• Tribology and Lubricants
• /
• v.33 no.3
• /
• pp.119-125
• /
• 2017

In this study, we perform a numerical analysis to predict the film thickness and lubrication regions for a thrust ball bearing under different operating conditions. Film thinning and replenishment affect the film thickness in starved lubrication. As the inlet meniscus position is brought to the edge of the Hertz contact, the thin film thickness is calculated as starved equation. We use a film replenishment model to determine the recovery film thickness between rolling elements. We use a hydrodynamic model to describe film recovery, that results from the effects of surface tension. In this model, we consider the surface tension gradient in fluid depression as the driving force for fluid recovery. We use Fourier transform method to determine the time-dependent depth of depressed oil. We calculate the change in the central film thickness graphically by using the recovery equation in starved elastohydrodynamic lubrication(EHL) under operating conditions that include numbers of balls, sliding velocity, applied force, and ambient film thickness. We evaluate the degree of starvation by using the distance from the center of the contact area to the meniscus position. Parched lubrication, a phenomenon where the film thickness decreases consistently, occurs at the severe condition. We determine optimal values with respect to the numbers of balls, and sliding velocity. The investigation can contribute to the design operating conditions for proper lubrication.

• Journal of Biosystems Engineering
• /
• v.3 no.2
• /
• pp.35-61
• /
• 1978

To find out the power tiller's travel and tractive characteristics on the general slope land, the tractive p:nver transmitting system was divided into the internal an,~ external power transmission systems. The performance of power tiller's engine which is the initial unit of internal transmission system was tested. In addition, the mathematical model for the tractive force of driving wheel which is the initial unit of external transmission system, was derived by energy and force balance. An analytical solution of performed for tractive forces was determined by use of the model through the digital computer programme. To justify the reliability of the theoretical value, the draft force was measured by the strain gauge system on the general slope land and compared with theoretical values. The results of the analytical and experimental performance of power tiller on the field may be summarized as follows; (1) The mathematical equation of rolIing resistance was derived as $$Rh=\frac {W_z-AC \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\] sin\theta_1}} {tan\phi \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]+\frac{tan\theta_1}{1}$$ and angle of rolling resistance as $$\theta _1 - tan^1\[ \frac {2T(AcrS_0 - T)+\sqrt (T-AcrS_0)^2(2T)^2-4(T^2-W_2^2r^2)\times (T-AcrS_0)^2 W_z^2r^2S_0^2tan^2\phi} {2(T^2-W_z^2r^2)S_0tan\phi}\] $$and the equation of frft force was derived as$$P=(AC+Rtan\phi)\[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]cos\phi_1 \ulcorner \frac {W_z \ulcorner{AC\[ [1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]sin\phi_1 {tan\phi[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\]+ \frac {tan\phi_1} { 1} \ulcorner W_1sin\alpha $$The slip coefficient K in these equations was fitted to approximately 1. 5 on the level lands and 2 on the slope land. (2) The coefficient of rolling resistance Rn was increased with increasing slip percent 5 and did not influenced by the angle of slope land. The angle of rolling resistance Ol was increasing sinkage Z of driving wheel. The value of Ol was found to be within the limits of Ol =2\ulcorner "'16\ulcorner. (3) The vertical weight transfered to power tiller on general slope land can be estim ated by use of th~ derived equation: $$R_pz= \frac {\sum_{i=1}^{4}{W_i}} {l_T} { (l_T-l) cos\alpha cos\beta \ulcorner \bar(h) sin \alpha - W_1 cos\alpha cos\beta$$The vertical transfer weight $R_pz$ was decreased with increasing the angle of slope land. The ratio of weight difference of right and left driving wheel on slop eland,$\lambda= \frac { {W_L_Z} - {W_R_Z}} {W_Z} $, was increased from ,$\lambda$=0 to$\lambda$=0.4 with increasing the angle of side slope land ($\beta = 0^\circ~20^\circ) (4) In case of no draft resistance, the difference between the travelling velocities on the level and the slope land was very small to give 0.5m/sec, in which the travelling velocity on the general slope land was decreased in curvilinear trend as the draft load increased. The decreasing rate of travelling velocity by the increase of side slope angle was less than that by the increase of hill slope angle a, (5) Rate of side slip by the side slope angle was defined as $ S_r=\frac {S_s}{l_s} \times$ 100( %), and the rate of side slip of the low travelling velocity was larger than that of the high travelling velocity. (6) Draft forces of power tiller did not affect by the angular velocity of driving wheel, and maximum draft coefficient occurred at slip percent of S=60% and the maximum draft power efficiency occurred at slip percent of S=30%. The maximum draft coefficient occurred at slip percent of S=60% on the side slope land, and the draft coefficent was nearly constant regardless of the side slope angle on the hill slope land. The maximum draft coefficient occurred at slip perecent of S=65% and it was decreased with increasing hill slope angle $\alpha$. The maximum draft power efficiency occurred at S=30 % on the general slope land. Therefore, it would be reasonable to have the draft operation at slip percent of S=30% on the general slope land. (7) The portions of the power supplied by the engine of the power tiller which were used as the source of draft power were 46.7% on the concrete road, 26.7% on the level land, and 13~20%; on the general slope land ($\alpha = O~ 15^\circ ,\beta = 0 ~ 10^\circ$) , respectively. Therefore, it may be desirable to develope the new mechanism of the external pO'wer transmitting system for the general slope land to improved its performance.l slope land to improved its performance.

