, Volume 47, Issue 1, pp 51–61 | Cite as

Experimental contact pattern analysis for a gear-rack system

  • Massimiliano Pau
  • Bruno Leban
  • Antonio Baldi
  • Francesco Ginesu


Gears perform their main task, namely load transmission, by means of very small contact areas originated by tooth interaction and thus, the analysis of phenomena occurring at the interface between mating teeth represents a critical issue in ensuring the optimal functioning of such devices. Nevertheless, while literature proposes a huge amount of numerical tooth contact analyses (TCA), a lack of experimental validation of such approaches is to be noted, since it is extremely difficult to inspect a contact interface which is, by its own nature, closed towards the outside world. One of the most promising techniques employed in investigating contact in metallic interfaces is based on the use of high frequency ultrasonic waves; their reflection from the interface (which is known to be related to contact conditions) can be graphically processed to build maps from which it is possible to assess geometrical features of the nominal contact area and, after a suitable calibration procedure, contact pressure distribution.

This study proposes the application of the ultrasonic method to investigate the contact of a tooth belonging to a spur gear with a plane, thus reproducing the case of a gear-rack system. Experimental tests were carried out under different conditions, including regular contacts, misalignments and excessive waviness of the teeth; in all cases analyzed, this technique exhibited interesting capabilities in faithfully reproducing the contact features, thus allowing us to state that it may represent a useful tool in arriving at a deeper insight into contact problems in gears and, above all, in effectively validating numerical TCA and wear models.


Spur gears Experimental Ultrasonic analysis Tooth contact analysis Contact area Contact pressure 



