ZF 5HP transmission

5HP is ZF Friedrichshafen AG's trademark name for its 5-speed automatic transmission models (5-speed transmission with Hydraulic converter and Planetary gearsets) for longitudinal engine applications, designed and built by ZF's subsidiary in Saarbrücken.

Key data

Gear ratiosTemplate:Efn

Model	First Deliv- ery	Gear						Total Span			Avg. Step	Components		Nomenclature
		R	1	2	3	4	5	Nomi- nal	Effec- tive	Cen- ter		Total	per GearTemplate:Efn	Gears Count	Cou- pling	Gear- sets	Input Shaft Diameter
Ravigneaux types														5Template:Efn	HTemplate:Efn	PTemplate:Efn
5HP 18 5HP 19	1990 1997	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	3 Gearsets 3 Brakes 4 Clutches	Template:Round				18 mm 19 mm
Simpson types
5HP 30	1992	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	3  Gearsets 3 Brakes 3 Clutches	Template:Round				30 mm
5HP 24	1996	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round	Template:Round						24 mm
Template:Notelist

1990: 5HP 18 & 1997: 5HP 19
— Ravigneaux planetary gearset types —

History

The Ravigneaux planetary gearset types were ZF's first 5-speed automatic transmission and introduced in 1990. They were produced through 2008 in different versions and were used in a wide range of vehicles. Since the successor model, the 6HP, could be manufactured at a significantly lower cost, most of the gearboxes were replaced shortly after its launch in 2000.

Planetary gearset concept

Improved fuel economy

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), which is a decisive factor in improving energy efficiency and thus reducing fuel consumption. In addition, the lower engine speed level improves the noise-vibration-harshness comfort and the exterior noise is reduced.

Increased manufacturing complexity

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.

Planetary gearset concept: manufacturing complexityTemplate:Efn

With Assessment	Output: Gear Ratios	Innovation ElasticityTemplate:Efn Δ Output : Δ Input	Input: Main Components
			Total	Gearsets	Brakes	Clutches
5HP 18/19 Ref. Object	$n_{O1}$ $n_{O2}$	TopicTemplate:Efn	$n_I=n_G+$ $n_B+n_C$	$n_{G1}$ $n_{G2}$	$n_{B1}$ $n_{B2}$	$n_{C1}$ $n_{C2}$
Δ Number	$n_{O1}-n_{O2}$		$n_{I1}-n_{I2}$	$n_{G1}-n_{G2}$	$n_{B1}-n_{B2}$	$n_{C1}-n_{C2}$
Relative Δ	Δ Output $\frac{n_{O1}-n_{O2}}{n_{O2}}$	$\frac{n_{O1}-n_{O2}}{n_{O2}}:\frac{n_{I1}-n_{I2}}{n_{I2}}$ $=\frac{n_{O1}-n_{O2}}{n_{O2}}$·$\frac{n_{I2}}{n_{I1}-n_{I2}}$	Δ Input $\frac{n_{I1}-n_{I2}}{n_{I2}}$	$\frac{n_{G1}-n_{G2}}{n_{G2}}$	$\frac{n_{B1}-n_{B2}}{n_{B2}}$	$\frac{n_{C1}-n_{C2}}{n_{C2}}$
5HP 18/19 4HP 14/16/18Template:Efn	5Template:Efn 4Template:Efn	ProgressTemplate:Efn	10 7	3Template:Efn 2Template:Efn	3 2	4 3
Δ Number	1		3	1	1	1
Relative Δ	Template:Round $\frac{1}{4}$	Template:Font colorTemplate:Efn $\frac{1}{4}:\frac{3}{7}=\frac{1}{4}$·$\frac{7}{3}=\frac{7}{12}$	Template:Round $\frac{3}{7}$	Template:Round $\frac{1}{2}$	Template:Round $\frac{1}{2}$	Template:Round $\frac{1}{3}$
5HP 18/19 4HP 20/22/24Template:Efn	5Template:Efn 4Template:Efn	ProgressTemplate:Efn	10 10	3Template:Efn 3	3 4	4 3
Δ Number	1		0	0	-1	1
Relative Δ	Template:Round $\frac{1}{4}$	∞Template:Efn $\frac{1}{4}:\frac{0}{10}=\frac{1}{4}$·$\frac{10}{0}=\frac{10}{0}$	Template:Round $\frac{0}{10}$	Template:Round $\frac{0}{3}$	Template:Round $\frac{-1}{4}$	Template:Round $\frac{1}{3}$
5HP 18/19 3-SpeedTemplate:Efn	5Template:Efn 3Template:Efn	Market PositionTemplate:Efn	10 7	3Template:Efn 2Template:Efn	3 3	4 2
Δ Number	2		3	1	0	2
Relative Δ	Template:Round $\frac{2}{3}$	Template:Font colorTemplate:Efn $\frac{2}{3}:\frac{3}{7}=\frac{2}{3}$·$\frac{7}{3}=\frac{14}{9}$	Template:Round $\frac{3}{7}$	Template:Round $\frac{1}{2}$	Template:Round $\frac{0}{3}$	Template:Round $\frac{2}{2}$
Template:Notelist

