= (b) The elastic cylinders are brought into contact at an angle a = 45° angle. The cylinders are characterized by the principal radii: R₁ = R₁₂ 0.05m and R = R' = ∞o. The two cylinders are pressed together with a force of 5kN. The relative radii of curvature can be found using the fundamental equations for elliptic contact. The equations for elliptic contact (on the formula sheet): 1 1 1 1 1 1 + = + + + R' R₁₂₁ R1 R₂ R" R" and 1 2 2 1 1 1 1 ↓ - ² = [ ( ²1 - ²2 ) ² + ( ²2 - 2²21 ) ² + 2 (2/27 - 12/17) (12/2 - 1/2 ) COS (202) 1¹/²2 a) (一般 +2 cos R" R' R₁ R R R₁ R₁ which under the present circumstances become: 1 1 1 1 2 + R" R' 0.05 (1.1) 0.05 0.05 and 2 1/2 1 1 1 π √2 1 1 R" R' [(0.05)² (0.05) ² +2 ·cos (2 (1.2) 0.05 0.05 0.05 The solution of the system radius of curvature is: leads to R' = 0.17m and R" = 0.029m. Accordingly, the effective relative R = √R'R" = √0.17 x 0.029 = 0.07m + +
= (b) The elastic cylinders are brought into contact at an angle a = 45° angle. The cylinders are characterized by the principal radii: R₁ = R₁₂ 0.05m and R = R' = ∞o. The two cylinders are pressed together with a force of 5kN. The relative radii of curvature can be found using the fundamental equations for elliptic contact. The equations for elliptic contact (on the formula sheet): 1 1 1 1 1 1 + = + + + R' R₁₂₁ R1 R₂ R" R" and 1 2 2 1 1 1 1 ↓ - ² = [ ( ²1 - ²2 ) ² + ( ²2 - 2²21 ) ² + 2 (2/27 - 12/17) (12/2 - 1/2 ) COS (202) 1¹/²2 a) (一般 +2 cos R" R' R₁ R R R₁ R₁ which under the present circumstances become: 1 1 1 1 2 + R" R' 0.05 (1.1) 0.05 0.05 and 2 1/2 1 1 1 π √2 1 1 R" R' [(0.05)² (0.05) ² +2 ·cos (2 (1.2) 0.05 0.05 0.05 The solution of the system radius of curvature is: leads to R' = 0.17m and R" = 0.029m. Accordingly, the effective relative R = √R'R" = √0.17 x 0.029 = 0.07m + +
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
Related questions
Question
can someone explain what has happened here. im not really sure why he has changed Cos(2a) to cos2pi/4 either.
Transcribed Image Text:=
(b) The elastic cylinders are brought into contact at an angle a = 45° angle. The cylinders are
characterized by the principal radii: R₁ = R₂ = 0.05m and R R = ∞. The two cylinders are
pressed together with a force of 5kN. The relative radii of curvature can be found using the fundamental
equations for elliptic contact. The equations for elliptic contact (on the formula sheet):
1
1
1
1
1
1
+
=
R"
+ + +
R' R₁₂ R₁ R₁₂ R
and
1/2
2
2
1
1
1
1
1
1
1
1
1
1
÷ ÷ - [(-+ )² + ( A - A ) ² - ¹ (A) (+) (²
+2
(一)(一般
cos (2a)
R" R'
R! R!!
R"
which under the present circumstances become:
1
2
1 1 1
+
R" R' 0.05
=
(1.1)
0.05
0.05
and
1/2
2
2
1
1
1
1
√2
- [(0.05)² + (0.05)
+2
·cos (2
=
(1.2)
R" R'
0.05
0.05
4
0.05
=
0.029m. Accordingly, the effective relative
The solution of the system leads to R' = 0.17m and R"
radius of curvature is:
Ř = √R¹R"
√0.17 x 0.029 = 0.07m
=
+
=
.
π
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