Tooth Contact Analysis


Non-Destructive Testing


Real Contact Area


Acoustic impedance of a medium


Reflection coefficient of the ultrasound wave


Finite Element


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Timoshenko S, Baud RV (1926) The strength of gear teeth. Mech Eng 48:1105–1109 Google Scholar
  2. 2.
    Jacobsen M (1955) Bending stresses in spur gear teeth: proposed new design factors based on a photoelastic investigation. Proc Inst Mech Eng 169:587–609 CrossRefGoogle Scholar
  3. 3.
    Allison IM, Hearn EJ (1980) A new look at the bending strength of gear teeth. Exp Mech 20(7):217–225 CrossRefGoogle Scholar
  4. 4.
    Rubayi NA, Tam HW (1979) Three-dimensional photoelastic study of stresses in rack gears. Exp Mech 19(5):153– 159 CrossRefGoogle Scholar
  5. 5.
    Shimamura S, Noguchi Y (1967) An analytical determination of speed factor in gear designs. Exp Mech 7(5):218–223 CrossRefGoogle Scholar
  6. 6.
    Lingaiah K, Ramachandra K (1977) Three-dimensional photoelastic study of the load-carrying capacity/face width ratio of Wildhaber-Novikov gears for automotive applications. Exp Mech 17(10):392–397 CrossRefGoogle Scholar
  7. 7.
    Lingaiah K, Ramachandra K (1976) Photoelastic optimization of the profiles of Wildhaber-Novikov gears. Exp Mech 16(3):116–120 CrossRefGoogle Scholar
  8. 8.
    Gamez-Montero PJ, Castilla R, Khamashta M, Codina E (2006) Contact problems of a trochoidal-gear pump. Int J Mech Sci 48(12):1471–1480 CrossRefMATHGoogle Scholar
  9. 9.
    Winter H, Höhn BR, Michaelis K, Kagerer E (1991) Measurement of pressure, temperature and film thickness in disk and gear contacts. In: Proc of the JSME international conference on motion and power transmissions, Hiroshima, Nov 23–26, pp 1038–1042 Google Scholar
  10. 10.
    Kagerer E, Königer ME (1989) Ion beam sputter deposition of thin film sensors for applications in highly loaded contacts. Thin Solid Films 182(1–2):333–344 CrossRefADSGoogle Scholar
  11. 11.
    Li S (2007) Effects of machining errors, assembly errors and tooth modifications on loading capacity, load-sharing ratio and transmission error of a pair of spur gears. Mech Mach Theory 42(6):698–726 CrossRefMATHGoogle Scholar
  12. 12.
    Li S (2007) Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors, assembly errors and tooth modifications. Mech Mach Theory 42(1):88–114 CrossRefMATHADSGoogle Scholar
  13. 13.
    Falah B, Gosselin C, Cloutier L (1998) Experimental and numerical investigation of the meshing cycle and contact ratio in spiral bevel gears. Mech Mach Theory 33(1–2):21–37 CrossRefMATHGoogle Scholar
  14. 14.
    Zhang J, Fang Z, Cao X, Deng X (2007) The modified pitch cone design of the hypoid gear: manufacture, stress analysis and experimental tests. Mech Mach Theory 42(2):147–158 CrossRefMATHGoogle Scholar
  15. 15.
    Luscher A, Houser D, Snow C (2000) An investigation of the geometry and transmission error of injection molded gears. J Inj Molding Technol 4(4):177–190 Google Scholar
  16. 16.
    Rademacher J (1968) Einfluss von Flankenrichtungsfehlern und Breitenballigkeiten auf die Tragfähikeit von Stirnradgetrieben. Ind-Anz 90(44):915–921 Google Scholar
  17. 17.
    International Organization for Standardization (1998) Technical report ISO/TR 10064-4, cylindrical gears—code of inspection practice—part 4: recommendations relative to surface texture and tooth contact pattern checking Google Scholar
  18. 18.
    Krachter H (1958) Einneuartiges verfahren zur messung von druckkraften mit ultraschall. Werkstatt Betr 5:246–248 Google Scholar
  19. 19.
    Masuko M, Ito Y (1969) Measurement of contact pressure by means of ultrasonic waves. Ann CIRP XVII:289–296 Google Scholar
  20. 20.
    Kendall K, Tabor D (1971) An ultrasonic study of the area of contact between stationary and sliding surfaces. Proc R Soc Lond Part A 323:321–340 CrossRefADSGoogle Scholar
  21. 21.
    Pau M (2005) Ultrasonic waves for effective assessment of wheel-rail contact anomalies. Proc Inst Mech Eng, F J Rail Rapid Transit 219:79–90 CrossRefGoogle Scholar
  22. 22.
    Aymerich F, Pau M (2004) Assessment of nominal contact area parameters by means of ultrasonic waves. J Tribol 126(4):639–645 CrossRefGoogle Scholar
  23. 23.
    Dwyer-Joyce RS, Drinkwater BW (2004) In situ measurement of contact area and pressure distribution in machine elements. Tribol Lett 14(1):41–52 CrossRefGoogle Scholar
  24. 24.
    Pau M, Leban B, Baldi A (2006) Experimental analysis of contact for the indentation of a flat rounded punch. Int J Solids Struct 43(25–26):7959–7965 CrossRefGoogle Scholar
  25. 25.
    Pau M, Aymerich F, Ginesu F (2001) Ultrasonic measurements of nominal contact area and contact pressure in a wheel-rail system. Proc Inst Mech Eng, F J Rail Rapid Transit 214(F4):231–244 Google Scholar
  26. 26.
    Pau M, Leban B, Baldi A (2008) Ultrasonic measurements of contact area and pressure distribution of a pneumatic tire on a rigid surface. Tire Sci Technol 36(1):43–62 CrossRefGoogle Scholar
  27. 27.
    Marshall MB, Lewis R, Dwyer-Joyce RS (2006) Characterisation of contact pressure distribution in bolted joints. Strain 42(1):31–43 CrossRefGoogle Scholar
  28. 28.
    Pau M, Baldi A (2007) Application of an ultrasonic technique to assess contact performance of bolted joints. J Press Vessel Technol 122(1):175–185 CrossRefGoogle Scholar
  29. 29.
    Marshall MB, Lewis R, Drinkwater BW, Dwyer-Joyce RS (2004) An ultrasonic approach for contact stress mapping in machine joints and concentrated contacts. J Strain Anal Eng Des 39(4):339–350 CrossRefGoogle Scholar
  30. 30.
    Pau M, Aymerich F, Ginesu F (2002) Distribution of contact pressure in wheel-rail contact area. Wear 253(1–2):265–274 CrossRefGoogle Scholar
  31. 31.
    Aymerich F, Pau M, Ginesu F (2003) Evaluation of nominal contact area and contact pressure distribution in a steel-steel interface by means of ultrasonic techniques. JSME Int J Ser C Mech Syst Mach Elem Manuf 46(1):297–304 Google Scholar
  32. 32.
    Quinn AM, Drinkwater BW, Dwyer-Joyce RS (2002) The measurement of contact pressure in machine elements using ultrasound. Ultrasonics 39(7):495–502 CrossRefGoogle Scholar
  33. 33.
    Váradi K, Kozma M, Poller R (1995) The effect of surface roughness on contact and stress states of spur gears. Tribotest J 2(1):25–35 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Massimiliano Pau
    • 1
  • Bruno Leban
    • 1
  • Antonio Baldi
    • 1
  • Francesco Ginesu
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of Cagliari, Piazza d’ArmiCagliariItaly

Personalised recommendations