Quality

Planetary gearset concept: gear ratio qualityTemplate:Efn

In-Depth AnalysisTemplate:Efn With Assessment And Torque RatioTemplate:Efn And Efficiency CalculationTemplate:Efn		Planetary Gearset: TeethTemplate:Efn			Count	Nomi- nalTemplate:Efn Effec- tiveTemplate:Efn	Cen- terTemplate:Efn
		Ravigneaux		Simple			Avg.Template:Efn
Model Type	Version First Delivery	S1Template:Efn R1Template:Efn	S2Template:Efn R2Template:Efn	S3Template:Efn R3Template:Efn	Brakes Clutches	Ratio Span	Gear StepTemplate:Efn
Gear	R		1	2	3	4	5
Gear RatioTemplate:Efn	$i_R$Template:Efn		$i_1$Template:Efn	$i_2$Template:Efn	$i_3$Template:Efn	$i_4$Template:Efn	$i_5$Template:Efn
StepTemplate:Efn	$-\frac{i_R}{i_1}$Template:Efn		$\frac{i_1}{i_1}$	$\frac{i_1}{i_2}$Template:Efn	$\frac{i_2}{i_3}$	$\frac{i_3}{i_4}$	$\frac{i_4}{i_5}$
Δ StepTemplate:EfnTemplate:Efn				$\frac{i_1}{i_2}:\frac{i_2}{i_3}$	$\frac{i_2}{i_3}:\frac{i_3}{i_4}$	$\frac{i_3}{i_4}:\frac{i_4}{i_5}$
Shaft Speed	$\frac{i_1}{i_R}$		$\frac{i_1}{i_1}$	$\frac{i_1}{i_2}$	$\frac{i_1}{i_3}$	$\frac{i_1}{i_4}$	$\frac{i_1}{i_5}$
Δ Shaft SpeedTemplate:Efn	$0-\frac{i_1}{i_R}$		$\frac{i_1}{i_1}-0$	$\frac{i_1}{i_2}-\frac{i_1}{i_1}$	$\frac{i_1}{i_3}-\frac{i_1}{i_2}$	$\frac{i_1}{i_4}-\frac{i_1}{i_3}$	$\frac{i_1}{i_5}-\frac{i_1}{i_4}$
Torque RatioTemplate:Efn	${\mu }_R$Template:Efn		${\mu }_1$Template:Efn	${\mu }_2$Template:Efn	${\mu }_3$Template:Efn	${\mu }_4$Template:Efn	${\mu }_5$Template:Efn
Efficiency ${\eta }_n$Template:Efn	$\frac{{\mu }_R}{i_R}$Template:Efn		$\frac{{\mu }_1}{i_1}$Template:Efn	$\frac{{\mu }_2}{i_2}$Template:Efn	$\frac{{\mu }_3}{i_3}$Template:Efn	$\frac{{\mu }_4}{i_4}$Template:Efn	$\frac{{\mu }_5}{i_5}$Template:Efn
5HP 18	Template:Convert 1990	38 34Template:Efn	34 98	32 76	3 4	Template:Round Template:Round Template:EfnTemplate:Efn	Template:Round
							Template:Font color Template:Efn
Gear	R		1	2	3	4	5
Gear RatioTemplate:Efn	Template:Font color		Template:Round $\frac{1,323}{361}$	Template:Font color	Template:Font color	1.0000 $\frac{1}{1}$	Template:Round $\frac{49}{66}$
Step	Template:Font colorTemplate:Efn		1.0000	Template:Font colorTemplate:Efn	Template:Font colorTemplate:Efn	1.4067	1.3469
Δ StepTemplate:Efn				1.2901	Template:Font colorTemplate:Efn	1.0444
Speed	Template:Font color		1.0000	1.8333	Template:Font color	3.6648	4.9363
Δ Speed	Template:Font color		1.0000	0.8333	Template:Font colorTemplate:Efn	1.0596	1.2715
Torque RatioTemplate:Efn	–3.9903 –3.9378		3.5344 3.4700	1.9581 1.9377	1.3861 1.3758	1.0000	0.7385 0.7366
