Theoretical investigation of sliding ratio on oscillatory roller transmission

Chaosheng Song,Changxu Wei,Caichao Zhu,Xuesong Du,Hailan Song 대한기계학회 2021 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.35 No.7

The contact pairs of oscillatory roller transmission are all high pairs, so the relative sliding occurs due to the different tangential velocity of the contact points. This paper derived the mathematical model and kinematic model of oscillatory roller transmission and proposed a new sliding ratio modeling method for oscillatory roller transmission based on the velocity decomposition. The impacts of geometry design parameters on sliding ratios for oscillatory roller transmission were studied. Results suggest that sliding ratios first decrease and then increase as the rotation angle of movable rolling teeth grows. However, for parametric studies, sliding ratios increase as the radius of disk cam and transmission ratio rise, and decrease as the radius of movable rolling teeth increases. The variation of the eccentricity of disk cam has a great influence on the fluctuating values of sliding ratios. The growth of the radius of movable rolling teeth and the eccentricity of disk cam significantly increase the peakto-peak values of sliding ratios. Relatively, the radius of disk cam and transmission ratio have small impact on sliding ratios. The results provide theoretical guidance for reducing friction and improving the mechanical efficiency of oscillatory roller transmission in engineering.

Computational investigation of three-faced blade errors on contact behaviors for face-hobbed hypoid gears

Chaosheng Song,Chengcheng Liang,Caichao Zhu,Kunming Liu,Siyuan Liu,Qianhong Huang 대한기계학회 2020 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.34 No.7

An accurate mathematical model of face-hobbed hypoid gear tooth surface based on the three-faced blade is established. The correctness of the mathematical model was verified by comparing the contact pattern results from KIMOS software and finite element tooth contact analysis. Then, the effects of tool errors on mesh characteristics of face-hobbed hypoid gear were investigated by loaded tooth contact analysis. Results show that the influences of pressure angle error and regrind angle error on contact pattern are obvious. The location of contact pattern moves from the root on the heel side to the top on the toe side of the tooth surface when the error value increases. The peak-to-peak value of transmission error gradually increases with those two types of errors. The influences of spheric radius error, rake angle error and cutting side relief angle error on contact behaviors are similar and not obvious for facehobbed hypoid gears.

Influences of machine-tool setting errors on mesh behavior for small-module spiral bevel gear

Chaosheng Song,Maohao Xia,Siyuan Liu,Chengcheng Liang 대한기계학회 2022 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.36 No.9

Due to the complex manufacturing process and numerous machine-tool settings, errors easily arise between the actual parameters and theoretical parameters of spiral bevel gear, which contributes to the deviation of geometrical morphology of gear flank. This type of gear pair is very sensitive to tooth flank deviations, and the deviations can affect the mesh behavior of the gear pair and then the performance of the entire device. To investigate the influence of different machine-tool setting errors on the mesh behavior of small-module spiral bevel gear, a mathematical model of this type of gear pair has been established based on the principle of duplex spread blade method, and the finite element analysis model has been developed under the rated condition. The horizontals and radial distances of pinion and wheel as well as the velocity ratio were selected to be investigated. The three machine-tool setting all makes the contact pattern move within the tooth flank. The minimum value of transmission error (TE) appears at the initial horizontal and radial distance. Negative values of the horizontal and radial distance and positive value of velocity ratio both can increase the root bending stress. The errors of machine-tool setting will increase the tooth contact stress. The main influential errors on mesh behavior of small-module spiral bevel gear are in proper order, horizontal, radial distance and velocity ratio. It is convenient and efficient to correct the tooth flanks in this order only by contrasting the contact pattern with the design after the rolling test.

Sliding friction effect on dynamics of crossed beveloid gears with small shaft angle

Song Chaosheng,Zhu Caichao,Liu Wenji 대한기계학회 2013 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.27 No.5

We propose a new method of incorporating the gear sliding friction model and loaded mesh model into an analytical nonlinear crossed beveloid geared vibration model to evaluate the mesh and dynamic characteristics. A 3-dimensional quasi-static loaded tooth contact analysis is employed and the derivation of distributed sliding friction forces and synthesis of frictions to the effective form is applied in the nonlinear dynamic analysis. Using the proposed method, the excitation effects of frictions on tooth mesh and dynamic responses at different load levels are found and investigated. The analysis results show that the existence of sliding frictions between the engaged teeth indeed tends to affect the contact pattern, normal load distribution and maximum contact pressure, but it is unsubstantial. The torque load effect of friction is found with greater degressive influence on mesh stiffness and transmission error at heavier load case. The magnitude and directionality of sliding friction on effective total engaged teeth exhibit less obvious variations than on each tooth due to the contributions from multiple teeth effect. Also, friction excitations tend to decrease the dynamic mesh force slightly for both light and heavy load cases.

