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Internal Combustion Engine - Automatic Transmission Matching for Next Generation Power Transfer Technology Development in Automotive Applications.


The current trend in step gear automatic transmissions is increasing number of forward gear ratios beyond 6, stabilizing for the moment at 8 to 10 in either transverse or longitudinal applications, [1, 2 and 3]. Simultaneously, technologies such as high efficiency gears, pumps, low spinloss bearings, seals and clutches, all coupled with aggressive calibration of shift patterns and early torque converter clutch lockup are being implemented on automatic transmissions to reduce losses and improve overall operational efficiency. Previous research on conventional powertrain matching optimal number of forward gear ratios and transmission technologies have largely only looked at current or near horizon engine designs see [4, 5. and 6]. A recent study, [7], have looked at over the horizon engine designs, integrating new technologies for drastically improved performance and what automatic transmissions pair best for fuel consumption on a given regulatory test schedule. In general, the authors have countered that the current trajectory of number of forward fixed gear ratios is unnecessary given the increased torque capability at low engine speeds and wider regions of minimum brake specific fuel consumption, BSFC, fewer forward gear ratios are required, potentially as few as four, see [7]. This study also proposed a new automatic transmission design, however, augmented with some form of parallel electrification to supplement the internal combustion engine. The aim of this investigation is to examine the validity of these claims through a detailed analysis approach considering engines with widely varying performance in a given vehicle application and propose alternative step gear automatic transmission concepts.

This investigation has two primary objectives, carried out using analytical methods and focused exclusively on conventional automotive powertrain machinery. The first objective was to determine design parameters for the next generation step gear automatic transmissions that best match the operating characteristics of current and anticipated future internal combustion engine designs based upon industry mega trends. Internal combustion engines will continue to increase torque output while reducing fuel consumption and emissions through mechanical design, controls and added features such as those mentioned by [8, 9, 10, 11, 12, 13,14, 15, 16, 17, 18]. These future internal combustion engines will have an increase in mean brake torque at lower engine speeds while also achieving lower BSFC over a wider range of engine speeds and brake mean effective pressures, BMEP. Figure 1 graphically highlights this trend in engine design and calibration, largely achieved through changes to valvetrain technology, combustion mechanism, friction reduction, downsizing, turbocharging and direct injection, see [8, 9, 10, 11, 12, 13] for details.

The second objective of this investigation is to present alternative step gear automatic transmission powerflow architectures that will synergize with previous research on conventional powertrain matching as well as the results contained in this investigation. The proposed transmission concepts are intended to match both current and future engine performance and vehicle applications. In general, the step gear automatic transmission concepts presented contain multiple input clutches, are layshaft versus planetary architecture principally to reduce rotating inertia, operating losses, increase acceleration performance capability and afford greater flexibility in individual forward gear ratio selection.


Conventional powertrain matching of internal combustion engines and step gear automatic transmissions has been a perennial activity amongst powertrain engineers and researchers, [1, 2, 2, 4, 5, 6, 7]. Recent analytical studies by [4, 5 and 6] highlight new technology integration combined with statistical approaches to select the optimal transmission design parameters for best fuel consumption. This investigation will continue this approach, using a fractional factorial design to assess quickly the influence of key parameters using an orthogonal array containing seven design parameters for step gear automatic transmissions arranged into 18 unique combinations. Each of the 18 transmission variants were then simulated with 8 different engines and 4 final drive axle ratios on a single vehicle application. The particulars of the analysis will be described in the subsequent sections, detailing the vehicle, engines, transmissions, test schedule, shift pattern creation and all other key assumptions. It is worth remarking that the parameter values defining the light duty, full size truck and all automatic transmissions are hypothetical paper designs and do not directly represent current or future product intent. The engines are a combination of existing designs and conjectural future engines extrapolated from the existing designs.


For this investigation a light duty, full size truck was considered as the principal candidate for analysis of future conventional powertrain matching. Such a vehicle was considered, as it is critical in the North American region market on a volume and per vehicle profit basis. It also represents the vehicle segment with the greatest opportunity to reduce greenhouse gas, GHG, emissions and fuel consumption on an absolute versus relative perspective. The vehicle is defined with a mass of 2200 kg, which assumes a significant amount of lightweighting from current generation light duty, full size trucks that are in the range of 2500 to 2600 kg. Road load power is expressed through a curve-fitting coast down coefficients with values of 150, 6.5 and 0.52 with units of N, N-s/m and [N-s.sup.2]/m, respectively. The road load power as a function of vehicle speed on a zero grade is shown in Figure 2, requiring roughly 20 kW of power at 100 kph.

