Calculation of chord tooth thickness and chord tooth height of double circular arc gear drive by Newton iteration method

Our country began to study the double circular arc gear from the mid-1960s, but entered the substantive research, test and application after 1975. After a series of analysis and industrial application, it is proved that the bearing capacity of double circular arc gear is higher than that of single circular arc gear. Double circular arc gear is a combination of convex arc and concave arc. It has a wide tooth thickness at the root of the tooth, which improves the bending strength at the root of the tooth. Under the same conditions, the number of contact points of double circular arc gear is more than that of single circular arc gear, which reduces the average load on each contact point.

The test results show that the bending strength and contact strength of double circular arc gear are 60% and 40% higher than that of single circular arc gear respectively. Its comprehensive load-bearing capacity is 40% higher than that of single circular arc gear. In technology, a pair of meshing gears can be machined with only one hob. The two advantages of double circular arc gear just overcome the two disadvantages of single circular arc gear. In addition, the load-carrying capacity of double circular arc gear with non hard tooth surface calculated by bending strength or surface contact strength is higher than that of involute gear under the same condition. Double circular arc gear is widely used in China, mainly in metallurgy, mining, petrochemical and other industries. Almost all reducers used for pumping units in China’s petroleum industry adopt double circular arc gears.

In the machining of double circular arc gear, machining error is the main reason for the displacement of gear basic tooth profile. It directly affects the meshing transmission quality and bearing capacity of gears. Therefore, in the processing field, it is often used to control the root circle diameter (or oblique diameter), the length of the common normal line of the convex tooth, the chord tooth thickness of the convex tooth and the limit deviation of the chord tooth depth to indirectly control the displacement of the basic tooth profile of the gear.

Generally, only one of the dimensions is measured to control the machining accuracy. When measuring the length of the common normal, the helical gear is limited by the tooth width; It is difficult to measure large module gear; In addition, it cannot be used to detect bevel gears and worm gears. In this case, the thickness of the indexing circle chord of the gear is usually measured.

In the past, the approximate method was often used to calculate the chord tooth thickness and chord tooth depth, but when the number of teeth is small and the helix angle is large, the calculation error is large. It is difficult to solve the transcendental equation by numerical method. Now, with the development and popularization of computer, it is no longer difficult to accurately calculate the chord tooth thickness and chord tooth depth by using computer program.

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