METHOD FOR DETERMINING THE WORN SHAPE OF A DEFORMABLE BODY
The invention features a method for determining the worn shape of a deformable body in sliding contact with a deformable substrate. A wear depth w in an inward normal direction is determined at select points on a surface of the deformable body at each point in time t by integration of the following equation: dw d τ = kT n v b where k is a material dependent variable determined by physical tests, T n is a contact pressure determined by finite element analysis of the deformable body in sliding contact with the deformable substrate at each point in time t, v is a constant sliding velocity between the deformable body and the deformable substrate, b is a constant determined by physical tests, and τ=t b is a computational time.
1 . A method for determining the worn shape of a deformable body in sliding contact with a deformable substrate comprising: determining a wear depth w in an inward normal direction at select points on a surface of the deformable body at each point in time t by integration of the following equation:
dw
d
τ
=
kT
n
v
b
where k is a material dependent variable determined by physical tests, T n is a contact pressure determined by finite element analysis of the deformable body in sliding contact with the deformable substrate at each point in time t, v is a constant sliding velocity between the deformable body and the deformable substrate, b is a constant, and τ=t b is a computational time.
2 . The method of claim 1 wherein computer software is used to determine the worn shape of the deformable body.
3 . The method of claim 1 wherein for mass loss data {M i }, i=1, . . . , n, observed at time {t i }, i=1, . . . , n, the material variable k and constant b are determined by minimization of the sum of squared residuals, SSR, between the mass loss data M i and the predicted mass loss m i with respect to the constants to be determined wherein
m
i
=
ρ
kN
(
vt
i
)
b
SSR
=
∑
i
=
1
n
(
M
i
-
m
i
)
2
and ρ is the density of the deformable body.
4 . The method of claim 1 wherein the deformable substrate comprises an abrasive felt.
5 . The method of claim 1 wherein the deformable substrate comprises a human skin-like substrate.
6 . The method of claim 1 wherein the deformable substrate comprises a substrate of human skin.
7 . The method of claim 1 wherein the deformable body comprises a lubricating member on a razor cartridge.
8 . The method of claim 1 wherein the material dependent variable k is a function of the process used in making the lubricating member.
9 . The method of claim 8 wherein the material dependent variable k is a function of the process conditions used in making the lubricating member.
10 . The method of claim 1 wherein the material dependent variable k is a function of the chemical formulation of the lubricating member.
11 . The method of claim 1 wherein the sliding contact is a finite sliding contact.
12 . A method for selecting a deformable body to be inserted into a razor blade cartridge, said method comprising the steps of:
a. selecting a desirable wear rate value for the deformable body,
b. providing a first deformable body,
c. providing a second deformable body different from the first deformable body,
d. determining a wear rate value over a defined period of time of the first deformable body and the second deformable body according to the following method:
i. determining a wear depth w in an inward normal direction at select points on a surface of the deformable body at each point in time t by integration of the following equation:
dw
d
τ
=
kT
n
v
b
where k is a material dependent variable determined by physical tests, T n is a contact pressure determined by finite element analysis of the deformable body in sliding contact with the deformable substrate at each point in time t, v is a constant sliding velocity between the deformable body and the deformable substrate, b is a constant, and τ=t b is a computational time,
e. selecting the deformable body from either the first deformable body or the second deformable body having the wear rate value closest to the desirable wear rate value.
13 . The method of claim 12 wherein the deformable body is secured on a razor cartridge.
14 . The method of claim 12 wherein computer software is used to determine the wear rate value of the first and second deformable body.
15 . The method of claim 12 wherein for mass loss data {M i }, i=1, . . . , n, observed at time {t i }, i=1, . . . , n, the material variable k and constant b are determined by minimization of the sum of squared residuals, SSR, between the mass loss data M i and the predicted mass loss m i with respect to the constants to be determined wherein
m
i
=
ρ
kN
(
vt
i
)
b
SSR
=
∑
i
=
1
n
(
M
i
-
m
i
)
2
and ρ is the density of the deformable body.
16 . The method of claim 12 wherein the deformable substrate comprises an abrasive felt.
17 . The method of claim 12 wherein the deformable substrate comprises a human skin-like substrate.
18 . The method of claim 13 wherein the deformable body is secured on the razor cartridge with an adhesive.
19 . The method of claim 13 wherein the deformable body is secured on the razor cartridge with mechanical securement.
20 . The method of claim 12 wherein the material dependent variable k is a function of the process used in making the lubricating member.