4.2 Power-Split Device (PSD), Planetary Gearing Nomographs & e-CVT Operation
Key Takeaways
- The standard Power-Split Device (PSD) consists of a simple epicyclic planetary gearset connecting the Sun gear to MG1, the Planet Carrier to the ICE crankshaft, and the Ring gear to MG2 and the final drive wheels.
- The planetary kinematic speed relationship is governed by $(R + S) \cdot N_c = R \cdot N_r + S \cdot N_s$, where $R$ is ring gear tooth count and $S$ is sun gear tooth count (typically yielding $N_s = 3.6 \cdot N_c - 2.6 \cdot N_r$).
- Torque applied at the planet carrier is divided in a strictly fixed mechanical ratio determined by gear tooth counts: typically ~72% direct mechanical torque to the ring gear and ~28% reaction torque to the sun gear (MG1), regardless of rotational speeds.
- The ICE cannot deliver propulsion torque to the ring gear without an equal and opposite reaction torque applied by MG1 at the sun gear; if MG1 free-wheels without electrical load, no torque reaches the wheels.
- Planetary nomographs (lever diagrams) illustrate operating states: in High-Speed Overdrive ('Herbie' mode), MG1 rotates backward while powered as a motor, and MG2 functions as a generator recirculating power back to MG1.
4.2 Power-Split Device (PSD), Planetary Gearing Nomographs & e-CVT Operation
The heart of the Toyota Hybrid Synergy Drive (THS), Ford e-CVT, and related power-split transaxles is the Power-Split Device (PSD). Unlike conventional automatic transmissions that utilize multi-plate friction clutches, brake bands, hydraulic torque converters, or variable-diameter conical pulleys with steel push-belts, the PSD achieves an infinite range of continuously variable gear ratios through the purely electronic speed and torque modulation of two electric motor-generators operating on an epicyclic planetary gearset.
1. Mechanical Architecture & Component Connections
A standard single-planetary Power-Split Device consists of three primary mechanical members:
+-----------------------------------------------------------------------------------------+
| POWER-SPLIT DEVICE (PSD) ARCHITECTURE |
| |
| +-----------------------------------------------+ |
| | RING (ANNULUS) GEAR | |
| | (Outer Internal Teeth: Typically 78 Teeth) | |
| | Connected to: MG2 Rotor & Final Drive Diff | |
| +-----------------------+-----------------------+ |
| | |
| +-----------------------+-----------------------+ |
| | PLANET PINIONS & CARRIER | |
| | (Set of 3 or 4 Pinions Meshed In Center) | |
| | Connected to: ICE Crankshaft via Damper | |
| +-----------------------+-----------------------+ |
| | |
| +-----------------------+-----------------------+ |
| | SUN GEAR | |
| | (Center External Teeth: Typically 30 Teeth)| |
| | Connected to: MG1 Rotor (Primary Gen) | |
| +-----------------------------------------------+ |
+-----------------------------------------------------------------------------------------+
Primary Member Allocations:
- Sun Gear (Center): Splined directly to the rotor shaft of Motor-Generator 1 (MG1). MG1 serves primarily as the high-voltage engine starter and electrical generator.
- Planet Carrier (Middle): Supports the pinion gears that orbit the sun gear while meshing simultaneously with the outer ring gear. The carrier is splined to the Internal Combustion Engine (ICE) crankshaft through a spring-loaded torsional damper plate (no disconnect clutch or fluid coupling).
- Ring Gear / Annulus (Outer): Possesses internal teeth meshed with the planet pinions. The ring gear hub is permanently splined to Motor-Generator 2 (MG2) and mechanically coupled through a counter-gear reduction set to the final drive differential and front drive wheels.
2. Planetary Kinematics & Mathematical Speed Formulas
The rotational speeds of the three planetary members are locked in a strict mechanical relationship governed by the tooth counts of the ring gear ($R$) and sun gear ($S$).
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| FUNDAMENTAL PLANETARY SPEED EQUATIONS |
| |
| Basic Epicyclic Formula: |
| (R + S) * N_carrier = (R * N_ring) + (S * N_sun) |
| |
| Dividing by R gives: |
| (1 + rho) * N_carrier = N_ring + (rho * N_sun) where rho = S / R |
| |
| Solving for Sun Gear Speed (MG1 Speed, N_s): |
| N_sun = [ (R + S) * N_carrier - (R * N_ring) ] / S |
| N_sun = (1 + R/S) * N_carrier - (R/S) * N_ring |
+-----------------------------------------------------------------------------------------+
Standard Gear Ratios in Common Transaxles
In popular transaxles (e.g., Toyota P410, P610, Ford HF35):
- Ring Gear Teeth ($R$) = 78 teeth
- Sun Gear Teeth ($S$) = 30 teeth
- Tooth Ratio $\frac{R}{S} = \frac{78}{30} = \mathbf{2.60}$
- Carrier Multiplier $(1 + \frac{R}{S}) = (1 + 2.60) = \mathbf{3.60}$
Substituting these values yields the definitive operating equation:
Worked Mathematical Kinematic Examples:
Scenario A: Pure Electric Vehicle Launch (EV Mode)
- Vehicle road speed corresponds to a Ring Gear (MG2) speed of $N_r = +1,000\text{ RPM}$ forward.
