• Transactions of the Korean Society of Mechanical Engineers
• /
• v.12 no.2
• /
• pp.206-214
• /
• 1988

To improve the surface waviness in the peripheral milling, the feedrate is controlled so that the cutting force measured in the normal direction to the workpiece is constant. A discrete time first order model between the feedrate and the tool deflection is derived for the control. It has been shown by the analysis that the tool deflection is directly related to the feedrate and largely affects the surface waviness during cutting. The experimental results shown that the surface waviness is drastically improved by the proposed methods.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
• /
• 1997.10a
• /
• pp.254-259
• /
• 1997

The measurement of surface roughness and waviness by means of noncontact method is an important area to be developed for GAC(Geometrical Adaptive Control) system. This paper deal with the design of noncontact in-process measurement system which measures the surface roughness and waviness during cylindrical grinding. This measuring system is simple and the apparatus proposed is composed of a laser unit, photodetector and optical system. During operation, the surface of a workpiece is continuously scanned by a laser beam. This method makes it possible to detect the surface roughness and waviness along the feed direction by control the spot diameter of laser beam. The experimental results show that the presence of chattering, loading and glazing can be detected sensitively along the feed directions.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2005.10a
• /
• pp.115-118
• /
• 2005

A workpiece with a large surface area is likely to be uneven due to form error and waviness. These geometric disturbances can cause inaccurate micro shapes to be formed when micro features are micro-grooved into the surface and cause the resulting workpiece to fail to function as desired. Thus, real-time measurement and compensation is required to guarantee the form accuracy of micro features while machining a workpiece with a large surface area. In this study, a method is suggested for real-time measurement of geometric error for the micro grooving of a large flat surface using a laser displacement sensor. The measurements are demonstrated for the workpieces with large surface areas and the experimental results show that the waviness and form error are well detected.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.11a
• /
• pp.297-303
• /
• 2001

This research presents an analytical model to characterize the ball bearing vibration due to the waviness in a rigid rotor supported by multi-row ball bearings considering centrifugal force and gyroscopic moment of ball. The effects of centrifugal force and gyroscopic moment are introduced to the kinematic constraints and force equilibrium equations. The waviness of ball and races is modeled by the superposition of sinusoidal function and it is introduced to position vectors of race curvature center to use the Hertzian contact theory in order to calculate the elastic deflection and nonlinear contact force resulting from the waviness while the rotor has translational and angular motion. They can be determined by solving the nonlinear equations of motion with five degrees of freedom by using the Runge-Kutta-Fehlberg algorithm. The accuracy of this research is validated by comparing with the results of the prior researches. It characterizes the vibration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing resulting from the waviness interaction.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.05a
• /
• pp.181-189
• /
• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness in a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time-varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i= 1,2,3..).

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.12
• /
• pp.2636-2646
• /
• 2002

This research presents an analytical model to investigate vibration due to ball bearing waviness in a rotating system supported by two or more ball bearings, taking account of the centrifugal force and gyroscopic moment of the ball. The waviness of rolling elements is modeled by the sinusoidal function, and it is incorporated into the position vectors of the race curvature center. The Hertzian con tact theory is applied to calculate the elastic deflection and nonlinear contact force while the rotor has translational and angular motions. Both the centrifugal force and gyroscopic moment of the ball and the waviness of the rolling elements are included in the kinematic constraints and force equilibrium equations of a ball to derive the nonlinear governing equations of the rotor, which are solved by using the Runge-Kutta-Fehlberg algorithm to determine the new position of the rotor. The proposed model is validated by the comparison of the results of the prior researchers. This research shows that the centrifugal force and gyroscopic moment of the ball plays the important role in determining the bearing frequencies, i.e. the principal frequencies, their harmonics and the sideband frequencies resulting from the waviness of the rolling elements of ball bearing. It also shows that the bearing vibration frequencies are generated by the waviness interaction not only between the rolling elements of one ball bearing but also between those of two or more ball bearings constrained by the rotor.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.12
• /
• pp.2647-2655
• /
• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness i n a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time -varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i=1,2,3..).

• Composites Research
• /
• v.12 no.1
• /
• pp.59-67
• /
• 1999

The effects of fiber waviness on tensile/compressive nonlinear elastic behaviors of graphite/epoxy unidirectional composite materials are studied theoretically and experimentally. New constitutive models are proposed to predict elastic properties and tensile/compressive nonlinear behaviors of composite materials. Three types of wavy pattern are considered: uniform, graded and localized fiber waviness. Complementary energy density and incremental method are used to incorporate the material and geometrical nonlinearities due to fiber waviness. Tensile/compressive tests are conducted on the specimens with fiber waviness. It is found that the predictions are in good agreement with the experimental results.

• 제어로봇시스템학회:학술대회논문집
• /
• 1987.10b
• /
• pp.232-236
• /
• 1987

To improve the surface waviness in the peripheral milling, since the tool deflection is largely affected by cutting force, the feedrate is controlled so that the cutting force measured in the normal direction to the workpiece is constant. A discrete time first order model between the feedrate and the tool deflection is derived for the control. The experimental results show that the surface waviness is greatly improved by the proposed method.

• Tribology and Lubricants
• /
• v.19 no.3
• /
• pp.123-132
• /
• 2003

The effect of surface texture on elastohydrodynamic lubrication (EHL) point contact of a ball Joint mechanism in small reciprocating compressors is studied numerically by using multigrid method. Pressure and film thickness profiles have been calculated for surface roughness with waviness of different orientations and transverse ridge and dent at minimum and maximum Hoes M parameter conditions. The influence of the amplitude and the wavelength of the surface roughness was also studied. Results show that the oblique waviness with orientation angle of 30$^{\circ}$generates the smallest minimum film thickness as compared with those of longitudinal, transverse, and other oblique roughness. The influence of transverse waviness on the minimum film thickness is smaller than for the longitudinal waviness case.