Efficiency ${\eta }_n$Template:Efn	0.9742 0.9614		0.9644 0.9468	0.9795 0.9693	0.9854 0.9780	1.0000	0.9948 0.9921
5HP 19	Template:Convert 1997	38 34Template:Efn	34 98	32 76	3 4	Template:Round Template:Round Template:EfnTemplate:Efn	Template:Round
							Template:Font color Template:Efn
Gear	R		1	2	3	4	5
Gear RatioTemplate:Efn	Template:Font color		Template:Round	Template:Font color	Template:Font color	1.0000	Template:Round
Actuated shift elements
Brake ATemplate:Efn				❶	❶		❶
Brake BTemplate:Efn	❶		❶
Brake CTemplate:Efn	❶		❶	❶
Clutch DTemplate:Efn			❶	❶	❶	❶
Clutch ETemplate:Efn	❶
Clutch FTemplate:Efn						❶	❶
Clutch GTemplate:Efn					❶	❶	❶
Geometric ratios: speed conversion
Gear RatioTemplate:Efn R & 1 OrdinaryTemplate:Efn Elementary NotedTemplate:Efn	$i_R=-\frac{R_2(S_3+R_3)}{S_2{R}_3}$			$i_1=\frac{R_1{R}_2(S_3+R_3)}{S_1{S}_2{R}_3}$
	$i_R=-\frac{R_2}{S_2}(1+\frac{S_3}{R_3})$			$i_1=\frac{R_1{R}_2}{S_1{S}_2}(1+\frac{S_3}{R_3})$
Gear RatioTemplate:Efn 2 & 3 OrdinaryTemplate:Efn Elementary NotedTemplate:Efn	$i_2=\frac{R_2(S_1+R_1)(S_3+R_3)}{S_1{R}_3(S_2+R_2)}$				$i_3=\frac{R_2(S_1+R_1)}{S_1(S_2+R_2)}$
	$i_2=\frac{(1+\frac{R_1}{S_1})(1+\frac{S_3}{R_3})}{1+\frac{S_2}{R_2}}$				$i_3=\frac{1+\frac{R_1}{S_1}}{1+\frac{S_2}{R_2}}$
Gear RatioTemplate:Efn 4 & 5 OrdinaryTemplate:Efn Elementary NotedTemplate:Efn	$i_4=\frac{1}{1}$			$i_5=\frac{R_2}{S_2+R_2}$
				$i_5=\frac{1}{1+\frac{S_2}{R_2}}$
Kinetic ratios: torque conversion
Torque RatioTemplate:Efn R & 1	${\mu }_R=-\frac{R_2}{S_2}{\eta }_0(1+\frac{S_3}{R_3}{\eta }_0)$			${\mu }_1=\frac{R_1{R}_2}{S_1{S}_2}{{\eta }_0}^{\frac{3}{2}}(1+\frac{S_3}{R_3}{\eta }_0)$
Torque RatioTemplate:Efn 2 & 3	${\mu }_2=\frac{(1+\frac{R_1}{S_1}{\eta }_0)(1+\frac{S_3}{R_3}{\eta }_0)}{1+\frac{S_2}{R_2}\cdot \frac{1}{{\eta }_0}}$				${\mu }_3=\frac{1+\frac{R_1}{S_1}{\eta }_0}{1+\frac{S_2}{R_2}\cdot \frac{1}{{\eta }_0}}$
Torque RatioTemplate:Efn 4 & 5	${\mu }_4=\frac{1}{1}$			${\mu }_5=\frac{1}{1+\frac{S_2}{R_2}\cdot \frac{1}{{\eta }_0}}$
Template:Notelist

1992: 5HP 30 & 1996: 5HP 24
— Simpson planetary gearset types —

History

The Simpson planetary gearset types were ZF's second 5-speed automatic transmission and introduced in 1992. They were produced through 2000 in different versions and were used in a wide range of vehicles. Since the successor model, the 6HP, could be manufactured at a significantly lower cost, most of the gearboxes were replaced shortly after its launch in 2000.