- ICE is shut down: $N_c = 0\text{ RPM}$.
- Calculate MG1 Sun Gear speed:
- Result: While MG2 drives the vehicle forward at 1,000 RPM, MG1 spins freely in the reverse direction at 2,600 RPM.
Scenario B: Highway Cruising at Constant Speed
- Vehicle is traveling at 65 mph; Ring Gear speed is $N_r = +2,200\text{ RPM}$.
- Hybrid ECU commands the ICE to run at its optimum fuel efficiency speed: $N_c = +2,000\text{ RPM}$.
- Calculate MG1 Sun Gear speed:
- Result: MG1 spins forward at 1,480 RPM in generator mode, providing reaction torque and supplying electricity to MG2.
3. Planetary Torque Distribution Mechanics
While rotational speeds vary infinitely depending on vehicle velocity and motor control, the torque distribution of a planetary gearset is mechanically fixed and unalterable.
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| PLANETARY TORQUE SPLIT PRINCIPLES |
| |
| Carrier Torque (T_c) = Ring Torque (T_r) + Sun Torque (T_s) |
| |
| Direct Mechanical Ring Torque: |
| T_ring = T_carrier * [ R / (R + S) ] = T_ICE * (78 / 108) = 72.22% of ICE Torque |
| |
| Sun Gear Reaction Torque: |
| T_sun = T_carrier * [ S / (R + S) ] = T_ICE * (30 / 108) = 27.78% of ICE Torque |
+-----------------------------------------------------------------------------------------+
The Fundamental Reaction Torque Rule
[!CRITICAL] The Lever Fulcrum Principle: The planet carrier acts as a class-1 or class-2 mechanical lever. For the engine to transfer its 72.2% direct torque to the ring gear, the sun gear (MG1) MUST provide an equal and opposite reaction torque (27.8%).
If MG1 is electrically disconnected (e.g., open high-voltage circuit, blown fuse, or inverter gate driver shutdown), the sun gear will spin freely with zero resistance. With no reaction torque at the sun gear, zero mechanical torque can be applied to the ring gear ($T_{\text{ring}} = 0$), and the vehicle cannot move under engine power alone.
4. Comprehensive Nomograph Analysis Across Operational States
A nomograph is a graphical lever chart used by hybrid calibration engineers and diagnostic technicians to visualize the rotational speeds of Sun, Carrier, and Ring gears. A straight line drawn across the three vertical axes represents the rigid mechanical kinematic constraint of the planetary gearset.
+-----------------------------------------------------------------------------------------+
| PLANETARY NOMOGRAPH LEVER DIAGRAM |
| |
| Speed (RPM) |
| ^ |
| +6000 | SUN (MG1) CARRIER (ICE) RING (MG2 / Wheels) |
| +5000 | | | | |
| +4000 | | | .......* (Max Accel) |
| +3000 | | .......* (Max ICE RPM) ...... |
| +2000 | * (Gen Mode) .... | * (Cruising) |
| +1000 | | * (Optimum ICE) | |
| 0 +-------------+-----------------------*----------------------------* (Zero Speed) |
| -1000 | | | (ICE Stopped) | |
| -2000 | | | | |
| -3000 | * (EV Reverse Spin) | | |
| +-------------+-----------------------+----------------------------+ |
| [ S ] [ C ] [ R ] |
| |<---- Ratio R=78 ---->|<------- Ratio S=30 ------->| |
+-----------------------------------------------------------------------------------------+
Detailed Analysis of the 6 Operational Nomograph States:
State 1: EV Mode (Electric Launch & Low Speed Driving)
- Kinematics: The vehicle is propelled solely by MG2 driving the ring gear forward ($N_r > 0$). The engine is shut off and stationary ($N_c = 0$).
- MG1 Behavior: MG1 rotates backward in the negative direction ($N_s < 0$). Because no fuel is injected, there is zero engine drag and zero tailpipe emissions.
- Maximum EV Speed Limit: Because MG1 has a maximum safe mechanical rotational limit (typically 10,000 to 14,000 RPM depending on generation), once vehicle speed exceeds roughly 42 to 65 mph (68 to 105 km/h), the ICE must spin ($N_c > 0$) to prevent MG1 from exceeding its maximum overspeed threshold.
State 2: Engine Cranking & Starting Sequence
- Kinematics: While stationary ($N_r = 0$) or moving ($N_r > 0$), the Hybrid ECU commands the inverter to energize MG1 as a powerful electric motor rotating in the positive forward direction ($N_s > 0$).
- Cranking Action: MG1 spins up rapidly, which raises the planet carrier speed ($N_c$) to approximately 1,000 RPM within 200–300 milliseconds.
