Linear ball guide design optimization considering stiffness, friction force, and basic dynamic load rating using particle swarm optimization

Van-Canh Tong,김경호,Chun Hong Park,Seong-Wook Hong 대한기계학회 2020 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.34 No.3

Linear-motion ball guides are one of the most common supporting elements in machine tools. Their design optimization is highly crucial for engineers and users because it can assist geometric and operating parameter selection and thereby aid in maximizing the stiffness and operating life while minimizing their friction. In this study, a multi-objective linear ball guide optimization process was performed using the particle swarm optimization (PSO). Five design parameters were selected for optimization: ball diameter, number of balls, groove curvature ratios for balls in contact with carriages and with rails, and initial contact angle. The design optimization objectives were radial stiffness, friction force, and basic dynamic load rating. The bearing stiffness and friction force were calculated using the numerical model proposed by the authors. The basic dynamic load rating was determined according to ISO 14728-1:2017. Pareto-optimal solutions were used to support optimal design parameter selection. The final selection of an optimal point from points satisfying the Pareto optimality was performed using the cooperative equilibrium point method. The simulation results indicated a good performance of the optimized linear ball guide. Finally, the effects of parametric uncertainties in the optimal design on the performance were extensively investigated through a sensitivity analysis.

Characteristics of tapered roller bearings in relation to roller profiles

TONG VAN CANH,홍성욱 대한기계학회 2015 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.29 No.7

This paper investigated the characteristics of tapered roller bearings (TRBs) including stiffness, displacement and contact pressure distributionin rollers, with consideration of the effects of roller profile and axial preload. To this end, a comprehensive modeling and computationprocedure for TRBs was presented. In this paper, TRBs with four typical roller profiles were examined: straight roller, and threemodified rollers such as chamfered, fully-crowned, and partially-crowned rollers. Simulation results showed that, under low axial preload,straight rollers provide higher stiffness and lower contact pressure than those of modified rollers owing to the larger contact area betweenroller and raceways. Under high axial preload, TRBs with modified rollers exhibited an improvement in reduction of peak contact pressurein rollers. Stiffnesses of TRBs were almost independent of roller profile when high preload is applied. Among the investigated rollerprofiles, the most effective pressure reduction was achieved with the partially-crowned roller.

Characteristics of Tapered Roller Bearing with Geometric Error

Van-Canh Tong,홍성욱 한국정밀공학회 2015 International Journal of Precision Engineering and Vol. No.

This study investigates the characteristics of a tapered roller bearing with bearing races that have geometric error. In particular, the out-of-roundness errors of the inner and outer races, which may occur during the manufacturing process or as a result of improper loadings, are considered. To this end, a dynamic model of a tapered roller bearing that includes out-of-roundness errors in its races was developed. The bearing model is assumed to be subjected to combined radial and axial loadings. From the developed model, the rotational angle-dependent characteristics regarding the bearing stiffness matrix, roller-race contact forces, and bearing displacements were obtained. The developed model was then validated by comparing the stiffness of an ideal tapered roller bearing from a commercial program with the quasistatic bearing stiffness of the developed model. Simulations were performed to investigate the effects of the geometric error on the characteristics of the tapered roller bearing. The errors were found to significantly affect the bearing stiffness and displacement as a result of the significant changes in the roller-race interaction. The stiffness characteristics of the tapered roller bearing with geometric error were further investigated along with the radial load and rotational speed effects.

Dynamic Analysis of Spindle Supported by Multiple Bearings of Different Types

Van-Canh Tong(통반칸),Gyu-Hyun Bae(배규현),Seong-Wook Hong(홍성욱) Korean Society for Precision Engineering 2015 한국정밀공학회지 Vol.32 No.2

This paper presents a dynamic modeling method for the indeterminate spindle-bearing system supported by multiple bearings of different types. A spindle-bearing system supported by ball and cylindrical roller bearings is considered. The de Mul’s bearing model is extended for calculating ball and cylindrical roller bearing stiffness matrices with inclusion of centrifugal force and gyroscopic moment. The dependence between spindle shaft reaction forces and bearing stiffness is effectively resolved using an iterative approach. The spindle rotor dynamics is established with the Timoshenko beam theory based finite elements. The spindle reaction forces, bearings stiffness and spindle natural frequencies are obtained with taking into account spindle radial load, ball bearing axial preload and rotational speed effects. The developed method is verified by comparing the simulation results with those from a commercial program.

