Meccanica

, Volume 47, Issue 3, pp 621–637

# Simulation of the running in process in external gear pumps and experimental verification

• Emiliano Mucchi
• Gianluca D’Elia
• Giorgio Dalpiaz
Article

## Abstract

Before marketing external gear pumps are subjected to a running in process to increase their efficiency. However, this is one of the most time-consuming tasks of the entire manufacturing process. Therefore, a mathematical model for optimizing the running in process can be a useful tool for time-to-market reduction. In particular, in this paper a model for the analysis of the dynamic behaviour of external gear pumps, developed by the authors in previous works, is modified and used for simulating the running in process. The modified model is presented and validated via experimental data. A good correlation between simulation and test results guarantees the effectiveness of the model in determining the amount and the distribution of the removed material during the running in process. A meaningful reduction (16%) of the global running in time has been achieved with the introduction of a modified running in process drawn from simulation results.

## Keywords

Gear pump Running in process Simulation Experimental verification

## Latin symbols

bb

Bearing block width (see Fig. 1b).

bk

Face width of gear k.

Boil

Oil bulk modulus.

Cr

Radial clearance in journal bearings.

fbxk

Bearing reaction applied to gear k in direction X.

fbyk

Bearing reaction applied to gear k in direction Y.

fmgm

Mean meshing force over one pitch.

fpxk

Pressure force applied to gear k in direction X.

fpyk

Pressure force applied to gear k in direction Y.

fpxkm

Mean value over one pitch of pressure force applied to gear k in direction X.

fpykm

Mean value over one pitch of pressure force applied to gear k in direction Y.

hb

Radial clearance between casing and bearing blocks.

hrn

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

hwk

Radial thickness of removed material for gear k.

Mm

Motor driving torque.

Mpk

Pressure torque applied to gear k.

Mpkm

Mean value over one pitch of pressure torque applied to gear k.

p

Pressure in the generic control volume.

pi

Pressure in isolated tooth space i.

pin

Pressure in the inlet volume.

pout

Pressure in the outlet volume.

pt

Pressure in the trapped volume.

Rb

rbk

Base radius of gear k.

rext

Outside radius of gears.

rk

Radius of the contact point for gear k (see Fig. 5, the expressions are given in [10]).

V

Volume of the generic control volume.

Vi

Volume of the isolated tooth space i.

Wkj

Volume of removed material by gear k during step j.

WTj

Volume of removed material by both gears during step j.

(xk,yk)

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

zk

Number of teeth of gear k.

## Greek symbols

αw

Pressure angle in working conditions.

ΔQ

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

θ

Angular displacement.

θk

Angular displacement of gear k.

θp

Angular pitch.

μ

Lubricant dynamic viscosity.

ρ

Oil density.

ψk

Angle coordinate along the casing housing for gear k (Fig. 1).

ψink

Angle limiting the isolated tooth spaces at the inlet side for gear k.

ψoutk

Angle limiting the isolated tooth spaces at the outlet side for gear k.

ω

Mean angular speed of gears in steady-state operational conditions.

## Subscripts

i

Denotes isolated spaces between teeth.

j

Denotes running in steps.

k=1,2

Denotes gears.

|k

Applied to gear k.

n, m

Number of isolated tooth spaces for gear 1 and 2, respectively.

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## Authors and Affiliations

• Emiliano Mucchi
• 1
Email author
• Gianluca D’Elia
• 1
• Giorgio Dalpiaz
• 1
1. 1.Department of EngineeringUniversity of FerraraFerraraItaly