Advertisement

Meccanica

, Volume 46, Issue 6, pp 1191–1212 | Cite as

Dynamic behavior of gear pumps: effect of variations in operational and design parameters

  • Emiliano MucchiEmail author
  • Giorgio Dalpiaz
  • Alessandro Rivola
Article

Abstract

This work presents a wide number of results about the influence that variations in terms of operational and design parameters play on the dynamic behavior of external gear pumps. These results are obtained by using a non-linear lumped-parameter kineto-elastodynamic model developed and experimentally assessed with the aim of including all the important dynamic effects. On the one hand, the effects of variations in the operational parameters—namely output pressure, rotational speed and oil viscosity—are analysed; on the other hand, the effects of modifications of some design parameters are shown: clearances and relief groove dimension. The results in terms of gear eccentricity, pressure evolution, pressure forces, gear accelerations and variable forces exciting the pump casing enlighten the dynamic behavior of gear pumps and give useful indications for design improvements and vibration and noise reduction. As regards specifically gear accelerations as well as forces exciting the casing, they strongly increase with both output pressure and rotational speed, but variations in rotational speed in the operational range give lower effects. Conversely, the modifications of the clearances give negligible effects, while the relief groove dimension is very important: the larger the relief grooves are, the higher the gear accelerations and forces exciting the casing become.

Keywords

External gear pumps Numerical dynamic analysis Gear accelerations Operational parameters Relief grooves Clearances Oil viscosity 

Nomenclature

Latin symbols

a

Center distance of gear pair.

Boil

Oil bulk modulus.

B

Dimension of the relief grooves.

Cr

Radial clearance in the journal bearing.

CT

Torsional viscous damping coefficient of the driving shaft.

h,l,w

Height, length, width of a generic fluid film element.

hrn

Radial clearance defined as the difference between the external radius of the gear and the internal radius of the casing (nominal).

fbxk,fbyk

Bearing reaction applied to gear k in directions X and Y, respectively.

fmg

Meshing force.

fpxk,fpyk

Pressure force applied to gear k in direction X and Y, respectively.

FecX,FecY

External forces applied to pump casing and plate in direction \(\mathrm{X}_{1}'\) and \(\mathrm{Y}_{1}'\), respectively.

FgcX,FgcY

Forces applied to pump casing and plate from gears in direction \(\mathrm{X}_{1}'\) and \(\mathrm{Y}_{1}'\), respectively.

FicX,FicY

Inertia forces concerning pump casing and plate in direction \(\mathrm{X}_{1}'\) and \(\mathrm{Y}_{1}'\), respectively.

FigX,FigY

Inertia forces concerning gears in direction \(\mathrm{X}_{1}'\) and \(\mathrm{Y}_{1}'\), respectively.

KT

Torsional stiffness of the driving shaft.

\(M_{ecO_{1}}\)

External moment applied to pump casing and plate about point O1.

\(M_{gcO_{1}}\)

Moment applied to pump casing and plate from gears about point O1.

\(M_{icO_{1}}\)

Inertia moment concerning pump casing and plate about point O1.

\(M_{igO_{1}}\)

Inertia moment concerning gears about point O1.

mk

Mass of gear k.

Mm

Motor driving torque.

Mpk

Pressure torque applied to gear k.

N

Maximum number of isolated tooth spaces.

Pb

Base pitch.

pi

Pressure in control volume i.

rb

Base radius.

Vi

Volume of control volume i.

t

Periodic time (0≤t<T).

T

Meshing period (T=60/nz, n is the rotational speed in rpm).

(xk,yk)

Coordinates of the centre of gear k in reference frame O k X k Y k .

z

Tooth number.

Greek symbols

αw

Pressure angle in operational conditions.

Δp

Pressure drop between adjacent control volumes.

ΔQ

Difference between the volumetric flow rate, coming into control volume i and coming out.

θ

Angular coordinate.

