Motor vehicle automatic transmission models
For the heavy-duty 5 speed automatic transmission, see
ZF Ecomat .
Motor vehicle
5HP is ZF Friedrichshafen AG 's trademark name for its 5-speed automatic transmission models (5 -speed transmission with H ydraulic converter and P lanetary gearsets) for longitudinal engine applications, designed and built by ZF 's subsidiary in Saarbrücken .
Gear Ratios[ a]
Model
First
Gear
Total Span
Avg.
Components
Nomenclature
R
1
2
3
4
5
Nomi-
Effec-
Cen-
Total
per[ b]
Gears
Cou-
Gear-
Input Shaft
Ravigneaux Types
5[ b]
H[ c]
P[ d]
5HP 18
1990
−4.096
3.665
1.995
1.407
1.000
0.742
4.936
4.936
1.650
1.491
3 Gearsets
2.000
18 mm
Simpson Types
5HP 30
1992
−3.684
3.553
2.244
1.545
1.000
0.787
4.517
4.517
1.672
1.458
3 Gearsets
1.800
30 mm
5HP 24
1996
−4.095
3.571
2.200
1.505
1.000
0.804
4.444
4.444
1.694
1.452
24 mm
^ Differences in gear ratios have a measurable, direct impact on vehicle dynamics, performance, waste emissions as well as fuel mileage
^ a b Forward gears only
^ Hydraulic torque converter · German : H ydraulischer Wandler oder Drehmomentwandler
^ Planetary gearing · German : P lanetenradsätze
[ edit ] Gearset Concept: Combined Parallel and Serial Coupled Gearset Concept For More Gears And Improved Cost-Effectiveness [ edit ] The 5HP 18 and 19 are a transmission family with purely serial power flow: components were simply added to enable more gears. This makes these transmissions larger, heavier, and more expensive. With 10 main components, progress was unsatisfactory: an obvious transitional solution. It is therefore the last conventionally designed transmission from ZF. All subsequent transmissions from ZF including the 8-speed transmission 8HP require fewer main components.
Gearset Concept: Cost-Effectiveness[ a]
With
Output:
InnovationElasticity [ b]
Input: Main Components
Total
Gearsets
Brakes
Clutches
5HP 18/19
n
O
1
{\displaystyle n_{O1}}
n
O
2
{\displaystyle n_{O2}}
Topic[ b]
n
I
=
n
G
+
{\displaystyle n_{I}=n_{G}+}
n
B
+
n
C
{\displaystyle n_{B}+n_{C}}
n
G
1
{\displaystyle n_{G1}}
n
G
2
{\displaystyle n_{G2}}
n
B
1
{\displaystyle n_{B1}}
n
B
2
{\displaystyle n_{B2}}
n
C
1
{\displaystyle n_{C1}}
n
C
2
{\displaystyle n_{C2}}
Δ Number
n
O
1
−
n
O
2
{\displaystyle n_{O1}-n_{O2}}
n
I
1
−
n
I
2
{\displaystyle n_{I1}-n_{I2}}
n
G
1
−
n
G
2
{\displaystyle n_{G1}-n_{G2}}
n
B
1
−
n
B
2
{\displaystyle n_{B1}-n_{B2}}
n
C
1
−
n
C
2
{\displaystyle n_{C1}-n_{C2}}
Relative Δ
Δ Output
n
O
1
−
n
O
2
n
O
2
{\displaystyle {\tfrac {n_{O1}-n_{O2}}{n_{O2}}}}
n
O
1
−
n
O
2
n
O
2
:
n
I
1
−
n
I
2
n
I
2
{\displaystyle {\tfrac {n_{O1}-n_{O2}}{n_{O2}}}:{\tfrac {n_{I1}-n_{I2}}{n_{I2}}}}
=
n
O
1
−
n
O
2
n
O
2
{\displaystyle ={\tfrac {n_{O1}-n_{O2}}{n_{O2}}}}
n
I
2
n
I
1
−
n
I
2
{\displaystyle {\tfrac {n_{I2}}{n_{I1}-n_{I2}}}}
Δ Input
n
I
1
−
n
I
2
n
I
2
{\displaystyle {\tfrac {n_{I1}-n_{I2}}{n_{I2}}}}
n
G
1
−
n
G
2
n
G
2
{\displaystyle {\tfrac {n_{G1}-n_{G2}}{n_{G2}}}}
n
B
1
−
n
B
2
n
B
2
{\displaystyle {\tfrac {n_{B1}-n_{B2}}{n_{B2}}}}
n
C
1
−
n
C
2
n
C
2
{\displaystyle {\tfrac {n_{C1}-n_{C2}}{n_{C2}}}}
5HP 18/194HP 14/16/18 [ c]
5[ d] [ d]
Progress[ b]
10
3[ e] [ e]
3
4
Δ Number
1
3
1
1
1
Relative Δ
0.250
1
4
{\displaystyle {\tfrac {1}{4}}}
0.583 [ b]
1
4
:
3
7
=
1
4
{\displaystyle {\tfrac {1}{4}}:{\tfrac {3}{7}}={\tfrac {1}{4}}}
7
3
=
7
12
{\displaystyle {\tfrac {7}{3}}={\tfrac {7}{12}}}
0.429
3
7
{\displaystyle {\tfrac {3}{7}}}
0.500
1
2
{\displaystyle {\tfrac {1}{2}}}
0.500
1
2
{\displaystyle {\tfrac {1}{2}}}
0.333
1
3
{\displaystyle {\tfrac {1}{3}}}
5HP 18/194HP 20/22/24 [ c]
5[ d] [ d]
Progress[ b]
10
3[ e]
3
4
Δ Number
1
0
0
-1
1
Relative Δ
0.250
1
4
{\displaystyle {\tfrac {1}{4}}}
∞ [ b]
1
4
:
0
10
=
1
4
{\displaystyle {\tfrac {1}{4}}:{\tfrac {0}{10}}={\tfrac {1}{4}}}
10
0
=
10
0
{\displaystyle {\tfrac {10}{0}}={\tfrac {10}{0}}}
0.000
0
10
{\displaystyle {\tfrac {0}{10}}}
0.000
0
3
{\displaystyle {\tfrac {0}{3}}}
−0.250
−
1
4
{\displaystyle {\tfrac {-1}{4}}}
0.333
1
3
{\displaystyle {\tfrac {1}{3}}}
5HP 18/19[ f]
5[ d] [ d]
Market Position[ b]
10
3[ e] [ e]
3
4
Δ Number
2
3
1
0
2
Relative Δ
0.667
2
3
{\displaystyle {\tfrac {2}{3}}}
1.556 [ b]
2
3
:
3
7
=
2
3
{\displaystyle {\tfrac {2}{3}}:{\tfrac {3}{7}}={\tfrac {2}{3}}}
7
3
=
14
9
{\displaystyle {\tfrac {7}{3}}={\tfrac {14}{9}}}
0.429
3
7
{\displaystyle {\tfrac {3}{7}}}
0.500
1
2
{\displaystyle {\tfrac {1}{2}}}
0.000
0
3
{\displaystyle {\tfrac {0}{3}}}
1.000
2
2
{\displaystyle {\tfrac {2}{2}}}
^ Progress increases cost-effectiveness and is reflected in the ratio of forward gears to main components. power flow:
parallel: using the two degrees of freedom of planetary gearsets
to increase the number of gears
with unchanged number of components serial: in-line combined planetary gearsets without using the two degrees of freedom
to increase the number of gears
a corresponding increase in the number of components is unavoidable ^ a b c d e f g h Innovation Elasticity Classifies Progress And Market Position
Automobile manufacturers drive forward technical developments primarily in order to remain competitive or to achieve or defend technological leadership. This technical progress has therefore always been subject to economic constraints
Only innovations whose relative additional benefit is greater than the relative additional resource input, i.e. whose economic elasticity is greater than 1, are considered for realization
The required innovation elasticity of an automobile manufacturer depends on its expected return on investment. The basic assumption that the relative additional benefit must be at least twice as high as the relative additional resource input helps with orientation
negative, if the output increases and the input decreases, is perfect 2 or above is good 1 or above is acceptable (red) below this is unsatisfactory (bold) ^ a b Direct Predecessor
To reflect the progress of the specific model change ^ a b c d e f plus 1 reverse gear
^ a b c d e of which 2 gearsets are combined as a compound Ravigneaux gearset
^ Reference Standard (Benchmark)
3-speed transmissions with torque converters have established the modern market for automatic transmissions and thus made it possible in the first place, as this design proved to be a particularly successful compromise between cost and performance
It became the archetype and dominated the world market for around 3 decades, setting the standard for automatic transmissions. It was only when fuel consumption became the focus of interest that this design reached its limits, which is why it has now completely disappeared from the market
What has remained is the orientation that it offers as a reference standard (point of reference, benchmark) for this market for determining progressiveness and thus the market position of all other, later designs
All transmission variants consist of 7 main components
Typical examples are
Gearset Concept: Quality [ edit ] The main objective in replacing the predecessor model was to improve vehicle fuel economy with extra speeds and a wider gear span to allow the engine speed level to be lowered (downspeeding).