- Reaction Torque Cancellation: When MG1 applies cranking torque to the carrier, a negative reaction torque is transmitted to the ring gear (which would tend to jerk the vehicle backward). To eliminate driveline shudder, the inverter commands MG2 to produce an equal and opposite forward counter-torque, creating a completely seamless engine start.
State 3: Normal Cruising & Continuous Power Split
- Kinematics: The vehicle travels at steady road speed ($N_r > 0$). The ICE runs at its optimal efficiency speed ($N_c \approx 1,500 - 2,500\text{ RPM}$). MG1 rotates forward ($N_s > 0$).
- Power Distribution:
- 72% of engine power flows mechanically to the wheels via the ring gear.
- 28% of engine power drives MG1 as a generator. The generated AC electricity is converted to DC by the inverter and routed directly to MG2 to provide supplementary electric propulsion at the ring gear.
State 4: Maximum Wide-Open Throttle (WOT) Acceleration
- Kinematics: The ICE is commanded to its maximum horsepower speed ($N_c \approx 5,000 - 6,000\text{ RPM}$). Ring gear speed ($N_r$) increases rapidly.
- Electrical Flow: MG1 generates maximum electrical power. Simultaneously, the high-voltage boost converter steps up battery voltage (up to 500V–650V DC), delivering maximum battery current combined with MG1 generator current into MG2. MG2 produces maximum peak torque, combining with the ICE mechanical torque at the ring gear for maximum total vehicle thrust.
State 5: High-Speed Overdrive / Electronic Recirculation ('Herbie' Mode)
- Kinematics: At very high vehicle speeds (e.g., 75–85 mph, $N_r = +3,500\text{ RPM}$) with low engine power demand ($N_c = +1,500\text{ RPM}$), the speed formula dictates that MG1 must spin in reverse:
- Electronic Recirculation Loop: To produce a forward reaction torque on the carrier while rotating in the negative direction, MG1 must operate as a motor drawing electrical energy.
- Power Flow: MG2 is driven by the ring gear and acts as a generator, sending electricity to the inverter, which powers MG1 as a motor. Power recirculates electronically from wheels $\to$ MG2 $\to$ Inverter $\to$ MG1 $\to$ Sun gear $\to$ Ring gear. This mode is known as Electronic Overdrive or 'Herbie' Mode.
State 6: Reverse Driving
- Kinematics: In power-split transaxles, there is no mechanical reverse gear, idler gear, or reverse hydraulic clutch.
- Reverse Operation: Reverse propulsion is achieved exclusively by reversing the 3-phase AC rotating magnetic field in the stator of MG2, driving the ring gear backward ($N_r < 0$).
- ICE & MG1 Status: The ICE remains shut off ($N_c = 0$). As the ring gear turns backward, MG1 spins forward in the positive direction ($N_s = -2.6 \cdot (-N_r) > 0$). If high torque or cabin heat is requested in reverse, the ICE can start and idle, with MG1 adjusting speed accordingly while MG2 maintains reverse wheel torque.
5. Advanced & Compound Power-Split Architectures
Motor Speed Reduction Planetary Sets (Toyota Gen 3/4/5)
In earlier hybrid generations, MG2 was coupled 1:1 with the ring gear. To increase MG2 efficiency and decrease its physical size and weight, modern transaxles incorporate a dedicated Planetary Motor Speed Reduction Gearset (reduction ratio typically 2.63:1) between MG2 and the counter-drive gear. This allows MG2 to operate at speeds up to 17,000 RPM, multiplying output torque to the wheels while slashing motor mass.
Lexus Multi-Stage Hybrid & GM 2-Mode Compound Systems
- Lexus Multi-Stage Hybrid System (RWD): Couples a standard two-motor power-split transaxle to a 4-speed automatic stepped planetary gear unit located downstream of the power-split device. By combining the e-CVT's infinite ratios with 4 mechanical gear ranges, the transmission provides 10 simulated virtual gear ratios, eliminating the 'rubber-band' engine drone and delivering high wheel torque from zero speed.
- GM 2-Mode Hybrid: Incorporates two epicyclic planetary gearsets, two internal motor-generators, and three to four multi-plate hydraulic clutches. It switches dynamically between Mode 1 (low-speed input-split) and Mode 2 (high-speed compound-split), plus four fixed mechanical gear ratios for heavy-duty towing efficiency.
A hybrid vehicle transaxle has a ring gear with 78 teeth and a sun gear with 30 teeth. If the vehicle is cruising at highway speed with the ring gear (MG2) spinning at +2,000 RPM and the engine (carrier) running at +1,800 RPM, what is the exact rotational speed of the sun gear (MG1)?
In a standard Toyota/Ford power-split planetary transaxle, what proportion of internal combustion engine torque is directly delivered to the ring gear and drive wheels mechanically?
During high-speed, light-load highway cruising (known as Electronic Overdrive or 'Herbie' mode), how do Motor-Generator 1 (MG1) and Motor-Generator 2 (MG2) operate within the power-split transaxle?