Effects of macro-parameters on vibration and radiation noise for high speed wheel gear transmission in electric vehicles

Xi Chen,Chaosheng Song,Caichao Zhu,Jianjun Tan,Najeeb Ullah 대한기계학회 2018 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.32 No.9

Considering flexible shafts, a coupled dynamic model for the gear transmission system of wheel reducer used in electric vehicle was developed. By combining the acoustics finite element modal for housing in Virtual Lab and the coupled dynamic model for gear transmission system, a simulation method was proposed for the prediction of the radiation noise for the wheel reducer. Then, the effects of different macro geometry gear parameters including pressure angle and helical angle on the dynamic response and radiation noise were investigated under the rated working condition. Results show that the peak-peak value of the transmission error dramatically falls in the starting zone, followed by an upward trend with the increase of the pressure angle for the low speed stage gear pair. The minimum transmission error and vibration acceleration occur when the pressure angle is 17°. The increase of the pressure angle does not affect the sound pressure level at the field point obviously. The design case with 17° pressure angle shows the optimum radiation noise level, which is 4.41dB less than the original model. Compared to the pressure angle, the helix angle has a major influence on the transmission error, vibration acceleration and acoustic radiation noise. With the increase of the helix angle, the time-varying transmission error curve becomes more smooth with a lower peak-peak value. Besides, the increase of helix angle results in lowering the varying and fluctuating trend of both vibration acceleration and acoustic radiation noise. The design case with 24° helix angle shows the prime radiation noise level, which is 7 dB less than the original scheme.

Influences of rubber cushion and bearing position on the mesh characteristics of small-module spiral bevel gear

Maohao Xia,Chaosheng Song,Chengcheng Liang,Siyuan Liu,Zhengminqing Li,Peitang Wei 대한기계학회 2021 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.35 No.12

A mathematical model of spiral bevel gear with the application of duplex spread blade method was established. A novel finite element model considering the configuration of shafts and bearings was developed. The influences of shafts, bearing position, and rubber cushion on the mesh characteristics of spiral bevel gear under different loads were investigated. Results show that the peak-to-peak value of transmission error and the ratio of contact area and high stress area all increase with the increase in loads. With the existence of rubber cushion, the contact pattern moves to the heel and root sides of the wheel flank, and the peakto-peak value of transmission error and root edge contact area increase. With the front bearing moving from the original position to the positive position, the peak-to-peak value of transmission error increases. With the movement of rear bearing position from negative to positive, the contact pattern moves to the heel and root sides of the wheel flank. The peak-to-peak value of transmission error increases, and the root edge contact area expands.

Tooth Thickness Error Analysis of Straight Beveloid Gear by Inclined Gear Shaping

Feihong Zhu,Chaosheng Song,Caichao Zhu,Xuesong Du 한국정밀공학회 2022 International Journal of Precision Engineering and Vol.23 No.4

In this paper, two approaches to calculate the tooth thickness error (TTE) of straight beveloid gear by tilt-type gear shaper were proposed. The first calculation approach of TTE was established by considering the change of pitch circle radius during the gear slotting process. The analytical tooth surface model of straight beveloid gear was derived by inclined gear shaping, and the tooth surface point set was obtained. Then, another calculation methodology of TTE was established based on the analytical straight beveloid gear model. Two approaches were employed to calculate the TTE of internal and external straight beveloid gear, respectively. And they were employed to validate each other, and the results show a good consistency. The influences of design parameters on TTE was analyzed. Results show that the internal/external straight beveloid gears have a convex/concave TTE along the tooth width direction while cutting by tilt-type gear shaper, which makes the tooth thickness of the heel and toe sides of beveloid gear thinned/thickened, respectively. The TTE of internal and external beveloid gear both increase with the increase of design cone angle, and decrease with the increase of modulus and number of teeth. For the same macro gear design parameters, the TTE of external beveloid gear is smaller than that of internal beveloid gear. The results of the two approaches show good consistency at the middle of tooth surface. The maximum difference between the results of two approaches gradually increases away from the middle of tooth surface, and it is positively correlated with the value of TTE.

