Novel Monitoring Method of Hypoid Gear Meshing Based on Thermal Network Model and Infrared Thermography Imagery

2016 ◽  
Author(s):  
Mitsuhiko Suzuki ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Temperature Distribution ◽  
Network Model ◽  
Tooth Surface ◽  
High Speed Photography ◽  
Hypoid Gear ◽  
Monitoring Method ◽  
Contact Conditions ◽  
Tooth Contact ◽  
Thermal Images ◽  
Thermal Network

Hypoid gears, used in automobile differentials, have a complex shape; thus, it is difficult to estimate tooth contact conditions. Therefore, a non-contact method of analysis is proposed for determining tooth contact conditions by using high-response thermography to analyze temperature distribution during meshing between the pinion and the gear. High-speed photography was performed using thermography and an extraction line was defined in the obtained thermal images to extract temperature data from them. Furthermore, we constructed a novel model to predict tooth surface temperature distribution during tooth meshing based on a thermal network model that represents the thermal conductivity of an object by a simple RC circuit. In this report, by comparing the temperature changes obtained from the thermal images with the calculated results, we identify the thermal properties of a material from the thermal images, and discuss the effects of parameters such as heat capacity and thermal resistance. The comparison shows that infrared tooth surface imagery is effective in estimating hypoid gear tooth meshing. That is, by using infrared image and a thermal network model, heat conduction in a gear can be considered. It was confirmed that it is possible to predict temperature rise on tooth surfaces due to gear meshing.

Novel Monitoring Method of Gear Meshing Using a High Response Infrared Thermography

2014 ◽  
Author(s):  
Kodai Niwa ◽  
Raphael Pihet ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Temperature Distribution ◽  
High Speed ◽  
Complex Shape ◽  
Thermal Image ◽  
Tooth Surface ◽  
High Speed Photography ◽  
Analysis Method ◽  
Monitoring Method ◽  
Contact Conditions ◽  
Geometry Error

The hypoid gear used in automobile differential has a complex shape, and the estimation of the contact conditions is difficult. Therefore we devised a method of analysis of the tooth contact conditions using a high reply thermography as a non-contact analysis method by analyzing the temperature distribution during meshing between the pinion and the gear. We decided to perform a high-speed photography used by thermography and defined the extraction line in a shot thermal image to extract the temperature data from the thermal images. The temperature distribution provided by extraction line shows a different temperature rising shape and the position of the tooth surface obtained using the extraction line moves up and down during the cycle of each tooth. This cyclic nature is in good accordance with the whirling of the shaft caused by the geometry error of the shaft center which was thought to have an influence on the contact conditions. In addition, as the extraction line was defined on the thermal image, it does not follow the movement of the gear, but the movement of the temperature distribution obtained using the extraction line matches the displacement of the gear by the whirling.

Tooth Meshing Estimation Based on Monitoring Rotational Vibration and Infrared Thermography Image of Hypoid Gear

2020 ◽  
Author(s):  
Ren Yamashita ◽  
Koki Mukaiyama ◽  
Hiroki Sakuda ◽  
Shota Matsui ◽  
Toshiki Hirogaki ◽  
...  
Keyword(s):  
Infrared Thermography ◽  
Automobile Industry ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Contact Conditions ◽  
Tooth Contact ◽  
Highly Sensitive ◽  
Rotational Vibration ◽  
Noise Vibration

Abstract Nowadays, the improvement in Noise Vibration Harshness (NVH) is one of the most important issues for meeting the needs of the user in the automobile industry. It is well-known that the tooth surface accuracy significantly influences the vibration in gear meshing. The hypoid gear used in the automobile differential has a complex shape, and estimation of the contact conditions is difficult. Therefore, we attempt to develop a novel method to analyze the tooth contact conditions by using highly sensitive infrared thermography with a high response; this method acts as a noncontact analysis that is based on monitoring the temperature distribution during meshing between the pinion and the gear surface. In this report, we designed three types of hypoid gears with different offsets to observe changes in the meshing phenomenon, which occurred due to the differences in the offset. Moreover, by employing accelerometers during a driving test, the dynamic behavior was also examined. Simultaneously, a tooth contact analysis was carried out using thermography. Consequently, the relationship between the rise in temperature at the tooth contact area and the tendency of the rotational vibration was elucidated.

