Gear Tooth Profile Cubic Curve Modification for Noiseless Pump Operation
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Solution Overview
Problem
Conventional rotary gear pumps with involute gears experience discontinuous contact paths, leading to rippled pressure and noise, making them unsuitable for high-precision and high-stability applications, and they can be damaged by trapped pressurized incompressible fluids during gear meshing.
Innovation Solution
A method to form a gear tooth profile using a cubic curve to modify the standard rack, ensuring the contact path is smooth and continuous, thereby preventing encapsulation and noise, by tangentially contacting the cubic curve with the basic tooth shape at specific points and parameterizing its coefficients with pressure angle, total tooth depth, and tooth width.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If involute gears are used in rotary gear pumps, then the gear structure is simple and easy to manufacture, but the contact path is discontinuous causing rippled pressure and noise
Solution Approach 1:
The patent applies curvature by replacing the straight-line contact segments of involute gears with a continuous curved contact path. The cubic curve is used to modify the rack tooth profile, creating a gear system where the contact path follows a smooth continuous curve rather than alternating between straight lines and arcs. This curvature transformation eliminates the discontinuities that cause pressure ripples and noise while maintaining manufacturing feasibility through the systematic cubic curve modification method.
Solution Approach 2:
The patent changes the geometric parameters of the gear tooth profile by introducing a cubic curve modification to the standard rack profile. The cubic curve coefficients are determined based on specific geometric constraints (tangential contact at midpoints of addendum, lateral, and dedendum), transforming the traditional involute parameters into a new parameter set that ensures continuous smooth contact. This parameter transformation resolves the contradiction by optimizing the contact path geometry while preserving the underlying gear generation process.
2Device complexity
If involute gears mesh with point contacts, then the gear structure is simple, but encapsulation forms trapping incompressible fluid and damaging the machine
Solution Approach 1:
The continuous curved contact path created by the cubic curve modification eliminates the point-contact moments that lead to encapsulation. By ensuring that the contact path maintains continuous tangential contact between gear teeth throughout the meshing process, the design prevents the formation of closed fluid pockets. The curved geometry ensures that fluid can continuously escape from the meshing zone, preventing pressure buildup that would damage the machine while maintaining relatively simple gear structures.
3Object-generated harmful factors
If a smooth continuous contact path is achieved, then noiseless operation and stable fluid supply are realized, but the tooth profile modification increases manufacturing complexity
Solution Approach 1:
The patent segments the tooth profile modification process into systematic steps: first establishing the cubic curve based on geometric constraints (tangential contact at three specific points), then using this curve to modify the rack profile, and finally generating the gear teeth through standard gearing processes. This segmentation of the modification process makes the complex manufacturing task manageable and repeatable, reducing the practical manufacturing complexity while achieving the smooth continuous contact path necessary for noiseless operation and stable fluid supply.
Solution Approach 2:
The cubic curve coefficients are determined through parameter relationships based on fundamental gear parameters (pressure angle, tooth depth, tooth width). By expressing the curve parameters in terms of these standard gear parameters, the modification process becomes systematically controllable and manufacturable. This parameter linkage ensures that the smooth contact path can be achieved through routine manufacturing processes rather than requiring complex custom fabrication, thus resolving the contradiction between performance improvement and manufacturing ease.
Data Source
AI summary
The present invention discloses a gear and a method for forming a tooth profile thereof. In the method of the present invention, a cubic curve is used to modify a basic tooth shape of a standard rack to obtain an amended basic tooth shape, wherein the cubic curve contacts tangentially with the basic tooth shape at the midpoint of a dedendum, a midpoint of a lateral and a midpoint of an addendum of the basic tooth shape. The amended basic tooth shape is reproduced to obtain an amended rack, and the amended rack is further used to generate a tooth profile of a desired gear.