Gear Sketch Generator
Involute spur gear builder with DXF output. Licensed under the MIT An open source, browser based utility for calculating and drawing involute spur gears. Teeth. Approximate Kind of Machine Name of Inventor or Developer Date Gear cutter Robert Hook of England Cut spur gears with a formed wheel. Gear generator Joseph Sexton of England Straight-sided milling cutter used to. Aug 1, Keywords: Spur gears, Tooth flank, Involute, Computational method. Let us consider a two dimensional gear tooth profile (not an involute in.
To find the instantaneous rotational speed of the tooth t at this time, the peripheral speed of the rim neutral circle determined by the steady rotational speed of the flexible external gear is divided by the radius of curvature COF.
The center of rotation of the rigid internal gear is the origin O. The instantaneous center of relative motion between the tooth t of the flexible external gear and the rigid internal gear is therefore on an extension of line segment OC. Define this as point Q. Point Q is at a position that externally divides line segment OC by the inverse ratio of the instantaneous rotational speeds of the gears.
Involute Gear Profile | KHK Gears
Select point P as the point of contact of flexible external gear tooth meshing and draw straight line QP. It follows from Camus' theorem that straight line QP is the normal of the tooth profile at this time. Take point R on s, draw lines connecting R with each of C and O, and define the points of intersection of their extensions with the tooth profile normal QP as A and B.
In this invention, point R is selected so that points A and B both fall on the same side of point P. In other words, the flexible external gear is given a concave tooth profile and the rigid internal gear is given a concave tooth profile.
Here involute curves having a common tooth profile normal at point P are newly adopted as the tooth profile of both gears. The overall meshing state of the teeth is also shown. As shown in the drawing, in involute tooth profiles imparted to the rigid gear and the flexible gear, the circles of curvature of the involute tooth profiles at the main meshing point P of the rigid tooth profile are made coincident with the conjugate circles of curvature according to the Euler-Savary equation to locate the conjugate circle of curvature of the flexible gear near the circle of curvature of its involute tooth profile at meshing point P.
The symbols in the drawing correspond to those in FIG. At places apart from point P, some amount of gap or some amount of interference may arise with increasing proximity to the major axis and increasing proximity to the minor axis. When interference arises, smooth meshing can be achieved by appropriately correcting the tooth crest. As can be seen from FIG. The maximum rim stress produced by meshing therefore appears at a place where bending stress produced by elliptical deformation is reduced, with no superimposition of the maximum rim stress produced by tooth meshing at the location of the major axis where bending stress produced by elliptical deformation of the rim of the flexible external gear is maximum.
This enhances the load capacity of the flexible external gear. Moreover, since in the flexible meshing type gear device the component of the load acting on a tooth in the radial direction is borne by the sphere of the wave generator under the tooth, the invention also has a favorable effect on the spherical load distribution of the wave generator. Specifically, incidence of maximum bending stress at the major axis owing to elliptical deformation is also the same at the inner ring of the wave generator so that a contribution can be made to reducing the spherical load in the vicinity of the major axis of the inner ring.
Involute Spur Gear Builder
The foregoing explanation relates to the main cross-section of the flexible external gear. As regards sections apart for the main cross-section in the directions of the opening portion and the diaphragm, relieving is preferable applied as shown in FIG.
In the case of a flat flexible meshing type gear device, however, relieving is not necessary. As explained in the foregoing, the invention establishes the tooth meshing regions of the two gears of a flexible meshing type gear device at locations apart from the major axis of the elliptical flexible external gear.
The bending stress produced in the vicinity of the major axis by the elliptical deformation and the tensile stress produced by tooth meshing are therefore prevented from being superimposed in the rim of the flexible external gear. In addition, the invention distributes the spherical load of the wave generator so that the maximum stress condition occurs at a location away from the neighborhood of the major axis. The invention therefore markedly enhances the load capacity of the flexible meshing type gear device.
The invention further utilizes the Euler-Savari equation that holds for tooth meshing in speed change gears to enable continuous contact in the region neighboring the main meshing point and adopts involute curves as the basic shape of both the convex and concave tooth profiles.
The invention therefore reduces machining cost to enable production of an inexpensive flexible meshing type gear device and, by enhancing tooth flank lubrication performance, increases the durability of the device. Claims 5 What is claimed is: However, gears with 16 teeth or less can be usable if their strength and contact ratio pose any ill effect. To prevent undercut, a positive correction must be introduced. A positive correction, as in Figure 3. Undercutting will get worse if a negative correction is applied.
The extra feed of gear cutter xm in Figures 3. And x is the profile shift coefficient. The condition to prevent undercut in a spur gear is: The profile shift coefficient without undercut x is: Profile shift is not merely used to prevent undercut, it can also be used to adjust the center distance between two gears. If a positive correction is applied, such as to prevent undercut in a pinion, the tooth tip is sharpened. Also, there are various unique ways of modifying gears. This section introduces some of most common methods.
Tooth profile adjustment is done by chamfering the tooth surface in order to make the incorrect involute profile on purpose.
Involute tooth profile generator for dating
This adjustment, enables the tooth to vault when it gets the load, so it can avoid interfering with the mating gear. This is effective for reducing noise and longer surface life. However, too much adjustment may create bad tooth contact as it is functions the same as a large tooth profile error. This method allows the gear to maintain contact in the central region of the tooth and permits avoidance of edge contact.
Crowning should not be larger than necessary as it will reduce the tooth contact area, thus weakening the gears strength. End relief is the chamfering of both ends of tooth surface. An advantage is that there will be no burrs on the tooth top. Also, the tip diameter is highly concentric with the pitch circle. Semitopping is the chamfering of the tooth's top corner, which is accomplished simultaneously with tooth generation.
Such a tooth end prevents corner damage and has no burrs. Topping and semitopping are independent modifications but, if desired, can be applied simultaneously. It is assumed that it is ideal to produce gears with no defects in tooth forms.
Not only is it impossible to avoid some errors, but even if the gears themselves are correct, the assembly process may introduce errors in parallelism of two shafts or eccentricity when mounting gears on the shafts. Even when the assembly is correctly done, because the gear material has elasticity, load on the gear may introduce deflection. For these reasons, the ideal meshing is not always assured.
In order to avoid these realistic deficiencies, it became a common practice to purposely deviate from the geometrically correct tooth forms. This is called tooth form modification. There are two types of tooth form modifications, modification of perpendicular cross section of tooth and modification of tooth line crowning.