Multi-domain simulation and dynamic analysis of the 3D loading and micromotion of continuous-contact helical gear pumps

Highlights

• A fully coupled multi-domain multi-physics dynamic system is presented.

• Three components of the loadings are explained and analyzed in detail.

• The patterns of 3D transient loadings and dynamics are discussed with simulation results.

• A design routine for the axial balancing mechanism of helical gear pumps is provided.

• The pattern of wear seen from experiments can be replicated by the wear model.

Abstract

This paper presents a multi-domain dynamic simulation model for continuous-contact helical gear pumps, which is an unconventional hydraulic pump design that is capable of canceling its kinematic flowrate variation. In this model, the fluid dynamics (in its lumped-element representation) are fully coupled in a closed feedback loop with other physical domains, including critical tribological interfaces, 3D dynamic loadings on the solid parts, dynamics, and micro-vibrations of the rotors. The model is compared to the analytical derivation and experimental measurements to prove its validity. The model can be used to provide predictive simulations for existing designs, or as a tool to optimize the design to provide better hydrostatic balancing for future iterations of hydraulic pump designs.

Introduction

External gear pump (EGP) is one of the most popular types of positive displacement pumps, with its advantages of simple assembly, robust operation, and low cost when compared to other types of positive displacement machines. External gear pumps have two gears that come into and out of mesh to produce flow. Typically, the external gear pump uses two identical gears rotating against each other, one gear is driven by a prime mover and it, in turn, drives the other gear. Each gear is supported by a shaft with bearings on both sides of the gear. External gear pumps have successful applications in many fields. These applications include, but are not limited to hydraulic control systems, fuel injection, automotive lubrication/transmission systems, high-pressure washings, and fluid transport systems.

In common with other positive displacement pumps, conventional external gear pumps based on involute teeth have a significant non-uniformity of the outlet flow. This non-uniformity of the flow, which is commonly referred to as flow ripple, is also associated with pressure ripple in the downstream hydraulic system and results in undesired system vibration and acoustic noise. Excessive noise emissions of hydraulic drives are preventing their applications in several sensitive application areas. Moreover, there is a recent trend in hydraulic control technology to replace the internal combustion engine as prime movers with electric motors. This trend puts the pump noise in a more prominent position. Therefore, there has been an increasing demand for low noise EGP designs.

The non-uniformity is given by both kinematics of the rotors and compressibility of the fluids. For relatively low-pressure operating conditions (<50 bar), the kinematic component is the dominant source of the ripple. Even at high-pressure operating conditions, with the compressibility of the fluids becoming significant, the kinematic component is still a major contributing factor that has to be taken into consideration. As discussed in [1], the non-uniformity given by the compressibility of the fluids decays faster than its kinematic counterpart as the impedance (resistance) of the hydraulic circuit increases. However, compared to other types of positive displacement machines, such as internal gear pumps, gerotors, and piston pumps, EGPs are considered to be a higher kinematic ripple source. This can be associated with the fact that for every tooth space volume, the volume displacement action for EGPs occurs only during the gear meshing, which corresponds to a small angular region compared to the whole revolution of the gears. Moreover, the kinematic ripple source can only be reduced by modifying the geometry of the rotor. There are many studies and patents on the minimization of the kinematic flow non-uniformity includes: Negrini [2] proposed the dual-flank EGP solution which significantly reduced the flow ripple generated by EGP based on single-flank EGPs; Manring and Kasaragadda [3] used different numbers of teeth for driver and drive gears; US Patent 5092751 [4] employs a split multi-stage spur gear pump design; Zhao and Vacca [5] performed optimization for dual-flank contact asymmetric involute spur gear pumps to reduce the kinematic flow ripple. Also, some studies have shown that the kinematic ripple in an external gear pump is affected by the porting geometry implemented in the meshing process (with the so-called relief groove) [6], [7]. As a general conclusion for traditional EGP designs based on involute teeth, it can be stated that their kinematic ripple source can only be reduced, but not eliminated.

An EGP design solution using helical rotors with a continuous-contact rotor profile was recently brought to the market. The particular geometry of the gears allows eliminating the kinematic ripple source. Besides the patents [8], [9], [10], [11], the discussion on this family of designs was pioneered by earlier researchers [12], [13], [14], [15], and the discussion is continued and still active nowadays [16], [17], [18], [19]. The previous work of the authors [20] on the design of continuous-contact helical external gear pump (CCHGP, also referred to as Helical Rotor Pump, or HRP, in some literature for example: [19]) presented an extensive geometric analysis on the working principle of this type of EGPs, and on the related kinematic features that allow eliminating the kinematic ripple. The previous work has indicated that the cancellation of the kinematic ripple source is given by the combined effect of the helical gear geometry and its continuous-contact type gear profiles. The sole use of one of two factors alone is not sufficient to reduce the kinematic ripple, and in most cases can make the situation worse. The previous work also indicates that only CCHGP designs with certain helical rotation angles manage to cancel the kinematic ripple source. CCHGP borrows most of the merits of EGPs, with its kinematic ripple source canceled, therefore it is highly suitable for the hydraulic systems that require quiet operations and no delivery flow pulsations, hydraulic elevators, forming machines, processes, and electro-hydraulic actuators for both fixed and mobile applications.

