Development of Conical Involute Gears (Beveloids) for Vehicle Transmissions

Conical involute gears used for marine transmissions are mostly helical conical involute gears. Besides these gears are not intersecting axis gears but also nonintersecting-nonparallel axis gears. The contact between tooth surfaces of a pair of gears is the point contact. Hence the tooth surface durability is generally small. In order to overcome this weak point, one of the authors invented a new type of conical gear, which is called conical Concave conical gear has higher tooth durability than the conventional conical involute gear. In this research, a new method to generate the helical Concave conical gear is presented. First the principle of generating method is introduced. Theoretical tooth surface is analyzed. Secondly test gears are ground. Tooth surfaces of the test gears are measured and compared with theoretical ones. Two tooth surfaces are in good agreement.

Dudley's Handbook of Practical Gear Design and Manufacture

A control method of finishing dimensions of a helical concave conical gear, called center-ball measurement, is newly developed. The tooth surface of the concave conical gear is different from that of the conical involute gear, which is concave compared to the tooth surface of the conical involute gear. So the over-ball measurement of the conical involute gear can not be used at it is, but can be applied to a special measuring conditions. This center-ball measurement is based on the over-ball measurement of the helical conical gear. But in this method, the measuring ball, which is composed of two hemispheres, must be used. So the over-ball diameter can not be measured, but a center-ball diameter, which is the distance between two ball centers, can be measured instead. In this research, first the measuring condition is established. Second the center-ball diameter is obtained analytically. Finally, the center-ball diameter is verified through experiments. The experiments prove that this method has opened a door to the control of finishing dimensions in hobbing and grinding of the helical concave conical gear.

Conical gear is an involute gear having a cone angle. When the conical gears are meshed on the intersecting axis or nonintersecting- nonparallel axis, the contact between tooth surfaces is a point contact. So the tooth surface strength is generally small. It is the Concave conical gear that was developed in order to overcome this weak point. Its tooth surface is a curved surface having the reverse crowning on the tooth surface of the conical gear. Conventionally, this tooth surface has been generated by the conical shaped wheel. By this method, however, it is not necessarily easy to make an ideal tooth surface. Therefore, we devised a new rack for generating the concave conical gear. This is the rack in which the tooth thickness of normal rack is corrected in the direction of the tooth trace. We obtained the theoretical tooth surface generated by the new rack. And, we made the gear having the theoretical tooth surface by the five axis machining center. In this research, first we developed a coordinate calculation method of the theoretical tooth surface, and next a 3D model, and finally an optimal tool path by using CAM. And we measured the curved line of the tooth surface in the plane of principal radii of curvature of the test gear and confirmed that this line agrees well with the ideal curved line. From the above results, the validity of this design and production system is confirmed.

Spur gears are simple to design and construct to actualize their usage in power transmission as well as for speed reduction or increase. The aim of this research work is to determine the effect of module variation on a 100Watt horizontal axis wind turbine (HAWT) spur gear drive. The solution is to determine and appropriately select gear parameter values based on design considerations and the significance is for enhanced machine reliability and balance with economic production. The method used involved the application of gear design principles, modelling the gears with AutoCAD, module variation and evaluation of induced bending stress at the gears root; gear diameter, tooth thickness and face width become bigger with choosing higher modules for cutting tooth size, with the largest diameter of 168.4mm and 80mm for driver and driven gear respectively and face width of 60mm from using a module of 6mm. Although, the total torque exerted remains constant at 7.9Nm and 3.8Nm for a 100W HAWT. The tangential force in meshed operation of the gears and induced bending stress kept reducing as module increased. The highest tangential force is 282.4N and corresponding induced bending stress is 26.1N/mm2 based on American Gear Manufacturers Association (AGMA) standard and the range of data analyzed, at the lowest module of 2mm. Selecting lower modules means that higher bending stresses will be induced at the gears root, but smaller production cost and more compact system with less space requirement. The lower bending stresses with increasing module will support higher load capacity of the gears due to the increasing face width and enhance the reliability of the HAWT in respect of its performance.
 Keywords: Module, Spur Gear, Power Transmission, Bending Stress, Wind Turbine