Optimal Tooth Modifications in Hypoid Gears

2004 ◽  
Vol 127 (4) ◽  
pp. 646-655 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Load Distribution ◽  
Angular Position ◽  
Point Contact ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Tool Profile

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and optimal diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in (Simon, V., 2000, “Load Distribution in Hypoid Gears,” ASME J. Mech. Des., 122, pp. 529–535) the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the diameter of the cutter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

Optimal Tooth Modifications in Hypoid Gears

2003 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Angular Position ◽  
Point Contact ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Tool Profile

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and by changing the cutter diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in [1] the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the cutter diameter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

Mathematical Model of Klingelnberg Cyclo-Palloid Hypoid Gear

2013 ◽  
Vol 341-342 ◽  
pp. 572-576 ◽  
Author(s):  
Jin Fu Du ◽  
Zong De Fang ◽  
Min Xu ◽  
Xing Long Zhao ◽  
Yu Min Feng
Keyword(s):  
Mathematical Model ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Tooth Surfaces ◽  
Normal Vectors

The geometry of the tooth surface is important for tooth contact analysis, load tooth contact analysis and the ease-off of gear pairs. This paper presents a mathematical model for the determination of the tooth geometry of Klingelnberg face-hobbed hypoid gears. The formulation for the generation of gear and pinion tooth surfaces and the equations for the tooth surface coordinates are provided in the paper. The surface coordinates and normal vectors are calculated and tooth surfaces and 3D tooth geometries of gear and pinion are obtained. This method may also applied to other face-hobbing gears.

The derivation of transformation matrix before and after thermal distortion for modification

2014 ◽  
Vol 229 (9) ◽  
pp. 1686-1692 ◽  
Author(s):  
Cheng Wang ◽  
Huan Yong Cui ◽  
Qing Ping Zhang
Keyword(s):  
Temperature Distribution ◽  
Contact Analysis ◽  
Transformation Matrix ◽  
Tooth Surface ◽  
Measured Temperature ◽  
Thermal Distortion ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Contact Points ◽  
Before And After

The transformation matrix before and after thermal distortion is deduced for modification. Firstly, the thermal distortion equation of tooth profile is deduced based on noninvolute characteristic caused by the change of temperature. Secondly, the equation of temperature distribution along the direction of tooth surface width is deduced according to the measured temperature of instantaneous contact points. By combining it with the equation of temperature change along the radial direction, the temperature distribution of whole gear can be given. Finally, the thermal distortion equation of tooth surface and the transformation matrix before and after thermal distortion are deduced. Illustrated by an example of a high-speed helical gear, the surface equation of thermal distortion is obtained by the above methods. Compared with tooth surface before thermal distortion, the tooth surface after thermal distortion has significant change. In addition, compared with the theoretical values, the calculated values have little difference. The derivation of transformation matrix before and after thermal distortion provides the basis of theory for modification using the method of tooth contact analysis and loaded tooth contact analysis.

Computational Study on Machine Settings for Face-Milled Hypoid Gears With Low Shaft Angles

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Xingyu Yang ◽  
Chaosheng Song ◽  
Caichao Zhu ◽  
Siyuan Liu ◽  
Chengcheng Liang
Keyword(s):  
Manufacturing Process ◽  
Computational Study ◽  
Cone Angle ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Contact Pattern ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Shaft Angle

Abstract Hypoid gear with small cone angle and large pitch cone distance can be directed at the transmission with low shaft angle (LSA). The manufacturing process has more freedoms of motion to control the tooth surface and ensure higher mesh performance. However, it is difficult to adjust the machine settings due to the extreme geometry. This paper focused on the manufacturing process and machine settings calculation of hypoid gear with low shaft angle (LSA hypoid gear). Based on the generating process, nongenerated gear, and generated pinion manufactured by circular cutter blade, the mathematic model of tooth surface of LSA hypoid gear was developed, and the expressions of principal directions and curvatures of LSA hypoid gear were derived. The relationship of curvatures between pinion and gear was also proposed. Then based on the basic relationships of two mating surfaces, an approach to determinate machine settings for LSA hypoid gear was proposed. Finally, the tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) were directed at the validation of machine settings’ derivation. TCA contact pattern results highly coincide with the preset values. And the LTCA contact pattern also highly coincides with TCA results, it can be considered that the determination approach of machine settings is valid. The TCA transmission error result also shows that the ratio of contact is quite large, which is a little bigger than 2. Thus, the load bearing ability and stability of LSA hypoid gear may be superior.

An Ease-Off Based Method for Loaded Tooth Contact Analysis of Hypoid Gears Having Local and Global Surface Deviations

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
M. Kolivand ◽  
A. Kahraman
Keyword(s):  
Gear Tooth ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Surface Deviations ◽  
Tooth Surfaces ◽  
Loaded Tooth Contact Analysis

Actual hypoid gear tooth surfaces do deviate from the theoretical ones either globally due to manufacturing errors or locally due to reasons such as tooth surface wear. A practical methodology based on ease-off topography is proposed here for loaded tooth contact analysis of hypoid gears having both local and global deviations. This methodology defines the theoretical pinion and gear tooth surfaces from the machine settings and cutter parameters, and constructs the surfaces of the theoretical ease-off and roll angle to compute for the unloaded contact analysis. This theoretical ease-off topography is modified based on tooth surface deviations and is used to perform a loaded tooth contact analysis according to a semi-analytical method proposed earlier. At the end, two examples, a face-milled hypoid gear set having local deviations and a face-hobbed one having global deviations, are analyzed to demonstrate the effectiveness of the proposed methodology in quantifying the effect of such deviations on the load distribution and the loaded motion transmission error.

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