• Tribology and Lubricants
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• v.23 no.4
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• pp.149-155
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• 2007

The CAD model of a elliptical gear for wire cutting has been developed. The rolling contact of pitch ellipses whose rotation axes coincide with their focus has been analyzed, and the perimeter of the pitch ellipse has been divided into equal-length segments by the number of teeth. A master tooth profile, which is a composite curve of circular arcs that represents involute, has been introduced. The elliptical gear has been designed by imposing the master tooth on the divided points of the pitch ellipse, and a full fillet has been achieved between neighbour teeth. Thus, the whole profile of an elliptical gear is a composite curve of arcs only, and consequently NC codes for wire cutting can be easily generated. Furthermore, a computer simulation program is developed to verify the mesh of the elliptical gear.

• Tribology and Lubricants
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• v.12 no.3
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• pp.115-122
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• 1996

In this paper, a finite difference method and the Newton-Raphson method are used to evaluate the Hamrock and Dowson's EHL film thickness formulas in elliptical contact problems. The minimum and central film thicknesses are compared with the Hamrock and Dowson's numerical results for various dimensionless parameters and with their film thickness formulas. The results of present analysis are more accurate and physically reasonable. The minimum film thickness formula is similar with the Hamrock and Dowson's results, however, the central film thickness formula shows large differences. Therefore, the Hamrock and Dowson's central film thickness formula should be replaced by following equation. $H_{c} = 4.88U^{0.68}G^{0.44}W^{0.096}(1-0.58e^{-0.60k})$ More accurate film thickness formula for general elliptical contact problems can be expected using present numerical methods and further research should be required.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.21 no.4
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• pp.335-340
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• 2008

In this study, novel structured thin ultrasonic rotary motor has been proposed. Ultrasonic motors are based on an elliptical motion on the surface of elastic body. Thin brass plate was used as a cross shaped vibrator and eight ceramic plates were attached on upper side and bottom side of the brass plate. From the thin stator, elliptical displacements of the four contact tips were obtained. To find the optimal size of the stator, motions of the motors were simulated using ATILA by changing length, width and thickness of the ceramics. The stators had commonly three resonance peaks and contact tips of the stator moved on tangential or normal trajectories at these resonance peaks. The maximum displacements at the resonance peaks were compared. As results, maximum displacements of the contact tips were obtained at the length of 16 mm, width of 6 mm and thickness of 0.4 mm. Changes of the resonance frequencies were inversely proportional to the length of ceramic and proportional to the width of ceramic. The motor was fabricated by using the designed stator. And, the characteristics of the motor were compared with the simulated results. When the motor was fabricated with these results, speed fo 935 rpm was obtained by input voltage of 25 Vrms at 93.5 kHz.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.5
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• pp.85-92
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• 1998

This present paper describes a mathematical model of profile shifted elliptical gears, and this model is based on the concepts of envelope theory and conjugate geometry between the blank and the straight-sided rack cutter. The geometric model of the rack cutter includes working regions generating involute curves and fillets for trocoidal curves, and furthermore the addendum modified coeff. is considered for avoiding undercutting. The addendum modified coeff. is changed linearly along with pitch curves and must be the same absolute value at both major semi-axis and minor semi-axis. If undercutting is at all pronounced, the undercut tooth not only are weakened in strength, but lose a small portion of the involute adjacent to the base circle, then this loss of involute may cause a serious reduction in the length of contact. A very effective method of avoiding undercutting is to use the so-called profile shifted gearing. Non-undercutting condition is examined with the change of eccentricity and addendum modified coeff. in elliptical gears and then the minimum number of tooth is proposed not to gernerate undercutting phenomenon.

