SME
Biomaterials
Implant design
Use this for “A hip liner with k = 1 × 10⁻⁶ mm³/(N·m) carries 2000 N and slides 20 mm a step, a million steps a year. How much wears away each year?”
Chart
One year: 5 × 40 mm³
This is an example. Type your own values to start a new problem.
V (mm³/yr)
=
k (mm³/(N·m))
×
F (N)
×
s (mm)
×
n
Vₜ (mm³)
=
V (mm³/yr)
×
t (years)
Formulas
V
=
k
×
F
×
s
×
n
40
=
1 ×
10
-6
×
2,000
×
0.02
×
1,000,000
Vₜ
=
V
×
t
200 = 40 × 5
Formulas are worked in m. The step-by-step shows the conversions.
Assumptions
•
Archard’s law: the volume worn grows with the load and the sliding distance, V = kF × distance.
•
One step is one gait cycle: the head slides the distance s across the liner once.
•
The wear factor k stays the same year after year, so the wear adds up evenly.
Step-by-step
WE KNOW
k = 1 × 10⁻⁶ mm³/(N·m), F = 2,000 N, s = 20 mm, n = 1,000,000, t = 5 years
FIND
wear each year (V), total wear (Vₜ)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to m).
s = 20 mm = 0.02 m (1 m = 1000 mm)
Step 2 · Find wear each year (V)
Use V = k × F × s × n
Archard’
s
law:
the
wear
factor
times
the
load
times
the
distance
slid
in
the
year,
s
times
n
.
V
=
10
-6
×
2,000
×
0.02
×
1,000,000
V
=
0.002
×
0.02
×
1,000,000
V
=
(4
×
10
-5
)
×
1,000,000
V
=
40
mm³/yr
Step 3 · Find total wear (Vₜ)
Use Vₜ = V × t
The same wear each year, so multiply by the years.
Vₜ = 40 × 5
Vₜ = 200 mm³
Check
Put the numbers back in. Both sides should match.
40
=
10
-6
×
2,000
×
0.02
×
1,000,000
✓
200 = 40 × 5 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.