A predictive simulation of a hydraulic pump/motor is challenging, as it is a complicated multi-physics problem, which typically requires multi-domain modeling. Methods like computational fluid dynamics (CFD) could be used to analyze detailed fluid flow characteristics. However, it misses numerous other crucial factors of consideration, such as some important tribological interfaces, the dynamics and vibrations of solid components, deformations and wears of machine parts, etc. These physics beyond fluid dynamics have a critical impact on some important machine characteristics, such as mechanical and volumetric efficiency, noise emission level, the longevity of the machine, etc., and in turn, provide influences back to the fluid dynamics. As a result, solo fluid dynamics simulation, even though it can provide high-resolution fluid flow data, usually generates results that are unpractical and non-predictive.

For the modeling of piston pumps, the most common approach is to couple the dynamics model of fluid pressure in the displacement chambers with one most important lubrication gap [21], [22], [23]. For piston pumps, the most critical lubrication interface can be identified as the interface between piston and cylinder, between slipper and swash-plate, or between the cylinder block and the valve plate, depending on the particular application. For gear pumps, gear/rotor positions and the lubrication interfaces are critical to the efficiencies of pumps. A lot of past research efforts ([24], [25], [26], etc.) have focused their studies on lubrication gaps in the journal bearings and between the gear axial surface and the housing to better predicts the volumetric and mechanical efficiencies of gear pumps. However, they all limited their scope to spur gear pumps, where the gear dynamics is limited to 2D transverse plane, and symmetry with respect to the axial direction can be assumed, therefore the analysis is greatly simplified.

When it comes to helical gear pumps, especially CCHGP type gear pumps, the force experienced by the gears/rotors is challenging to analyze, given its complicated geometry. As indicated by the previous work [20], in the meshing zone and within the same toothspace, CCHGP pumps have high pressure in the volume above the axial sealing surface, and low pressure below the axial sealing surface, and this becomes one of the major sources for force imbalance. Therefore, the resulting loading for the gear has a 3D fashion: its axial component of the force and radial components of moments also need to be taken into account. As a result, the dynamics (or micro-motion) of gears will also manifest in its 3D fashion under such 3D dynamic loading. 3D rotor dynamics, such as misalignment and axial mismatching, have been found of crucial impact on the efficiencies of hydraulic pumps [27]. Although they are less discussed for external spur gear pumps, they must be addressed for helical gear pumps such as CCHGPs. To accurately predict the 3D gear dynamics and resulting lubrication gap performance and pump efficiencies, the effect of multiple lubrication gaps must be taken into consideration simultaneously, including the bearings and axial lubrication gaps on both sides of both gears.

The previous work by the authors on CCHGP [20] focused on the machine kinematics and fluid dynamics level, revealing the characters of internal pressure buildup and outlet flow/pressure ripples, however, it misses analyzing the influence of the 3D fluid-pressure distribution exerting on the 3D rotor geometry, resulting in imbalance mode of solid parts, and corresponding balancing strategy. This consideration is imperative for the design and modeling of helical gear pumps or CCHGPs; without a proper balancing of the solid parts, a helical gear pump will have very low efficiency when operating, or simply not fail to work. Also, the previous work assumed perfect axial balancing of the rotors, without providing the strategy and specific design to achieve such nearly perfect balancing. Furthermore, in order for the fluid dynamics model in the previous work to predict the flow efficiency with reasonable accuracy, it requires a sophisticated calibration or modeling of the gear positions. In other words, the model presented in [20] is an incomplete model that cannot work on itself. The missing parts, together with other challenging parts including casing wear, the vibration modes of the rotors, will be particularly addressed by the current paper, to complete the whole picture of the simulation model.

This paper presents a multi-domain multi-physics dynamical model for helical external gear pumps with complicated meshing geometry, where the fluid dynamics is fully coupled with evaluations of dynamics force/loading, dynamics and vibrations (micromotions) of rotors, computations/modeling of lubrication interfaces. The proposed model not only serves as a predictive model for existing pump designs, but also can be used as a tool for design optimization for improved designs. For example, hydrostatic balancing is an important design consideration for gear pumps, as the balancing of the solid components of a gear pump will greatly influence the performance of several important lubrication gaps, and will, in turn, affect the mechanical and volumetric efficiencies of a pump, as well as its noise emission. With such a model, better balancing mechanisms can be designed to improve the mechanical and volumetric efficiencies of this type of pump, and optimized the design of the solid parts to reduces its vibrations, noises. Also, the wear typically produced by external gear machines operated at high-pressure conditions, but in 3D fashion for helical gear pumps, can be predicted by the proposed model, which is another originality of this work.

The structure of the paper is as follows: first, the basics of the CCHGP design are introduced to support the considerations made in the rest of the paper, then the fluid-pressure dynamics model already presented by the authors in [20] is briefly reviewed and is used as a basis for the modeling work presented in this paper. Next, the force analysis will be presented, including the forces on the axial and radial surfaces of the helical gears, as well as the contact force between two gears. It is then followed by the discussion of the micro-motion model which models the dynamic response of the gears and force allocation between four sets of journal-bearings on both ends. Next, in Section 6, the results from the simulation model will be compared to analytical derivation, experimental measurements. In addition, the dynamic characteristics will be compared and discussed in different hydrostatic balancing design scenarios, shedding light on the appropriate balancing strategy of CCHGP as a highly promising hydraulic pump design.