Gear Ratio Analysis[ a]
In-Depth Analysis[ b] [ c] [ d]
Planetary Gearset: Teeth[ e]
Count
Nomi-[ f] [ g]
Cen-[ h]
Ravigneaux
Simple
Avg.[ i]
Model
Version
S1 [ j] 1 [ k]
S2 [ l] 2 [ m]
S3 [ n] 3 [ o]
Brakes
Ratio
Gear[ p]
Gear
R
1
2
3
4
5
Gear[ b]
i
R
{\displaystyle {i_{R}}}
[ b]
i
1
{\displaystyle {i_{1}}}
[ b]
i
2
{\displaystyle {i_{2}}}
[ b]
i
3
{\displaystyle {i_{3}}}
[ b]
i
4
{\displaystyle {i_{4}}}
[ b]
i
5
{\displaystyle {i_{5}}}
[ b]
Step[ p]
−
i
R
i
1
{\displaystyle -{\frac {i_{R}}{i_{1}}}}
[ q]
i
1
i
1
{\displaystyle {\frac {i_{1}}{i_{1}}}}
i
1
i
2
{\displaystyle {\frac {i_{1}}{i_{2}}}}
[ r]
i
2
i
3
{\displaystyle {\frac {i_{2}}{i_{3}}}}
i
3
i
4
{\displaystyle {\frac {i_{3}}{i_{4}}}}
i
4
i
5
{\displaystyle {\frac {i_{4}}{i_{5}}}}
Δ Step[ s] [ t]
i
1
i
2
:
i
2
i
3
{\displaystyle {\tfrac {i_{1}}{i_{2}}}:{\tfrac {i_{2}}{i_{3}}}}
i
2
i
3
:
i
3
i
4
{\displaystyle {\tfrac {i_{2}}{i_{3}}}:{\tfrac {i_{3}}{i_{4}}}}
i
3
i
4
:
i
4
i
5
{\displaystyle {\tfrac {i_{3}}{i_{4}}}:{\tfrac {i_{4}}{i_{5}}}}
Shaft
i
1
i
R
{\displaystyle {\frac {i_{1}}{i_{R}}}}
i
1
i
1
{\displaystyle {\frac {i_{1}}{i_{1}}}}
i
1
i
2
{\displaystyle {\frac {i_{1}}{i_{2}}}}
i
1
i
3
{\displaystyle {\frac {i_{1}}{i_{3}}}}
i
1
i
4
{\displaystyle {\frac {i_{1}}{i_{4}}}}
i
1
i
5
{\displaystyle {\frac {i_{1}}{i_{5}}}}
Δ Shaft[ u]
0
−
i
1
i
R
{\displaystyle 0-{\tfrac {i_{1}}{i_{R}}}}
i
1
i
1
−
0
{\displaystyle {\tfrac {i_{1}}{i_{1}}}-0}
i
1
i
2
−
i
1
i
1
{\displaystyle {\tfrac {i_{1}}{i_{2}}}-{\tfrac {i_{1}}{i_{1}}}}
i
1
i
3
−
i
1
i
2
{\displaystyle {\tfrac {i_{1}}{i_{3}}}-{\tfrac {i_{1}}{i_{2}}}}
i
1
i
4
−
i
1
i
3
{\displaystyle {\tfrac {i_{1}}{i_{4}}}-{\tfrac {i_{1}}{i_{3}}}}
i
1
i
5
−
i
1
i
4
{\displaystyle {\tfrac {i_{1}}{i_{5}}}-{\tfrac {i_{1}}{i_{4}}}}
Torque[ c]
μ
R
{\displaystyle \mu _{R}}
[ c]
μ
1
{\displaystyle \mu _{1}}
[ c]
μ
2
{\displaystyle \mu _{2}}
[ c]
μ
3
{\displaystyle \mu _{3}}
[ c]
μ
4
{\displaystyle \mu _{4}}
[ c]
μ
5
{\displaystyle \mu _{5}}
[ c]
Efficiency
η
n
{\displaystyle \eta _{n}}
[ d]
μ
R
i
R
{\displaystyle {\frac {\mu _{R}}{i_{R}}}}
[ d]
μ
1
i
1
{\displaystyle {\frac {\mu _{1}}{i_{1}}}}
[ d]
μ
2
i
2
{\displaystyle {\frac {\mu _{2}}{i_{2}}}}
[ d]
μ
3
i
3
{\displaystyle {\frac {\mu _{3}}{i_{3}}}}
[ d]
μ
4
i
4
{\displaystyle {\frac {\mu _{4}}{i_{4}}}}
[ d]
μ
5
i
5
{\displaystyle {\frac {\mu _{5}}{i_{5}}}}
[ d]
5HP 18
310 N⋅m (229 lb⋅ft )
3834 [ v]
34 32
3
4.9363[ g] [ q]
1.6495
1.4906 [ p]
Gear
R
1
2
3
4
5
Gear[ b]
−4.0960[ q] [ g]
−
1
,
323
323
{\displaystyle -{\tfrac {1,323}{323}}}
3.6648
1
,
323
361
{\displaystyle {\tfrac {1,323}{361}}}
1.9990 [ r]
7
,
938
3
,
971
{\displaystyle {\tfrac {7,938}{3,971}}}
1.4067 [ p] [ t] [ u]
294
209
{\displaystyle {\tfrac {294}{209}}}
1.0000
1
1
{\displaystyle {\tfrac {1}{1}}}
0.7424
49
66
{\displaystyle {\tfrac {49}{66}}}
Step
1.1176 [ q]
1.0000
1.8333 [ r] 1.4211 [ p] 1.4067
1.3469
Δ Step[ s]
1.2901
1.0102 [ t] 1.0444
Speed
-0.8947
1.0000
1.8333
2.6053
3.6648
4.9363
Δ Speed
0.8947
1.0000
0.8333
0.7719 [ u] 1.0596
1.2715
Torque[ c]
–3.9903
3.5344
1.9581
1.3861
1.0000
0.7385
Efficiency
η
n
{\displaystyle \eta _{n}}
[ d]
0.9742
0.9644
0.9795
0.9854
1.0000
0.9948
5HP 19
325 N⋅m (240 lb⋅ft )
3834 [ v]
34 32
3
4.9363[ g] [ q]
1.6495
1.4906 [ p]
Gear
R
1
2
3
4
5
Gear[ b]
−4.0960[ q] [ g]
3.6648
1.9990 [ r] 1.4067 [ p] [ t] [ u] 1.0000
0.7424
Actuated Shift Elements
Brake A[ w]
❶
❶
❶
Brake B[ x]
❶
❶
Brake C[ y]
❶
❶
❶
Clutch D[ z]
❶
❶
❶
❶
Clutch E[ aa]
❶
Clutch F[ ab]
❶
❶
Clutch G[ ac]
❶
❶
❶
Geometric Ratios: Speed Conversion
Gear[ b] [ ad] [ ae]
i
R
=
−
R
2
(
S
3
+
R
3
)
S
2
R
3
{\displaystyle i_{R}=-{\frac {R_{2}(S_{3}+R_{3})}{S_{2}R_{3}}}}
i
1
=
R
1
R
2
(
S
3
+
R
3
)
S
1
S
2
R
3
{\displaystyle i_{1}={\frac {R_{1}R_{2}(S_{3}+R_{3})}{S_{1}S_{2}R_{3}}}}
i
R
=
−
R
2
S
2
(
1
+
S
3
R
3
)
{\displaystyle i_{R}=-{\tfrac {R_{2}}{S_{2}}}\left(1+{\tfrac {S_{3}}{R_{3}}}\right)}
i
1
=
R
1
R
2
S
1
S
2
(
1
+
S
3
R
3
)
{\displaystyle i_{1}={\tfrac {R_{1}R_{2}}{S_{1}S_{2}}}\left(1+{\tfrac {S_{3}}{R_{3}}}\right)}
Gear[ b] [ ad] [ ae]
i
2
=
R
2
(
S
1
+
R
1
)
(
S
3
+
R
3
)
S
1
R
3
(
S
2
+
R
2
)
{\displaystyle i_{2}={\frac {R_{2}(S_{1}+R_{1})(S_{3}+R_{3})}{S_{1}R_{3}(S_{2}+R_{2})}}}
i
3
=
R
2
(
S
1
+
R
1
)
S
1
(
S
2
+
R
2
)
{\displaystyle i_{3}={\frac {R_{2}(S_{1}+R_{1})}{S_{1}(S_{2}+R_{2})}}}
i
2
=
(
1
+
R
1
S
1
)
(
1
+
S
3
R
3
)
1
+
S
2
R
2
{\displaystyle i_{2}={\tfrac {\left(1+{\tfrac {R_{1}}{S_{1}}}\right)\left(1+{\tfrac {S_{3}}{R_{3}}}\right)}{1+{\tfrac {S_{2}}{R_{2}}}}}}
i
3
=
1
+
R
1
S
1
1
+
S
2
R
2
{\displaystyle i_{3}={\tfrac {1+{\tfrac {R_{1}}{S_{1}}}}{1+{\tfrac {S_{2}}{R_{2}}}}}}
Gear[ b] [ ad] [ ae]
i
4
=
1
1
{\displaystyle i_{4}={\frac {1}{1}}}
i
5
=
R
2
S
2
+
R
2
{\displaystyle i_{5}={\frac {R_{2}}{S_{2}+R_{2}}}}
i
5
=
1
1
+
S
2
R
2
{\displaystyle i_{5}={\tfrac {1}{1+{\tfrac {S_{2}}{R_{2}}}}}}
Kinetic Ratios: Torque Conversion
Torque[ c]
μ
R
=
−
R
2
S
2
η
0
(
1
+
S
3
R
3
η
0
)
{\displaystyle \mu _{R}=-{\tfrac {R_{2}}{S_{2}}}\eta _{0}\left(1+{\tfrac {S_{3}}{R_{3}}}\eta _{0}\right)}
μ
1
=
R
1
R
2
S
1
S
2
η
0
3
2
(
1
+
S
3
R
3
η
0
)
{\displaystyle \mu _{1}={\tfrac {R_{1}R_{2}}{S_{1}S_{2}}}{\eta _{0}}^{\tfrac {3}{2}}\left(1+{\tfrac {S_{3}}{R_{3}}}\eta _{0}\right)}
Torque[ c]
μ
2
=
(
1
+
R
1
S
1
η
0
)
(
1
+
S
3
R
3
η
0
)
1
+
S
2
R
2
⋅
1
η