Planetary gearset concept

Improved fuel economy

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), which is a decisive factor in improving energy efficiency and thus reducing fuel consumption. In addition, the lower engine speed level improves the noise-vibration-harshness comfort and the exterior noise is reduced.

Reduced manufacturing complexity

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. In order to avoid a further increase in manufacturing complexity while expanding the number of gear ratios, ZF switched from the conventional design method—in which the planetary gearset concept was limited to a purely serial or in-line power flow—to a more modern design method that utilizes a planetary gearset concept with combined parallel and serial power flow. This was only possible thanks to computer-aided design and has resulted in a globally patented gearset concept. 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 8HP has become the new reference standard (benchmark) for automatic transmissions.

Planetary gearset concept: manufacturing complexityTemplate:Efn

With Assessment	Output: Gear Ratios	Innovation ElasticityTemplate:Efn Δ Output : Δ Input	Input: Main Components
			Total	Gearsets	Brakes	Clutches
5HP 30/24 Ref. Object	$n_{O1}$ $n_{O2}$	TopicTemplate:Efn	$n_I=n_G+$ $n_B+n_C$	$n_{G1}$ $n_{G2}$	$n_{B1}$ $n_{B2}$	$n_{C1}$ $n_{C2}$
Δ Number	$n_{O1}-n_{O2}$		$n_{I1}-n_{I2}$	$n_{G1}-n_{G2}$	$n_{B1}-n_{B2}$	$n_{C1}-n_{C2}$
Relative Δ	Δ Output $\frac{n_{O1}-n_{O2}}{n_{O2}}$	$\frac{n_{O1}-n_{O2}}{n_{O2}}:\frac{n_{I1}-n_{I2}}{n_{I2}}$ $=\frac{n_{O1}-n_{O2}}{n_{O2}}$·$\frac{n_{I2}}{n_{I1}-n_{I2}}$	Δ Input $\frac{n_{I1}-n_{I2}}{n_{I2}}$	$\frac{n_{G1}-n_{G2}}{n_{G2}}$	$\frac{n_{B1}-n_{B2}}{n_{B2}}$	$\frac{n_{C1}-n_{C2}}{n_{C2}}$
5HP 30/24 4HP 14/16/18Template:Efn	5Template:Efn 4Template:Efn	ProgressTemplate:Efn	9 7	3 2Template:Efn	3 2	3 3
Δ Number	1		2	1	1	0
Relative Δ	Template:Round $\frac{1}{4}$	Template:Font colorTemplate:Efn $\frac{1}{4}:\frac{2}{7}=\frac{1}{4}$·$\frac{7}{2}=\frac{7}{8}$	Template:Round $\frac{2}{7}$	Template:Round $\frac{1}{2}$	Template:Round $\frac{1}{2}$	Template:Round $\frac{0}{3}$
5HP 30/24 4HP 20/22/24Template:Efn	5Template:Efn 4Template:Efn	ProgressTemplate:Efn	9 10	3 3	3 4	3 3
Δ Number	1		-1	0	-1	0
Relative Δ	Template:Round $\frac{1}{4}$	Template:RoundTemplate:Efn $\frac{1}{4}:\frac{-1}{10}=\frac{1}{4}$·$\frac{10}{-1}=\frac{10}{-4}$	Template:Round $\frac{-1}{10}$	Template:Round $\frac{0}{3}$	Template:Round $\frac{-1}{4}$	Template:Round $\frac{0}{3}$
5HP 30/24 3-SpeedTemplate:Efn	5Template:Efn 3Template:Efn	Market PositionTemplate:Efn	9 7	3 2Template:Efn	3 3	3 2
Δ Number	2		2	1	0	1
Relative Δ	Template:Round $\frac{2}{3}$	Template:RoundTemplate:Efn $\frac{2}{3}:\frac{2}{7}=\frac{2}{3}$·$\frac{7}{2}=\frac{7}{3}$	Template:Round $\frac{2}{7}$	Template:Round $\frac{1}{2}$	Template:Round $\frac{0}{3}$	Template:Round $\frac{1}{2}$
Template:Notelist

