# The forming principle and transmission characteristics of helical gear tooth profile curved surface

The helical gear is used to transmit the rotary motion between the parallel axis and the staggered axis, and the tooth surface of the gear is the helical surface. It can be considered that the helical surface is formed by the helical motion of the end tooth profile, or the helical surface is formed by the helical motion of the axial tooth profile. The so-called axial tooth profile is formed by the intersection of the plane of the axis of the helical surface and the helical surface.

In parallel shaft external meshing gear transmission, the helix angle on the two gear pitch cylinders is the same, while the direction is opposite. In cross shaft transmission, the helix angle of the two gears may not be the same. For simplicity, we use the term “helical gear” to denote a gear with two parallel axes, and “helical gear” to denote a gear with two staggered axes. It must be noted that in both cases, the tooth surface of the gear is a helical surface, and the helical gear is also a cylindrical gear with helical teeth. If we only look at a single gear, the helical gear and the helical gear are exactly the same, but because of the relative position of their axes, their transmission principle is also different. There are many kinds of combination forms of helical gear pair, such as straight gear, helical gear, helical gear, worm all the way gear. Although the combination forms of worm and helical gear are different, they all have the same characteristics: the two axes are staggered in space, and the profile is involute cylinder or involute helicoid.

The involute helicoid can be formed by a straight generatrix making a spiral motion. This line and radius are. The tangent point of the cylinder of, in the spiral motion, the inclination angle of the straight generatrix of a helix should be selected so that it is tangent to the helix, and the cylinder with radius is called the base cylinder. The section of an involute helicoid that is cut by a plane perpendicular to the axis of spiral motion is the involute of a circle of radius.

Involute cylindrical gear is one of the most widely used parts in mechanical transmission. With the development of the machine towards high speed, heavy load and low noise, the helical gear including helical gear is more and more widely used due to its unique transmission characteristics:

1) It is convenient to realize the transmission between any shaft intersection angles. The shaft intersection angle of the helical gear transmission is the included angle of the projection of the two gear axes on the common section of the two wheel segment cylinder passing through the two wheel meshing nodes. If the rotation directions of the two wheels are the same, the intersection angle of the axes is the sum of the helix angles of the two wheels. Therefore, given the intersection angle of the two shafts, the transmission between the staggered shafts in space can be realized as long as the two helix angles are properly distributed. This advantage is incomparable to other gear mechanisms which can realize the transmission of spatial staggered shaft.

2) The point contact between the teeth of the cross helical gear is not sensitive to the errors of the angle and the center distance in the process of installation. This is also very beneficial for its installation, adjustment and inspection. In other words, helical gears have unique advantages in matching center distance and reducing outline size.

3) The minimum number of teeth without undercut of helical gear is less than that of straight gear.

4) Because the teeth of helical gears are of spatial helical shape, the points on the same cylindrical surface are not engaged at the same time, which can disperse the influence of manufacturing error on transmission.

5) When the transmission ratio of a pair of helical gears is fixed, the diameter of two wheels can be arbitrarily selected to meet the requirements of center distance as long as the helix angle and the size of cutter are changed, or when the diameter of two wheels is fixed, the different transmission ratio can be obtained by changing the helix angle. In addition, the direction of the helix angle can be changed from the driving wheel to the direction of rotation. These characteristics bring great convenience to the transmission design.

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