4
Torque Converters

4.1 Introduction

The invention of fluid couples, over a hundred years ago, was credited to H. Foettinger [1]. The fluid couple, with two elements, the impeller as input and the turbine as output, was later improved by adding the reactor between the two elements to become the torque converter. These hydraulic devices were first applied in the driving systems of ship propellers. The development of torque converters for applications in automotive powertrains dates back to the 1920s [1]. In the US automotive industry, fluid couples were already being applied in the 1930s in transmissions for production passenger cars and city buses [2]. The application of torque converters in automatic transmissions of passenger cars started to take off in the mid 1940s. By the late 1940s, automatic transmissions with torque converters were already in mass production [3,4]. The market demand for family cars grew rapidly in the booming economy after WWII, and this called for the development of automatic transmissions for passenger automobiles that would offer comfort and operation easiness. Torque converter, due to its input and output characteristics, proved to be a perfect fit between the engine output and the transmission input. The application of torque converters in the automotive industry was so widespread that more than 70% of passenger automobiles sold in 1960 in the USA were already equipped with automatic transmissions with these devices [5]. It can be stated that torque converter equipped automatic automobiles are indispensable for daily transportation in today’s society.

Although torque converters can be applied in a variety of machinery, their application in automotive transmissions is by far the most dominant. Today the vast majority of automatic vehicles, if not all of them, are equipped with one of the three types of automatic transmissions: (1) conventional automatic transmission that is commonly termed just automatic transmission (AT) since it had been applied in the industry almost exclusively for decades before the other two types were applied in significant scale: (2) continuously variable transmissions (CVT), and (3) dual‐clutch transmissions (DCT). Torque converters are applied in all ATs and in the vast majority of CVTs. It is not necessary to use torque converters in DCTs since the vehicle launch is realized by controlling the slippage of one of the dual clutches. However, Honda recently developed a DCT that is equipped with a torque converter to improve vehicle launch control and applied it for a popular passenger car [6]. It is likely that the market share of automatic vehicles equipped with torque converters will still grow, as customers in emerging markets are buying more driver‐friendly automobiles.

The in‐depth research and development conducted by the US automotive industry in the 1940s and 1950s established the standards for torque converter design and application for automotive transmissions. Pioneering works on torque converter design, manufacturing, and applications can be found in the SAE publication [4] “Design Practices: Passenger Car Automatic Transmissions”. This publication provides a collection of classic technical papers that detailed the operation, analysis, and design optimization of torque converters [3,5,7–11]. The advancement and maturity of torque converter technologies today is thanks to the original technical contributions represented in these papers.

The objective of this chapter is to provide readers a systematic description on the structure, operation principles, and input–output characteristics of torque converters. The chapter starts in Section 4.2 with the basic structure and geometry of torque converters with lock‐up capability and a qualitative analysis on the functionality. Then Section 4.3 follows on with the mechanism of fluid circulation and torque multiplication, including topics on fluid velocity diagrams, analysis of the angular momentum of automatic transmission fluid (ATF) circulating inside the torque converter, and torque formulations on the three torque converter elements. Section 4.4 presents the torque capacity formulation and input–output characteristics of torque converters. The section ends with the modeling of the joint operation of the complete vehicle system that consists of engine, torque converter, transmission, and the vehicle itself. The conventions on torque converter terminologies in SAE publications are used throughout this chapter wherever appropriate. For detailed torque converter blade designs, readers are referred to specific SAE publications and guidelines [3,5].

4.2 Torque Converter Structure and Functions

Torque converters used in automatic transmissions today consist of four elements: impeller, reactor, turbine, and pressure plate. The impeller, reactor, and turbine are basic elements that realize the functionality of a torque converter. The pressure plate is designed to lock up the torque converter as a mechanical link between the engine and the transmission input. As shown in Figure 4.1, the impeller, which is also called the “pump”, is always rigidly connected to the engine flywheel; the turbine is the output element and is connected to the transmission input; and the reactor or stator is placed between the impeller and the turbine. The reactor is fixed with the outer race of a one‐way clutch whose inner race is grounded to the transmission housing and is thus allowed to rotate in only one direction. The torque converter cover is welded to the impeller and forms an enclosure with the impeller, which contains the turbine, the reactor, and the automatic transmission fluid (ATF). The pressure plate is splined to the turbine shaft and is machined with a friction surface. When the pressure plate is pushed against the inside wall of the cover by the ATF under pressure, the friction generated on the contacting surfaces of the cover and the pressure plate will lock up the torque converter, forming a mechanical coupling between the engine and transmission. The pressure plate assembly includes a torsional spring damper which cushions the impacts during locking up.

Image described by caption and surrounding text.

Figure 4.1 Torque Converter Elements.