Quality

Planetary gearset concept: gear ratio qualityTemplate:Efn

In-Depth AnalysisTemplate:Efn With Assessment And Torque RatioTemplate:Efn And Efficiency CalculationTemplate:Efn		Planetary Gearset: TeethTemplate:Efn			Count	Nomi- nalTemplate:Efn Effec- tiveTemplate:Efn	Cen- terTemplate:Efn
		Simpson		Simple			Avg.Template:Efn
Model Type	Version First Delivery	S1Template:Efn R1Template:Efn	S2Template:Efn R2Template:Efn	S3Template:Efn R3Template:Efn	Brakes Clutches	Ratio Span	Gear StepTemplate:Efn
Gear	R		1	2	3	4	5
Gear RatioTemplate:Efn	$i_R$Template:Efn		$i_1$Template:Efn	$i_2$Template:Efn	$i_3$Template:Efn	$i_4$Template:Efn	$i_5$Template:Efn
StepTemplate:Efn	$-\frac{i_R}{i_1}$Template:Efn		$\frac{i_1}{i_1}$	$\frac{i_1}{i_2}$Template:Efn	$\frac{i_2}{i_3}$	$\frac{i_3}{i_4}$	$\frac{i_4}{i_5}$
Δ StepTemplate:EfnTemplate:Efn				$\frac{i_1}{i_2}:\frac{i_2}{i_3}$	$\frac{i_2}{i_3}:\frac{i_3}{i_4}$	$\frac{i_3}{i_4}:\frac{i_4}{i_5}$	$\frac{i_4}{i_5}:\frac{i_5}{i_6}$
Shaft Speed	$\frac{i_1}{i_R}$		$\frac{i_1}{i_1}$	$\frac{i_1}{i_2}$	$\frac{i_1}{i_3}$	$\frac{i_1}{i_4}$	$\frac{i_1}{i_5}$
Δ Shaft SpeedTemplate:Efn	$0-\frac{i_1}{i_R}$		$\frac{i_1}{i_1}-0$	$\frac{i_1}{i_2}-\frac{i_1}{i_1}$	$\frac{i_1}{i_3}-\frac{i_1}{i_2}$	$\frac{i_1}{i_4}-\frac{i_1}{i_3}$	$\frac{i_1}{i_5}-\frac{i_1}{i_4}$
Torque RatioTemplate:Efn	${\mu }_R$Template:Efn		${\mu }_1$Template:Efn	${\mu }_2$Template:Efn	${\mu }_3$Template:Efn	${\mu }_4$Template:Efn	${\mu }_5$Template:Efn
Efficiency ${\eta }_n$Template:Efn	$\frac{{\mu }_R}{i_R}$Template:Efn		$\frac{{\mu }_1}{i_1}$Template:Efn	$\frac{{\mu }_2}{i_2}$Template:Efn	$\frac{{\mu }_3}{i_3}$Template:Efn	$\frac{{\mu }_4}{i_4}$Template:Efn	$\frac{{\mu }_5}{i_5}$Template:Efn
5HP 30	Template:Convert 1992	40 100	32 108	38 97	3 3	Template:Round Template:Round Template:EfnTemplate:Efn	Template:Round
							Template:Font color Template:Efn
Gear	R		1	2	3	4	5
Gear RatioTemplate:Efn	Template:Round $-\frac{70}{19}$		Template:Round $\frac{135}{38}$	Template:Round $\frac{175}{78}$	Template:Font color	Template:Font color	Template:Font color
Step	1.0370		1.0000	1.5835	Template:Font colorTemplate:Efn	Template:Font colorTemplate:Efn	1.2714
Δ StepTemplate:Efn				1.0904	Template:Font colorTemplate:Efn	1.2151
Speed	–0.9643		1.0000	1.5835	2.2995	3.5526	Template:Font color
Δ Speed	0.9643		1.0000	0.5835	0.7161	1.2531	Template:Font colorTemplate:Efn
Torque RatioTemplate:Efn	–3.5078 –3.4217		3.5016 3.4761	2.2059 2.1870	1.5272 1.5183	1.0000	0.7782 0.7738
Efficiency ${\eta }_n$Template:Efn	0.9521 0.9288		0.9856 0.9784	0.9832 0.9748	0.9885 0.9827	1.0000	0.9894 0.9839
5HP 24	Template:Convert 1996	36 93	32 100	35 90	3 3	Template:Round Template:Round Template:EfnTemplate:Efn	Template:Round
							Template:Font colorTemplate:Efn
Gear	R		1	2	3	4	5
