VM191

VM191
Hertz Contact Between Two Cylinders

Overview

Reference:

N. Chandrasekaran, W. E. Haisler, R. E. Goforth, "Finite Element Analysis of Hertz Contact Problem with Friction", Finite Elements in Analysis and Design, Vol. 3, 1987, pp. 39-56.

Analysis Type(s):

Static Analysis (ANTYPE = 0)

Element Type(s):

2D/3D Node-to-Surface Contact Elements (CONTA175)

2D Structural Solid Elements (PLANE182)

3D Structural Solid Elements (SOLID185)

Input Listing:

vm191.dat

Test Case

Two long cylinders of radii R₁ and R₂, in frictionless contact with their axes parallel to each other are pressed together with a force per unit length, F. Determine the semi-contact length b and the approach distance d.

Figure 294: Hertz Contact Between Two Cylinders Problem Sketch

Material Properties

Geometric Properties

Cylinder 1:

E₁ = 30000 N/mm²

ν₁ = 0.25

Cylinder 2:

E₂ = 29120 N/mm²

ν₂ = 0.3

R₁ = 10 mm

R₂ = 13 mm

F = 3200 N/mm

Analysis Assumptions and Modeling Notes

Each analysis uses two load steps; in the first load step a small imposed displacement is used on the upper cylinder to engage contact, whereas in the second load step the imposed displacement is deleted and the force load is applied.

The problem is solved in four different ways:

Contact Algorithm: Augmented Lagrangian - KEYOPT(2) = 0

2D analysis with PLANE182 and CONTA175
3D analysis with SOLID185 and CONTA175

Contact Algorithm: Lagrange Multiplier - KEYOPT(2) = 3

2D analysis with PLANE182 and CONTA175
3D analysis with SOLID185 and CONTA175

Plane stress condition is modeled using a unit thickness slice through the cylinders. The region modeled is shown shaded in the problem sketch. The ESURF command is used to automatically generate the contact and target elements between "contactor" nodes on the upper cylinder and "target" nodes on the lower cylinder. The default value of contact stiffness FKN is chosen while performing a solution using Augmented Lagrangian contact algorithm (KEYOPT(2) = 0) whereas no contact stiffness input is required to be specified while performing a solution using Lagrange Multiplier contact algorithm (KEYOPT(2) = 3).

Results Comparison

		Target	Mechanical APDL	Ratio
CONTA175 - Algorithm: Augmented Lagrangian KEYOPT(2) = 0
PLANE182	d,mm	-0.4181	-0.4219	1.009
PLANE182	b,mm	1.20	1.1609	0.967
SOLID185	d,mm	-0.4181	-0.4280	1.024
SOLID185	b,mm	1.20	1.1609	0.967
CONTA175 - Algorithm: Lagrange Multiplier KEYOPT(2) = 3
PLANE182	d,mm	-0.4181	-0.4181	1.000
PLANE182	b,mm	1.20	1.1609	0.967
SOLID185	d,mm	-0.4181	-0.4190	1.002
SOLID185	b,mm	1.20	1.1609	0.967