The Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes

2014 ◽  
Author(s):  
Giorgio Figliolini ◽  
Hellmuth Stachel ◽  
Jorge Angeles
Keyword(s):  
Tangent Plane ◽  
Line Contact ◽  
Screw Axis ◽  
Fundamental Step ◽  
Involute Gear ◽  
Involute Gears ◽  
Instant Screw Axis

Camus’ concept of Auxiliary Surface (AS) is extended to the case of involute gears with skew axes. In the case at hand, we show that the AS is an orthogonal helicoid whose axis a) lies in the cylindroid and b) is normal to the instant screw axis of one gear with respect to its meshing counterpart; in general, the helicoid axis is skew with respect to the latter. According to the spatial version of Camus’ Theorem, any line attached to the AS, in particular any generator g of AS itself, can be chosen to generate a pair of conjugate flanks with line contact. While the pair of conjugate flanks is geometrically feasible, as they always share a line of contact and the tangent plane at each point of this line, there are poses where the flanks even have a common Disteli axis. Then there is a G2-contact at the striction point and the two surfaces penetrate each other. The outcome is that the surfaces are not realizable as tooth flanks. Nevertheless, this is a fundamental step towards the synthesis of the flanks of involute gears with skew axes.

The Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Giorgio Figliolini ◽  
Hellmuth Stachel ◽  
Jorge Angeles
Keyword(s):  
Smooth Surface ◽  
Tangent Plane ◽  
Line Contact ◽  
Planar Surface ◽  
Screw Axis ◽  
Bevel Gears ◽  
Involute Gears ◽  
G2 Continuity ◽  
Instant Screw Axis

Camus' concept of auxiliary surface (AS) is extended to the case of involute gears with skew axes. In the case at hand, we show that the AS is an orthogonal helicoid whose axis (a) lies in the cylindroid and (b) is normal to the instant screw axis of one gear with respect to its meshing counterpart; in general, the helicoid axis is skew with respect to the latter. According to the spatial version of Camus' Theorem, any line or surface attached to the AS, in particular any line L of AS itself, can be chosen to generate a pair of conjugate flanks with line contact. While the pair of conjugate flanks is geometrically feasible, as they always share a line of contact and the tangent plane at each point of this line, they even have the same curvature, G2-continuity, when L coincides with the instant screw axis (ISA). This means that the two surfaces penetrate each other, at the same common line. The outcome is that the surfaces are not realizable as tooth flanks. Nevertheless, this is a fundamental step toward the synthesis of the flanks of involute gears with skew axes. In fact, the above-mentioned interpenetration between the tooth flanks can be avoided by choosing a smooth surface attached to the AS, instead of a line of the AS itself, which can give, in particular, the spatial version of octoidal bevel gears, when a planar surface is chosen.

The Synthesis of the Axodes of RCCC Linkages

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Giorgio Figliolini ◽  
Pierluigi Rea ◽  
Jorge Angeles
Keyword(s):  
Ruled Surface ◽  
Line Contact ◽  
Output Function ◽  
Input Output ◽  
Screw Axis ◽  
Dual Algebra ◽  
Synthesis Procedure ◽  
Instant Screw Axis ◽  
Four Bar Linkage

As the coupler link of an RCCC linkage moves, its instant screw axis (ISA) sweeps a ruled surface on the fixed link; by the same token, the ISA describes on the coupler link itself a corresponding ruled surface. These two surfaces are the axodes of the linkage, which roll while sliding and maintaining line contact. The axodes not only help to visualize the motion undergone by the coupler link but also can be machined as spatial cams and replace the four-bar linkage, if the need arises. Reported in this paper is a procedure that allows the synthesis of the axodes of an RCCC linkage. The synthesis of this linkage, in turn, is based on dual algebra and the principle of transference, as applied to a spherical four-bar linkage with the same input–output function as the angular variables of the RCCC linkage. Examples of RCCC linkages are included. Moreover, to illustrate the generality of the synthesis procedure, it is also applied to a spherical linkage, namely, the Hooke joint, and to the Bennett linkage.