Gear RatioTemplate:Efn	Template:Font color		Template:Round $\frac{25}{7}$	Template:Round $\frac{11}{5}$	Template:Font color	Template:Font color	Template:Font color
Step	Template:Font colorTemplate:Efn		1.0000	1.6234	1.4621	Template:Font colorTemplate:Efn	1.2419
Δ StepTemplate:Efn				1.1103	Template:Font colorTemplate:Efn	1.2094
Speed	Template:Font color		1.0000	1.6234	2.3736	3.5714	Template:Font color
Δ Speed	Template:Font color		1.0000	0.6234	0.7502	1.1979	Template:Font colorTemplate:Efn
Torque RatioTemplate:Efn	–3.8985 –3.8025		3.5200 3.4943	2.1630 2.1445	1.4880 1.4795	1.0000	0.7959 0.7918
Efficiency ${\eta }_n$Template:Efn	0.9520 0.9285		0.9856 0.9784	0.9832 0.9748	0.9889 0.9833	1.0000	0.9902 0.9851
Actuated shift elements
Brake ATemplate:Efn					❶		❶
Brake BTemplate:Efn				❶
Brake CTemplate:Efn	❶		❶
Clutch DTemplate:Efn			❶	❶	❶	❶
Clutch ETemplate:Efn						❶	❶
Clutch FTemplate:Efn	❶
Geometric ratios: speed conversion
Gear RatioTemplate:Efn R & 2 OrdinaryTemplate:Efn Elementary NotedTemplate:Efn	$i_R=-\frac{S_2(S_1+R_1)(S_3+R_3)}{S_1{R}_2{S}_3}$			$i_2=\frac{(S_2+R_2)(S_3+R_3)}{S_2{R}_3+S_3(S_2+R_2)}$
	$i_R=-\frac{S_2}{R_2}(1+\frac{R_1}{S_1})(1+\frac{R_3}{S_3})$			$i_2=\frac{1}{\frac{1}{1+\frac{R_3}{S_3}}+\frac{1}{(1+\frac{R_2}{S_2})(1+\frac{S_3}{R_3})}}$
Gear RatioTemplate:Efn 1 & 5 OrdinaryTemplate:Efn Elementary NotedTemplate:Efn	$i_1=\frac{S_3+R_3}{S_3}$		$i_5=\frac{S_2(S_1+R_1)(S_3+R_3)}{S_2(S_1+R_1)(S_3+R_3)+S_1{R}_2{S}_3}$
	$i_1=1+\frac{R_3}{S_3}$		$i_5=\frac{1}{1+\frac{\frac{R_2}{S_2}}{(1+\frac{R_1}{S_1})(1+\frac{R_3}{S_3})}}$
Gear RatioTemplate:Efn 3 & 4 OrdinaryTemplate:Efn Elementary NotedTemplate:Efn	$i_3=\frac{(S_1(S_2+R_2)+R_1{S}_2)(S_3+R_3)}{S_2(S_1+R_1)(S_3+R_3)+S_1{R}_2{S}_3}$					$i_4=\frac{1}{1}$
	$i_3=\frac{1}{\frac{1}{\frac{1}{1+\frac{S_1}{R_1}}+\frac{1+\frac{R_2}{S_2}}{1+\frac{R_1}{S_1}}}+\frac{1}{(1+\frac{S_2}{R_2}(1+\frac{R_1}{S_1}))(1+\frac{R_3}{S_3})}}$
Kinetic ratios: torque conversion
Torque RatioTemplate:Efn R & 1	${\mu }_R=-\frac{S_2}{R_2}{\eta }_0(1+\frac{R_1}{S_1}{\eta }_0)(1+\frac{R_3}{S_3}{\eta }_0)$				${\mu }_1=1+\frac{R_3}{S_3}{\eta }_0$
Torque RatioTemplate:Efn 2 & 5	${\mu }_2=\frac{1}{\frac{1}{1+\frac{R_3}{S_3}{\eta }_0}+\frac{1}{(1+\frac{R_2}{S_2}{\eta }_0)(1+\frac{S_3}{R_3}{\eta }_0)}}$				${\mu }_5=\frac{1}{1+\frac{\frac{R_2}{S_2}\cdot \frac{1}{{\eta }_0}}{(1+\frac{R_1}{S_1}{\eta }_0)(1+\frac{R_3}{S_3}{\eta }_0)}}$
Torque RatioTemplate:Efn 3 & 4	${\mu }_3=\frac{1}{\frac{1}{\frac{1}{1+\frac{S_1}{R_1}\cdot \frac{1}{{{\eta }_0}^{\frac{1}{3}}}}+\frac{1+\frac{R_2}{S_2}{{\eta }_0}^{\frac{1}{2}}}{1+\frac{R_1}{S_1}\cdot \frac{1}{{{\eta }_0}^{\frac{1}{3}}}}}+\frac{1}{(1+\frac{S_2}{R_2}{{\eta }_0}^{\frac{1}{2}}(1+\frac{R_1}{S_1}{{\eta }_0}^{\frac{1}{3}}))(1+\frac{R_3}{S_3}{\eta }_0)}}$						${\mu }_4=\frac{1}{1}$
Template:Notelist