• Journal of Biosystems Engineering
• /
• v.3 no.2
• /
• pp.34-34
• /
• 1978

To find out the power tiller's travel and tractive characteristics on the general slope land, the tractive p:nver transmitting system was divided into the internal an,~ external power transmission systems. The performance of power tiller's engine which is the initial unit of internal transmission system was tested. In addition, the mathematical model for the tractive force of driving wheel which is the initial unit of external transmission system, was derived by energy and force balance. An analytical solution of performed for tractive forces was determined by use of the model through the digital computer programme. To justify the reliability of the theoretical value, the draft force was measured by the strain gauge system on the general slope land and compared with theoretical values. The results of the analytical and experimental performance of power tiller on the field may be summarized as follows; (1) The mathematical equation of rolIing resistance was derived as $$Rh=\frac {W_z-AC \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\] sin\theta_1}} {tan\phi \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]+\frac{tan\theta_1}{1}$$ and angle of rolling resistance as $$\theta _1 - tan^1\[ \frac {2T(AcrS_0 - T)+\sqrt (T-AcrS_0)^2(2T)^2-4(T^2-W_2^2r^2)\times (T-AcrS_0)^2 W_z^2r^2S_0^2tan^2\phi} {2(T^2-W_z^2r^2)S_0tan\phi}\] $$and the equation of frft force was derived as$$P=(AC+Rtan\phi)\[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]cos\phi_1 ? \frac {W_z ?{AC\[ [1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]sin\phi_1 {tan\phi[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\]+ \frac {tan\phi_1} { 1} ? W_1sin\alpha $$The slip coefficient K in these equations was fitted to approximately 1. 5 on the level lands and 2 on the slope land. (2) The coefficient of rolling resistance Rn was increased with increasing slip percent 5 and did not influenced by the angle of slope land. The angle of rolling resistance Ol was increasing sinkage Z of driving wheel. The value of Ol was found to be within the limits of Ol =2? "'16?. (3) The vertical weight transfered to power tiller on general slope land can be estim ated by use of th~ derived equation: $$R_pz= \frac {\sum_{i=1}^{4}{W_i}} {l_T} { (l_T-l) cos\alpha cos\beta ? \bar(h) sin \alpha - W_1 cos\alpha cos\beta$$The vertical transfer weight $R_pz$ was decreased with increasing the angle of slope land. The ratio of weight difference of right and left driving wheel on slop eland,$\lambda= \frac { {W_L_Z} - {W_R_Z}} {W_Z} $, was increased from ,$\lambda$=0 to$\lambda$=0.4 with increasing the angle of side slope land ($\beta = 0^\circ~20^\circ) (4) In case of no draft resistance, the difference between the travelling velocities on the level and the slope land was very small to give 0.5m/sec, in which the travelling velocity on the general slope land was decreased in curvilinear trend as the draft load increased. The decreasing rate of travelling velocity by the increase of side slope angle was less than that by the increase of hill slope angle a, (5) Rate of side slip by the side slope angle was defined as $ S_r=\frac {S_s}{l_s} \times$ 100( %), and the rate of side slip of the low travelling velocity was larger than that of the high travelling velocity. (6) Draft forces of power tiller did not affect by the angular velocity of driving wheel, and maximum draft coefficient occurred at slip percent of S=60% and the maximum draft power efficiency occurred at slip percent of S=30%. The maximum draft coefficient occurred at slip percent of S=60% on the side slope land, and the draft coefficent was nearly constant regardless of the side slope angle on the hill slope land. The maximum draft coefficient occurred at slip perecent of S=65% and it was decreased with increasing hill slope angle $\alpha$. The maximum draft power efficiency occurred at S=30 % on the general slope land. Therefore, it would be reasonable to have the draft operation at slip percent of S=30% on the general slope land. (7) The portions of the power supplied by the engine of the power tiller which were used as the source of draft power were 46.7% on the concrete road, 26.7% on the level land, and 13~20%; on the general slope land ($\alpha = O~ 15^\circ ,\beta = 0 ~ 10^\circ$) , respectively. Therefore, it may be desirable to develope the new mechanism of the external pO'wer transmitting system for the general slope land to improved its performance.

