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Complex Impedance Measurement Applied to Short-Time Contact Between Colliding Steel Surfaces

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Abstract

The complex impedance method was developed for measuring the transient behaviors of short-time contacts between colliding steel surfaces, by using an alternating current circuit with a high frequency of 500 kHz at a high sampling rate of 20 MHz. The method was applied to estimate the lubrication effects of simple test lubricants acting at a short-time contact with a duration of 110 μs occurring between a free-falling steel ball and a stationary steel plate, where to minimize the hydrodynamic lubrication effect, the test lubricant was provided on the steel plate as a homogeneous thin film with a thickness of 30 μm. An advantage of the method is in the detection of the beginning and end of the contact. Particularly for wet conditions, although they were apparently unclear in the output voltage signal from the circuit, the modulus of the complex impedance detected them with high accuracy. In addition, using the modulus and argument of the complex impedance, the metallic contact ratio and residual film thickness at the short-time contact can be estimated quantitatively. By using the metallic contact duration determined by the metallic contact ratio, the differences in the boundary lubrication effects were quantified for the selected base oils (i.e., n-decane, n-dodecane, n-tetradecane, and n-hexadecane) and the 30-mM oleic acid solutions dissolved in the base oils at the short-time contact, although the differences in the lubricants did not change the shape of the plastic indentation formed on the steel plate.

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Abbreviations

a :

Dimensionless coefficient

b :

Dimensionless coefficient

C f :

Capacitance of lubricant film

d :

Thickness of lubricant film

d min :

Residual film thickness

e r :

Coefficient of restitution

f :

Frequency

f 0 :

Frequency of alternator

\(\bar{F}\) :

Mean contact force

g :

Gravitational constant

h 0 :

Initial height of ball

I 1 :

Amplitude of I *1

I *1 :

Alternating current

j :

Imaginary unit

L :

Inductance

m :

Mass of ball

\(\bar{P}\) :

Mean contact pressure

p p :

Plastic flow pressure

r :

Radial position

R :

Resistance of fixed resistor

R m :

Resistance of metallic contact

S :

Apparent contact area

S f :

Area covered with lubricant film

S m :

Area of metallic contact

S m,max :

Maximum of S m

S m,SP :

S m during stable period

S m0 :

S m for dry condition

S m0,max :

Maximum of S m0

S max :

Maximum of S

S SP :

S during stable period

t :

Time

t A :

Time at beginning of contact

t B :

Time at end of contact

t C :

Time of branching

T MC :

Metallic contact duration

V 0 :

Amplitude of V *0

V *0 :

Alternating voltage (input voltage)

V 1 :

Amplitude of V *1

V *1 :

Alternating voltage (output voltage)

Y :

Yield stress

z :

Vertical position

Z :

Modulus of Z *

Z 0 :

Z for dry condition

Z SP :

Z during stable period

Z * :

Complex impedance of contact

Z *t :

Total complex impedance of circuit

α :

Metallic contact ratio

α max :

Maximum of α

β :

Radius of ball

δ :

Indentation depth

Δt :

Duration of contact

ε :

Permittivity of lubricant

ε 0 :

Permittivity of vacuum

ε r :

Relative permittivity

ζ :

Acceleration

η :

Viscosity

θ :

Argument of Z *

θ 0 :

θ for dry condition

θ SP :

θ during stable period

π :

Circular constant

σ :

Resistance of metallic contact for unit area

φ :

Phase difference

ω :

Angular frequency

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Authors and Affiliations

  1. Faculty of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya, Yokohama, 240-8501, Japan

    Takahiro Nihira, Kazuyoshi Manabe & Ken Nakano

  2. Department of Mechanical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika, Tokyo, 125-8585, Japan

    Chiharu Tadokoro

  3. Faculty of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama, 240-8501, Japan

    Shingo Ozaki

Authors
  1. Takahiro Nihira
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  2. Kazuyoshi Manabe
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  3. Chiharu Tadokoro
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  4. Shingo Ozaki
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  5. Ken Nakano
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Corresponding author

Correspondence to Ken Nakano.

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Nihira, T., Manabe, K., Tadokoro, C. et al. Complex Impedance Measurement Applied to Short-Time Contact Between Colliding Steel Surfaces. Tribol Lett 57, 29 (2015). https://doi.org/10.1007/s11249-015-0478-5

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