Single piece heavy duty wheel
A wheel rim including a flange profile on a tire side of an open end flange of the wheel rim, the flange profile defined by the equation: y 1 = ( a Theta 1 + 1 ( 1 + Exp ( a Theta 3 + a Theta 4 · X 1 ) ) aTheta 5 ) · a Theta 2 wherein, for 0≤X 1 ≤1, aTheta1 is between −1.004 to −0.974, aTheta2 is between −−1.049 to −1.0182, aTheta3 is between −3.601 to −2.760, aTheta4 is between 18.791 to 25.965, and aTheta5 is between 0.185 to 0.277.
1. A wheel rim comprising:
a first flange profile on a tire side of an open end flange of the wheel rim, the first flange profile defined by the equation:
y
1
=
(
a
Theta
1
+
1
(
1
+
Exp
(
a
Theta
3
+
a
Theta
4
·
X
1
)
)
aTheta
5
)
·
a
Theta
2
wherein, for 0≤X 1 ≤1, aTheta1 is between −1.004 to −0.974, aTheta2 is between −1.049 to −1.0182, aTheta3 is between −3.601 to −2.760, aTheta4 is between 18.791 to 25.965, and aTheta5 is between 0.185 to 0.277.
2. The wheel rim of claim 1 , wherein aTheta1 is −0.989, aTheta2 is 1.034, aTheta3 is −3.181, aTheta4 is 22.378, and aTheta5 is 0.231.
3. The wheel rim of claim 1 , wherein
a second flange profile on an inboard side of the open end flange of the wheel rim is defined by the equation:
y
2
=
(
b
Theta
1
+
1
(
1
+
Exp
(
b
Theta
3
+
b
Theta
4
·
X
2
)
)
bTheta
5
)
·
b
Theta
2
+
(
Alpha
0
+
Alpha
1
·
X
2
+
Alpha
2
·
X
2
2
+
Alpha
3
·
X
2
3
)
wherein, for 0≤X2≤1, bTheta1 is between −1.319 to −1.065, bTheta2 is between 0.0001 to 6.277, bTheta3 is between −7.536 to −2.786, bTheta4 is between 7.384 to 16.538, bTheta5 is between −0.234 to −0.159, Alpha0 is 0, Alpha1 is between −3.534 to −0.0001, Alpha2 is between 1.090 to 13.597, and Alpha3 is between −16.537 to −10.472.
4. The wheel rim of claim 3 , wherein bTheta1 is −1.192, bTheta2 is 3.126, bTheta3 is −5.161, bTheta4 is 11.961, bTheta5 is −0.197, Alpha0 is 0, Alpha1 is −1.500, Alpha2 is 7.343, and Alpha3 is −13.505.
5. The wheel rim of claim 3 , further comprising a third flange profile connecting the first flange profile and the second flange profile, the third flange profile having a first portion and a second portion, wherein:
the first portion is defined by the equation:
y 3 =Beta0+Beta1· X 3 +Beta2· X 3 2 +Beta3· X 3 3 +Beta4· X 3 4 ,
wherein, for 0≤X 3 ≤1, Beta0 is between −874.899 to −347.942, Beta1 is between 1651.049 to 3667.375, Beta2 is between −5733.990 to −2841.300, Beta3 is between 2125.823 to 3969.923, and Beta4 is between 1027.410 to −586.633; and
the second portion is defined by the equation:
X 4 =Constant
for y 2 <y<y 3 .
6. The wheel rim of claim 5 , wherein Beta0 is −611.42, Beta1 is 2659.212, Beta2 is −4287.640, Beta3 is 3047.873, and Beta4 is −807.023.
7. The wheel rim of claim 5 , further comprising a disc end flange mirroring the open end flange.
8. The wheel rim of claim 5 , further comprising:
a first angle wall extending from the disc end flange toward the open end flange;
a second angle wall extending from the open end flange toward the disc end flange; and
a drop well connecting the first angle wall and the second angle wall.
9. The wheel rim of claim 8 , further comprising a mounting flange extending radially inward from the disc face, the mounting flange having a plurality of bolt holes.