Study on the effect of tooth blank parameters on mesh behavior of aviation bevel gear considering thin web and narrow rim structure

Shuaitao Zhao,Chaosheng Song,Siyuan Liu,Cheng Xu,Caichao Zhu 대한기계학회 2023 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.37 No.7

This study establishes the mathematical model of aviation spiral bevel gear with tilt structure by considering the spatial relationship between cutter and gear blank involved machine-tool settings, and builds a finite element model for the spiral bevel gear with a thin web and narrow rim structure. It also investigates the influence law of different parameters of gear blank on the mesh characteristics. Results show that the decrement of the thickness of the rim does not influence the position of contact pattern. When the thickness of the rim is reduced, the tooth root stress shows an increasing trend and the peak-to-peak value of the transmission errors first decreases and then increases. A reduction of the web causes the position of contact pattern moving slightly from the center part to the heel. When the web thickness gets lower, the tooth root stress greatly declines, while the peak-to-peak value of the transmission errors keeps rising. When increasing the number of rows of the hole, the position of contact pattern gradually shifts from the middle to the heel, the changes of tooth root stress are not obvious, and the peak-to-peak value of the transmission errors initially decreases, but then increases afterwards.

Computational Studies on Mesh Stiffness of Paralleled Helical Beveloid Gear Pair

Ruihua Sun,Chaosheng Song,Caichao Zhu,Yawen Wang,Xingyu Yang 한국정밀공학회 2021 International Journal of Precision Engineering and Vol.22 No.1

Considering the asymmetrical left and right tooth profiles including the transient curve at the tooth root region and the varying thickness along the axial direction due to the cone angle, we build the accurate profile curve model including the transient curve at the tooth root of helical beveloid gear with machining parameters to solve the problem of non-applicability of real digital model. According to the feature of gear shape varying along tooth width direction, we introduced the slicing method and derived its grouping formula. Finally, the efficient and accurate slicing-based mesh stiff ness calculation model of paralleled helical beveloid gears was proposed using potential energy theory. Then, mesh stiff ness was calculated using finite element contact model for comparison and verification. Finally, the impacts of macro geometry parameters including cone angle, normal pressure angle, helix angle, tooth width and addendum coefficient on single and total mesh stiff ness were analyzed. The calculated mesh stiff ness correlates well with the results from FEM with the maximum peak error is 4.8%. Results show that the tooth width shows an obvious incremental impact on average total mesh stiff ness. When the pressure angle, helix angle, cone angle and addendum coefficient increase, the average total mesh stiff ness increases first and then decreases. For the fluctuating value, it increases as the tooth width, helix angle and cone angle increase. However, the pressure angle and addendum coefficient show an opposite impact on the fluctuating value.

Research on Tolerance Design of 2K-V Reducer with Beveloid Gear Considering the Effect of Anti-Backlash

Zhiying Cui,Chaosheng Song,Feihong Zhu,Caichao Zhu 한국정밀공학회 2024 International Journal of Precision Engineering and Vol.25 No.2

A mathematical model for calculating the lost motion of the 2K-V reducer with beveloid gear was established, considering the influence of assembly-induced error factors and the effect of backlash elimination. Sensitivity analysis was conducted on each error factor, and in combination with actual manufacturing processes, a set of tolerance correction values was designed using the Monte Carlo method. Based on these tolerance values, prototype manufacturing and performance testing were carried out. The validity of the proposed theoretical model was verified through experimental validation. The results indicate that three significant factors affecting the overall lost motion are the radial clearance of the tapered roller bearing, the backlash of the involute spline, and the radial runout of the small tooth difference gear. The tolerance correction reduced the difficulty of actual manufacturing, allowing the three highly sensitive error ranges to be relaxed to 757.58 times, 1.26 times, and 8.63 times of their original values, when the lost motion of the whole machine is less than 1arcmin.