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


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.

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a :

Center distance of gear pair.

B oil :

Oil bulk modulus.

B :

Dimension of the relief grooves.

C r :

Radial clearance in the journal bearing.

C T :

Torsional viscous damping coefficient of the driving shaft.

h,l,w :

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

h rn :

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

f bxk, f byk :

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

f mg :

Meshing force.

f pxk, f pyk :

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

F ecX,F ecY :

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

F gcX,F gcY :

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

F icX,F icY :

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

F igX,F igY :

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

K T :

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.

m k :

Mass of gear k.

M m :

Motor driving torque.

M pk :

Pressure torque applied to gear k.

N :

Maximum number of isolated tooth spaces.

P b :

Base pitch.

p i :

Pressure in control volume i.

r b :

Base radius.

V i :

Volume of control volume i.

t :

Periodic time (0≤t<T).

T :

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

(x k ,y k ):

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

z :

Tooth number.

α w :

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.

θ p :

Angular pitch.

μ :

Oil dynamic viscosity.

ω :

Angular speed.

i=1,…,N :

Denotes isolated tooth space volumes (control volumes).


Denotes gears.


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Correspondence to Emiliano Mucchi.

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Mucchi, E., Dalpiaz, G. & Rivola, A. Dynamic behavior of gear pumps: effect of variations in operational and design parameters. Meccanica 46, 1191–1212 (2011). https://doi.org/10.1007/s11012-010-9376-y

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