10. The wheel rim of claim 5 , wherein the wheel rim is formed from at least one of steel, aluminum, steel alloys, aluminum alloys, or combinations thereof.
11. The wheel rim of claim 7 , wherein the wheel has a maximum load rating, wherein the wheel has a weight, and wherein an increase in the maximum load rating by a factor of 1.5 results in a corresponding increase in the weight of the wheel by a factor of 1.3.
12. The wheel rim of claim 11 , wherein the wheel has a maximum tire pressure rating, and wherein an increase in the maximum tire pressure rating by a factor of 1.375 results in a corresponding increase in the weight of the wheel by a factor of 1.298.
13. A method for making a wheel comprising:
forming the wheel by at least one of forging or casting the wheel, the wheel having a disc face at a disc end, an opposing open end, and a wheel rim extending between the disc face and the open end, the wheel rim including:
a first flange profile on a tire side of an open end flange of the wheel rim, the first flange profile defined by the equation:
y
1
=
(
a
Theta
1
+
1
(
1
+
Exp
(
a
Theta
3
+
a
Theta
4
·
X
1
)
)
aTheta
5
)
·
a
Theta
2
wherein, for 0≤X 1 ≤1 01, a Theta1 is between −1.004 to −0.974, aTheta2 is between −1.049 to −1.0182, aTheta3 is between −3.601 to −2.760, aTheta4 is between 18.791 to 25.965, and aTheta5 is between 0.185 to 0.277.
14. The method of claim 13 , wherein aTheta1 is −0.989, aTheta2 is 1.034, aTheta3 is −3.181, aTheta4 is 22.378, and aTheta5 is 0.231.
15. The method of claim 13 , wherein the step of forming further comprises forming a second flange profile on an inboard side of the open end flange of the wheel rim, the second flange profile defined by the equation:
y
2
=
(
b
Theta
1
+
1
(
1
+
Exp
(
b
Theta
3
+
b
Theta
4
·
X
2
)
)
bTheta
5
)
·
b
Theta
2
+
(
Alpha
0
+
Alpha
1
·
X
2
+
Alpha
2
·
X
2
2
+
Alpha
3
·
X
2
3
)
wherein, for 0≤X 2 ≤1 is between −1.319 to −1.065, bTheta2 is between 0.0001 to 6.277, bTheta3 is between −7.536 to −2.786, bTheta4 is between 7.384 to 16.538, bTheta5 is between −0.234 to −0.159, Alpha0 is 0, Alpha1 is between −3.534 to −0.0001, Alpha2 is between 1.090 to 13.597, and Alpha3 is between −16.537 to −10.472.
16. The method of claim 15 , wherein bTheta1 is −1.192, bTheta2 is 3.126, bTheta3 is −5.161, bTheta4 is 11.961, bTheta5 is −0.197, Alpha0 is 0, Alpha1 is −1.500, Alpha2 is 7.343, and Alpha3 is −13.505.
17. The method of claim 15 , wherein the step of forming further comprises forming a third flange profile connecting the first flange profile and the second flange profile, the third flange profile having a first portion and a second portion, wherein:
the first portion is defined by the equation:
y 3 =Beta0+Beta1· X 3 +Beta2· X 3 2 +Beta3· X 3 3 +Beta4· X 3 4 ,
wherein, for 0≤X 3 ≤1, Beta0 is between −874.899 to −347.942, Beta1 is between 1651.049 to 3667.375, Beta2 is between −5733.990 to −2841.300, Beta3 is between 2125.823 to 3969.923, and Beta4 is between 1027.410 to −586.633; and
the second portion is defined by the equation:
X 4 =Constant
for y 2 <y<y 3 .
18. The method of claim 17 , wherein the wheel rim further comprises a disc end flange mirroring the open end flange.
19. The method of claim 18 , wherein the wheel is forged or cast from at least one of steel, aluminum, steel alloys, aluminum alloys, or combinations thereof.
20. The method of claim 17 , wherein X 4 =1.