Geometrical design of skew conical involute gear drives in approximate line contact

2009 ◽  
Vol 223 (9) ◽  
pp. 2201-2211 ◽  
Author(s):  
S H Wu ◽  
S J Tsai
Keyword(s):  
Power Transmission ◽  
Design Approach ◽  
Line Contact ◽  
Contact Sensitivity ◽  
Axis Ratio ◽  
Edge Contact ◽  
Involute Gear ◽  
Surface Durability ◽  
Gear Drives ◽  
Conical Gear

A novel design for skew conical involute gear drives in approximate line contact is proposed. Such a drive has a contact ellipse with a large major-to-minor-axis ratio, which allows it to overcome the weakness of conical gear drives for application in power transmission. This gearing design approach is characterized by reduced edge contact sensitivity and increased surface durability. The edge contact sensitivity that can arise with this kind of gear drive due to assembly or manufacturing errors is evaluated by analysing the value of the shift of the line of action caused by such errors. The surface durability is evaluated by calculating the Hertz stress. Some guidelines are developed based on the analysis of the influence of the gearing parameters on the edge contact sensitivity and the surface durability made possible using this design approach for conical gear drives in the approximate line contact. The guidelines are summarized and, finally, a practical example is given to demonstrate the feasibility of the approximate line contact design.

Generation of Noncircular Bevel Gears With Free-Form Tooth Profile and Curvilinear Tooth Lengthwise

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Fangyan Zheng ◽  
Lin Hua ◽  
Xinghui Han ◽  
Dingfang Chen
Keyword(s):  
Screw Theory ◽  
Mapping Method ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Free Form ◽  
Arc Length ◽  
Screw Axis ◽  
Bevel Gears ◽  
Generating Method ◽  
Instant Screw Axis

Noncircular bevel gear is applied to intersecting axes, realizing given function of transmission ratio. Currently, researches are focused mainly on gear with involute tooth profile and straight tooth lengthwise, while that with free-form tooth profile and curvilinear tooth lengthwise are seldom touched upon. Based on screw theory and equal arc-length mapping method, this paper proposes a generally applicable generating method for noncircular bevel gear with free-form tooth profile and curvilinear tooth lengthwise, covering instant screw axis, conjugate pitch surface, as well as the generator with free-form tooth profile and curvilinear tooth lengthwise. Further, the correctness of the proposed method is verified through illustrations of computerized design.

Effect of tooth waist order parameters of double involute gears on lubrication performance of gear drive

2016 ◽  
Vol 68 (6) ◽  
pp. 671-675 ◽  
Author(s):  
Zhimin Fan ◽  
Wanfeng Zhou ◽  
Ruixue Wang ◽  
Na Wang
Keyword(s):  
Elastohydrodynamic Lubrication ◽  
Reference Value ◽  
Tooth Profile ◽  
Order Parameters ◽  
Content Type ◽  
Oil Film ◽  
Gear Drive ◽  
Involute Gear ◽  
Lubrication Performance ◽  
Involute Gears

Purpose The purpose of this paper is to derive a new lubrication model of double involute gears drive and study the effect of the tooth waist order parameters of double involute gears on lubrication performance. Design/methodology/approach The new lubrication model of double involute gears drive was established according to the meshing characteristics of double involute gears drive and the finite length line contact elastohydrodynamic lubrication theory. Numerical calculation of the lubrication model of gear drive was conducted using the multigrid method. Findings The results show that the oil film necking phenomenon and the oil film pressure peak emerged at the tooth waist order area and the tooth profile ends, and when compared with involute gear, the lubrication performance at the tooth waist order area is better than that at the tooth profile ends. The effect of tooth waist order parameters on lubrication performance at the tooth waist order area was greater than that at other areas. Originality/value This research will promote the application of the double involute gear as soon as possible, and it has the reference value for other types of gears.