Current and Future Engines

A survey across multiple original equipment manufacturers of this vehicle segment shows a wide array of internal combustion engines offered, as the prime source of propulsion. Engines range from gasoline to diesel, naturally aspirated to turbocharged, with the latest generation variable valve timing, direct fuel injection and potentially cylinder deactivation. For this investigation, three engine variants with characteristics covering the width of applications in the current market place were selected and included in the analysis array. A fourth engine was created from an existing base engine data set to represent a future engine design with a modified maximum brake torque envelop, namely, higher torque output below 2000 rpm achieved through a specific turbocharging strategy, see [10] for example. Engine fuel consumption will most likely continue to decrease with future engine designs as engineering and technologies progress. To examine the influence improved fuel consumption will have on step gear automatic transmission gearing selection the BSFC maps for all four engines were scaled in certain speed-torque regions. The approximate scaling is based upon engine technologies and strategies mentioned in the literature, [8, 9, 10, 11, 12, 11, 14, 15, 16, 17, 18], for example. These hypothetical engines then became derivatives of their base engines with the same specific torque output, but will lower and wider BSFC contours in the core operating region of nearly all regulatory test schedules. To facilitate direct comparison of optimal transmission design parameter selection, the maximum brake torque output of all the engines was held fixed while fuel consumption was scaled. The details of these engines and the fuel map scaling is detailed in the next sections.

Large Displacement V8 Gasoline with Cylinder Deactivation

The large displacement gasoline V8 engine is one of the more common prime movers found in the light duty, full size truck segment and is included in this investigation. The particular engine has cylinder deactivation, V8 to V4, to reduce fuel consumption. Peak torque output is slightly above 500 Nm as noted in Figure 3. Baseline engine performance is noted in the left plot of Figure 3 and the reduced fuel consumption map is shown on the right. Minimum fuel consumption is around 245 g/kW-hr for the baseline engine, occurring between 1000 and 4000 rpm, and 225 to 400 Nm. The minimum BSFC island was increased in size and depth, spanning the same speed range, but opened to 200 Nm, dropping to a specific consumption of 200 g/kW-hr.

Downsized Turbocharged V6 Gasoline

Another engine entry in the light duty truck market are downsized, turbocharged, abbreviated DSB, direct injected V6 gasoline engines, which were also included in this study. The performance data for the baseline and reduced BSFC island variants of this engine are included in Figure 4. Maximum engine torque is at 600 Nm at roughly 3000 to 5000 rpm and a minimum BSFC of 230 g/kW-hr at a roughly 2750 rpm and 350 Nm. The hypothetical, reduced fuel consumption engine variant greatly expands the minimum BSFC island at 200 g/kW-hr to occur between speeds of 1200 to 3700 rpm and torques of 180 Nm upwards of 450 Nm. The reduced BSFC engine variant represents an approximate reduction of 13% in fuel consumption.

Turbocharged Diesel V6

A new engine entry into the light duty truck market is the turbocharged diesel V6. Utilization of such an engine will likely be expanded in this particular vehicle segment to improve emissions sufficiency and performance capabilities of the vehicle. As noted in Figure 5, engine torque output peaks at 550 Nm across a narrow speed range with minimum BSFC occurring throughout the typical driving range above 250 Nm. A reduction in fuel consumption of approximately 7% was assumed with the reduced BSFC variant achieved largely through combustion efficiency improvements found with methods reported by [9 and 10].

Future Downsized Turbocharged V6 Gasoline

It is anticipated that the megatrends in DSB gasoline engines will continue in future automotive powertrain applications with continued effort to increase torque capability and reduce fuel consumption. To capture this trend in engine design, a hypothetical engine was created to include in the analysis matrix. The particular engine presented here was an extrapolation of engine presented in Figure 4, with torque output increased in the 1200 to 3000 rpm range as noted in Figure 6. Similarly, BSFC was scaled in certain operating ranges to expand the minimum island to be highly aggressive. This particular engine represents the best-case scenario for engine performance to influence transmission gearing selection for potentially showing if any direct correlation exists to enable a reduction in the number of fixed gear ratios.

