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User:Kaboldy
Notations of planetary gearing elements for the next table
[1]
Name
Number of teeth
Speed
D
r
i
v
i
n
g
{\displaystyle {\color {blue}Driving}\,}
z
{\displaystyle {\color {blue}z}\,}
n
{\displaystyle {\color {blue}n}\,}
A
u
x
i
l
i
a
r
y
d
r
i
v
i
n
g
{\displaystyle {\color {magenta}Auxiliary\ driving}\,}
z
{\displaystyle {\color {magenta}z}\,}
n
{\displaystyle {\color {magenta}n}\,}
D
r
i
v
e
n
{\displaystyle {\color {red}Driven}\,}
z
{\displaystyle {\color {red}z}\,}
n
{\displaystyle {\color {red}n}\,}
F
i
x
e
d
{\displaystyle Fixed\,}
z
{\displaystyle z\,}
n
{\displaystyle n\,}
P
l
a
n
e
t
a
r
y
{\displaystyle {\color {green}Planetary}\,}
z
{\displaystyle {\color {green}z}\,}
n
{\displaystyle {\color {green}n}\,}
P
l
a
n
e
t
a
r
y
{\displaystyle {\color {cyan}Planetary}\,}
z
{\displaystyle {\color {cyan}z}\,}
n
{\displaystyle {\color {cyan}n}\,}
Sketch and output speed of planetary gearings
Sketch
Output speed
Sketch
Output speed
Sketch
Output speed
Sketch
Output speed
n
=
n
(
1
+
z
z
)
{\displaystyle {\color {red}n}={\color {blue}n}(1+{\frac {z}{\color {red}z}})}
n
=
n
(
1
−
z
z
)
{\displaystyle {\color {red}n}={\color {blue}n}(1-{\frac {z}{\color {red}z}})}
n
=
n
(
0
+
z
z
)
{\displaystyle {\color {red}n}={\color {blue}n}(0+{\frac {z}{\color {red}z}})}
n
=
n
(
cos
β
+
z
z
)
{\displaystyle {\color {red}n}={\color {blue}n}(\cos \beta +{\frac {z}{\color {red}z}})}
n
=
n
(
1
+
z
z
z
z
)
{\displaystyle {\color {red}n}={\color {blue}n}(1+{\frac {{\color {green}z}z}{\color {cyan}z\color {red}z}})}
n
=
n
(
1
+
z
z
z
z
)
{\displaystyle {\color {red}n}={\color {blue}n}(1+{\frac {{\color {green}z}z}{\color {cyan}z\color {red}z}})}
n
=
n
1
(
1
+
z
z
z
z
)
{\displaystyle {\color {red}n}={\color {blue}n}{\frac {1}{(1+{\dfrac {{\color {green}z}z}{\color {cyan}z\color {red}z}})}}}
n
=
n
1
(
1
+
z
z
z
z
)
{\displaystyle {\color {red}n}={\color {blue}n}{\frac {1}{(1+{\dfrac {{\color {green}z}z}{\color {cyan}z\color {red}z}})}}}
n
=
n
(
1
+
z
z
)
{\displaystyle {\color {red}n}={\color {blue}n}(1+{\frac {z}{\color {red}z}})}
n
=
n
(
1
+
z
z
)
{\displaystyle {\color {red}n}={\color {blue}n}(1+{\frac {z}{\color {red}z}})}
n
=
n
(
1
+
z
z
)
{\displaystyle {\color {red}n}={\color {blue}n}(1+{\frac {z}{\color {blue}z}})}
n
=
n
(
1
+
z
z
)
{\displaystyle {\color {red}n}={\color {blue}n}(1+{\frac {z}{\color {blue}z}})}
n
=
n
z
z
z
z
{\displaystyle {\color {red}n}={\color {blue}n}{\dfrac {{\color {cyan}z}z}{{\color {green}z}{\color {red}z}}}}
n
=
n
1
−
z
z
z
z
1
+
z
z
{\displaystyle {\color {red}n}={\color {blue}n}{\frac {1-{\dfrac {z\color {green}z}{\color {cyan}z\color {red}z}}}{1+{\dfrac {z}{\color {blue}z}}}}}
n
=
n
1
−
z
z
z
z
1
+
z
z
{\displaystyle {\color {red}n}={\color {blue}n}{\frac {1-{\dfrac {z\color {green}z}{\color {cyan}z\color {red}z}}}{1+{\dfrac {z}{\color {blue}z}}}}}
n
=
n
1
1
+
z
z
{\displaystyle {\color {red}n}={\color {blue}n}{\dfrac {1}{1+{\dfrac {z}{\color {blue}z}}}}}
n
=
n
1
1
−
z
z
z
z
{\displaystyle {\color {red}n}={\color {blue}n}{\dfrac {1}{1-{\dfrac {{\color {cyan}z}z}{{\color {green}z}{\color {blue}z}}}}}}
n
=
n
1
1
−
z
z
z
z
{\displaystyle {\color {red}n}={\color {blue}n}{\dfrac {1}{1-{\dfrac {{\color {cyan}z}z}{{\color {green}z}{\color {blue}z}}}}}}
n
=
n
1
−
z
z
z
z
1
+
z
z
{\displaystyle {\color {red}n}={\color {blue}n}{\frac {1-{\dfrac {z\color {green}z}{\color {cyan}z\color {red}z}}}{1+{\dfrac {z}{\color {blue}z}}}}}
n
=
n
(
1
−
z
z
z
z
)
{\displaystyle {\color {red}n}={\color {blue}n}(1-{\frac {{\color {green}z}z}{\color {cyan}z\color {red}z}})}
n
=
n
[
1
−
(
n
n
−
1
)
z
z
]
{\displaystyle {\color {red}n}={\color {blue}n}\left[1-\left({\frac {\color {magenta}n}{\color {blue}n}}-1\right){\frac {\color {magenta}z}{\color {red}z}}\right]}
n
=
n
[
1
−
(
n
n
−
1
)
z
z
]
{\displaystyle {\color {red}n}={\color {blue}n}\left[1-\left({\frac {\color {magenta}n}{\color {blue}n}}-1\right){\frac {\color {magenta}z}{\color {red}z}}\right]}
n
=
n
1
+
n
z
n
z
1
+
z
z
{\displaystyle {\color {red}n}={\color {blue}n}{\frac {1+{\dfrac {\color {magenta}n\color {magenta}z}{\color {blue}n\color {blue}z}}}{1+{\dfrac {\color {magenta}z}{\color {blue}z}}}}}
n
=
n
1
+
n
z
n
z
1
+
z
z
{\displaystyle {\color {red}n}={\color {blue}n}{\frac {1+{\dfrac {\color {magenta}n\color {magenta}z}{\color {blue}n\color {blue}z}}}{1+{\dfrac {\color {magenta}z}{\color {blue}z}}}}}
Reference
edit
^
Pattantyús Gépész- és Villamosmérnökök Kézikönyve 3. tom. Műszaki Könyvkiadó, Budapest, 1961. p.632.
![{\displaystyle {\color {red}n}={\color {blue}n}\left[1-\left({\frac {\color {magenta}n}{\color {blue}n}}-1\right){\frac {\color {magenta}z}{\color {red}z}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9239bbfe93b3c73d416cf065b5349fa212e6faf3)