0
{\displaystyle \mu _{2}={\tfrac {\left(1+{\tfrac {R_{1}}{S_{1}}}\eta _{0}\right)\left(1+{\tfrac {S_{3}}{R_{3}}}\eta _{0}\right)}{1+{\tfrac {S_{2}}{R_{2}}}\cdot {\tfrac {1}{\eta _{0}}}}}}
μ
3
=
1
+
R
1
S
1
η
0
1
+
S
2
R
2
⋅
1
η
0
{\displaystyle \mu _{3}={\tfrac {1+{\tfrac {R_{1}}{S_{1}}}\eta _{0}}{1+{\tfrac {S_{2}}{R_{2}}}\cdot {\tfrac {1}{\eta _{0}}}}}}
Torque[ c]
μ
4
=
1
1
{\displaystyle \mu _{4}={\tfrac {1}{1}}}
μ
5
=
1
1
+
S
2
R
2
⋅
1
η
0
{\displaystyle \mu _{5}={\tfrac {1}{1+{\tfrac {S_{2}}{R_{2}}}\cdot {\tfrac {1}{\eta _{0}}}}}}
^ Revised 14 January 2026Nomenclature
S
n
=
{\displaystyle S_{n}=}
R
n
=
{\displaystyle R_{n}=}
C
n
=
{\displaystyle \color {gray}{C_{n}=}}
carrier or planetary gear carrier (not needed)
s
n
=
{\displaystyle s_{n}=}
r
n
=
{\displaystyle r_{n}=}
c
n
=
{\displaystyle c_{n}=}
n
=
{\displaystyle n=}
i
n
=
{\displaystyle i_{n}=}
ω
1
;
n
=
ω
t
=
{\displaystyle \omega _{1;n}=\omega _{t}=}
ω
2
;
n
=
{\displaystyle \omega _{2;n}=}
T
1
;
n
=
T
t
=
{\displaystyle T_{1;n}=T_{t}=}
T
2
;
n
=
{\displaystyle T_{2;n}=}
μ
n
=
{\displaystyle \mu _{n}=}
η
n
=
{\displaystyle \eta _{n}=}
i
0
=
{\displaystyle i_{0}=}
η
0
=
{\displaystyle \eta _{0}=}
^ a b c d e f g h i j k l m Gear Ratio (Transmission Ratio)
i
n
{\displaystyle i_{n}}
The gear ratio
i
n
{\displaystyle i_{n}}
is the ratio of
input shaft speed
ω
1
;
n
{\displaystyle \omega _{1;n}}
to output shaft speed
ω
2
;
n
{\displaystyle \omega _{2;n}}
and therefore corresponds to the reciprocal of the shaft speeds
i
n
=
1
ω
2
;
n
ω
1
;
n
=
ω
1
;
n
ω
2
;
n
=
ω
t
ω
2
;
n
{\displaystyle i_{n}={\frac {1}{\frac {\omega _{2;n}}{\omega _{1;n}}}}={\frac {\omega _{1;n}}{\omega _{2;n}}}={\frac {\omega _{t}}{\omega _{2;n}}}}
^ a b c d e f g h i j k l Torque Ratio (Torque Conversion Ratio)
μ
n
{\displaystyle \mu _{n}}
The torque ratio
μ
n
{\displaystyle \mu _{n}}
is the ratio of
output torque
T
2
;
n
{\displaystyle T_{2;n}}
to input torque
T
1
;
n
{\displaystyle T_{1;n}}
minus efficiency losses
and therefore corresponds (apart from the efficiency losses) to the reciprocal of the shaft speeds too
μ
n
=
i
n
η
n
;
η
0
=
ω
1
;
n
η
n
;
η
0
ω
2
;
n
=
T
2
;
n
η
n
;
η
0
T
1
;
n
{\displaystyle \mu _{n}=i_{n}\eta _{n;\eta _{0}}={\frac {\omega _{1;n}\eta _{n;\eta _{0}}}{\omega _{2;n}}}={\frac {T_{2;n}\eta _{n;\eta _{0}}}{T_{1;n}}}}
whereby
η
n
;
η
0
{\displaystyle \eta _{n;\eta _{0}}}
0
≤
η
n
;
η
0
≤
1
{\displaystyle 0\leq \eta _{n;\eta _{0}}\leq 1}
^ a b c d e f g h i Efficiency
The efficiency
η
n
{\displaystyle \eta _{n}}
from the torque ratio
in relation to the gear ratio (transmission ratio)
η
n
=
μ
n
i
n
{\displaystyle \eta _{n}={\frac {\mu _{n}}{i_{n}}}}
Power loss for single meshing gears
is in the range of 1 % to 1.5 %
helical gear pairs, which are used to reduce noise in passenger cars, are in the upper part of the loss range
spur gear pairs, which are limited to commercial vehicles due to their poorer noise comfort, are in the lower part of the loss range Corridor for torque ratio and efficiency
in planetary gearsets, the stationary gear ratio
i
0
{\displaystyle i_{0}}
is formed via the planetary gears and thus by two meshes
for reasons of simplification, the efficiency for both meshes together is commonly specified there
the efficiencies
η
0
{\displaystyle \eta _{0}}
stationary ratio
i
0
{\displaystyle i_{0}}
of
η
0
=
0.9800
{\displaystyle \eta _{0}=0.9800}
and
η
0
=
0.9700
{\displaystyle \eta _{0}=0.9700}
for both interventions together
The corresponding efficiency
for single-meshing gear pairs is
η
0
1
2
{\displaystyle {\eta _{0}}^{\tfrac {1}{2}}}
at
0.9800
1
2
=
0.98995
{\displaystyle 0.9800^{\tfrac {1}{2}}=0.98995}
and
0.9700
1
2
=
0.98489
{\displaystyle 0.9700^{\tfrac {1}{2}}=0.98489}
^ Layout
Input and output are on opposite sides
Planetary gearset 2 (the outer Ravigneaux gearset) is on the input (turbine) side
Input (turbine) shafts are, if actuated, S1 , C1 /C2 (the common carrier of the compound Ravigneaux gearset), and R1 /S2
Output shaft is C3 ^ Total Ratio Span (Total Gear/Transmission Ratio) Nominal
ω
2
;
n
ω
2
;
1
=
ω
2
;
n
ω
2
;
1
ω
2
;
n
ω
2
;
1
ω
2
;
1
ω
2
;
n
=
1
ω
2
;
1
1
ω
2
;
n
=
ω
t
ω
2
;
1
ω
t
ω
2
;
n
=
i
1
i
n
{\displaystyle {\frac {\omega _{2;n}}{\omega _{2;1}}}={\frac {\frac {\omega _{2;n}}{\omega _{2;1}\omega _{2;n}}}{\frac {\omega _{2;1}}{\omega _{2;1}\omega _{2;n}}}}={\frac {\frac {1}{\omega _{2;1}}}{\frac {1}{\omega _{2;n}}}}={\frac {\frac {\omega _{t}}{\omega _{2;1}}}{\frac {\omega _{t}}{\omega _{2;n}}}}={\frac {i_{1}}{i_{n}}}}
A wider span enables the
downspeeding when driving outside the city limits
increase the climbing ability
when driving over mountain passes or off-road
or when towing a trailer ^ a b c d e Total Ratio Span (Total Gear Ratio/Total Transmission Ratio) Effective
ω
2
;
n
m
a
x
(
ω
2
;
1
;
|
ω
2
;
R
|
)
=
m
i
n
(
i
1
;
|
i
R
|
)
i
n
{\displaystyle {\frac {\omega _{2;n}}{max(\omega _{2;1};|\omega _{2;R}|)}}={\frac {min(i_{1};|i_{R}|)}{i_{n}}}}
The span is only effective to the extent that
the reverse gear ratio
matches that of 1st gear
see also Standard R:1 Digression
is usually longer than 1st gear the effective span is therefore of central importance for describing the suitability of a transmission because in these cases, the nominal spread conveys a misleading picture which is only unproblematic for vehicles with high specific power Market participants