θp

Angular pitch.

μ

Oil dynamic viscosity.

ω

Angular speed.

Subscripts

i=1,…,N

Denotes isolated tooth space volumes (control volumes).

k=1,2

Denotes gears.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kojima E, Nagakura H (1982) Characteristic of fluidborne noise generated by fluid power pump (1st report, mechanism of generation of pressure pulsation in axial piston pump). Bull JSME, 25(199):46–53 CrossRefGoogle Scholar
  2. 2.
    Kojima E, Shinada M, Yoshino T (1984) Characteristic of fluidborne noise generated by fluid power pump (2nd report, pressure pulsation in balanced vane pump). Bull JSME, 27(225):475–482 CrossRefGoogle Scholar
  3. 3.
    Kojima E, Shirada M (1984) Characteristic of fluidborne noise generated by fluid power pump (3rd report, discharge pressure pulsation of external gear pump). Bull JSME, 27(232):2188–2195 CrossRefGoogle Scholar
  4. 4.
    Ichikawa T, Yamaguchi K (1971) On pulsation of delivery pressure of gear pump (in the case of a long delivery pipeline). Bull JSME, 14(78):1304–1312 CrossRefGoogle Scholar
  5. 5.
    Vacca A, Franzoni G, Casoli P (2007) On the analysis of experimental data for experimental gear machines and their comparison with simulation results. In: Proceedings of IMECE2007, Seattle, USA, November 11–15, 2007, pp 1–9 Google Scholar
  6. 6.
    Mucchi E, Dalpiaz G, Rivola A (2010) Elasto-dynamic analysis of a gear pump, part II: meshing phenomena and simulation results. Mech Syst Signal Process 24:2180–2197 ADSCrossRefGoogle Scholar
  7. 7.
    Dalpiaz G, del Rincón Fernández A Mucchi E, Rivola A (2005) Experimental validation of a model for the dynamic analysis of gear pumps. In: Proceedings of Novem 2005, Saint Raphael, France, April 2005 Google Scholar
  8. 8.
    Mucchi E, Dalpiaz G, Fernàndez del Rincòn A (2010) Elasto-dynamic analysis of a gear pump, part I: pressure distribution and gear eccentricity. Mech Syst Signal Process 24:2160–2179 ADSCrossRefGoogle Scholar
  9. 9.
    The Mathworks (2001) Matlab, version 6.1, release 12.1, May 2001 Google Scholar
  10. 10.
    Bonacini C, Borghi M (1990) Calcolo delle pressioni nei vani fra i denti di una macchina oleodinamica ad ingranaggi esterni. Oleodinamica-pneomatica. Novembre:128–134 Google Scholar
  11. 11.
    Mancò S, Nervegna N (1989) Simulation of an external gear pump and experimental verification. In: Proceedings of the International symposium on fluid power, Tokyo, 13–16 March 1989, pp 139–152 Google Scholar
  12. 12.
    Miccoli G, Vagnoni P (1988) Determinazione per via sperimentale dei carichi sul corpo di una pompa ad ingranaggi esterni. Oleodinamica-pneumatica, Novembre:145–155 Google Scholar
  13. 13.
    Mancò S, Nervegna N (1993) Pressure transients in an external gear hydraulic pump. In: Proceedings of the 2nd international symposium on fluid power, Tokyo, 6–9 September 1993, pp 221–228 Google Scholar
  14. 14.
    Childs D, Moes H, Van Leeuwen H (1977) Journal bearing impedance descriptions for rotordynamic application. J Lubr Technol 99:198–214 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Emiliano Mucchi
    • 1
    Email author
  • Giorgio Dalpiaz
    • 1
  • Alessandro Rivola
    • 2
  1. 1.Engineering Department in FerraraUniversità degli Studi di FerraraFerraraItaly
  2. 2.DIEMUniversity of BolognaBolognaItaly

Personalised recommendations