Transmission Design Parameter Fractional Factorial Design - L18 Orthogonal Array

The design parameters for step gear automatic transmissions and shift pattern constraints incorporated into an L18 orthogonal array for analyzing the optimal matching of engine and transmission for performance are explained in the proceeding four sections.

Transmission Design Parameters

Table 1 contains the transmission parameters in the L18 orthogonal array, which includes number of fixed gear ratios, ratio progression, top gear and launch gear ratios, scaling factor for transmission spinloss, gear architecture and fundamental shift pattern constraints. These parameters were considered as they define the foundation of the step gear automatic for engine matching as well as determine overall performance potential. Scaling the transmission spinloss was included to encompass the variation that might be realized in actual parasitic losses that are highly dependent on powerflow selection, transmission layout and gear architecture. Gear architecture is included as a separate parameter, namely to differential spinloss from gear mesh efficiency as there are distinctly different values between planetary and layshaft transmission designs. A third option, layshaft with winding path, is a particular case of a layshaft transmission design that achieves unique gear ratios through multiple meshes of parallel axis gears, sometimes incorporating multiple countershafts. Such an architecture can increase the availability of fixed gear ratios while reducing the number of rows of gear pairs, but at the sacrifice of mesh efficiency. Appendix A of the paper contains the exact L18 orthogonal array layout and allocates each parameter into a unique transmission design and shift pattern specification, see Table A1 for more details.

The intermediate gear ratios for all the transmissions were determined using the same methodology described in [6] to achieve the ratio progressions defined as geometric, equally spaced ratio step size, linear, linearly decreasing step size from first step to last step and logarithmically decreasing ratio step sizes. The overall ratio spreads, OAR, that were produced from the combinations of launch and top gear ratios are summarized in Table 2, ranging from 6.92 to 10.00. This range covers existing step gear designs but goes beyond to consider extremely wide ratio spreads not currently available in automotive applications.

Transmission Losses

As reported by a number of case studies on automatic transmission design, such as [3, 4, 5., 6 and 19, 20, 21], parasitic losses can significantly influence fuel consumption. A uniform approach to developing spinloss values was utilized such that it could more readily be understood what influence it has on transmission engineering and minimize the opportunity for it to obscure the objectives of the study. For each of the unique transmission combinations created from Table 1 and Table A1 in Appendix A, a spinloss table was created as a function of input speed, input torque and gear state. The general form of the spinloss, which includes losses at open clutch(es), bearings and seals, is shown in Figure 7 for a 10 speed transmission at line pressures of 500 and 1200 kPa and input speeds between 1000 and 2500 kPa. The spinloss calculations were developed by looking at existing planetary and layshaft transmission designs at a nominal warm operating temperature.

The spinloss dependency on line pressure originates from input torque, which dictates lube pressure and flow to the transmission. For all transmissions, line pressure, [P.sub.lim], was a fixed relationship for all gear states given by,

[mathematical expression not reproducible] (1).

which is input torque, [T.sub.input] times a gain of 2.25 plus an offset of 200 kPa. Maximum line pressure was set at 2100 kPa, corresponding to a maximum input torque of 845 Nm, which is typical of an automatic transmission to be matched to the output of the engines considered for this investigation. As part of the orthogonal array parameters, spinloss was scaled +/- 30% or held at the nominal values. For lay shaft transmissions, the nominal values were reduced by 15% to reflect the lower losses associated with this type of architecture, namely splash lubrication and minimal open clutches.

Separate from spinloss is the parasitic losses associated with a high pressure hydraulic pump to actuate clutches and shift forks as well as provide lube flow. Pump losses were included as a separate input to the analysis, being a function of input speed and line pressure requirement. The same pump design was applied to all transmission in the orthogonal array, featuring binary action to reduce losses. The value of torque consumed to operate the transmission pump ranged between 1.25 to 6 Nm depending on operating conditions and mode of the pump.

A third parasitic loss mechanism included is gear mesh efficiency, or torque loss due to friction at the mesh interface for gear teeth. For planetary transmissions, the values were a function of gear ratio, having lowest values in the 97% range at launch ratios, peaking at 100% at 1:1 ratio and dropping back to 98 to 99% at top gear ratio. A gear mesh efficiency of 98% was applied to all gear ratios for layshaft transmission architectures with the exception of those considered to have winding path gear ratios. For the latter type of layshaft one third of the fixed gear states were considered to have winding paths, primarily in the intermediate gear ratios and were assigned a value of 96% to account for the additional meshes participating in torque transfer.