• Journal of the Korean Society for Precision Engineering
• /
• v.28 no.3
• /
• pp.285-291
• /
• 2011

The error motion of a machine tool spindle directly affects the surface errors of machined parts. The error motions of the spindle are not desired errors in the three linear direction motions and two rotating motions. Those are usually due to the imperfect of bearings, stiffness of spindle, assembly errors, external force or unbalance of rotors. The error motions of the spindle have been needed to be decreased to desired goal of spindle's performance. The level of error motion is needed to be estimated during the design and assembly process of the spindle. In this paper, the estimation method for the five degree of freedom (5 D.O.F) error motions of the spindle is suggested. To estimate the error motions of the spindle, waviness of shaft and bearings, external force model was used as input data. And, the estimation models are considering geometric relationship and force equilibrium of the five degree of the freedom. To calculate error motions of the spindle, not only imperfection of the shaft, bearings, such as rolling element bearing, hydrostatic bearing, and aerostatic bearing, but also driving elements such as worm, pulley, and direct driving motor systems, were considered.

• Journal of Korean Society of Steel Construction
• /
• v.14 no.6
• /
• pp.711-720
• /
• 2002

A 3-D numerical model, which could demonstrate the static and dynamic responses of a curved bridge more precisely with the moving vehicles, was developed The dynamic response induced by the centrifugal rolling motion of vehicle was identified according to the variations of the partial grade and the curvature of the slab. Dynamic characteristics of the curved bridge with the moving vehicle were analyzed under the condition of support types and two different support systems. Parametric studies were conducted to compare the efficiency of load distribution in the curved bridge. In general, while the vehicle was crossing the curved bridge, negative reaction occurred in the inside of the girder. The final result showed that the support system located outside the girder was more advantageous than other systems, and the characteristics of load distributions differed from the others in the various conditions of support systems.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.16 no.1
• /
• pp.29-36
• /
• 2008

In this paper, the orbital forming analysis of an automotive hub bearing was studied to predict forming performances using the explicit finite element method. To find an efficient solution technique for the orbital forming, axisymmetric finite element models and 3D solid element models were solved and numerically compared. The time scaling and mass scaling techniques were introduced to reduce the excessive computational time caused by small element size in case of the explicit finite element method. It was found from the numerical simulations on the orbital forming that the axisymmetric element models showed the similar results to the 3D solid element models in forming loads whereas the deformations at the inner race of bearing were quite different. Finally the strains at the inner race of bearing and the forming forces to the peen were measured for the same product of the numerical model by test, and were compared with the 3D solid element results. It was founded that the test results were in good agreements with the numerical ones.