Applications

Variants and applications

Model	Car ModelTemplate:Efn
1990: 5HP 18 · 1997: 5HP 19 · Ravigneaux planetary gearset types
5HP 18Template:Efn	Template:Div col 1992–1993 BMW E32 — 730i M60B30 1992–1995 BMW E34 — 525i M50B25TÜ 1992–1995 BMW E34 — 530i M60B30 1992–1995 BMW E34 — 525tds M51D25 1995–2000 BMW E38 — 725tds M51D25 1994–1996 BMW E38 — 730I M60B30 1993–1996 BMW E36 — M3 S50B30US 1995–1999 BMW E36 — 328i M52B28 - BMW Part No A5S 310Z 1996–1998 BMW E38 — 728i/iL M52B28 1997–1999 BMW E36 — M3 3.2 S52B32 1995–1999 BMW E39 — 523i M52B25 1995–1999 BMW E39 — 528i M52B28 1995–1999 BMW E39 — 525tds M51D25 1991–1999 BMW E36 — 320i
5HP 19Template:Efn	Template:Div col 2001–2003 BMW E46 — 330Ci M54B30 2001–2003 BMW E46 — 330i M54B30 2000–2003 BMW E46 — 320i M52TUB20/ M54B22 2000– BMW E46 — 323Ci M52TUB25 2000– BMW E46 — 323i M52TUB25 2000– BMW E46 — 328i M52TUB28 2000– BMW E38 — 728i M52TUB28 2001–2003 BMW E46 — 325Ci M54B25 2001–2003 BMW E46 — 325i M54B25 1998–2000 BMW E39 — 520i M52TUB20 1998–2000 BMW E39 — 523i M52TUB25 1998–2000 BMW E39 — 528i M52TUB28 2000–2004 BMW E39 — 520i M54B22 2000–2004 BMW E39 — 525i M54B25 2000–2004 BMW E39 — 530i M54B30 2002–2005 BMW E85 — Z4 (M54 engine)
5HP 19FLTemplate:Efn	Template:Div col 1996–2001 Audi A4 (B5) 2.8 V6 1997–2003 Audi A4 (B5) 1.8T 1997–1999 Audi A8 (D2) 3.7 V8 1998–2001 Audi A6 (C5) 2.8 V6 1998–2003 Volkswagen Passat GLS 1.8T 1998–2003 Volkswagen Passat GLS 2.8 V6 1998–2003 Volkswagen Passat GLX 2.8 V6 2003– Volkswagen Passat GL 1.8T 2004–2005 Volkswagen Passat GLS 2.0 TDI [ZF 1060 030106, VW GMR], [A73 Torque Converter]
5HP 19FLATemplate:Efn	Template:Div col 1996–2001 Audi A4 (B5) 2.8 V6 quattro 1997–2001 Audi S4 (B5) 2.7 V6 'biturbo' quattro 1997–2005 Audi A4 (B5) and Audi A4 (B6) 1.8 T quattro 1998–2001 Audi A6 (C5) 2.8 V6 quattro 2000–2003 Audi A6 2.7 V6 biturbo quattro 2000–2003 Volkswagen Passat GLS V6 4motion 2.8 V6 2000–2003 Volkswagen Passat GLX V6 4motion 2.8 V6 2004–2005 Volkswagen Passat GLS 4motion 1.8T 2001–2003 Audi allroad quattro 2.7 V6 biturbo 2002–2005 Audi A4 (B6) 3.0 V6 quattro 2002–2003 Audi A6 (C5) 3.0 V6 quattro 2002–2003 Volkswagen Passat 4.0 W8 4motion