Manufacturers naturally have no interest in specifying the effective span Users have not yet formulated the practical benefits that the effective span has for them The effective span has not yet played a role in research and teaching Contrary to its significance
the effective span has therefore not yet been able to establish itself
either in theory or in practice. End of digression ^ Ratio Span's Center
(
i
1
i
n
)
1
2
{\displaystyle (i_{1}i_{n})^{\frac {1}{2}}}
The center indicates the speed level of the transmission
Together with the final drive ratio
it gives the shaft speed level of the vehicle ^ Average Gear Step
(
ω
2
;
n
ω
2
;
1
)
1
n
−
1
=
(
i
1
i
n
)
1
n
−
1
{\displaystyle \left({\frac {\omega _{2;n}}{\omega _{2;1}}}\right)^{\frac {1}{n-1}}=\left({\frac {i_{1}}{i_{n}}}\right)^{\frac {1}{n-1}}}
There are
n
−
1
{\displaystyle n-1}
n
{\displaystyle n}
with decreasing step width
the gears connect better to each other
shifting comfort increases ^ Sun 1: sun gear of gearset 1: inner Ravigneaux gearset
^ Ring 1: ring gear of gearset 1: inner Ravigneaux gearset
^ Sun 2: sun gear of gearset 2: outer Ravigneaux gearset
^ Ring 2: ring gear of gearset 2: outer Ravigneaux gearset
^ Sun 3: sun gear of gearset 3
^ Ring 3: ring gear of gearset 3
^ a b c d e f g Standard 50:50
With steadily decreasing gear steps (yellow highlighted line Step )
and a particularly large step from 1st to 2nd gear
the lower half of the gear steps (between the small gears; rounded down, here the first 2) is always larger
and the upper half of the gear steps (between the large gears; rounded up, here the last 2) is always smaller
than the average gear step (cell highlighted yellow two rows above on the far right)lower half: smaller gear steps are a waste of possible ratios (red bold)
upper half: larger gear steps are unsatisfactory (red bold) ^ a b c d e f Standard R:1
The ideal reverse gear has the same transmission ratio as 1st gear
no impairment when maneuvering
especially when towing a trailer
a torque converter can only partially compensate for this deficiency
Plus 11.11 % minus 10 % compared to 1st gear is good
Plus 25 % minus 20 % is acceptable (red) Above this is unsatisfactory (bold) see also Total Ratio Span (Total Gear/Transmission Ratio) Effective ^ a b c d Standard 1:2
With continuously decreasing gear steps (yellow marked line Step )
the largest gear step is the one from 1st to 2nd gear, which
for a good speed connection and
a smooth gear shift
must be as small as possible
A gear ratio of up to 1.6667 : 1 (5 : 3) is good
Up to 1.7500 : 1 (7 : 4) is acceptable (red) Above is unsatisfactory (bold) ^ a b From large to small gears (from right to left)
^ a b c d Standard STEP
Gear steps should
increase: Δ Step (first green highlighted line Δ Step ) is always greater than 1As progressive as possible: Δ Step is always greater than the previous step
Not progressively increasing is acceptable (red) Not increasing is unsatisfactory (bold) ^ a b c d Standard SPEED
Shaft speed differences should
increase: Δ Shaft Speed (second line marked in green Δ (Shaft) Speed ) is always greater than the previous one
1 difference smaller than the previous one is acceptable (red) 2 consecutive ones are a waste of possible ratios (bold) ^ a b inner and outer sun gears of the Ravigneaux planetary gearset are inverted
^ Blocks R1 (ring gear of the inner Ravigneaux gearset) and S2 (sun gear of the outer Ravigneaux gearset)
^ Blocks C1 /C2 (the common carrier of the compound Ravigneaux gearset)
^ Blocks S3
^ Couples S1 (sun of the inner Ravigneaux gearset) with the input (turbine)
^ Couples R1 (ring gear of the inner Ravigneaux gearset) and S2 (sun gear of the outer Ravigneaux gearset) with the input (turbine)
^ Connects C1 /C2 (the common carrier of the compound Ravigneaux gearset) with the input (turbine)
^ Couples S3 with R3
^ a b c Ordinary Noted
For direct determination of the gear ratio ^ a b c Elementary Noted
Alternative representation for determining the transmission ratio
Contains only operands
With simple fractions of both central gears of a planetary gearset
Or with the value 1
As a basis
For reliable
And traceable
Determination of torque conversion ratio and efficiency
[ edit ] Gearset Concept: Combined Parallel and Serial Coupled Gearset Concept For More Gears And Improved Cost-Effectiveness [ edit ] With planetary transmissions, the number of gears can be increased conventionally by adding additional gearsets as well as brakes and clutches, or conceptually by switching from serial to combined parallel and serial power flow. The conceptual way requires a computer-aided design. The resulting progress is reflected in a better ratio of the number of gears to the number of components used compared to existing layouts.
The 5HP 30 and 24 are the first transmission family with combined parallel and serial power flow to prevent these transmission from becoming larger, heavier, and more expensive. With 9 main components, it saves 1 component compared to the 5HP 18 and 19 family. No subsequent transmissions from ZF including the 8-speed transmission 8HP require more main components.
