correct formation of the profile assures uniform transmission of the angular velocity from the conducting wheel to the driven one. Profile errors result non-uniform gait, noise and pulsation in the teeth and in bearings. The aim of this paper is the determination of the profile errors using the theoretical profile as reference. The experiment was carried out using a coordinate measuring machine. The real profile is constructed by theoretical equations. The errors are determined comparing these two sets of surfaces, the theoretical and the measured profile. These errors are presented in a graphical user interface (GUI) made by the authors. This GUI is parameterized, so it can be used to evaluate any gear.

Study on Cutting Less-Teeth Gear with the Slotting Tool

In this paper, firstly, the common equation of involute gear profile was derived with the slotting tool, based on the principle of Envelope Method & Coordinate Transform. Secondly, different equqtions of the involute and transition curve were solved with different gear profiles of slotting tool through some mathmatical substitution. Finally, the model of gear profile equation was bulit with the software Pro/E. After verification, it proved that all derived equations, which can be used to establish the accurate 3D model of gear, are correct.

Research on Application of NC Polish-Grinding of Valve Stem and Instantaneous Compensation of Grinding Wheel

According to the example of using a common grinding and composition of parts processing movement and achievement elements, the design of construction of special NC technologies in ordinary grinding machine was formulated. . The grinding and polish-grinding were performed by using two NC systems in series to achieve multi-axis movement. The function and application scope of NC technology were expanded because the instantaneous compensation of the grinding wheel and the polish-grinding wheel were performed under a rectangular coordinate system and a polar coordinate system by using an open loop NC system. The application of surface recovery of grinding wheel by NC reconstruction and extension applications of processing the track of involute curve were referred.

A study on cutting errors in the tooth profiles of the spur gears manufactured in CNC milling machine

In this study, the cutting errors in the tooth profile of the spur gears which are manufactured by end mill according to radial cutting method in three-axis CNC milling machine are investigated. According to this method, a mathematical approach in order to investigate the cutting errors of the tooth profile is presented. Then, mathematical expressions determining the error quantity in the tooth profile curve are derived by using this approach, and a programme is developed in the MATLAB. Parameters such as module (m), tooth number (N), pressure angle (∅) and cutting angle (αm) in the programme are changed, and the cutting errors of the involute tooth profile according to the obtained results are interpreted graphically. As a result, it is seen that the cutting errors in the involute curve increase according to increments of m, N, ∅ and αm.

Cutting Geometry and Base-Cone Parameters of Manufacturing Hypoid Gears by Generating-Line Method

Generating-line method, which is based on the generating process of spherical involute curve, is a new processing theory of cutting ideal spherical involute gears. Based on the principle of the new method, this paper expands the traditional geometrical relationship into the cutting geometry of generating-line method, and proposes the base-cone parameters with their formulas to provide necessary parameters for further study. The application examples, such as establishing the coordinate systems and the equation of gear generating line, show the importance of these researches, and the example of calculating geometric parameters illustrate the way to adjust the base-cone parameters. It can be seen from the researches, the cutting geometry contains the tangent relationships between two base cones and a base plane respectively, and the planar conjugated relationship between two generating lines of pinion and gear. The base-cone parameters determine the relationships among base cones, base plane and generating lines. If some of the base-cone parameters need to be adjusted, it can be realized by modify the value of the parameter r 2 , e or Z 0 .

Accurate Calculation on Bending Stress of the Tooth Root of the Involute Cylindrical Gear

A gear’s finite-element model has been set up according to the parameter functions of the involute and tooth root curve, single and double tooth meshing region have been obtained according to the results of contact analysis. A tooth root’s bending stress has been calculated when meshing in the ultimate position in single tooth meshing region, and this stress has been contrasted with the results of a classical method as the maximum of a circle. The results of theoretical method were far away from that of finite-element calculation before being modified and were a little larger than the later after being modified. Reasons leading to this difference have been analyzed.

Study for the Verification of the Tooth Profile Accuracy of the Automatic Gear Design Program

The gear is a major mechanical element for the power transmission between two adjacent axes. Even though tooth profile of the gear is made of involute and cycloid curve, involute curved gear is generally used by the easiness of the fabrication and assembly. There are lots of studies for the gear design but mostly weighted toward to the drawing production and two dimensional modeling. And because the exclusive three dimensional gear design program is costly high, it is only used at the very confined fields. In this study, we developed automatic gear design program to create three dimensional model and gear profile of the spur and helical gear with involute tooth profile by using user development program named Visual LISP on the AutoCAD and compared each gear tooth profile which is created by automatic design program and commercial program named KissSoft, Inventor utilizing exclusive reverse engineering program named RapidForm XOV and performed gear fabrication through wire cutting electric discharge machining and after that, we compared gear measured data which was made by three dimensional scanner and made by the fabricated gear to check accuracy of the gear profiles. And also checked interference and undercut of the gear tooth by using gear driving motor.

216103 ディスク型SOFC流路における旋回流れの特性(一般05 流体力学・流体工学2)

In the present study, we investigated characteristics of a swirling flow in an air channel of a disk shape planar solid oxide fuel cell (SOFC) by using a particle image velocimetry (PIV). In the case of applying circle involute shape current collectors in a lower section of the air channel, the swirling flow maintained constant speed in the free stream region toward the channel exit. This is because a flow passage consisting of two adjacent involute curves functions as a constant-area channel. Furthermore, when involute shape current collectors were arranged in the reverse direction of involute support plates installed in the upper section of the air channel, a flow uniformity was achieved over the wide range of Reynolds numbers by optimizing flow directions.