The last energy loss mechanism included relates to transmission shift dynamics. During upshift or downshift events, energy loss due to slipping clutches and engine torque reductions during upshift events was included as part of the powertrain model. As discussed in [22], this is a nontrivial loss of energy and as the number of forward gears increases, so too does the number of shifts performed on a given test schedule. As will be discussed later, this aspect of automatic transmission operation can hinder the potential benefit of increasing the number of gear states as more energy is consumed by the transmission through higher frequency of shift events if not compensated by achieving engine operation that significantly reduces fuel consumption.

Launch Device

All transmissions in the orthogonal array were considered to have a torque converter and lockup clutch as the launch device irrespective of the gear architecture, e.g. planetary vs. layshaft, which would typically see wet clutches. This was done to simplify the analysis and eliminate the energy utilization benefits of various launch device types. It also facilitates the comparison solely on the effect of the fundamental transmission design versus the combination of transmission and launch device. Two torque converter K-factors were used to match the performance of the four engines analyzed. A low K-factor unit for the large displacement V8 gasoline engine was utilized, while a higher K-factor unit for the smaller turbocharged engines to enable more rapid rises in engine speed on launch and lockup clutch release events was considered. In addition, the torque converter is used only at launch, with the lockup clutch applied right at the 1-2 upshift and fully locked through all power on operation and for non-fueled coast down conditions. The torque converter clutch is released immediately following engine refueling during vehicle coast down. This attribute of operating strategy further marginalizes the choice of a torque converter for all transmission simulations.

Shift Pattern

The assumption of shift pattern constraints and transmission operating point can also be a significant contributor to overall performance and fuel consumption. Thus, it was included as one parameters in the L18 orthogonal array. The goal was to demonstrate overall effect on fuel consumption relative to design parameters and if the relative influence varies greatly between drastically different engines. A thorough discussion on all the shift pattern constraints and assumptions can be rather lengthy, so the major assumptions and strategies employed in this investigation are summarized in Table 3 as well as Table A2 in Appendix A.

The exact procedure for creating the shift pattern has previously been detailed at length in [5 and 6], which roughly approximates the approaches reported by [23 and 24]. The foundation of finding the optimal gear state is predicated on a minimum search function on the metric of mass flow rate of fuel at the engine normalized by power delivered at the axle. This method comprehends the net efficiency of the entire powertrain and driveline in selection of the optimal gear state for minimum fuel consumption. Additionally, system constraints are imposed upon this raw shift map to include the requirement to meet road load power as well as typical hardware limitations such as pump limits, drivetrain resonances, vehicle NVH and drive quality constraints. A typical shift pattern for a particular 10 speed transmission studied in the L18 investigation is shown in Figure 8.

Fin al Drive Axle Ratios

Four final drive axle ratios were added to the analysis matrix for each engine and transmission combination. The exact final drive ratios used in the analysis are provided in Table 4. An axle efficiency of 96% percent was assumed across all operating torques and speeds.

Test Schedules

The Worldwide Light Duty Test Procedure, WLTP, see Figure 9, was the single regulatory test schedule prescribed for this study. It was selected as it nearly equivalently approximates the fuel consumption performance and operating points realized through combining the Federal Test Procedure, FTP, and US06 test schedules without having to simulate both and calculate a composite fuel consumption. All simulation runs were made with the assumption of a warmed up and constant operating temperature powertrain at 90 C.

To compliment fuel consumption performance on the WLPT, an acceleration performance simulation for 0 to 100 kph was also run for the LI8 orthogonal array and all engine variants and final drive axle ratios. The key metric of interest is time to reach 100 kph form a vehicle standstill.


A total of 576 simulation runs were required to run all combinations of the L18 orthogonal array, 8 engines and 4 final drive axle ratios for the WLPT test schedule. An equal number of simulations were required for acceleration performance. The results of the analysis will be presented with specific focus on design parameters and shift pattern strategy that yield the best performance for fuel consumption and acceleration. Direct comparison will be made between the baseline engines and those created with reduced fuel consumption and distinctly wider regions of low BSFC.