Torque converters provide several important functions for vehicle powertrain systems:

  1. To multiple the engine output torque at lower turbine rotational velocity, which corresponds to low vehicle speed. This function is very useful since it helps launch the vehicle quickly and smoothly while the engine is running in a low torque RPM range. The torque multiplication is realized by the reactor which is not allowed to rotate by the one‐way clutch at low turbine speed and thus provides a reaction through the ATF to the turbine. Without the reactor, the impeller and the turbine just form a fluid couple between the engine and the transmission input.
  2. To form a fluid couple between the engine and the transmission after the turbine speed gets close to the impeller speed. As the turbine speed increases to a certain point, termed the coupling point, the ATF circulating inside the torque converter will enter the reactor from the turbine in such a way that its impact on the reactor blades starts to turn the reactor in the direction allowed by the one‐way clutch. The torque multiplication function no longer exists after the coupling point, and the torque converter becomes a fluid couple. Functioning as a fluid couple, the torque converter dampens the dynamic transients in the powertrain system and enhances transmission shift smoothness.
  3. To provide crawl and hill holding capability. This function can be considered as the combined result of functions (a) and (b). When an automatic vehicle is stopped with the engine running at idle, the small engine output torque will be transmitted by the torque converter to the transmission input, generating sufficient driving force to move the vehicle forward at low speed on level ground. If the vehicle is stopped in an uphill position, this driving force prevents the vehicle from slipping backward up to a certain grade percentage even if the brake pedal is not pressed.
  4. To provide a mechanical link between the engine and the transmission. When the torque converter functions as a fluid couple, the torque on the turbine is the same as the torque on the impeller, but the turbine speed always lags behind the impeller speed. This represents a power loss due to the friction between the ATF and the converter interior surfaces, internal ATF leakage, and turbulence. This power loss is converted to an ATF temperature rise. After the torque converter is locked by the pressure plate, it just becomes a mechanical link with no more power loss.

4.2.1 Torque Multiplication and Fluid Coupling

The torque multiplication mechanism in a torque converter can be analysed qualitatively as follows. As the impeller turns with the engine, automatic transmission fluid (ATF) enters the torque converter and soon fills it up. The ATF then circulates continuously within the torque converter between the impeller, turbine, and reactor. To simplify the analysis on ATF circulation, let’s consider the circulation of a single drop of ATF. This drop enters the impeller at the juncture between the reactor and the impeller, and then travels outward on the surface of an impeller blade due to the centrifugal effect from the impeller rotation. It then enters the turbine at the juncture between the impeller and the turbine, producing an impact on the turbine. This impact from the ATF causes the turbine to rotate. After entering the turbine, the fluid drop travels on the surface of a turbine blade toward the juncture between the turbine and the reactor. When the fluid drop exits the turbine and enters the reactor, it may impact either side of the reactor blade, depending on the direction of the absolute velocity of the fluid drop in its circulation motion. The force from this impact tends to rotate the reactor in the direction conducive to the ATF flow. However, due to the constraint from the one‐way clutch, the reactor is only allowed to rotate in one direction, as shown in Figure 4.2. If the fluid drop impacts the blade side such that the rotation of the reactor is not allowed by the one‐way clutch, it will be deflected or redirected upon impact, resulting in a reaction to the turbine blade and increasing the torque on the turbine. If the fluid drop impacts the other side of the reactor blade, the impact force will then turn the reactor as allowed by the one‐way clutch. The motion of the fluid drop is thus continuous without deflection, resulting in no reaction to the turbine and thus no turbine torque increment. The torque converter then functions as a fluid couple.

Torque converter stator with one-way clutch at the center indicated by a line with arrows labeled Rotation allowed (top) and ATF flow redirected (middle) and another arrow marked with “X” (bottom).

Figure 4.2 Reaction from the reactor.

The absolute velocity of the fluid drop circulating in the torque converter is the vector sum of its relative velocity with respect to the blade and the transfer velocity with the blade. The relative velocity is in the direction tangential to the blade and the transfer velocity is caused by the rotation of a torque converter element and is perpendicular to the radial direction. Therefore, both the magnitude and the direction of the absolute velocity of the fluid drop at the turbine exit, or the reactor entrance, depend on the angular velocity of the turbine. Because of the design of the blade geometry, the ATF impact force when it enters the reactor cannot turn the reactor when the turbine angular velocity is low, resulting in the turbine torque increasing as mentioned previously. The absolute velocity of the fluid drop will change as the turbine angular velocity increases. At some point, the direction of the fluid drop velocity at the turbine exit or the reactor entrance will be such that the fluid drop enters the reactor from the blade side which produces the impact to turn the reactor in the direction allowed by the one‐way clutch. This point is defined as the coupling point of the torque converter. If not locked up, the torque converter just behaves as a fluid couple, with equal torque on the impeller and the turbine, and with the turbine speed lagging behind the impeller speed by a small amount.

4.2.2 Torque Converter Locking up

There is an apparent power loss when a torque converter functions as a fluid couple because the turbine speed lags behind the impeller speed. Torque converters with lock‐up clutch are designed to salvage that power loss. The unlocked and locked positions of a torque converter are shown in Figure 4.3a and 4.3b respectively. In the locked position shown in Figure 4.3b, applied ATF flows between the turbine shaft and the fixed support that is splined with the reactor, and empties the right side of the pressure plate. The pressure plate is thus pressed by the ATF on its left side against the cover to lock up the torque converter. Note that the AFT enters the pressure plate apply side (left side as shown) from the converter inside through the small gap between the turbine and the impeller and holes drilled on the turbine shell. In the unlocked position shown in Figure 4.3a, released AFT enters the right side of the pressure plate to disengage the clutchFigure. There are other designs of torque converter locking clutch. For example, a multiple disk clutch can be placed between the turbine and the converter cover, with friction disks and plates splined to a hub and a drum attached to the turbine and the cover respectively. In this design, the hydraulic circuit for the engagement and release of the lock‐up clutch can be separated from the ATF circuit for the torque converter operation.

Unlocked (left) and locked (right) positions of a torque converter with parts labeled Turbine, Impeller, Reactor, Pressure plate, Converter cover, Friction area, Torsional spring, and Contact.