Gearset Concept: Cost-Effectiveness[ a]
With
Output:
InnovationElasticity [ b]
Input: Main Components
Total
Gearsets
Brakes
Clutches
5HP 30/24
n
O
1
{\displaystyle n_{O1}}
n
O
2
{\displaystyle n_{O2}}
Topic[ b]
n
I
=
n
G
+
{\displaystyle n_{I}=n_{G}+}
n
B
+
n
C
{\displaystyle n_{B}+n_{C}}
n
G
1
{\displaystyle n_{G1}}
n
G
2
{\displaystyle n_{G2}}
n
B
1
{\displaystyle n_{B1}}
n
B
2
{\displaystyle n_{B2}}
n
C
1
{\displaystyle n_{C1}}
n
C
2
{\displaystyle n_{C2}}
Δ Number
n
O
1
−
n
O
2
{\displaystyle n_{O1}-n_{O2}}
n
I
1
−
n
I
2
{\displaystyle n_{I1}-n_{I2}}
n
G
1
−
n
G
2
{\displaystyle n_{G1}-n_{G2}}
n
B
1
−
n
B
2
{\displaystyle n_{B1}-n_{B2}}
n
C
1
−
n
C
2
{\displaystyle n_{C1}-n_{C2}}
Relative Δ
Δ Output
n
O
1
−
n
O
2
n
O
2
{\displaystyle {\tfrac {n_{O1}-n_{O2}}{n_{O2}}}}
n
O
1
−
n
O
2
n
O
2
:
n
I
1
−
n
I
2
n
I
2
{\displaystyle {\tfrac {n_{O1}-n_{O2}}{n_{O2}}}:{\tfrac {n_{I1}-n_{I2}}{n_{I2}}}}
=
n
O
1
−
n
O
2
n
O
2
{\displaystyle ={\tfrac {n_{O1}-n_{O2}}{n_{O2}}}}
n
I
2
n
I
1
−
n
I
2
{\displaystyle {\tfrac {n_{I2}}{n_{I1}-n_{I2}}}}
Δ Input
n
I
1
−
n
I
2
n
I
2
{\displaystyle {\tfrac {n_{I1}-n_{I2}}{n_{I2}}}}
n
G
1
−
n
G
2
n
G
2
{\displaystyle {\tfrac {n_{G1}-n_{G2}}{n_{G2}}}}
n
B
1
−
n
B
2
n
B
2
{\displaystyle {\tfrac {n_{B1}-n_{B2}}{n_{B2}}}}
n
C
1
−
n
C
2
n
C
2
{\displaystyle {\tfrac {n_{C1}-n_{C2}}{n_{C2}}}}
5HP 30/244HP 14/16/18 [ c]
5[ d] [ d]
Progress[ b]
9
3[ e]
3
3
Δ Number
1
2
1
1
0
Relative Δ
0.250
1
4
{\displaystyle {\tfrac {1}{4}}}
0.875 [ b]
1
4
:
2
7
=
1
4
{\displaystyle {\tfrac {1}{4}}:{\tfrac {2}{7}}={\tfrac {1}{4}}}
7
2
=
7
8
{\displaystyle {\tfrac {7}{2}}={\tfrac {7}{8}}}
0.286
2
7
{\displaystyle {\tfrac {2}{7}}}
0.500
1
2
{\displaystyle {\tfrac {1}{2}}}
0.500
1
2
{\displaystyle {\tfrac {1}{2}}}
0.000
0
3
{\displaystyle {\tfrac {0}{3}}}
5HP 30/244HP 20/22/24 [ c]
5[ d] [ d]
Progress[ b]
9
3
3
3
Δ Number
1
-1
0
-1
0
Relative Δ
0.250
1
4
{\displaystyle {\tfrac {1}{4}}}
−2.500 [ b]
1
4
:
−
1
10
=
1
4
{\displaystyle {\tfrac {1}{4}}:{\tfrac {-1}{10}}={\tfrac {1}{4}}}
10
−
1
=
10
−
4
{\displaystyle {\tfrac {10}{-1}}={\tfrac {10}{-4}}}
−0.100
−
1
10
{\displaystyle {\tfrac {-1}{10}}}
0.000
0
3
{\displaystyle {\tfrac {0}{3}}}
−0.250
−
1
4
{\displaystyle {\tfrac {-1}{4}}}
0.000
0
3
{\displaystyle {\tfrac {0}{3}}}
5HP 30/24[ f]
5[ d] [ d]
Market Position[ b]
9
3[ e]
3
3
Δ Number
2
2
1
0
1
Relative Δ
0.667
2
3
{\displaystyle {\tfrac {2}{3}}}
2.333 [ b]
2
3
:
2
7
=
2
3
{\displaystyle {\tfrac {2}{3}}:{\tfrac {2}{7}}={\tfrac {2}{3}}}
7
2
=
7
3
{\displaystyle {\tfrac {7}{2}}={\tfrac {7}{3}}}
0.286
2
7
{\displaystyle {\tfrac {2}{7}}}
0.500
1
2
{\displaystyle {\tfrac {1}{2}}}
0.000
0
3
{\displaystyle {\tfrac {0}{3}}}
0.500
1
2
{\displaystyle {\tfrac {1}{2}}}
^ Progress increases cost-effectiveness and is reflected in the ratio of forward gears to main components. power flow:
parallel: using the two degrees of freedom of planetary gearsets
to increase the number of gears
with unchanged number of components serial: in-line combined planetary gearsets without using the two degrees of freedom
to increase the number of gears
a corresponding increase in the number of components is unavoidable ^ a b c d e f g h Innovation Elasticity Classifies Progress And Market Position
Automobile manufacturers drive forward technical developments primarily in order to remain competitive or to achieve or defend technological leadership. This technical progress has therefore always been subject to economic constraints
Only innovations whose relative additional benefit is greater than the relative additional resource input, i.e. whose economic elasticity is greater than 1, are considered for realization
The required innovation elasticity of an automobile manufacturer depends on its expected return on investment. The basic assumption that the relative additional benefit must be at least twice as high as the relative additional resource input helps with orientation
negative, if the output increases and the input decreases, is perfect 2 or above is good 1 or above is acceptable (red) below this is unsatisfactory (bold) ^ a b Direct Predecessor
To reflect the progress of the specific model change ^ a b c d e f plus 1 reverse gear
^ a b of which 2 gearsets are combined as a compound Ravigneaux gearset
^ Reference Standard (Benchmark)
3-speed transmissions with torque converters have established the modern market for automatic transmissions and thus made it possible in the first place, as this design proved to be a particularly successful compromise between cost and performance
It became the archetype and dominated the world market for around 3 decades, setting the standard for automatic transmissions. It was only when fuel consumption became the focus of interest that this design reached its limits, which is why it has now completely disappeared from the market
What has remained is the orientation that it offers as a reference standard (point of reference, benchmark) for this market for determining progressiveness and thus the market position of all other, later designs
All transmission variants consist of 7 main components
Typical examples are
Gearset Concept: Quality [ edit ] The main objective in replacing the predecessor model was to improve vehicle fuel economy with extra speeds and a wider gear span to allow the engine speed level to be lowered (downspeeding).