Computerized generation and simulation of meshing of modified spur and helical gears manufactured by shaving

The influence of operating condition on acoustic emission (AE) generation during meshing of helical and spur gear

In this study, we call an internal gear having conical angle as the internal conical gear. In the case of conjugating with spur gear, this gear can transmit rotational motion between intersecting shafts. Also in the case of conjugating with conical gear, there is possibility of adjusting backlash by axial movement. Therefore, as a first step of the study we obtain theoretical tooth surface of the internal conical gear cut by gear shaper. Next we measured tooth surface of the test gears and compared them with theoretical one. Finally the tooth-bearing test confirms that theoretical analyses holds true.

Purpose Crossed helical gears have point contact and their surfaces are subject to high surface stress. Contact stress and root tooth stress are the most common sources of failure in crossed helical gear. This paper aims to study the load-carrying capacity and performance of crossed helical gear teeth with different gear tooth profiles. To overcome defects and reduce the sensitivity to small shaft angle changes. The combined tooth profile is designed to reduce the bending stresses, contact stresses and tooth deflection, and prevent pinion failure in the gearbox. Design/methodology/approach The principle of the method is a line contact is introduced instead of a point contact between two teeth in mesh with each other. The tooth surface of the helical gear is designed and cut by a modified tool. Higher normal pressure angles like 25° and 35° are used. The modified involute is accomplished to eliminate interference between the teeth. Engineering software packages have been applied to generate all crossed helical gears gear profiles. The modification is compounding curves consisting of an epicycloid-involute-hypocycloid gear teeth profile generated by the cutter modified. Findings The stresses in the crossed helical gear teeth profile were reduced by increasing the normal pressure angle values. Using a 35° pressure angle the enhancement percentage in contact stress and teeth fillet region will be about 29.345% and 15.421%, respectively. The best enhancement in a gear’s resistance is the epicycloid-involute-hypocycloid gear teeth profile. The enhancement was 32.610% and 18.588%. The skew in line of action in skewed helical gear will be sensitive when the crossing angles are small. Their teeth surface tends to be easily worn out; however, the wearing process will be reduced by using a proposed gear teeth profile. Practical implications The gear teeth to be modified are cut by a shaper process. The modifying rack cutter of this study can be used as a reference for creating a different helical gears sample. The helical teeth surface is modified to become an envelope of the other. This makes an original point contact change into a line contact. The epicycloid-involute-hypocycloid gear teeth profile is preferred for a higher contact ratio and a large load capacity. This work explicitly introduces a new method of kinematic consideration to improve the load capacity of crossed helical gear. Originality/value This paper showed some novel results by the unique shape of the rack-cutter designed to generate different helical angles and different gear positions. In the future, it will make valuable contributions to the further development of the dynamic performance of a crossed helical gear system through the study in the field of using asymmetric teeth profiles of helical gears with tip relief as the manner to enhance the crossed helical gear performance. Investigation of crossed helical gear by applying a predesigned parabolic function of transmission error enables the absorption of linear discontinuous functions caused by misalignment.

In this paper we present the modalities to obtain, by a CAD soft, the solids that materialize the conical gears. The procedure is similar to the industrial ones for the cutting of the teeth of the conical gears and it assumes the existence of the generator tool and a raw material. The algorithm of the method permits the obtaining of any gears, no matter the shape of the tooth, its inclination etc. Finally, we present an application for the obtaining of a gear with two wheels with straight teeth.