Basic Principle and Mathematical Model of Cutting Hypoid Gears by Generating Line Method

Generating line method, which is based on the generating process of spherical involute curve, is a new processing theory of cutting ideal spherical involute gears. This paper proposed the geometry and basic principle of cutting hypoid gears by this method, and defined the planar conjugated relationship between generating lines of the pinion and gear. A mathematical model of tooth surfaces is established based on cutting process. This model can be applied to any shapes and parameters of the gear generating line.

Study of Gear Profile Curve Equation for Less-Teeth Gear Transmission

Due to the shortage of complete design material and mature manufacturing method, less teeth gear (1-7 teeth) transmission has many restrictions in practice nowadays. In this paper, applying the principles of using rack cutter to cut involute gear by using generating methods, we established the dynamic coordinate system and the static coordinate system. By using coordinate transformation method, we derived the equations of gear profile involute and dedendum transition curve. After using Pro/E to plot the end profile of less-teeth gears, we did the 3D modeling and the simulation of the less teeth gear. We also improved a general hobber machine and manufactured less teeth gears successfully. The derivation method of gear profile curve in this paper has lucid concepts which make it quite clear and easy to understand, therefore, it provides theoretical basis to the design, the manufacturing and detection of the less teeth gear.

1313 正弦曲線で構成される歯形を基準ラックとするプラスチック歯車 : 動力損失低減および負荷容量増加の可能性(歯車の動力損失,一般講演)

Power distribution by the plastic gear is decreased for the lighten machine and the compact machine. Also, the reduction of a few energy losses, too, is wanted for the global environmental problem. Gears with a different profile from the involute curve could be effective for the reduction of energy loss in gearing systems, and could enable them to be small and light. The present paper describes plastic gears with a sine curve profile, and analytically discusses their possibility of reducing the energy loss. As a result, it is confirmed that gears with a sine curve profile have smaller sliding between tooth flanks than ones with the involute curve, and would enable the energy loss to be reduced.

The CAM System for Scroll Profile with Three CNC Interpolations

The scroll profile is complex with involute curve and high precision is required. Owing to the interpolation method has significant effects on the dynamic behaviour and to obtain the flexibility of the machining, this paper focuses on the development of a computer-aided manufacturing methodology for precision scroll by the combination of curve fitting and CNC interpolation. In this paper, the method for design and manufacture of the scroll profile is established based on the differential geometry and the enveloping theory. The cutter location using the cylindrical end mill is derived and the cutting path sequences are planned. Three types curve fitting methods: linear fitting, circular biarcs curve fitting, and NURBS curve fitting are adopted to approximate the toolpath of the scroll profile. The error control is used as the basis for generating appropriate toolpath to ensure the machining accuracy. The circular biarcs fitting and NURBS curve fitting can obtain continuous smooth toolpath. In the identical chordal deviation, the circular biarcs curve fitting provides the best performance. The toolpath generated by the proposed method is verified through the solid cutting simulation and the trial-cut on a three-axis machine tool.

Application of Generalized NAUT B-Spline Curveon Circular Domain to Generate Circle Involute

In the present paper, we use generalized B-Spline curve in trigonometric form on circular domain, to capture the transcendental nature of circle involute curve and uncertainty characteristic of design. The required involute curve get generated within the given tolerance limit and is useful in gear design. Keywords—Bezier,Circle Involute, NAUT B-Spline, Spur Gear.

Virtual Design and Structural Optimization of Dry Twin Screw Vacuum Pump with a New Rotor Profile

Twin screw vacuum pump is an important kind of dry vacuum pump, which is widely used in the oil-free vacuum system. The design of the screw rotor profile directly influences the working performance and manufacture cost of the screw pumps. In this paper, a new rotor profile for twin screw vacuum pump is introduced which is comprised of the cycloid curve, the dedendum circle arc, the involute curve and the addendum circle arc. The processes of three-dimensional modeling, motion simulation, interference checking and structural optimization for twin screw vacuum pumps are studied by means of Solidworks software. The works provide theoretical basis for optimal designing and reference for test prototype manufacturing. The results showed the performance of the vacuum pump according with the designer’s intention.

Involute Spur Gear Template Development by Parametric Technique Using Computer Aided Design

There are many methods available for developing profiles of gear and spline teeth. Most of the techniques are inaccurate because they use only an approximation of the involute curve profile. The parametric methoddeveloped in this paper provides accurate involute curve creation usingformulas and exact geometric equations. In addition, the involute curve byequation technique allows using either Cartesian in terms of X, Y, and Z orcylindrical coordinate systems to create the involute curve profile. Sincespur gear geometry is controlled by a few basic parameters, a generic gearcan be designed by three common parameters namely the pressure angle (a), the module (m), and the number of teeth (z). Most of the present day CAD systems have no built-in tool for designing such gears. This paper is an attempt in utilizing the concept of parametric technology to develop atemplate gear. The gear so developed has true involute profile, which is arealistic design. This will allow making changes to the gear design by using parametric input. If one gear file is developed using this parametrictechnology, with which, different size and variety of spur gears can becreated. The specific objective is to design and develop a template spur gear with 3 module, 30 Teeth, 20° pressure angle based on parametric technique by using CATIA V5R14 package. The later portion it is shown how this model may be retrieved and utilized for developing gears of different modules and number of teeth with change in these input parameters.Keywords: Parametric design, Template gear, involute curve, x and y coordinates, Laws for x and y co-ordinates, Extrapolated spline, circularpattern, extrusion