5HP 19HLTemplate:Efn	Template:Div col 1998–2003 Porsche 911 Carrera 996 3.4 2002–2003 Porsche 911 Targa 996 3.6
5HP 19HLATemplate:Efn	Template:Div col 1999–2003 Porsche 911 Carrera 996 3.6 1999–2003 Porsche 911 Carrera 4S 996 3.6Template:Efn 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
1992: 5HP 30 · 1996: 5HP 24 · Simpson planetary gearset types
5HP 30Template:Efn	Template:Div col 1992–1995 BMW E34 — 540i M60/B40 1995–1997 BMW E39 — 540i M62/B44 1998–2001 BMW E39 — 540i M62/B44TU 1992–1994 BMW E32 — 740i M60/B40 1994–1995 BMW E38 — 740i M60/B40 1996–1997 BMW E38 — 740i M62/B44 1992–1994 BMW E32 — 740iL M60/B40 1994–1995 BMW E38 — 740iL M60/B40 1996–1997 BMW E38 — 740iL M62/B44 1998-2001 BMW E38 — 740d M67/D40 1994–2001 BMW E38 — 750iL M73/B54 1993–1995 BMW E31 — 840i M60/B40 1995–1996 BMW E31 — 840Ci M62/B44 1994–1997 BMW E31 — 850Ci M73/B54 1998–2003 Rolls-Royce Silver Seraph 5.4 V12 1998–2000 Bentley Arnage 4.4 V8 1999–2003 Aston Martin DB7 Vantage 6.0 V12 1999–2003 Aston Martin DB7 Vantage Volante 6.0 V12
5HP 24Template:Efn	Template:Div col 1996–1997 BMW E31 — 840Ci M62/B44 1997–2001 BMW E38 — 735i M62/B35 1997–2001 BMW E38 — 735iL M62/B35 1997–2001 BMW E38 — 740i M62/B44 1997–2001 BMW E38 — 740iL M62/B44 1998–2001 BMW E38 — 730d M57 1997–2003 BMW E39 — 540i M62/B44 2000–2003 BMW E39 — Alpina D10 Bi-turbo 1997-2003 Jaguar XJ Sport 3.2 V8 1997–2002 Jaguar XK8 V8 4.0L 1998–2003 BMW E53 — X5 4.4i 1998–2002 Jaguar XJ8 4.0 V8 1998–2001 Jaguar XJ8 Vanden Plas 4.0 V8 1998–2001 Jaguar XJ8 L 4.0 V8 2001–2003 BMW E53 — 4.6is V8 2002–2003 BMW Z8 — Alpina 4.8 V8 2002–2003 Jaguar XJ Sport 4.0 V8 2003–2005 Range Rover (L322) — With BMW M62/B44 engine
5HP 24ATemplate:Efn	Template:Div col 1997–2003 Audi A8 (D2) 4.2 V8 2001–2002 Audi A8 (D2) 6.0 W12 1998–2003 Audi S8 (D2) 4.2 V8 1999–2004 Audi A6 (C5) 4.2 V8 1999–2004 Audi S6 (C5) 4.2 V8 2000–2003 Audi A8L (D2) 4.2 V8 2002–2004 Audi RS6 (C5) 4.2 biturbo V8 2002–2011 Volkswagen Phaeton (Typ 3D)
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See also

• List of ZF transmissions