Increase Of Helix Angle Research Articles

曲げ剛性に基づくテーパエンドミルのたわみの解析

Tapered end mills are indispensable cutters for machining of inclined surface with conventional type of numerical controlled machine tools, for instance side surface of mold and die. But, the cutter deflection problem of tapered end mills has not been analized. This paper therefore tries to analyze cutter deflection by statical load based on flexural rigidity of cutter and aims at presenting basic data on tool design and improvement of cutting method. The main results are as follows: (1) Flexural rigidity and equivalent diameter of tapered end mill are calculated by cross-sections of the tool. And the model consists of truncated cones is generated in order to calculate a deflection of the tapered end mill. (2) Calculating method of deflection of the center axis of the truncated cones model by statical load are shown. (3) Deflection curve of the cutter axis by statical load on end of the tool is calculated, and obtained following results. (i) In case of 4 teeth, the maximum deflection of the tool for one-half of tapered angle α=2° is smaller than that for α=3°. But the maximum values of tapered end mills are about 35% for α=2° and 29% for a=3°greater than that of assumed square end mills. (ii) In case of 2 teeth, the deflection changes depend on the direction of load, and maximum value is about 1.5 times the minimum value. But the range of fluctuation of deflection decreases about one-half for α=2° and 3° with increase of helix angle from 24° to 45° respectively.

Upper‐Bound Prediction of Cable Damping under Cyclic Bending

A theoretical formulation has been proposed for obtaining upper bounds to single‐layer helical strand damping under cyclic bending to a constant radius of curvature. The model employs an alternative interwire/interlayer friction formulation to the traditional rigid‐plastic Coulomb model: this, then, enables one to follow the no‐slip‐to‐full‐slip friction transition over the individual contact patches. Results are presented for cables in which the helical outer wires only touch the core and also for spiral strands with no core whose outer wires just touch each other in line contact. Parametric studies show that the traditional Coulomb friction model tends to grossly overestimate cable damping for large radii of curvature such as those found in connection with vortex shedding dynamic instabilities of, for example, overhead transmission lines and underwater cables where the maximum amplitude of vibration is of the order of one cable diameter. For small enough radii of curvature, however, the present model's predictions approach those based on the Coulomb rigid‐plastic model. It is found that cable damping may be increased by increasing the number of wires and/or decreasing the helix angle. However, for sufficiently large levels of radii of curvature and cable axial strain, the present theory suggests that for certain ranges of helix angle, increasing helix angle leads to increases in cable damping that can only be predicted with the newly proposed model, which takes no‐slip‐to‐full‐slip interwire friction interaction into account.

ドリル加工におけるバリ生成に関する研究 バリ生成時の材料の変形状態

This paper deals with exit burrs produced in drilling. The development of yielded, deformed and strain-hardened area is investigated respectively by Finite Element Method(FEM), Grid Method(GM) and Hardness Distribution Measurement(HDM) to clarify the burr formation mechanism. In FEM, the drill exit part of workpiece is divided into 198 triangle elements and 119 nodes. For GM and HDM, aluminum alloy(A6030 in JIS) plates of 10mm thickness are drilled under various cutting conditions with drills of 8mm diameter and various helix angles. And also the measurement of cutting forces is done at the same time. The plastic deformation of workpiece starts at the drill point part, and then occurs mainly at the outer corner part. Both plastic deformation and burr become small as the helix angle increases. Burr shapes are divided mainly into two types. One is a small even burr with or without a conical hat chip. The other is a large burr shaped like a petal. The difference of the two burrs is caused by the formation of a conical hat chip.

Wear of involute helical and circular-arc gears (A comparative study)

The paper presents a comparative study between wear of gears of circular-arc tooth profile having a relative radius of curvature in the axial sense of between 0.4 times and 1.4 times that in the normal plane and wear of involute helical gears based on previous investigations from a research programme carried out at Mansoura University Laboratories. The comparison revealed that wear of involute helical gears is greater than that of gears of circular-arc tooth profile for light and medium tooth loads. For heavily loaded gears, wear of cicrular-arc gears exceeds that of involute helical gears owing to an increase in hertzian deformations and their effect on the lubrication characteristics. The amount of difference in wear increases with increasing helix angle and/or decreasing oil viscosity.

Wear of gear of circular-arc tooth-profile: effect of helix angle and oil viscosity

The results are presented of an experimental investigation carried out at Mansoura University Laboratories aimed at studying the effect of change of helix angle and lubricating oil on wear of a relatively new type of gearing of circular-arc tooth-profile. Eighteen pairs of gears of 6 DP, 91.5 mm pitch diameter and different helix angles were run in power circulating gear test rig at different speeds and transmitting different loads, and the gears were lubricated with oils of different viscosities. It was found that wear increases with increasing helix angle and decreases with increase of oil viscosity. Variations of amount of wear with all the test variables are presented.

