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


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.

This is a preview of subscription content, log in to check access.


b b :

Bearing block width (see Fig. 1b).

b k :

Face width of gear k.

B oil :

Oil bulk modulus.

C r :

Radial clearance in journal bearings.

f bxk :

Bearing reaction applied to gear k in direction X.

f byk :

Bearing reaction applied to gear k in direction Y.

f mgm :

Mean meshing force over one pitch.

f pxk :

Pressure force applied to gear k in direction X.

f pyk :

Pressure force applied to gear k in direction Y.

f pxkm :

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

f pykm :

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

h b :

Radial clearance between casing and bearing blocks.

h rn :

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

h wk :

Radial thickness of removed material for gear k.

M m :

Motor driving torque.

M pk :

Pressure torque applied to gear k.

M pkm :

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

p :

Pressure in the generic control volume.

p i :

Pressure in isolated tooth space i.

p in :

Pressure in the inlet volume.

p out :

Pressure in the outlet volume.

p t :

Pressure in the trapped volume.

R b :

Journal bearing radius

r bk :

Base radius of gear k.

r ext :

Outside radius of gears.

r k :

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

V :

Volume of the generic control volume.

V i :

Volume of the isolated tooth space i.

W kj :

Volume of removed material by gear k during step j.

W Tj :

Volume of removed material by both gears during step j.

(x k ,y k ):

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

z k :

Number of teeth of gear k.

α w :

Pressure angle in working conditions.

ΔQ :

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

θ :

Angular displacement.

θ k :

Angular displacement of gear k.

θ p :

Angular pitch.

μ :

Lubricant dynamic viscosity.

ρ :

Oil density.

ψ k :

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

ψ ink :

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

ψ outk :

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

ω :

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

i :

Denotes isolated spaces between teeth.

j :

Denotes running in steps.


Denotes gears.

| k :

Applied to gear k.

n, m :

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


  1. 1.

    Frith RH, Scott W (1996) Comparison of an external gear pump wear model with test data. Wear 196:64–71

    Article  Google Scholar 

  2. 2.

    Frith RH, Scott W (1994) Wear in external gear pumps. Wear 172:121–126

    Article  ADS  Google Scholar 

  3. 3.

    Gellrich R, Kunz A, Beckmann G, Broszeit E (1995) Theoretical and practical aspects of the wear of vane pumps. Part A. Adaptation of a model for predictive wear calculation. Wear 181–183:862–867

    Google Scholar 

  4. 4.

    Tian HH, Addie GR, Pagalthivarthi KV (2005) Determination of wear coefficients for erosive wear prediction through Coriolis wear testing. Wear 259:160–170

    Article  Google Scholar 

  5. 5.

    Koç E, Kurbant AO, Hooke CJ (1997) An analysis of the lubrication mechanisms of the bush-type bearings in high pressure pumps. Tribology Internationl 30(8):553–560

    Article  Google Scholar 

  6. 6.

    Koç E, Hooke CJ (1997) An experimental investigation into the design and performance of hydrostatically loaded floating wear plates in gear pumps. Wear 209:184–192

    Article  Google Scholar 

  7. 7.

    Paltrinieri F, Milani M, Borghi M (2002) Modelling and simulation hydraulically balance external gear pumps. In: 2nd international FPNI PhD symposium of fluid power, Modena, Italy, 3–6 July 2002

    Google Scholar 

  8. 8.

    Borghi M, Milani M, Paltrinieri F, Guidetti M (2001) Influenza del rodaggio sulle condizioni di funzionamento di macchine volumetriche ad ingranaggi esterni. In: Proceedings of the 56th ATI national congress, Naples, 10–14 September 2001, pp 69–79 (in Italian)

    Google Scholar 

  9. 9.

    Mucchi E (2007) Dynamic analysis of external gear pumps by means of non linear models and experimental techniques. PhD thesis, EnDIF—Engineering Department in Ferrara, Ferrara, Italy, March 2007

  10. 10.

    Mucchi E, Dalpiaz G, Rivola A (2010) Elasto-dynamic analysis of a gear pump. Part II. Meshing phenomena and simulation results. Mechanical Systems and Signal Processing 24:2180–2197

    Article  ADS  Google Scholar 

  11. 11.

    Dalpiaz G, Mucchi E, D’Elia G, Fernández del Rincón A (2006) Pressure phenomena in dynamic analysis of external gear pumps. In: Proceedings of international conference on noise and vibration engineering, Leuven, Belgium, pp 3605–3620

    Google Scholar 

  12. 12.

    Dalpiaz G, Fernández del Rincón 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, pp 1–12

    Google Scholar 

  13. 13.

    Borghi M, Milani M, Toderi G (1996) Sul calcolo della spinta sulle fiancate nelle macchine oleodinamiche ad ingranaggi esterni. In: Proceedings of the 51st ATI national congress, Udine, Italy, 16–20 September 1996, pp 1675–1688 (in Italian)

    Google Scholar 

  14. 14.

    Borghi M, Dilani D, Paltrinieri F, Zardin B (2005) Studying the axial balance of external gear pumps. In: SAE international

    Google Scholar 

  15. 15.

    Mucchi E, Dalpiaz G, Rivola A (2010) Dynamic behaviour of gear pumps: effect of variations in operational and geometrical parameters. Meccanica 18:1–22

    Google Scholar 

  16. 16.

    Mucchi E, Dalpiaz G, Fernàndez del Rincòn A (2010) Elasto-dynamic analysis of a gear pump. Part I. Pressure distribution and gear eccentricity. Mechanical Systems and Signal Processing 24:2160–2179

    Article  ADS  Google Scholar 

  17. 17.

    Kuang JH, Yang YT (1992) An estimate of mesh stiffness and load sharing ration of a spur gear pair. In: International power transmission and gearing conference. ASME, New York

    Google Scholar 

  18. 18.

    Bonacini C, Borghi M (1991) Calcolo delle pressioni nei vani fra i denti di una macchina oleodinamica ad ingranaggi esterni. Oleodinamica-Pneumatica (in Italian)

  19. 19.

    Childs D, Moes H, Van Leeuwen H (1977) Journal bearing impedance descriptions for rotordynamic application. Transactions of the ASME 99(2):198–214

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Emiliano Mucchi.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mucchi, E., D’Elia, G. & Dalpiaz, G. Simulation of the running in process in external gear pumps and experimental verification. Meccanica 47, 621–637 (2012).

Download citation


  • Gear pump
  • Running in process
  • Simulation
  • Experimental verification