• Wind and Structures
• /
• v.35 no.2
• /
• pp.83-92
• /
• 2022

When the rolling stocks run on the curve, the external rail has to be lifted to a certain level to balance the centrifugal force acting on the train body. Under such a situation, passengers may feel uncomfortable, and the slanted vehicle has the potential overturning risks at high speed. This paper conducted a wind tunnel test in an annular wind tunnel with φ=3.2 m based on a 1/20^th scaled high-speed train (HST) model. The sensitivity of Reynolds effects ranging from Re = 0.37×10⁶ to Re = 1.45×106 was tested based on the incoming wind from U=30 m/s to U=113 m/s. The wind speed covers the range from incompressible to compressible. The impact of roll angle ranging from γ=0° to γ=4° on train aerodynamics was tested. In addition, the boundary layer development was also analyzed under different wind speeds. The results indicate that drag and lift aerodynamic coefficients gradually stabilized and converged over U=70 m/s, which could be regeared as the self-similarity region. Similarly, the thickness of the boundary layer on the floor gradually decreased with the wind speed increase, and little changed over U=80 m/s. The rolling moment of the head and tail cars increased with the roll angle from γ=0° to γ=4°. However, the potential overturning risks of the head car are higher than the tail car with the increase of the roll angle. This study is significant in providing a reference for the overturning assessment of HST.

• Structural Engineering and Mechanics
• /
• v.30 no.6
• /
• pp.679-698
• /
• 2008

On marine vessels, delicate instruments such as navigation radars are normally mounted on ship masts. However the vibrations at the top of mast where the radar is mounted often cause serious deterioration in radar-tracking resolution. The most serious problem is caused by the rotational vibrations at the top of mast that may be due to wind loading, inertial loading from ship rolling and base excitations induced by the running propeller. This paper presents a method of semi-active vibration control using magneto-rheological (MR) dampers to reduce the rotational vibration of the mast. In the study, the classical optimal control algorithm, the independent modal space control algorithm and the double input - single output fuzzy control algorithm are employed for the vibration control. As the phenomenological model of an MR damper is highly nonlinear, which is difficult to analyse, a back- propagation neural network is trained to emulate the inverse dynamic characteristics of the MR damper in the analysis. The trained neural network gives the required voltage for each MR damper based on the displacement, velocity and control force of the MR damper quickly. Numerical simulations show that the proposed control methods can effectively suppress the rotational vibrations at the top of mast.

• The Journal of the Acoustical Society of Korea
• /
• v.14 no.2
• /
• pp.80-91
• /
• 1995

A theoretical models has been prepared which describes the noise generated by tire/road interaction for the tire structure-borne sound analysis. The model begin with a set of thin shell equations describing the motion of the belt of a radial ply tire, as drived by Bohm('mechanisms of the belted tire', Igeniur-Archiv, XXXV, 1966). Structural quantities required for these equations are derived from material properties of the tire. The rolling shape of a tire is computed from the steady-state limit of these equations. Vibrational response of the tire is treated by the full dependent shell equations. The force input at the tire/road interface is calculated on the basis of tread geometry and distribution of contact patch pressure. Radiation of noise is calculated by a simpson integral. Using the programs, the effect on noise of various tire design variations is computed and discussed. Trends which lead to quiet tire design are identified.

• Journal of Power System Engineering
• /
• v.7 no.3
• /
• pp.48-53
• /
• 2003

This paper deals with the control of a horizontally placed flexible rotor levitated by electromagnets in a multi-input/multi-output (MIMO) active magnetic bearing(AMB) system. AMB is a kind of novel high performance bearing which can suspend the rotor by magnetic force. Its contact-free manner between the rotor and stator results in it being able to operate under much higher speed than conventional rolling bearings with relatively low power losses, as well as being environmental-friendly technology for AMB system having no wear and no lubrication requirements. In this MIMO AMB system, the rotor is a complex mechanical system, it not only has rigid body characteristics such as translational and slope motion but also bends as a flexible body. Reduced order nominal model is computed by consideration of the first 3 mode shapes of rotor dynamics. Then, the $H_{\infty}$ control strategy is applied to get robust controller. Such robustness of the control system as the ability of disturbance rejection and modeling error is guaranteed by using $H_{\infty}$ control strategy. Simulation results show the validation of the designed control system and the modeling method to the rotor.