Gear Ratio Analysis[ a]
In-Depth Analysis[ b] [ c] [ d]
Planetary Gearset: Teeth[ e]
Count
Nomi-[ f] [ g]
Cen-[ h]
Simpson
Simple
Avg.[ i]
Model
Version
S1 [ j] 1 [ k]
S2 [ l] 2 [ m]
S3 [ n] 3 [ o]
Brakes
Ratio
Gear[ p]
Gear
R
1
2
3
4
5
Gear[ b]
i
R
{\displaystyle {i_{R}}}
[ b]
i
1
{\displaystyle {i_{1}}}
[ b]
i
2
{\displaystyle {i_{2}}}
[ b]
i
3
{\displaystyle {i_{3}}}
[ b]
i
4
{\displaystyle {i_{4}}}
[ b]
i
5
{\displaystyle {i_{5}}}
[ b]
Step[ p]
−
i
R
i
1
{\displaystyle -{\frac {i_{R}}{i_{1}}}}
[ q]
i
1
i
1
{\displaystyle {\frac {i_{1}}{i_{1}}}}
i
1
i
2
{\displaystyle {\frac {i_{1}}{i_{2}}}}
[ r]
i
2
i
3
{\displaystyle {\frac {i_{2}}{i_{3}}}}
i
3
i
4
{\displaystyle {\frac {i_{3}}{i_{4}}}}
i
4
i
5
{\displaystyle {\frac {i_{4}}{i_{5}}}}
Δ Step[ s] [ t]
i
1
i
2
:
i
2
i
3
{\displaystyle {\tfrac {i_{1}}{i_{2}}}:{\tfrac {i_{2}}{i_{3}}}}
i
2
i
3
:
i
3
i
4
{\displaystyle {\tfrac {i_{2}}{i_{3}}}:{\tfrac {i_{3}}{i_{4}}}}
i
3
i
4
:
i
4
i
5
{\displaystyle {\tfrac {i_{3}}{i_{4}}}:{\tfrac {i_{4}}{i_{5}}}}
i
4
i
5
:
i
5
i
6
{\displaystyle {\tfrac {i_{4}}{i_{5}}}:{\tfrac {i_{5}}{i_{6}}}}
Shaft
i
1
i
R
{\displaystyle {\frac {i_{1}}{i_{R}}}}
i
1
i
1
{\displaystyle {\frac {i_{1}}{i_{1}}}}
i
1
i
2
{\displaystyle {\frac {i_{1}}{i_{2}}}}
i
1
i
3
{\displaystyle {\frac {i_{1}}{i_{3}}}}
i
1
i
4
{\displaystyle {\frac {i_{1}}{i_{4}}}}
i
1
i
5
{\displaystyle {\frac {i_{1}}{i_{5}}}}
Δ Shaft[ u]
0
−
i
1
i
R
{\displaystyle 0-{\tfrac {i_{1}}{i_{R}}}}
i
1
i
1
−
0
{\displaystyle {\tfrac {i_{1}}{i_{1}}}-0}
i
1
i
2
−
i
1
i
1
{\displaystyle {\tfrac {i_{1}}{i_{2}}}-{\tfrac {i_{1}}{i_{1}}}}
i
1
i
3
−
i
1
i
2
{\displaystyle {\tfrac {i_{1}}{i_{3}}}-{\tfrac {i_{1}}{i_{2}}}}
i
1
i
4
−
i
1
i
3
{\displaystyle {\tfrac {i_{1}}{i_{4}}}-{\tfrac {i_{1}}{i_{3}}}}
i
1
i
5
−
i
1
i
4
{\displaystyle {\tfrac {i_{1}}{i_{5}}}-{\tfrac {i_{1}}{i_{4}}}}
Torque[ c]
μ
R
{\displaystyle \mu _{R}}
[ c]
μ
1
{\displaystyle \mu _{1}}
[ c]
μ
2
{\displaystyle \mu _{2}}
[ c]
μ
3
{\displaystyle \mu _{3}}
[ c]
μ
4
{\displaystyle \mu _{4}}
[ c]
μ
5
{\displaystyle \mu _{5}}
[ c]
Efficiency
η
n
{\displaystyle \eta _{n}}
[ d]
μ
R
i
R
{\displaystyle {\frac {\mu _{R}}{i_{R}}}}
[ d]
μ
1
i
1
{\displaystyle {\frac {\mu _{1}}{i_{1}}}}
[ d]
μ
2
i
2
{\displaystyle {\frac {\mu _{2}}{i_{2}}}}
[ d]
μ
3
i
3
{\displaystyle {\frac {\mu _{3}}{i_{3}}}}
[ d]
μ
4
i
4
{\displaystyle {\frac {\mu _{4}}{i_{4}}}}
[ d]
μ
5
i
5
{\displaystyle {\frac {\mu _{5}}{i_{5}}}}
[ d]
5HP 30
560 N⋅m (413 lb⋅ft )
40
32
38
3
4.5169[ g] [ q]
1.6716
1.4578 [ p]
Gear
R
1
2
3
4
5
Gear[ b]
−3.6842
−
70
19
{\displaystyle -{\tfrac {70}{19}}}
3.5526
135
38
{\displaystyle {\tfrac {135}{38}}}
2.2436
175
78
{\displaystyle {\tfrac {175}{78}}}
1.5449 [ p] [ t]
275
178
{\displaystyle {\tfrac {275}{178}}}
1.0000 [ p]
1
1
{\displaystyle {\tfrac {1}{1}}}
0.7865[ u]
70
89
{\displaystyle {\tfrac {70}{89}}}
Step
1.0370
1.0000
1.5835
1.4522 [ p] 1.5449 [ p] 1.2714
Δ Step[ s]
1.0904
0.9400 [ t] 1.2151
Speed
–0.9643
1.0000
1.5835
2.2995
3.5526
4.5169
Δ Speed
0.9643
1.0000
0.5835
0.7161
1.2531
0.9643 [ u]
Torque[ c]
–3.5078
3.5016
2.2059
1.5272
1.0000
0.7782
Efficiency
η
n
{\displaystyle \eta _{n}}
[ d]
0.9521
0.9856
0.9832
0.9885
1.0000
0.9894
5HP 24
440 N⋅m (325 lb⋅ft )
36
32
35
3
4.4435[ g] [ q]
1.6943
1.4519 [ p]
Gear
R
1
2
3
4
5
Gear[ b]
−4.0952[ q] [ g]
−
86
21
{\displaystyle -{\tfrac {86}{21}}}
3.5714
25
7
{\displaystyle {\tfrac {25}{7}}}
2.2000
11
5
{\displaystyle {\tfrac {11}{5}}}
1.5047 [ t]
161
107
{\displaystyle {\tfrac {161}{107}}}
1.0000 [ p]
1
1
{\displaystyle {\tfrac {1}{1}}}
0.8037[ u]
86
107
{\displaystyle {\tfrac {86}{107}}}
Step
1.1467 [ q]
1.0000
1.6234
1.4621 1.5047 [ p] 1.2419
Δ Step[ s]
1.1103
0.9717 [ t] 1.2094
Speed
-0.8721
1.0000
1.6234
2.3736
3.5714
4.4435
Δ Speed
0.8721
1.0000
0.6234
0.7502
1.1979
0.8721 [ u]
Torque[ c]
–3.8985
3.5200
2.1630
1.4880
1.0000
0.7959
Efficiency
η
n
{\displaystyle \eta _{n}}
[ d]
0.9520
0.9856
0.9832
0.9889
1.0000
0.9902
Actuated Shift Elements
Brake A[ v]
❶
❶
Brake B[ w]
❶
Brake C[ x]
❶
❶
Clutch D[ y]
❶
❶
❶
❶
Clutch E[ z]
❶
❶
Clutch F[ aa]
❶
Geometric Ratios: Speed Conversion
Gear[ b] [ ab] [ ac]
i
R
=
−
S
2
(
S
1
+
R
1
)
(
S
3
+
R
3
)
S
1
R
2
S
3
{\displaystyle i_{R}=-{\frac {S_{2}(S_{1}+R_{1})(S_{3}+R_{3})}{S_{1}R_{2}S_{3}}}}
i
2
=
(
S
2
+
R
2
)
(
S
3
+
R
3
)
S
2
R
3
+
S
3
(
S
2
+
R
2
)
{\displaystyle i_{2}={\frac {(S_{2}+R_{2})(S_{3}+R_{3})}{S_{2}R_{3}+S_{3}(S_{2}+R_{2})}}}
i
R
=
−
S
2
R
2
(
1
+
R
1
S
1
)
(
1
+
R
3
S
3
)
{\displaystyle i_{R}=-{\tfrac {S_{2}}{R_{2}}}\left(1+{\tfrac {R_{1}}{S_{1}}}\right)\left(1+{\tfrac {R_{3}}{S_{3}}}\right)}
i
2
=
1
1
1
+
R
3
S
3
+
1
(
1
+
R
2
S
2
)
(
1
+
S
3
R
3
)
{\displaystyle i_{2}={\tfrac {1}{{\tfrac {1}{1+{\tfrac {R_{3}}{S_{3}}}}}+{\tfrac {1}{\left(1+{\tfrac {R_{2}}{S_{2}}}\right)\left(1+{\tfrac {S_{3}}{R_{3}}}\right)}}}}}
Gear[ b] [ ab] [ ac]
i
1
=
S
3
+
R
3
S
3
{\displaystyle i_{1}={\frac {S_{3}+R_{3}}{S_{3}}}}
i
5
=
S
2
(
S
1
+
R
1
)
(
S
3
+
R
3
)
S
2
(
S
1
+
R
1
)
(
S
3
+
R
3
)
+
S
1
R
2
S
3
{\displaystyle i_{5}={\frac {S_{2}(S_{1}+R_{1})(S_{3}+R_{3})}{S_{2}(S_{1}+R_{1})(S_{3}+R_{3})+S_{1}R_{2}S_{3}}}}
i
1
=
1
+
R
3
S
3
{\displaystyle i_{1}=1+{\tfrac {R_{3}}{S_{3}}}}
i
5
=
1
1
+
R
2
S
2
(
1
+
R
1
S
1
)
(
1
+
R
3
S
3
)
{\displaystyle i_{5}={\tfrac {1}{1+{\tfrac {\tfrac {R_{2}}{S_{2}}}{\left(1+{\tfrac {R_{1}}{S_{1}}}\right)\left(1+{\tfrac {R_{3}}{S_{3}}}\right)}}}}}
Gear[ b] [ ab] [ ac]
i
3
=
(
S
1
(
S
2
+
R
2
)
+
R
1
S
2
)
(
S
3
+
R
3
)
S
2
(
S
1
+
R
1
)
(
S
3
+
R
3
)
+
S
1
R
2
S
3
{\displaystyle i_{3}={\frac {(S_{1}(S_{2}+R_{2})+R_{1}S_{2})(S_{3}+R_{3})}{S_{2}(S_{1}+R_{1})(S_{3}+R_{3})+S_{1}R_{2}S_{3}}}}
i
4
=
1
1
{\displaystyle i_{4}={\frac {1}{1}}}
i
3
=
1
1
1
1
+
S
1
R
1
+
1
+
R
2
S
2
1
+
R
1
S
1
+
1
(
1
+
S
2
R
2
(
1
+
R
1
S
1
)
)
(
1
+
R
3
S
3
)