Figure 4.3 Torque converter lock‐up mechanism.

4.3 ATF Circulation and Torque Formulation

In a torque converter, power is transmitted from the impeller to the turbine by ATF circulation inside the torque converter. Based on Newton’s second law, the torque applied on a torque converter element is equal to the change of angular moment with respect to time of the AFT circulating inside the element from the entrance to the exit. The angular momentum of a single drop in the AFT continuum depends on its velocity and position inside the torque converter. Computational fluid dynamics can be applied to study the ATF circulation as a continuum for torque converter dynamic behavior and design optimization [10]. To simplify the problem, the torque formulations in this section will be based on the concept of the mean effective flow, or design path, as defined in SAE publications on torque converters [4]. In this simplified formulation, AFT circulation as a continuum is assumed to be equivalent to the mean effective flow along the design path. For readers’ convenience, the text throughout this section will follow SAE conventions in terminologies and definitions on torque converters.

4.3.1 Terminologies and Definitions

The section view (i.e. the view on a plane that contains the axis) of a torque converter is shown in Figure 4.4. This section view is commonly termed the torus section, which is used to define the geometry, dimension and other features of a torque converter as described in the following.

Left: Torque converter with parts labeled Reactor, Shell, Core, Impeller, Element line, Pressure plate, Design path, One-way clutch, etc. Right: Torque converter with arrows labeled r2, r3, r1, rc, rs, and γ.

Figure 4.4 Torque converter terminologies and definitions.

Design path: The design path is a circle on the torus section that is assumed to be the mean flow path of ATF circulating as a continuum in the three elements of the torque converter. The ATF circulating velocity is always tangential to the design path, as shown in Figure 4.4a. There are an infinite number of axial sections or torus sections, and the design paths on all torus sections form a circular tube about the converter axis.

Shell: The shell is the outside boundary of the AFT continuum and is physically the inside wall of the shell of a torque converter element. The inside walls of the shells of the three elements jointly form a tube‐like surface.

Core: The core is the inside boundary of the ATF continuum and is physically the outside wall of the core of a torque converter element. ATF is contained between the core and the shell in the torque converter. The core is also a tube‐like surface.

Element line: The element line is perpendicular to the design path on the torus section and is used for the design of blade geometry [3]. A set of element lines is arranged on the torus section on each element and the position of each element line is defined by the angle γ formed by the element line with respect to the vertical axis. The element line intersects the shell and the core on a torus section at radius rs and rc respectively, as shown in Figure 4.4b.

Maximum diameter of flow path: As shown in Figure 4.4b, the maximum diameter of flow path D is defined at the point in the ATF flow circuit that is the farthest from the converter axis. It is actually the outer diameter of the shell. The maximum flow path diameter is the most important design parameter that determines the torque converter torque capacity, as will be shown later.

Entrance and exit radii: These radii are at the junctures between the three elements. The radius at reactor exit and impeller entrance is r1, the radius at impeller exit and turbine entrance is r2, and the radius at turbine exit and reactor entrance is r3. In design practice, images, and r2 is approximately equal to r1.

ATF flow area: The flow area is measured between the core and the shell of an element in the direction perpendicular to the AFT circulation velocity. This area is formed by an element line in Figure 4.4b performing a full revolution about the converter axis. The ATF flow area is denoted as A and can be calculated by the following equation in terms of radii rs and rc, and angle γ defined by an element line:

For optimized torque converter performance, it is beneficial to keep the flow area A approximately a constant along the design path. This is possible by properly designing the shape and dimension of the shell and the core, as demonstrated in the classic paper by V.J. Jandasek [3].

Blade entrance and exit angles: The blade surface of a converter element is highly three dimensional. In each element, the blade surface intersects the circulating tube surface formed by the design path, as shown in Figure 4.5. The curve of this intersection is called the mean blade curve and is used to define the blade geometry. The ATF motion in an element is assumed to be equivalent to the motion of an ATF drop along the mean blade curve.

Image described by caption and surrounding text.

Figure 4.5 Mean blade curve.

The motion of an ATF drop along the mean blade curve on an impeller blade is shown in Figure 4.6. At any point P along the mean blade curve, the absolute velocity of the ATF drop is the vector sum of two velocities, namely, the relative velocity whose direction is along the tangent to the mean blade curve, and the transfer velocity whose direction is perpendicular to radial direction at point P. Following the convention in SAE publications, the absolute velocity, the relative velocity, and the transfer velocity are denoted by V, W, and U respectively, with a subscript indicating element and bold letters or arrows indicating vectors. Denoted by F in Figure 4.5, the circulating velocity is tangent to the design path and is contained in the axial section. A prime is used for a velocity component at the entrance of an element to distinguish it from the exit. The angle between the relative velocity and the transfer velocity is defined as the blade angle. Geometrically, the blade angle is formed between the tangent to the mean blade curve and the normal to the axial plane at point P. The blade angles at the entrance and the exit are the entrance angle and exit angle respectively.

Image described by caption and surrounding text.

Figure 4.6 AFT velocities and blade angle definition.

ATF mass circulating rate: It is apparent that the ATF volumetric circulating rate is (AF). The ATF has a constant density ρ since it is considered incompressible. The ATF mass circulating rate, i.e. the ATF mass flow (images, is therefore also a constant in the converter elements if leakage is not considered. Similar to a centrifugal pump, the mass circulating rate in a torque converter is proportional to the impeller (pump) speed. For a given impeller speed, the mass circulating rate in a converter element can be assumed to be a constant, resulting in a constant circulating velocity F since the circulating area A is a almost constant by design.