WLTP Fuel Consumption

The analysis results for the WLTP fuel consumption simulations will be presented as a delta g C[O.sub.2]/km from all transmissions in the L18 orthogonal array relative to a parameter for a given engine and all four axle ratios. The Equations 2 through 4 summarize these calculations. Equation 2 represents the average performance, [Y.sub.n], for a row in the L18 orthogonal array which is a single transmission taken for an engine and the four final drive axle ratios. The average of all 18 transmission designs is computed using Equation 3, which is the overall average of all 18 row averages of the L18 orthogonal array. To find the average effect of each design parameter or shift pattern, Equation 2 is modified to compute the average within a parameters, e.g. all 10 speed variants are averaged together to compute 10 speed average performance. The delta in g C[O.sub.2]/km for a parameter is then found by subtracting the overall mean of the L18 array from a parameter specific average as given by Equation 4.

[mathematical expression not reproducible] (2)

[mathematical expression not reproducible] (3)

[DELTA]g C[O.sub.2]/km = [[bar.y].sub.n] - [[bar.y].sub.m] (4)

Presenting the data as a delta from overall mean for each parameter allows all engine variants to be compared succinctly on one plot. Figure 10, shows the main effects of the L18 orthogonal for the baseline engine variants. Downsized turbocharged engines are designated by the acronym, DSB, standing for downsized boosted. The local optimum for number of gear ratios is approximately 9 to 12. This conclusion agrees strongly with the findings of [3, 5 and 6]. Marginal contribution to C[O.sub.2] reduction is noted in Figure 10 from the overall average from ratio progression and top or launch gear ratios. As expected, scaling spinloss (bearings, seals, open clutches) of the transmission has a big of a contribution as number of gears, as was previously reported by [5 and 6]. The results for gear architecture show planetary and layshaft architectures with no considerable difference as the greatest percentage of time on schedule is spent in top gear where gear mesh efficiencies are nearly equivalent. Layshaft architectures that utilize winding paths shows a 1 g C[O.sub.2]/km penalty in fuel consumption from the overall average due to markedly lower mesh efficiency for a third of the gear ratios, thus it is an expected result. Interestingly, for this investigation, the parameter that showed the largest change in fuel consumption is the shift pattern constraints imposed upon the automatic transmissions operation. The constraints that changed most between shift patterns 1 and 2 are minimum operating speed per gear state, with the results aligning with that reported by [5]. From shift pattern 2 to shift pattern 3, the differences are the hysteresis pairing between upshift and downshift, reduced to 1.5 kph and a higher numerical gear ratio that fuel cutoff is used under vehicle deceleration, yielded an additional 4 to 5 g C[O.sub.2]/km reduction in fuel consumption.

The results for the four engine variants with reduced fuel consumption and wider minimum BSFC regions are shown in the mean effects plot of Figure 11. Largely, the results for these engine variants matches to that found in the baseline engines. To get the lowest fuel consumption, 9 to 12 gears are the most favorable, although for the diesel engine, 12 gears and potentially beyond is best. Logarithmic ratio progression produces the best C[O.sub.2] solution for the downsized, turbocharged engines, where for the V8 engine ratio progression has little effect. Launch and top gear ratios show identical trend and influence on CO2 as with the baseline engines in Figure 10. The diesel engine is the only variant that produces improved results with numerically lower top gear ratio. All other parameters for the orthogonal array are equivalent between baseline and reduced fuel consumption engines. The results for this subset of the investigation runs counter to the claims of [7] that future engines with wide BSFC islands and reduced fuel consumption match best with automatic transmissions with fewer forward gear ratios. The exception to this is if an automatic transmission with fewer gear ratios operates with substantially lower parasitic losses and has technology enablers for an overly aggressive downspeed shift pattern and drive quality that tolerates minimum spacing of shift lines, e.g. minimal shift hysteresis.

Table 5 shows the average fuel consumption improvement noted between the baseline and hypothetical, reduced fuel consumption engine variants across all the permutations of step gear automatic transmissions and axle ratios modeled in the L18 array. The percent improvement is noted to range from a modest 2%, representing combustion enhancements alone, to greater than 14.5%, representing wholesale engine hardware and combustion strategy changes. These figures align with the predicted improvements in engine performance noted in research reported by [9, 10, 15 and 16].