Motion Simulation of Gears and Cams Using Working Model

1997 ◽  
Author(s):  
Shih-Liang Wang
Keyword(s):  
Complex Geometry ◽  
Gear Tooth ◽  
Tooth Profile ◽  
Line Contact ◽  
Motion Simulation ◽  
The Past ◽  
Working Model ◽  
Simulation Engine ◽  
Involute Gear ◽  
Involute Surface

Abstract Motion simulation of mechanism of line contact like gears and cams has been difficult in the past. With Working Model, NURBS based complex geometry can be modeled fairly easily, and its simulation engine can animate this type of mechanism accurately. In this paper several Working Model files are developed for visualization and analysis. An algorithm to generate involute gear tooth profile is introduced in this paper for the involute and a portion of non-involute surface.

Simulation and Analysis about Different Pressure Angle in Involute Gears Based on Neural Network

2014 ◽  
Vol 540 ◽  
pp. 88-91 ◽  
Author(s):  
Jun Xiao ◽  
Xu Lei Deng ◽  
Jia Ning He ◽  
Wu Xing Ma ◽  
Yan Li ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Learning Process ◽  
Theoretical Basis ◽  
Nonlinear Mapping ◽  
Pressure Angle ◽  
Involute Gear ◽  
Transmission Design ◽  
Involute Gears ◽  
The Neural Networks

This article introduced neural network, discusses the neural networks model and its learning process. Using the MATLAB environment research and analysis the involute gear undercutting relationship, which under different pressure angles. In the number of teeth or modulus has been scheduled environment apply the nonlinear mapping characteristics of neural networks to involute gear undercutting do a more accurate simulation. This provides a theoretical basis for different pressure angle involute gear in gear transmission design.

Optimizing involute gear design for maximum bending strength and equivalent pitting resistance

2007 ◽  
Vol 221 (4) ◽  
pp. 479-488 ◽  
Author(s):  
V Spitas ◽  
C Spitas
Keyword(s):  
Bending Strength ◽  
Power Transmission ◽  
Optimization Procedure ◽  
Contact Ratio ◽  
Element Analysis ◽  
Gear Design ◽  
Involute Gear ◽  
Involute Gears ◽  
High Power Transmission ◽  
Complex Algorithm

Standard involute gear designs dominate high-power transmission applications because they combine sufficient bending strength with high pitting resistance, while retaining an adequate contact ratio. In this paper, a non-standard, optimal alternative involute gear design has been presented, which has the same pitting resistance as the standard involute gears but exhibits maximum resistance to bending. The optimization procedure is based on the complex algorithm, where the root stress, as calculated through tabulated boundary element analysis values, is the objective function and the active constraints include all of the kinematical, manufacturing and geometrical conditions, which must be satisfied by the optimal design, including the pitting resistance. The results indicate that optimal designs can achieve up to 8.5 per cent reduction of the fillet stress. Two-dimensional photoelasticity was used to verify the optimization results.

Can non-standard involute gears of different modules mesh?

2006 ◽  
Vol 220 (8) ◽  
pp. 1305-1313 ◽  
Author(s):  
C Spitas ◽  
V Spitas
Keyword(s):  
Bending Strength ◽  
Gear Tooth ◽  
Sliding Velocity ◽  
Initial Investigation ◽  
Involute Gear ◽  
Involute Gears ◽  
Gear Systems ◽  
Standard Designs

Under the current standardized involute gear systems, meshing of gears of different modules is a practical impossibility. However, by performing a fresh reinterpretation of the well-established fundamental meshing principles, a more insightful form for the compatibility equations that govern involute gear tooth generation and meshing can be obtained. This article reports some first non-standard designs based on this analysis that allows gears of different modules to mesh. By the same token, standard gears can be manufactured with non-standard hobs and vice versa. Initial investigation suggests that practical benefits such as increasing the root bending strength without affecting the pitting resistance and the sliding velocity can be achieved that may justify such deviation from standard designs.

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