The concept of conjugate curves is put forward based on the definition of continuous and tangent contact, and the basic conditions of conjugation contact between a pair of conjugate curves are given. The fundamental principle of conjugate curves for gear transmission is provided: The normal vector to arbitrary direction of contact angle is calculated; the meshing equation is derived and the necessary and sufficient conditions of conjugation meshing for these curves are demonstrated simultaneously; the corresponding conjugated curve can be identified and line of action is also deduced with this method. A general conjugation model is therefore established according to the aforementioned theory and the result is demonstrated with parallel axis gearing as well as cylindrical helix. The geometric properties of conjugation in arbitrary contact angle direction are revealed and the characteristics of meshing motion of conjugate curves are discussed. The versatility of the principle and the outstanding contact features become obvious with treating any gear transmission. The freedom of selecting contact curve suggests the possibility of optimal conjugation design. The results provide a new method for the generation of gear tooth profile and lay a solid foundation for the further study of the gear meshing theory of conjugate curves.

The Principle of Conjugate Curves for Gear Transmission

In view of the axial force produced in the working process of double arc helical gear hydraulic pump, the theory of differential equation of curve and curved surface was utilized so that the calculation formula of axial force was obtained and the relationship between the axial force and structure parameters of gears was clarified. In order to balance the axial force, the pressure oil in the high pressure area was introduced into the end face of the plunger to press the plunger against the gear shaft, and the hydrostatic bearing whose type is plunger at the end of the shaft was designed. In order to verify the balance effect of axial force, the leakage owing to end clearance and volume efficiency of gear hydraulic pump before and after the balancing process was analyzed. This paper provides a new analysis idea and balance scheme for the axial force produced in the working process of the double arc helical gear hydraulic pump, which can reduce the leakage owing to end clearance caused by the axial force and improve the volume efficiency of the gear hydraulic pump.

Analysis of axial force of double circular arc helical gear hydraulic pump and design of its balancing device

The most widely of hydraulic applications power employed source that including low manufacturing costs and good performance are defined as the external gear pumps. In this study, the using of unstandard gears and influence on the performance of gear pumps are studied. These influences include pulsation factor of flow rate, flow rate of pump and trapped volume between two meshing gears. Matlab software has been used to evaluate performance by modifying algorithm and deriving the equations of pump flow rate. The unstandard gear is used in the study undertaken with +0.3 Rack shift coefficient. Results indicated the using of unstandard gears increase flow rate and reduce the trapped volume and pulsation flow rate factor. It was concluded that the factor of pulsation flow rate reduces as increase of teeth number which leads to pulsation flow rate stabilization.

Numerical Analysis of Standard - Unstandard Gears for an External Gear Pumps

For solving the problems that the flux and pressure of involute gear pump are pulsatile,single arc gear pump for the instant displacement and displacement are analyzed by the way of sweeping area.The law of the change and the key influence factor is studied.Comparing with involute gear pump,the instant displacement is in direct proportion to the angular velocity of the gear and stable without pulsation.The displacement of single arc gear pump is only associate with it is own paramerer with out the effect of the movement.

Analysis of Single Arc Gear Pump for Flow Output Property

A new tooth profile gear,involute-circular gear,is proposed by integrating involute gear's advantageous edges with circular tooth gear's advantages in this research.The concept of involute-circular gear is also defined,namely that choosing two single-valued curves which are corresponding engaged from the involute profiles between driving and driven wheels respectively,and replacing involute profile with the convex and concave circular arc separately to form new tooth profile at any point of these curves.According to differential geometry,the equation of tooth surface is established based on method of coordinates transformation.Insensitivity to central distance variation on involute-circular gear is discussed.The analyzed results indicate that the transformation ratio remains still unchanged as long as the gear pair can keep meshing drive,even if central distance generates change.An example of this gearing was presented and calculated,and 3D models of a pair of gears are established.The results offer theoretical supports for further studies on the involute-circular gear and reference value for the design and machining of gear.

Generation Principle and Mathematical Models of Involute-circular Gear

Aiming at the problems of the general involute external gear pump, a gear pump with double circular arc helical gear as motion pair is proposed. Based on the comparison and analysis of their meshin...

https://journals.sagepub.com/doi/pdf/10.1177/1687814018767003

Weifeng Han

Papers

Profile design and displacement analysis of the low pulsating gear pump

A New Linear Cutting Experimental Machine for Disc-Cutter Rock Breaking with High-Pressure Water Jets Assisted