{\displaystyle i_{3}={\tfrac {1}{{\tfrac {1}{{\tfrac {1}{1+{\tfrac {S_{1}}{R_{1}}}}}+{\tfrac {1+{\tfrac {R_{2}}{S_{2}}}}{1+{\tfrac {R_{1}}{S_{1}}}}}}}+{\tfrac {1}{\left(1+{\tfrac {S_{2}}{R_{2}}}\left(1+{\tfrac {R_{1}}{S_{1}}}\right)\right)\left(1+{\tfrac {R_{3}}{S_{3}}}\right)}}}}}
Kinetic Ratios: Torque Conversion
Torque[ c]
μ
R
=
−
S
2
R
2
η
0
(
1
+
R
1
S
1
η
0
)
(
1
+
R
3
S
3
η
0
)
{\displaystyle \mu _{R}=-{\tfrac {S_{2}}{R_{2}}}\eta _{0}\left(1+{\tfrac {R_{1}}{S_{1}}}\eta _{0}\right)\left(1+{\tfrac {R_{3}}{S_{3}}}\eta _{0}\right)}
μ
1
=
1
+
R
3
S
3
η
0
{\displaystyle \mu _{1}=1+{\tfrac {R_{3}}{S_{3}}}\eta _{0}}
Torque[ c]
μ
2
=
1
1
1
+
R
3
S
3
η
0
+
1
(
1
+
R
2
S
2
η
0
)
(
1
+
S
3
R
3
η
0
)
{\displaystyle \mu _{2}={\tfrac {1}{{\tfrac {1}{1+{\tfrac {R_{3}}{S_{3}}}\eta _{0}}}+{\tfrac {1}{\left(1+{\tfrac {R_{2}}{S_{2}}}\eta _{0}\right)\left(1+{\tfrac {S_{3}}{R_{3}}}\eta _{0}\right)}}}}}
μ
5
=
1
1
+
R
2
S
2
⋅
1
η
0
(
1
+
R
1
S
1
η
0
)
(
1
+
R
3
S
3
η
0
)
{\displaystyle \mu _{5}={\tfrac {1}{1+{\tfrac {{\tfrac {R_{2}}{S_{2}}}\cdot {\tfrac {1}{\eta _{0}}}}{\left(1+{\tfrac {R_{1}}{S_{1}}}\eta _{0}\right)\left(1+{\tfrac {R_{3}}{S_{3}}}\eta _{0}\right)}}}}}
Torque[ c]
μ
3
=
1
1
1
1
+
S
1
R
1
⋅
1
η
0
1
3
+
1
+
R
2
S
2
η
0
1
2
1
+
R
1
S
1
⋅
1
η
0
1
3
+
1
(
1
+
S
2
R
2
η
0
1
2
(
1
+
R
1
S
1
η
0
1
3
)
)
(
1
+
R
3
S
3
η
0
)
{\displaystyle \mu _{3}={\tfrac {1}{{\tfrac {1}{{\tfrac {1}{1+{\tfrac {S_{1}}{R_{1}}}\cdot {\tfrac {1}{{\eta _{0}}^{\tfrac {1}{3}}}}}}+{\tfrac {1+{\tfrac {R_{2}}{S_{2}}}{\eta _{0}}^{\tfrac {1}{2}}}{1+{\tfrac {R_{1}}{S_{1}}}\cdot {\tfrac {1}{{\eta _{0}}^{\tfrac {1}{3}}}}}}}}+{\tfrac {1}{\left(1+{\tfrac {S_{2}}{R_{2}}}{\eta _{0}}^{\tfrac {1}{2}}\left(1+{\tfrac {R_{1}}{S_{1}}}{\eta _{0}}^{\tfrac {1}{3}}\right)\right)\left(1+{\tfrac {R_{3}}{S_{3}}}\eta _{0}\right)}}}}}
μ
4
=
1
1
{\displaystyle \mu _{4}={\tfrac {1}{1}}}
^ Revised 14 January 2026Nomenclature
S
n
=
{\displaystyle S_{n}=}
R
n
=
{\displaystyle R_{n}=}
C
n
=
{\displaystyle \color {gray}{C_{n}=}}
carrier or planetary gear carrier (not needed)
s
n
=
{\displaystyle s_{n}=}
r
n
=
{\displaystyle r_{n}=}
c
n
=
{\displaystyle c_{n}=}
n
=
{\displaystyle n=}
i
n
=
{\displaystyle i_{n}=}
ω
1
;
n
=
ω
t
=
{\displaystyle \omega _{1;n}=\omega _{t}=}
ω
2
;
n
=
{\displaystyle \omega _{2;n}=}
T
1
;
n
=
T
t
=
{\displaystyle T_{1;n}=T_{t}=}
T
2
;
n
=
{\displaystyle T_{2;n}=}
μ
n
=
{\displaystyle \mu _{n}=}
η
n
=
{\displaystyle \eta _{n}=}
i
0
=
{\displaystyle i_{0}=}
η
0
=
{\displaystyle \eta _{0}=}
^ a b c d e f g h i j k l m Gear Ratio (Transmission Ratio)
i
n
{\displaystyle i_{n}}
The gear ratio
i
n
{\displaystyle i_{n}}
is the ratio of
input shaft speed
ω
1
;
n
{\displaystyle \omega _{1;n}}
to output shaft speed
ω
2
;
n
{\displaystyle \omega _{2;n}}
and therefore corresponds to the reciprocal of the shaft speeds
i
n
=
1
ω
2
;
n
ω
1
;
n
=
ω
1
;
n
ω
2
;
n
=
ω
t
ω
2
;
n
{\displaystyle i_{n}={\frac {1}{\frac {\omega _{2;n}}{\omega _{1;n}}}}={\frac {\omega _{1;n}}{\omega _{2;n}}}={\frac {\omega _{t}}{\omega _{2;n}}}}
^ a b c d e f g h i j k l m Torque Ratio (Torque Conversion Ratio)
μ
n
{\displaystyle \mu _{n}}
The torque ratio
μ
n
{\displaystyle \mu _{n}}
is the ratio of
output torque
T
2
;
n
{\displaystyle T_{2;n}}
to input torque
T
1
;
n
{\displaystyle T_{1;n}}
minus efficiency losses
and therefore corresponds (apart from the efficiency losses) to the reciprocal of the shaft speeds too
μ
n
=
i
n
η
n
;
η
0
=
ω
1
;
n
η
n
;
η
0
ω
2
;
n
=
T
2
;
n
η
n
;
η
0
T
1
;
n
{\displaystyle \mu _{n}=i_{n}\eta _{n;\eta _{0}}={\frac {\omega _{1;n}\eta _{n;\eta _{0}}}{\omega _{2;n}}}={\frac {T_{2;n}\eta _{n;\eta _{0}}}{T_{1;n}}}}
whereby
η
n
;
η
0
{\displaystyle \eta _{n;\eta _{0}}}
0
≤
η
n
;
η
0
≤
1
{\displaystyle 0\leq \eta _{n;\eta _{0}}\leq 1}
^ a b c d e f g h i j Efficiency
The efficiency
η
n
{\displaystyle \eta _{n}}
from the torque ratio
in relation to the gear ratio (transmission ratio)
η
n
=
μ
n
i
n
{\displaystyle \eta _{n}={\frac {\mu _{n}}{i_{n}}}}
Power loss for single meshing gears
is in the range of 1 % to 1.5 %
helical gear pairs, which are used to reduce noise in passenger cars, are in the upper part of the loss range
spur gear pairs, which are limited to commercial vehicles due to their poorer noise comfort, are in the lower part of the loss range Corridor for torque ratio and efficiency
in planetary gearsets, the stationary gear ratio
i
0
{\displaystyle i_{0}}
is formed via the planetary gears and thus by two meshes
for reasons of simplification, the efficiency for both meshes together is commonly specified there
the efficiencies
η
0
{\displaystyle \eta _{0}}
stationary ratio
i
0
{\displaystyle i_{0}}
of
η
0
=
0.9800
{\displaystyle \eta _{0}=0.9800}
and
η
0
=
0.9700
{\displaystyle \eta _{0}=0.9700}
for both interventions together
The corresponding efficiency
for single-meshing gear pairs is
η
0
1
2
{\displaystyle {\eta _{0}}^{\tfrac {1}{2}}}
at
0.9800
1
2
=
0.98995
{\displaystyle 0.9800^{\tfrac {1}{2}}=0.98995}
and
0.9700
1
2
=
0.98489
{\displaystyle 0.9700^{\tfrac {1}{2}}=0.98489}
^ Layout
Input and output are on opposite sides
Planetary gearset 1 is on the input (turbine) side
Input shafts are, if actuated, S1 , C2 , S3 , and R1
Output shaft is C3 ^ Total Ratio Span (Total Gear/Transmission Ratio) Nominal
ω
2
;
n
ω
2
;
1
=
ω
2
;
n
ω
2
;
1
ω
2
;
n
ω
2
;
1
ω
2
;
1
ω
2
;
n
=
1
ω
2
;
1
1
ω
2
;
n
=
ω
t
ω
2
;
1
ω
t
ω
2
;
n
=
i
1
i
n
{\displaystyle {\frac {\omega _{2;n}}{\omega _{2;1}}}={\frac {\frac {\omega _{2;n}}{\omega _{2;1}\omega _{2;n}}}{\frac {\omega _{2;1}}{\omega _{2;1}\omega _{2;n}}}}={\frac {\frac {1}{\omega _{2;1}}}{\frac {1}{\omega _{2;n}}}}={\frac {\frac {\omega _{t}}{\omega _{2;1}}}{\frac {\omega _{t}}{\omega _{2;n}}}}={\frac {i_{1}}{i_{n}}}}
A wider span enables the
downspeeding when driving outside the city limits
increase the climbing ability