Vibration of Helical Gears : Part 2 Experimental Investigation

Dynamic strain and accelerations of three-directional vibrations of helical gears are measured and their natural frequencies, modes and exciting force are discussed in comparison with those of spur gears. Some interesting facts are found : As in spur gears, in helical gears also the most prominent natural frequency is the one which corresponds to torsional vibration of the geared system. Some natural frequencies and modes which are not found in spur gears appear in vibrations of helical gears. As the result of resonance in these frequencies the axial vibration level and dynamic load of helical gears both increase to some extent. The exciting force due to periodic variation of tooth stiffness decreases with an increase of helix angle. Any remarkable difference is not found between levels of exciting forces of two pairs of helical gears having same helix angle but different face widths.

Geometry of Bent Continuous-Filament Yarns1

Expressions are derived for determining theoretically the number of filaments accommodatable in successive con centric rings in a multifilament yarn cross section as a function of yam twist and filament diameter. Increasing filament ellipticity with increasing twist is considered. Numerical values are tabulated for several typical filament diameters and a range of yam twists. The yarn packing factor is also given. Photomicrographs of model yarns illustrate that migra tion of filaments occurs with increasing twist; filaments are forced outward from one ring to the next as their ellipticity is increased. Photographs of bent, multifilament model yams show evidence of an increase in helix angle of the filaments on the inside of the bend and a decrease of those on the outside of the bend. A change of filament packing density upon bending is also evident. An increase in packing density on the inside of the bend and a decrease on the outside is observed for some degrees of bending; however, for severe bending the packing density appears to decrease throughout. Analytical results are presented graphically for the curvature and change in curvature of the filaments in a bent, twisted yam as a function of filament position in the yam cross section, yam twist, and radius of curvature. The most significant findings relate to the locations within the yam cross section of the maximum and minimum curvature and changes in curvature. A discussion of the classic geometrical model of a bent yarn as it relates to fiber mobility is included.

The surface roughness of drilled hole in aluminum alloys

The surface roughness of drilled hole is affected by many factors. In the present studies, the effects of drill shapes and drilling conditions on the surface roughness of various aluminum alloys were pursued by experiments. The results obtained were as follows.(1) The materials to be drilled were arranged in ascending order of the degree of surface roughness as follows: 24ST3 <17ST3 <56SH <61ST3. The above order just corresponded with the descending order of strengths of the materials.(2) The effect of helix angle with a constant point angle (118°) was as follows: the surface roughness was more improved with the increase of helix angle and reached the best state at 35° of helix angle. The effect of point angle with a constant helix angle (27°) on the surface roughness was not very great, but the roughness was slightly improved outside the range of 90 130° of point angle.(3) The surface roughness was greater with the increase in cutting speed or feed.(4) The surface roughness was improved when the chips continously flowed in coiled form. There would be a close connection between the chip flow angle at drill edge and the surface roughness finished.

Thread Forms of Milled Worms: Progress Report No. 3 of the A.S.M.E. Special Research Committee on Worm Gears

Abstract This paper is a continuation of the material on helicoidal sections given in the author’s paper on “Worm-Wheel Contact” presented before the Society in December, 1926. It covers the equations necessary to determine the thread form of milled and ground threads in various sections and also the sections of a helicoid formed by a straight-sided lathe tool, set toward the helix angle of a thread. This last helicoid is a convolute helicoid with the inclination of its generatrix in the opposite direction to that of the helix. As an example, the worm used in the drive AW-3 in Progress Report No. 2 of the A.S.M.E. Special Research Committee on Worm Gears has been analyzed and the coordinates of the thread form in an axial section have been determined when the thread is produced by a lathe tool, a 4-in.-diameter thread milling cutter, a 12-in.-diameter grinding wheel, and by the flat side of a grinding wheel which would produce an involute helicoid. This analysis shows that the form in the axial section of a thread produced by a lathe tool, tipped toward the helix angle, will be concave. That produced by a milling cutter may be concave, convex, or a form of double curvature, depending upon the diameter of the cutter, angle of thread, diameter and lead of screw, and depth of thread. The curvature increases with a reduction in thread angle and an increase in helix angle. The milled forms become more convex with an increase in the diameter of the cutter or grinding wheel. This paper is another attempt to introduce more mathematics in the machine shop to the end that we may know more definitely the conditions with which we are contending.