Internal Gear Pump Trochoidal Tooth Profile Cusp Prevention
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Solution Overview
Problem
Internal gear pumps with trochoidal curve tooth profiles often form cusps at the addendum edges, leading to increased Hertz stress, abrasion, vibration, and noise, and existing corrections result in reduced mechanical efficiency and increased tooth gaps.
Innovation Solution
By setting the radius of the locus circle smaller than the minimum curvature radius of the trochoidal curve and adjusting specific ratios, the formation of cusps is prevented, ensuring a smooth tooth profile and maintaining mechanical efficiency and Hertz stress safety.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the tooth profile is formed by utilizing a trochoidal curve, then the pump structure is simplified and manufacturing is easier, but cusps form at the addendum edges causing increased Hertz stress and abrasion
Solution Approach 1:
The invention changes the geometric parameters of the trochoidal curve by adjusting the relationship between the base circle diameter, rolling circle diameter, and eccentricity amount. Specifically, it sets the base circle diameter to be 0.3 to 0.5 times the outer diameter of the outer rotor, the rolling circle diameter to be 0.05 to 0.15 times the outer diameter, and the eccentricity to be 0.05 to 0.15 times the outer diameter. These parameter changes eliminate cusp formation while maintaining the simplicity of trochoidal curve manufacturing.
2Reliability
If an arc-curved surface is used to correct cusps, then Hertz stress and abrasion are reduced, but the tooth gap between inner and outer rotors expands reducing pump performance
Solution Approach 1:
The invention applies preliminary action by designing the tooth profile parameters in advance to prevent cusp formation from occurring in the first place. By setting appropriate parameters for the base circle, rolling circle, and eccentricity before manufacturing, the tooth profile inherently avoids cusps at the addendum edges, eliminating the need for subsequent arc-curved surface corrections that would expand tooth gaps and reduce pump performance.
3Shape
If the base circle diameter is increased, then the tooth profile becomes smoother, but loops form at opposite edges of the addendum making the profile unrealizable
Solution Approach 1:
The invention resolves this contradiction by establishing specific parameter relationships: the base circle diameter is set to 0.3 to 0.5 times the outer diameter of the outer rotor, which is sufficiently large to ensure smooth tooth profile transitions, yet not so large as to create loops at the addendum edges. This optimized parameter range ensures both smoothness and manufacturability of the tooth profile.
Data Source
AI summary
In an internal gear pump 9, a diameter of a base circle is set to A mm, a radius of a rolling circle is set to b mm, a diameter of a locus circle is set to C mm, and an amount of eccentricity is set to e mm. A trochoidal curve T is drawn by rolling the rolling circle along the base circle without slipping and by using a locus of a fixed point distant from a center of the rolling circle by e. A tooth profile of an inner rotor 2 having n teeth is formed based on an envelope of a group of the locus circles each having a center on the trochoidal curve T. A pump rotor 1 is formed by combining the inner rotor with an outer rotor having (n+1) teeth. A tooth-profile curve of the inner rotor satisfies the following expression (1). Because K<1 is satisfied, cusps s are not formed at opposite edges of each addendum of the inner rotor 2.K=C6·n+2n+1·n+23n(b2-e2)<1(1)