• Journal of Mechanical Science and Technology
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• v.16 no.2
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• pp.182-191
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• 2002

The reliable stress intensity factor analysis is required for fracture mechanics design or safety evaluation of mechanical joints at which cracks often initiate and grow. It has been reported that cracks in mechanical joints usually nucleate as corner cracks at the faying surface of joints and grow as elliptical arc through cracks. In this paper, three dimensional finite element analyses are performed for elliptical arc through cracks in mechanical joints. Thereafter stress intensity factors along elliptical crack front including two surface points are determined by the virtual crack closure technique. Virtual crack closure technique is a method to calculate stress intensity factor using the finite element analysis and can be applied to non-orthogonal mesh. As a result, the effects of clearance on the stress intensity factor are investigated and crack shape are then predicted.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.20 no.2
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• pp.23-31
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• 2021

Surface texturing is a promising route to reduce the friction forces between two surfaces in sliding contact. To this end, the fabrication of micro dimples is one of the most widely used surface texturing methods. According to published results, textured surfaces with elliptical micro dimples offer the best friction performance. Therefore, we fabricated elliptical micro dimples on carbon steel (SM45C) by using dual frequency vibration assisted machining. High and low frequencies of 16.3 kHz and 230 Hz were applied to the 3D resonant elliptical vibrator. The 3D resonant elliptical vibrator with a triangular cubic boron nitride insert was assembled on a computer numerically controlled turning lathe. Oval micro dimples of various profiles were manufactured on carbon steel. In terms of the profile of the elliptical micro dimples, the experimental results indicated that the average micro dimple width and depth were 112 ㎛ and 7.7 ㎛. These dimensions are closely related to the cutting conditions and can be easily controlled.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1998.10a
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• pp.212-218
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• 1998

This paper presents a study of the elastohydrodynamic lubrication of elliptical contacts where lubricant entrainment coincides with the major axis of the Hertzian contact ellipse. A finite difference method and the Newton-Raphson method are applied to analyze the problem. Film contours and pressure distributions are compared with the results for lubricant entrainment coincides with the minor axis. Variations of the minimum and central film thicknesses with the radius ratio are also examined. Therefore, the present numerical scheme can be used generally in the analysis of the EHL of elliptical contacts where the lubricant entraining vector did not coincide with either of the principal axis of the conjunction.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.572-577
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• 1997

This present paper describes a mathematical model of profile elliptical gears, and this model is based on the concepts of envelop theory and conjugate geometry between the blank and the straight-sided rack cutter. The geometric model of the rack cutter includes working regions generating involute curves andd fillets for trocoidal curves, and furthermore the addendum modified coeff,is considered for avoiding undercutting. The addendum modified coeff, is changed linearly along with pitch curves and must be the must be the same absolute value at both major semi-axis and minor semi-axis. If undercutting is at all pronounced, the undercut tooth not only are weakened in strength, but lose a small portion of the involute adjacent to the base circle, then this loss of involute may ncause a serios reduction in the length of contact. A very effective method of avoiding undercutting is to use the so-called profile shifted gearing. Non-undercutting conditon is examined with the change of eccentricity and addendum modefied coeff. in elliptical gears and then the minimum number of tooth is proposed not to gernerate undercutting phenomenon.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.3
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• pp.397-408
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• 1988

The study is concerned with the theoretical and experimental investigation of the elliptical bulge test. The elliptical bulge test is analyzed by using a rigid-plastic finite element method incorporating large deformation and normal anisotropy. Thin elliptical diaphragms of mild steel are bulged for three aspect ratios. The contact problem the die round and the sheet is successfully solved by using a skew boundary condition. It is shown that the proper consideration of die radius and normal anisotropy is very significant. The relation between bulging pressure and deformation is obtained. It has been found that the pole is nearly under proportional straining during deformation. The instability criterion by maximum load condition enables the effective prediction of instability pressure. The computional results are in good agreement with experimental results and to be very useful for a better understanding of the elliptical bulge test.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.10
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• pp.1671-1677
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• 2001

Cracks at mechanical fastener holes usually nucleate as elliptical comer cracks at the faying surface of the mechanical joints and grow as elliptical arc through cracks. The weight function method for elliptical arc through cracks at mechanical fastener holes has been developed and verified in the part I of this study. In part H, applying the weight function method, the effects of the amount of clearance on the mixed-mode stress intensity (actors are investigated and the change of crack shape is predicted from the analysis for various crack shapes. The stress intensity factors leer inclined crack are analyzed and critical angle at which mode I stress intensity factor becomes maximum is determined.