REDUCTION OF CONTACT STRESSES USING INVOLUTE GEARS WITH ASYMMETRIC TEETH

Asymmetrical involute gears have a different value of the operating pressure angle for right and left side of the gear. These teeth are suitable for one direction of rotation. Such teeth enable to change the length of the generating line. They enable to improve the value of reduced radii of curvature. Asymmetrical teeth allow reducing the values of Hertz's pressures, especially on the root of the teeth. Hertz pressures are directly related to the asymmetry.


INTRODUCTION
In practice, cogwheels with involute gears are used the most. Their production is common and their accuracy is aceptable. [1][2][3][4][5][6][7]. However, to lower the value of contact stresses, gears with asymmetric teeth might be more suitable. Their price should not be a main criterion when working with them. With a well-designed gear with asymmetrical teeth, a considerable decrease in the values of contact stresses can be noticed, and in some cases also a decrease in vibrations. From this point of view, the spur gears with non-symmetrical teeth are becoming a great alternative. [1][2].

SUITABLE TOOTH DESIGN AREA FOR GEAR WITH ASYMMETRIC TEETH
The driving side has a differnet pressure angle than the opposite side, and therefore an asymetrical tooth is being created. An angle larger than 20° is more advantageous for the driving side. The angle of the opposite side has a considerable influence only during the reverse movement. Base circle diameter significantly decreases with increasing pressure angle. The larger the difference between the angles of a profile, the more pronounced is the asymmetry, and hence there is a significant difference between the diameters of the base circle. [1].
An asymmetrical tooth, an axis of tooth, and a pitch circle are drawn on Fig. 1. The circular pitch measured on the pitch circle is identical for the left and right side. The tooth thickness, measured mostly on a top land, is changing relative to the angle of stress, which influences the ability to create a correct tooth.   These parameters imply a possible design area of an accurate tooth creation, which satisfies the geometrical parameters. An area for accurate tooth creation for parameters z1=17, ha * =1 is shown in Fig. 3. For a certain number of teeth, based on an angle αL, the values of the angle on the right side can be determined in the graph (Fig. 3). For example, z1=17, ha * =1, αL=20° can have an angle αP in the interval < 20°, 38.5°>. This area decreases in size with a smaller number of teeth.  The limits values of the angles α for the right and left side, with a full degree precision for the left side and 0,5° precision for the right side, for a various amount of teeth are mentioned in Tab. 1. The values of half top land tooth thickness are also mentioned there. The value z2hL is the limit value of the number of teeth, for the gear ratio u=1. If the number of teeth is greater than z2hL, point A is outside the interval N1N2 (interference). For a larger gear ratio, the value of the limit of the teeth z2h increases.

THE RADII OF CURVATURE AND HERTZ PRESSURES
A view of various sides of the tooth, where the length of the contact line and radii are changing, is on Fig. 4.The change of pressure angle α leads to changes in the radii of curvature (Fig. 4), which affect the Hertz pressures. Tab. 2 shows the values of the radii of curvature, mesh points A, C. [1]. The value of Hertz pressure is changing in relation to the contact point. It has the least advantageous values in the place of the first mesh point, at the dedendum of the pinion.
The regular values of the pressure in the gearing can be approximately determined in a following matter: For symmetrical gearing, if the pressure value of 100% is at the pitch point, then this value at the dedendum is approximately 150% and approximately 95% at the top of the pinion in relation to the gearing geometry. [8]. The values of the pressures can Reduction of contact stresses using involute gears with asymmetric teeth 183.
be determined based on the circumference force. The second option is to determine these values on the basis of normal force, which value changes depending only on the amount of tooth pairs in the mesh, and is constant for a single contact. Double tooth contact is also being considered in the calculation. Reduced radius of curvature ρR for the mesh points: The change corresponding to the change in stresses at a specific point can be seen in Fig. 2. For example, for values z1= z2=17, ha * =1, an angle αL=18° is the stress at the pitch point C with the value 100%, in point A with 162%, and decreases for angle αP=39,5° to 77% in point C, and to 57% in point A. If the angle of the driving side is 39,5°, the values of stresses are considerably more advantageous.
Hertz pressure by tangential force

CONCLUSION
The use of gears with asymmetric teeth can be a good alternative to reduce Hertz pressures. Well-designed gearing can be achieved to reduce the size, significantly reduce contact stresses especially in the dedendum of the pinion.
This paper was written in the framework of Grant Project VEGA: "1/0688/12-Research and application of universal regulation system in order to master the source of mechanical systems excitation."