PurposeThis paper aims to present an analytical approach for the determination of helical gear tooth geometry and introduces the necessary parameters. Tooth geometry including tooth chamfer, involute curve, root fillet, helix as well as tooth microgeometry can be obtained using the presented approach.Design/methodology/approachThe presented analytical approach involves deriving the equivalent equations at the transverse plane rather than the normal plane. Moreover, numerical evaluation of microgeometry modifications is presented for tooth profile, tooth lead and flank twist.FindingsAn analytical approach is presented and equations are derived and explained in detail for helical gear tooth geometry calculation, including tooth microgeometry. Method 1, which was presented by Lopez and Wheway (1986) for obtaining the root fillet, is examined and it is proven that it does not work accurately for helical gears, but rather it works perfectly in the case of spur gears. Changing the normal plane parameters in Method 1 to the transverse plane ones does not give correct results. Two alternative methods, namely, Methods 2 and 3, are developed in the current research for the calculation of the tooth root fillet of helical gears. The presented methods and also the numerical evaluation presented for microgeometry modification are examined against the geometry obtained from Windows LDP software. The results show very good agreement, and it is feasible to apply the approach using the presented equations.Originality/valueIn the gear design process, it is important to model the correct gear tooth geometry and deliver all related dimensions and calculations accurately. However, the determination of helical gear tooth geometry has not been presented adequately by equations to facilitate gear modelling. The detailed helical gear tooth root has been enveloped using software tools that can simulate the cutter motion. Deriving those equations, presented in this article, provides gear design engineers and researchers with the possibility to model helical gears and perform design calculations in a structured, applicable and accurate method.

The new estimation formula of coefficient of friction in rolling-sliding contact surface under mixed lubrication condition for the power loss reduction of power transmission gears

In order to address the impact of reduced transmission stability and reliability caused by volume reduction on the quality of gear transmission, this article proposes a multi-objective optimization model for nonlinear dynamic load transmission errors of double helical gears. This study aims to introduce a multi-objective design method for gear transmission, using the volume and smooth reliability of helical gears as objective functions, and establish a multi-objective optimization design mathematical model for helical cylindrical gear transmission. In order to solve this multi-objective optimization problem, we utilized the optimization toolbox in the scientific calculation software MATLAB with examples. The results show that after the joint optimization design of volume and coincidence degree, it is calculated that the volume after the joint optimization design is still 2.2624 × 107 mm3, and the coincidence degree is 5.9908. After rounding, the design result is m n = 3 , Z 1 = 31 , β = 20 ∘ , Ψ d = 1.2 {m}_{{\rm{n}}}=3,{Z}_{1}=31,\beta ={20}^{\circ },{\Psi }_{{\rm{d}}}=1.2 . The optimization design results show that the joint optimization design with the minimum volume and the maximum coincidence as the objective function can reduce the volume and improve the output stability of the helical gear.

Performance of gear transmissions affects the performance of mechanical equipment. It is necessary to develop more reliable gear pitch and tooth thickness accuracy detection methods in order to evaluate gear transmission performance and detect gear pitch and tooth thickness accuracy more accurately. Based on the basic theory of gears, binocular vision technology, and statistical principles, a new method that measures gear pitch and tooth thickness using machine vision is proposed: coaxial multi-ring detection (MCD). There is no contact, no damage, and a high degree of efficiency with this method. Using this method, we are able to detect the pitch and thickness accuracy of each gear tooth multiple times within the tooth width range and in multiple directions perpendicular to the gear axis. We statistically analyze the measurement results to determine the gear’s most accurate detection results. The measurement method for gear machining accuracy is investigated using the coaxial multi-ring detection method. The statistical analysis of multiple measurement results is carried out, and the measurement results obtained are highly consistent with those of the gear detection center. In conclusion, the measurement results of this method are highly reliable, and they can be used as a reliable basis for evaluating gear transmission performance.

As the helical gear is widely used as transmission part in the planetary gear train system, a six-degree-of-freedom bending-torsion-axis coupling dynamic model is established for the helical gear. In order to analyze the influence of the tooth profile modification on the gear meshing transmission, the tooth profile modification model is established, and the modification curve equation is analyzed by different curves. The results are substituted into the dynamic model of the original helical gear transmission, and a five-degree-of-freedom dynamic equation systematically considering tooth profile modification is obtained. The numerical simulation results show that the external stimulation, the tooth side gap and other factors have great influence on the vibration of the gear transmission, and the reasonable tooth profile curve can effectively reduce the system amplitude.