Speed ratio: The torque converter speed ratio, denoted as is, is defined as the angular velocity of the turbine divided by the angular velocity of the impeller, i.e. images. As an operating parameter, the speed ratio is used to define a range of variables related to torque converter performance, as will be detailed later.

Torque ratio: The torque converter torque ratio, denoted as iq, is defined as the torque on the turbine or the output torque divided by the torque on the impeller or the input torque, i.e. images. For a typical torque converter used for automatic transmissions, the torque ratio varies between the stall ratio, which is approximately equal to 2.0, to the coupling torque ratio which is always equal to 1.0.

Efficiency: The torque converter efficiency is the ratio between the output power and the input power. Apparently, the efficiency is equal to the multiplication of the speed ratio and the torque ratio, i.e. images.

4.3.2 Velocity Diagrams

Since the AFT circulation is assumed to be along the design path that is always on the axial plane, the transfer velocity is always perpendicular to the circulating velocity. Geometrically, the directions of the circulating velocity and the transfer velocity are respectively along the two mutually perpendicular tangents at point P on the surface of the circulating tube. These two tangents define the tangent plane of the circulating tube surface at point P. Since the mean blade curve is the intersection between the blade surface and the circulating tube surface, the tangent line to the mean blade curve at point P must be on the tangent plane. Therefore, the circulating velocity F, the transfer velocity U, and the relative velocity W are contained within the tangent plane at point P to the surface of the circulating tube shown in Figure 4.5. At any point along the design path, the absolute velocity of an ATF drop is the vector sum of its relative velocity and transfer velocity as follows:

The magnitude of the transfer velocity depends on the element angular velocity and the radial distance to the converter axis. Velocity diagrams for ATF circulation can be constructed for the three converter elements based on Eq. (4.2) and blade geometry under various operation conditions. Figure 4.7 shows the velocity diagrams when the reactor is not turning and the converter functions as a torque multiplier.

Image described by caption and surrounding text.

Figure 4.7 Velocity diagrams for impeller, turbine, and reactor.

While drawing the velocity diagrams shown in Figure 4.7, the angular velocities of the impeller ωi is considered as given and the circulating speed F is also a given constant. The velocity components are shown on the plane formed by the transfer velocity U and circulating velocity F. The drawing starts at the impeller entrance with radius r1. The magnitude of the transfer velocity at the impeller entrance, images, is equal to ωir1, and the angle between the relative velocity images and the transfer velocity images is the impeller blade entrance angle images. The circulating velocity F is the projection of the absolute velocity V1 on the tangential direction to the design path and the tangential component S1 is the projection of the absolute velocity V1 on the tangential direction of the plane of rotation, with subscript 1 indicating radius r1.

After entering the impeller, the ATF drop moves along the mean blade curve of the impeller blade surface toward the exit at radius r2. At the impeller exit, the magnitude of the transfer velocity Ui is higher than that at the entrance and is equal to ωir2. The angle between the relative velocity Wi and the transfer velocity Ui is the impeller exit angle αi. The velocity diagram is uniquely defined since the magnitude of circulating velocity F is a constant. Based on the velocity diagrams for the impeller at the entrance and exit, there exist the following relations between the impeller velocity components:

(4.4)images

At the turbine entrance, the ATF absolute velocity V2 is the same as that at the impeller exit. For a given turbine angular velocity ωt, the magnitude of the transfer velocity images is calculated as ωtr2. The relative velocity images is then determined by the vector parallelogram. At the turbine exit, the magnitude of the transfer velocity Ut is calculated as ωtr3. The relative velocity Wt is along the blade tangent that forms the exit angle αt with the transfer velocity Ut. The velocity diagram at the turbine exit leads to the following relation on the velocity components:

When the reactor is not turning, the transfer velocity for the ATF moving on the reactor blade is zero. The absolute velocity at the reactor entrance is the same as that at the turbine exit. The velocity diagrams at the reactor entrance and exit can be easily constructed as shown at the top of Figure 4.7.

The velocity diagrams in Figure 4.7 illustrate the velocity components of ATF circulating inside the torque converter and the relationship between them. Several important observations and design recommendations can be made about these diagrams for a better understanding on blade geometry and ATF circulation:

  • The geometric blade exit angle is equal to the angle formed between the relative velocity and the transfer velocity, but the same is not true in general for the geometric blade entrance angle. This can be explained by the velocity diagrams at the impeller exit and the turbine entrance in Figure 4.7. The impeller exit angle αi is the same as the angle formed between the ATF relative velocity Wi and the transfer velocity Ui, whose vector sum determines the AFT absolute velocity V1. The AFT absolute velocity at the turbine entrance is the same as V1 due to AFT flow continuity. The relative velocity images is determined by the velocity parallelogram defined by V1 and the transfer velocity images which depends on the turbine angular velocity ωt. Therefore, the angle between the relative velocity images and the transfer velocity images, denoted as images in Figure 4.7, is generally not equal to the geometric turbine blade entrance angle. As a matter of fact, there exists only one turbine angular velocity at which the geometric blade entrance angle will be equal to the angle formed between the relative velocity images and the transfer velocity images. The same is true for the entrance angles for the reactor and the impeller.
  • To minimize ATF flow shock loss at an exit and entrance juncture, the blade entrance angle should be equal to the angle formed between the relative velocity and the transfer velocity. However, this is not possible since torque converter elements turn at different speeds that affect the ATF velocity direction. According to the research data in SAE publication [4], the angles between the relative velocity and the transfer velocity at the entrances of the impeller and the reactor, images and images, as denoted in Figure 4.7, vary in wide ranges from around 30° to 150° while at the turbine entrance, the angle varies in a much narrower range between about 22° to 45°. As recommended in [3,4], the entrance angles of the impeller, turbine, and reactor are optimized at a speed ratio of 0.7 for optimized results in stall torque ratio, efficiency, high coupling speed, and characteristics. Typical blades that provide the optimized trade‐off between stall ratio, efficiency, and coupling characteristics are also recommended in SAE publication [4]. For example, a torque converter with a 12 inch design path diameter, the blade angles are designed as: images, images; images, images, images.
  • The velocity diagrams in Figure 4.7 are constructed for the torque converter operation when the reactor is not turning. As shown at the top of Figure 4.7, the absolute AFT velocity at the reactor entrance V3 is directed in such a way that the impact of the ATF flow upon the reactor blade cannot turn the reactor because of the constraint from the one‐way clutch. As the turbine speed increases, the magnitude of the transfer velocity Ut will also increase and thus the direction of V3 will change, as shown in the velocity diagram at the turbine exit. The angle between V3 and the tangential direction on the plane of rotation, images shown in Figure 4.7, varies gradually from a value larger than 90° to a value smaller than 90°. When this happens, the impact of the ATF flow upon the reactor blade will cause the reactor to turn in the direction allowed by the one‐way clutch. The torque converter then reaches the coupling point and functions just as fluid couple.

4.3.3 Angular Momentum of ATF Flow and Torque Formulation

For an ATF drop circulating inside the torque converter, its angular momentum about the converter axis is the cross product between its position vector from the axis and its linear momentum. The component of the angular momentum of the ATF drop about the converter axis is equal to (msr), where m is its mass, s is the tangential component of its absolute velocity on the plane of rotation, and r is its radial distance from the converter axis. For simplicity, the AFT is assumed to be circulating inside the torque converter as a continuum along the design path. The change of ATF circulation status over time Δt is shown in Figure 4.8 for the impeller. At any arbitrary time t during torque converter operation, the ATF continuum is fully contained between the core and the shell of the impeller, as shown in Figure 4.8a. At time images, a small amount of the ATF continuum moves into the impeller at the entrance and the same amount moves out of the impeller at the exit since the ATF is assumed to be incompressible, as shown in Figure 4.8b. The mass of the ATF amount moving into or moving out of the impeller is equal to (AFΔtρ), where ρ is the mass density of the ATF, A is the ATF flow area in Eq. 4.1, and F is the ATF circulating velocity. The angular momentum of the ATF amounts that moves into or out of the impeller are therefore (AFΔtρs1r1) and (AFΔtρs2r2) respectively, with r1 as the radius at the impeller entrance and r2 as the radius at the impeller exit. As can be observed from Figure 4.8, the only change on the status of the ATF continuum over time Δt occurs at the impeller entrance and exit. According to the principle of angular impulse and momentum, the following equation applies to the ATF continuum contained between the core and shell of the torque converter impeller:

where the left side is the angular impulse of torque Ti that is applied to the ATF continuum over time Δt and the right side is the change of angular momentum of the ATF continuum contained inside the impeller. It is obvious that the torque applied to the impeller by the ATF continuum has the same magnitude as Ti, which can be determined by dividing Eq. (4.6) on both sides by Δt, i.e.

Image described by caption and surrounding text.

Figure 4.8 Angular momentum change of ATF continuum over time Δt.

The torque equation for the turbine and reactor can be derived by following the same procedure, as presented in the following:

(4.8)images

It is apparent that the sum of the torque on the impeller, turbine, and reactor is equal to zero, i.e. images, since the torque converter as a whole body must be in equilibrium. The torque equations, Eqs (4.7–4.9), can also be expressed as follows by the substitution of S1, S2, and S3 from Eqs (4.3–4.5):

(4.11)images
(4.12)images

As can be observed from the torque equations above, the torque applied to a converter element depends on many variables, including the angular velocities of converter elements, the ATF circulating velocity, the ATF mass density, the blade geometry, the design path contour, and the converter dimensions.

4.4 Torque Capacity and Input–Output Characteristics

Equations (4.10–4.12) can be further simplified for the formulation of the torque applied to a torque converter element. As an example, let us consider the torque applied to the impeller formulated by Eq. (4.10). For a given torque converter, the following observations and assumptions can be made on the torque converter design parameters and operation variables in Eq. (4.10):

  • The radii at the impeller entrance and exit, r1 and r2, are proportional to the maximum diameter of the flow path, i.e. images and images, where λ1 and λ2 are proportionality factors.
  • The ATF circulating velocity F is proportional to the mean transfer velocity on the design path and depends on the speed ratio of the torque converter, i.e. images, with λF as the proportionality factor. Function λ(is) describes the dependence of the circulating velocity on the speed ratio.
  • The AFT flow area A, designed as a near constant, is proportional to the square of maximum diameter of the flow path, i.e. images, with λA as the proportionality factor.