Analysis of the Stiffness and Fatigue Life of Double-Row Angular Contact Ball Bearings

Van-Canh Tong(통반칸),Seong-Wook Hong(홍성욱) Korean Society for Precision Engineering 2017 한국정밀공학회지 Vol.34 No.11

This paper presents an analysis of the stiffness and fatigue life of double-row angular contact ball bearings (D-ACBBs). To this end, a comprehensive quasi-static model was developed for D-ACBBs subjected to five degree-of-freedom (DOFs) loading and displacement. The model was verified by a commercial computational program. A rigorous numerical investigation was performed, based on the developed model regarding the effects of external load, rotational speed, axial clearance, bearing arrangement, and angular misalignment on the stiffness and fatigue life of the D-ACBB. The D-ACBB was subjected to negative axial clearance and yielded improved performance in terms of fatigue life and stiffness. The effect of angular misalignment on the bearing fatigue life was found to be significantly dependent on the amount of axial clearance. The moment stiffness of the D-ACBB in a back-to-back arrangement was higher than the face-to-face arrangement owing to the increased effective load center distance, whereas the radial stiffness and fatigue life were almost unchanged for back-to-back and face-to-face arrangements.

Vibration Analysis of Flexible Rotor with Angular Contact Ball Bearings Using a General Bearing Stiffness Model

Van-Canh Tong(통반칸),Seong-Wook Hong(홍성욱) Korean Society for Precision Engineering 2018 한국정밀공학회지 Vol.35 No.12

The vibration analysis of flexible rotor systems supported by angular contact ball bearings is presented. Vibration analysis of rotor-ball bearing systems has often been performed via simplification of supporting bearings as linear springs with constant stiffness. In this study, an improved model of rotor-ball bearing systems was proposed. It utilizes a general bearing model based on response and time-dependent bearing characteristics. The system equations of motion were established using the finite-element method and numerically solved using the Newmark-β method. The method was used to recalculate the bearing stiffness matrices at every interval of numerical integration as a function of the instantaneous bearing displacements using a separated five-degrees-of-freedom bearing model. The method was verified via comparison with experimental data available in the literature. The extended simulations were conducted to investigate the unbalanced responses of a rotor-ball bearing system using the proposed and conventional methods. Numerical results showed a meaningful discrepancy between the vibrational responses obtained by the proposed model using the response and timedependent bearing stiffness model and the traditional constant-stiffness model.

Characteristics of Tapered Roller Bearing Subjected to Combined Radial and Moment Loads

Van-Canh Tong,Seong-Wook Hong 한국정밀공학회 2014 International Journal of Precision Engineering and Vol.1 No.4

This paper investigates characteristics of the TRB such as displacements, contact forces between roller and inner ring, outer ring and flange, contact angle between roller and flange, load distribution along roller, and stiffness matrix, when the TRB is subjected to combined radial and moment loads. Understanding of these characteristics deserves attention for developing more sustainable TRBs. To this end, a five-degree-of-freedom model of TRB is employed. Unlike other studies, this paper takes TRB displacements as unknown variables and determines them by iteratively solving the roller and bearing equilibrium equations. A new formula for load variation in rollers is also presented by using an integration technique. The developed method is validated by comparing preliminary results with those from a reference program. The characteristics of TRBs subjected to combined radial and moment loads are simulated as a function of roller profile and rotational speed.

Analysis of tapered roller bearing characteristics with consideration for thermal effects

Van-Canh Tong,Seong Wook Hong 한국생산제조학회 2014 한국생산제조시스템학회 학술발표대회 논문집 Vol.2014 No.9(2)

Modeling and analysis of double-row cylindrical roller bearings

Van-Canh Tong,홍성욱 대한기계학회 2017 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.31 No.7

This paper presented a four Degrees-of-freedom (DOF) quasi-static model for Double-row Cylindrical roller bearings (D-CRBs). In practice, a D-CRB may be replaced by an equivalent pair of two Single-row Cylindrical roller bearings (S-CRBs). However, this simplification may introduce some errors due to the dimensional difference between a D-CRB and two S-CRBs and the complexity in modeling and analysis due to the indeterminate problems associated with two S-CRBs. The model developed in this paper provided an accurate method for the performance evaluation of systems containing D-CRBs, and it reduced complexity of the indeterminate problem. This study rigorously compared the performances of a D-CRB and a pair of S-CRBs having equivalent geometry. A parametric study was carried out on the effects of bearing loading, radial clearance, and angular misalignment on the D-CRB internal load distribution, stiffness, and fatigue life.

Modeling of Moving Table with Linear Roller Guides Subjected to Geometric Errors In Guide Rails

Van-Canh Tong,Sun-Woong Kwon,Seong-Wook Hong 한국정밀공학회 2020 International Journal of Precision Engineering and Vol.21 No.10

This paper presents a model of a linear roller guide that considers geometric errors in rails. A five degree-of-freedom model of a table supported by linear roller guides with guide rail errors was built to determine table-motion errors during its motion along erroneous rails. The model was verified by comparing the simulated displacements of a linear guide estimated by the proposed model and those by an existing transfer-function method. Two types of geometric errors were considered for the guide rail: general form and waviness errors. The influence of external load, initial preload, and a few important parameters of the rail—such as wavelength and amplitude—on the displacement of the carriage and table were investigated extensively. The simulation results demonstrated the ability of the model to obtain complicated motion errors for moving tables with a number of supporting linear guides subjected to guide errors.