when driving over mountain passes or off-road
or when towing a trailer ^ a b c d Total Ratio Span (Total Gear Ratio/Total Transmission Ratio) Effective
ω
2
;
n
m
a
x
(
ω
2
;
1
;
|
ω
2
;
R
|
)
=
m
i
n
(
i
1
;
|
i
R
|
)
i
n
{\displaystyle {\frac {\omega _{2;n}}{max(\omega _{2;1};|\omega _{2;R}|)}}={\frac {min(i_{1};|i_{R}|)}{i_{n}}}}
The span is only effective to the extent that
the reverse gear ratio
matches that of 1st gear
see also Standard R:1 Digression
is usually longer than 1st gear the effective span is therefore of central importance for describing the suitability of a transmission because in these cases, the nominal spread conveys a misleading picture which is only unproblematic for vehicles with high specific power Market participants
Manufacturers naturally have no interest in specifying the effective span Users have not yet formulated the practical benefits that the effective span has for them The effective span has not yet played a role in research and teaching Contrary to its significance
the effective span has therefore not yet been able to establish itself
either in theory or in practice. End of digression ^ Ratio Span's Center
(
i
1
i
n
)
1
2
{\displaystyle (i_{1}i_{n})^{\frac {1}{2}}}
The center indicates the speed level of the transmission
Together with the final drive ratio
it gives the shaft speed level of the vehicle ^ Average Gear Step
(
ω
2
;
n
ω
2
;
1
)
1
n
−
1
=
(
i
1
i
n
)
1
n
−
1
{\displaystyle \left({\frac {\omega _{2;n}}{\omega _{2;1}}}\right)^{\frac {1}{n-1}}=\left({\frac {i_{1}}{i_{n}}}\right)^{\frac {1}{n-1}}}
There are
n
−
1
{\displaystyle n-1}
n
{\displaystyle n}
with decreasing step width
the gears connect better to each other
shifting comfort increases ^ Sun 1: sun gear of gearset 1
^ Ring 1: ring gear of gearset 1
^ Sun 2: sun gear of gearset 2
^ Ring 2: ring gear of gearset 2
^ Sun 3: sun gear of gearset 3
^ Ring 3: ring gear of gearset 3
^ a b c d e f g h i j Standard 50:50
With steadily decreasing gear steps (yellow highlighted line Step )
and a particularly large step from 1st to 2nd gear
the lower half of the gear steps (between the small gears; rounded down, here the first 2) is always larger
and the upper half of the gear steps (between the large gears; rounded up, here the last 2) is always smaller
than the average gear step (cell highlighted yellow two rows above on the far right)lower half: smaller gear steps are a waste of possible ratios (red bold)
upper half: larger gear steps are unsatisfactory (red bold) ^ a b c d e Standard R:1
The ideal reverse gear has the same transmission ratio as 1st gear
no impairment when maneuvering
especially when towing a trailer
a torque converter can only partially compensate for this deficiency
Plus 11.11 % minus 10 % compared to 1st gear is good
Plus 25 % minus 20 % is acceptable (red) Above this is unsatisfactory (bold) see also Total Ratio Span (Total Gear/Transmission Ratio) Effective ^ Standard 1:2
With continuously decreasing gear steps (yellow marked line Step )
the largest gear step is the one from 1st to 2nd gear, which
for a good speed connection and
a smooth gear shift
must be as small as possible
A gear ratio of up to 1.6667 : 1 (5 : 3) is good
Up to 1.7500 : 1 (7 : 4) is acceptable (red) Above is unsatisfactory (bold) ^ a b c From large to small gears (from right to left)
^ a b c d e Standard STEP
Gear steps should
increase: Δ Step (first green highlighted line Δ Step ) is always greater than 1As progressive as possible: Δ Step is always greater than the previous step
Not progressively increasing is acceptable (red) Not increasing is unsatisfactory (bold) ^ a b c d e Standard SPEED
Shaft speed differences should
increase: Δ Shaft Speed (second line marked in green Δ (Shaft) Speed ) is always greater than the previous one
1 difference smaller than the previous one is acceptable (red) 2 consecutive ones are a waste of possible ratios (bold) ^ Blocks S1
^ Blocks C1
^ Blocks R3
^ Connects S2 and S3 with the input (turbine)
^ Connects R1 with the input (turbine)
^ Connects C1 with the input (turbine)
^ a b c Ordinary Noted
For direct determination of the gear ratio ^ a b c Elementary Noted
Alternative representation for determining the transmission ratio
Contains only operands
With simple fractions of both central gears of a planetary gearset
Or with the value 1
As a basis
For reliable
And traceable
Determination of the torque conversion ratio and efficiency
[ edit ]
Introduced in MY 1991 on the BMW E36 320i/325i and E34 5 Series.
Input torque maximum is 310 N⋅m (229 lb⋅ft )
Weight: ~75 kg (165 lb )Oil capacity: ~10.5 L (11.1 US qt )Applications [ 1]
Applications [ 1]
BMW — longitudinal engine , rear wheel drive
Applications [ 1]
Volkswagen Group — longitudinal engine transaxle , front-wheel drive
Applications [ 1]
Volkswagen Group — longitudinal engine , transaxle permanent four-wheel drive
1999 (DRN/EKX) transmissions used Induction speed sensors and 2000+ (FAS) transmissions used Hall Effect sensors. These transmissions are mechanically the same, but are not interchangeable.
Applications [ 1]
Porsche — longitudinal engine rear engine transaxle
Applications [ 1]
Porsche — longitudinal engine rear engine transaxle
Porsche — mid-engine design flat-six engine , 5-speed tiptronic #1060, rear-wheel drive A87.01-xxx, A87.02-xxx, A87.21-xxx , [5HP19FL Valve Body, Solenoids, and Speed Sensor. Different Wiring Harness.] [Speed Sensor/Pulser part # ZF 0501314432]
1997-2004 Porsche Boxster 986 2.5 6-cyl
1997-2004 Porsche Boxster 986 2.7 6-cyl
1997-2004 Porsche Boxster 986 3.2 6-cyl
2005–2008 Porsche Boxster 987 2.7 6-cyl
2005–2008 Porsche Boxster S 987 3.4 6-cyl
2005–2008 Porsche Cayman 987 2.7 6-cyl
2005–2008 Porsche Cayman S 987 3.4 6-cyl
[ edit ]
Applications [ 1]
Applications [ 1]
Applications [ 1]