With these observations, Eq. (4.10) can then be translated into the following form:

where the ATF mass density ρ is a constant, the proportional factors are also constants, and the entrance angle images and exit angle αi are determined from the AFT velocity diagrams. As mentioned previously, these angles are not exactly the same as the geometric blade angles and largely depend on the relative angular velocity between the impeller and the turbine which is defined by the speed ratio at a given impeller angular velocity. Therefore, for a given torque converter that turns at a given impeller angular velocity, the torque applied to the impeller can be formulated by:

where k represents the whole term before images in Eq. (4.13) and only depends on the speed ratio during the operation of a given torque converter. In the convention of SAE standard publications, the impeller RPM is used in the impeller torque formulation. By replacing ωi with images in the equation above, the torque applied to the impeller is then represented by:

where C is called the torque capacity coefficient, and is similar to k in Eq. (4.14), depends only on the speed ratio for a given torque converter. It should be emphasized here that the torque capacity coefficient C reflects the effects of the geometry design parameters, such as blade angles, entrance and exit radii, and ATF circulating area, on the performance of a torque converter. Extensive dyno testing is required to obtain the relationship between the torque capacity coefficient and the speed ratio. Based on test data, the torque capacity coefficient is plotted versus the speed ratio for the determination of operation status of a given torque converter [11]. Similar to the formulation of the impeller torque, the turbine torque can also be formulated by an equation that resembles Eq. (4.15), where the impeller RPM ni is replaced by the turbine RPM nt, as follows:

where Ct is the capacity coefficient for the turbine torque and, similar to C in Eq. (4.15), depends only on the speed ratio for a given torque converter. It follows directly from Eqs (4.15) and (4.16) that the torque ratio iq, defined as images, also depends on the speed ratio only. It can also be observed from either of these equations that the torque transmitted by a torque converter is proportional to the fifth power of the maximum diameter of the flow path. A 20% increase on the converter size would increase the torque capacity by 2.5 times. This is advantageous for torque converter applications in the automotive industry since a small range of converter dimensions will cover various vehicle power requirements.

4.4.1 Torque Converter Capacity Factor

In torque converter design and applications, the torque capacity factor, or K‐factor as commonly termed, is used to present the relationship between the torque and the speed, typically of the impeller, for a torque converter with particular dimension and blade geometry design. The value of the K‐factor is equal to the ratio between the impeller speed and the square root of the impeller torque:

where ni is the impeller speed in RPM and Ti is the impeller torque in ft.lb. Comparing Eqs (4.17) and (4.15), it is obvious that the K‐factor is related to the torque capacity coefficient C by the following equation:

For a given converter, D is a constant and thus the K‐factor only depends on the speed ratio is. If the values of capacity factor C at different speed ratios have been obtained from the test on a given torque converter, then the values of the K‐factor can be easily obtained from Eq. (4.18). In practice, the K‐factor is often directly obtained through testing. In the dyno test setup, the impeller is connected to an electric motor with controllable torque, and the turbine is connected to a loader with measurable torque load. During the test, the input torque, i.e. the torque applied to the impeller by the motor, is kept as a constant. The test then runs at different torque loads. The speeds of the impeller and the turbine are measured when dynamic equilibrium is achieved on the dyno system. The torques and speeds of the impeller and turbine are then used to calculate the speed ratio, the torque ratio, the efficiency, and the torque capacity factor by Eq. (4.17). Typically, the torque ratio, the torque capacity factor, and the efficiency are plotted versus the speed ratio in the so‐called torque converter characteristic plot, as shown in Figure 4.9.

Image described by caption and surrounding text.

Figure 4.9 Torque converter characteristic plot.

Note that the US customary unit is used in Figure 4.9, where torque is in ft.lb. Similarly, the torque converter characteristics can also be plotted in SI unit, with torque in Nm and the value of K‐factor converted accordingly. Several observations can be made on typical torque converter characteristics from Figure 4.9:

  • When the speed ratio is zero, i.e. the turbine is not turning, the torque ratio is the highest and is termed the stall ratio. As the speed ratio increases from zero to 0.9, the torque ratio decreases from the stall ratio to 1.0. The torque converter reaches the coupling point when the torque ratio is 1.0 and it then just behaves as a fluid couple if unlocked.
  • The curve for K‐factor versus speed ratio is upward in shape, with gradual increment with respect to the speed ratio until the coupling point. After the coupling point, the K‐factor increases very sharply as the speed ratio approaches 1.0, rendering accurate data reading impractical.
  • The torque converter efficiency increases from zero at stall to about 0.9 near the coupling point. It increases further after the coupling point as the speed ratio increases and the torque ratio stays at 1.0. However, there is always a power loss since the turbine always lags behind the impeller if the torque converter is unlocked. To save the power loss, which translates into fuel economy worsening, the torque converter is unlocked only for operation conditions such as launching, crawl and hill holding, and transmission shifting process.
  • The stall ratio helps launch the vehicle quickly and smoothly. Typically, torque converters used for passenger vehicle transmissions have a stall ratio in the neighborhood of 2.0.
  • As implied by Eq. (4.17), the value of K‐factor is equal to the impeller speed scaled by images. This is validated by the plot in Figure 4.9, which is based on the test setup where a constant torque is applied to the impeller. As shown in Figure 4.9, the curve for torque capacity is parallel to the curve of the impeller speed up to the coupling point. The discrepancy after the coupling point is caused by the sharp increase of K‐factor and impeller speed versus the speed ratio.
  • In addition, it is worthwhile to point out that the impeller speed (i.e. the engine speed), as shown in Figure 4.9 increases monotonically versus the speed ratio, providing the driver a desirable feel when the vehicle is being accelerated. This feature can be guaranteed by the optimized design of blade entrance and exit angles of the torque converter.

4.4.2 Input–Output Characteristics

As mentioned previously, the plot shown in Figure 4.9 is established based the test data when a constant torque is applied to the impeller. This constant torque, which is used in the test to obtain the input–output characteristics of the torque converter, should be chosen as the maximum or near maximum torque of the engine to which the torque converter is matched. As observed in Eqs (4.17) and (4.18), the torque capacity factor is theoretically unrelated to the input torque on the impeller and is only the characteristics of the torque converter dimension and geometry design. Therefore, the relationship between the torque ratio, the torque capacity factor, and the efficiency versus the speed ratio shown in Figure 4.9 should be applicable for other operation conditions of the torque converter within allowable discrepancy in engineering practice. The small discrepancy is mainly due to the shock loss of ATF flow caused by turbulence at blade entrance and exit, friction between AFT flow and surfaces of blades, core, and shell, and AFT leakages inside the torque converter.

The operation status of a torque converter is defined by four parameters: the angular velocities of the impeller and turbine, ωi and ωt, and the torques on the impeller and turbine, Ti and Tt. These four operation parameters are linked to each other by the characteristics of the torque converter through the following equations:

(4.19)images
(4.20)images

(4.21)images
(4.22)images
(4.23)images

where the torque ratio iq and the torque capacity factor K are functions of the speed ratio is, in the form of a data file or a plot, and are characteristic of a given torque converter, as illustrated in Figure 4.9. Obviously, the speed ratio is is the key to the determination of the torque converter operation status.

4.4.3 Joint Operation of Torque Converter and Engine

When a torque converter is matched to an engine, it is important to know how the turbine torque, i.e. the input torque to the transmission, behaves with respect to the speed ratio. For a given engine, the output torque is a function of its RPM with a specific throttle opening. The engine RPM is the same as the impeller speed ni. If the impeller–flywheel inertia is not considered, then the impeller torque Ti is the same as the engine output torque Te, and the turbine torque is then the engine torque multiplied by the torque ratio, that is, images. As a function of the speed ratio is, the torque ratio is defined by the joint operation status of the torque converter and the engine. The joint operation between the engine and the torque converter can be quantitatively analysed by model simulation to be discussed later in this section. A simple graphic method, proposed in SAE publications [4], can be used to determine the speed ratio and torque capacity factor for the converter–engine joint operation, as demonstrated in Figure 4.10.

Image described by caption and surrounding text.

Figure 4.10 Joint converter–engine operation status.

The engine torque plotted in Figure 4.10 is at a fixed throttle opening. For example, the wide open throttle (WOT) engine torque can be plotted for acceleration performance analysis. The engine torque capacity factor, which is denoted as Ke and is equal to images, is then plotted accordingly. The Ke factor is characteristic of the engine at a given throttle opening. At any given speed ratio is, the converter torque capacity factor K and the torque ratio iq can be found from the characteristic plot of the torque converter matched to the engine, such as the one shown in Figure 4.9. When the converter–engine system reaches dynamic balance, the converter torque capacity factor is equal to the engine torque capacity factor, i.e. images. A horizontal line is drawn at the value of the converter torque capacity factor K in Figure 4.10. The intersection of this horizontal line and the plot of the engine torque capacity factor Ke defines the converter–engine joint operation status. The vertical line drawn at the intersection will then intersect the engine torque plot and the horizontal axis, leading to the determination of the engine torque Te or impeller torque Ti, and the corresponding engine RPM. The turbine torque and speed are then determined as iqTe and isne respectively. Repeating the steps by varying the speed ratio in the interval [0, 1] monotonically, the turbine torque Tt and turbine speed nt can be found for the speed ratio from the stall status to the coupling point, corresponding to the engine output at a specified throttle opening. Note that the graphical method described here can be used to assess how well the torque converter is matched to the engine in terms of intended objectives. For example, the converter–engine joint operation status corresponding to the stall ratio near the engine maximum torque would provide the best acceleration performance at vehicle launch.

If the converter torque capacity factor and the torque ratio are given as functions of the speed ratio, and the engine torque at a specified throttle opening is given as a function of its RPM, then the joint converter–engine operation status from stall to coupling, with the speed ratio is varying from 0 to 1, can be determined numerically by the following set of equations:

(4.26)images
(4.27)images
(4.28)images

where Eq. (4.24) defines the engine torque capacity factor Ke at a given throttle opening as a function of the engine speed ne. The engine speed is determined by Eq. (4.25) by iteration for a speed ratio in the interval [0, 1], based on the equality of K and Ke. The torque on the impeller and turbine, and the turbine speed, are then determined by Eqs (2.26), (2.27) and (2.28) respectively.

4.4.4 Joint Operation of Torque Converter and Vehicle Powertrain

As a coupling that connects the engine output with the transmission input, the torque converter interacts dynamically with the vehicle powertrain system. The mass moment of inertia of the impeller–flywheel assembly is a part of the system and should be considered in the system dynamics. Figure 4.11 illustrates the dynamic model for vehicle powertrain systems equipped with a torque converter. As shown in the figure, the vehicle mass has been replaced by its equivalent mass moment of inertia (Iv) and the road load by its equivalent torque (Tload) on the output of the final drive. The overall powertrain ratio is the multiplication of the transmission ratio and the final drive ratio (itia).

Image described by caption and surrounding text.

Figure 4.11 Torque converter equipped powertrain system.

There are clearly two degrees of freedom for the dynamics of the lumped mass system shown in Figure 4.11: one is the angular velocity of the impeller–flywheel assembly, ωe or ωi, and the other is the angular velocity of the turbine, ωt, which is related to the vehicle speed V and tire radius r as images, if tire slippage is not considered. Based on Newton’s second law, two equations of motion can be written for the system:

where Ii is the mass moment of inertia of the impeller–flywheel assembly, η is the combined efficiency of the transmission and final drive, and Te is the engine output torque. Note that the engine torque is not the same as the impeller torque Ti since the impeller–flywheel assembly has a mass moment of inertia that can be accelerated quickly. The equivalent road load torque is calculated from the road load formulated by Eq. (1.14) in Chapter 1 by the following equation:

(4.31)images

where the vehicle speed is related to the turbine angular velocity as: images. The system of two ordinary differential equations formed by Eqs (4.29) and (4.30) governs the motion of the whole vehicle. An initial condition must be provided to solve the equation system for the dynamic status of the vehicle system. When the vehicle is launched from rest at a specified engine throttle opening, the vehicle speed or the turbine angular velocity and the speed ratio are both zero at time zero, and the impeller angular velocity at time zero, images, can be found using the graphical method described previously or using Eqs (4.24) and (4.25). The initial condition for the equation system is then defined as:

At a specified engine throttle opening, the engine output torque Te is a function of its angular velocity. The impeller torque and the turbine torque are determined by the torque converter input–output characteristics in terms of the speed ratio. Therefore, combined with the initial condition defined by Eq. (4.32), the equation system formed by Eqs (4.29) and (4.30) can be solved for the velocity–time relationship of the vehicle during launch. If wide open engine throttle opening is specified, the solution will lead to the capacity performance in terms of vehicle acceleration.

References

  1. Gott, P.G., Changing Gears: The Development of the Automotive, Society of Automotive Engineers, 1991, ISBN 1‐56091‐099‐2.
  2. Jandasek, J., Turbine Clutch Smooths Car Operation – Reduces Stress and Fatigue Failures, Automotive Industries, September 12. 1931, pp. 396–400.
  3. Jandasek, J., Design of Single‐Stage, Three‐Element Torque Converter, SAE Special Publication SP‐186, Jan. 1961.
  4. SAE Transmission/Axle/Driveline Forum Committee, Design Practices: Passenger Car Automatic Transmissions, Third Edition, AE‐18, SAE Publication, 1994, ISBN 1‐56091‐506‐4.
  5. Upton, E.W., Application of Hydrodynamic Drive Units to Passenger Car Automatic Transmissions, Volume 1, 1962.
  6. Machida, S., Yagi, N., Miyata, K., Sadakiyo, M., Okaji, T., and Yamane, T., Development of 8‐speed DCT with Torque Converter for Midsize Vehicles, Article of Honda R&D Technical Review, Vol. 26, No. 2., 2014.
  7. By R.R. and Mahoney, J.E., Technology Needs for the Automotive Torque Converter – Part 1: Internal Flow, Blade Design and Performance, SAE Paper No. 880482.
  8. Blomquist, A.P. and Mikel, S.A., The Chrysler Torque Converter Lock‐up Clutch, SAE Paper No. 780100.
  9. Hiramatsu, T., Akagi, T., and Yoneda, H., Control Technology of Minimal Slip‐Type Torque Converter Clutch, SAE Paper No. 850460.
  10. Tsangarides, M.C. and Tobler W.E., Dynamic Behaviour of a Torque Converter with Centrifugal Bypass Clutch, SAE Paper No. 850461.
  11. Numazawa, A., Ushijima, F. and Fukumura, K., An Experimental Analysis of Fluid Flow in a Torque Converter, SAE Paper No. 830571.

Problem

  1. A vehicle of the following data is equipped with a four‐speed AT. The ratios are: 2.84 (1st), 1.60 (2nd), 1.0 (3rd), 0.7 (4th). The final drive ratio is 2.84. The torque converter characteristics and the engine WOT output torque are the same as in the example problem solved previously in this chapter. The vehicle is being driven on level ground in the first gear with the torque converter unlocked.
    1. Present the differential equation system with the initial condition for the WOT performance simulation model of the vehicle in first gear. Assume the vehicle is launched at the same condition as in the example.
    2. Determine the engine angular acceleration and vehicle acceleration when the vehicle is just launched from standstill.
    3. Starting from time zero and using a step size of t = 0.2, solve the differential equation system by hand for one step, i.e. find the engine RPM and vehicle speed 0.2 second after launch.
    4. Establish the computer model to implement the dynamic model shown in Figure 4.11, using the formulation consisting of Eqs (4.29) and (4.30) and other related equations in this chapter. Use your model to simulate vehicle performance dynamics during launch from rest to the time when the torque converter becomes a fluid couple. Plot the engine speed, engine torque, vehicle speed and acceleration, and the speed ratio against time during the vehicle launch process.
    Vehicle data:
    Front axle weight: 1290 lb Rear axle weight: 1240 lb
    Center of gravity height: 18 inch Wheel base: 100 in.
    Air drag coefficient: 0.31 Frontal projected area: 20 sq.ft
    Tire radius: 10.0 in. Roll resistance coefficient: 0.02
    Powertrain efficiency: 0.92 Mass moment of inertia of engine–impeller: 0.3 lb.ft2