Acceleration Performance

The effect of the parameters in the L18 orthogonal array on 0 to 100 kph time for all engine, step gear automatic transmission and final drive axle ratio combinations is displayed as the delta time in seconds from the overall mean time as was computed for fuel consumption with Equations 2 through 4. Figure 12 shows the mean effects plot for the influence of key design parameters and shift pattern constraint on 0 to 100 kph time. No differentiation between baseline and the reduced fuel consumption, wide BSFC island engine variants was necessary since both engines were considered to have the same maximum engine torque curves. As expected, shift pattern constraints had no influence as the shift patterns were setup for best acceleration under full engine torque demand. Selection of gear architecture has a strong influence on acceleration performance, mainly due to the lower inertia of a layshaft transmission. The result is more torque at the transmission output for a layshaft versus planetary design of similar specifications. The higher torque transfer efficiency of the layshaft design without winding path gear ratios also leads to lower torque loss across the transmission from input to output shaft. Not surprising, the best acceleration times come with the highest numerical launch gear, dropping 0 to 100 kph time by 0.1 seconds by using a 5.50:1 over a 4.50:1 launch gear ratio.

Also of note in Figure 12 is that top gear ratio shows some degree of influence for the diesel and future DSB V6 engines, which appears to be a questionable result. Top gear is not reached within 100 kph at full engine torque, but the methodology in which intermediate gear ratios were determined was based upon the specification of launch and top gear ratios. For example, considering a geometric ratio progression 10 speed transmission with a launch gear ratio of 4.50:1 paired with top gear ratios of 0.65:1 and 0.55:1, the former would result in smaller ratio step sizes of 1.22 versus 1.26 for the latter. Thus, the depending on how well the ratio steps align with the shift pattern and maximum engine torque curve will influence what top gear ratio produces the best acceleration performance. More simply put, the gear spacing, a.k.a. ratio step sizes, for the shift events that occur up to 100 kph and matching to the maximum engine torque curve will strongly influence acceleration performance. This finding can also be noted in the number of forward gear ratios and ratio progression, with results aligning for all engines with the exception of future DSB V6 engine. The optimal number of gears for each engine variant for best acceleration time is easiest explained by looking at the maximum torque curves contained in Figure 13.

For the future DSB V6 engine, torque output drops off sharply above 5000 rpm, whereas the other engines considered have a gradual reduction in torque as maximum engine speed is reached. In the latter case, additional forward gears with smaller ratio step sizes prevent engine operation at peak torque because the upshifted gear does not drop engine speed low enough on the torque curve. The shape and features of any engine then will dictate what transmission gearing will match best for acceleration performance. This in large part explains the opposing trends noted in Figure 12 with respect to number of forward gear ratios and acceleration performance for 0 to 100 kph.

Optimal Step Gear Automatic Transmission Design

The results of the L18 orthogonal array for step gear automatic transmission design and shift pattern constraint parameters showed that the transmission features yielding the best fuel consumption generally converged for current and future engine designs. For acceleration performance, however, the features producing the best results do not necessarily correlate with those for fuel consumption and can vary greatly depending on the details of the characteristic shape of the engines maximum torque curve. Thus, there is no one size fits all step gear automatic transmission design and a weighting of requirements has to be balanced between fuel consumption, acceleration and drive/shift quality, which has not been part of the discussion in this study. The ideal step gear automatic transmission design would facilitate flexibility in individual gear ratio selection without having to change the fundamental architecture to adapt to various engine and vehicle applications.

Fuel Consumption

From a fuel consumption perspective, the following attributes yield the best performance on the WLTP test schedule for current and future gasoline or diesel engines applied to a light duty, full size trucks:

* At least 9 forward gear ratios

* Low parasitic loss content - hydraulic pump, open clutches, bearings and seals

* High gear mesh efficiency

* Launch device and primary isolator that facilitates lower engine speed operation and early lockup - downspeeding

* Top gearratio of 0.65:1 for gasoline engines, 0.55:1 fordiesels

* Launch gear has minimal influence on fuel consumption

* Logarithmic ratio progression to quickly transition from launch to numerically low gear ratios

* Small ratio step sizes can be reduce shift hysteresis constraints


The key step gear transmission design and operating point parameters that provide the best acceleration performance are described in the following list:

* High numerical launch gear ratio, > 5.00:1, 5.50:1 preferred

* Low rotating inertia for transmission components, preference to layshaft vs. planetary gear architecture

* Low parasitic losses from a high mechanically efficient and actuated design

* Number of gears and ratio progression are highly dependent on engine maximum torque capability and shape of torque near maximum engine speed

* If engine torque gradually tapers at maximum speed, more forward gear ratios with geometric spacing are preferred

* If engine torque drops drastically over a wide speed range as maximum engine speed is reached, fewer gears, 6 or 7, with large, logarithmically spaced ratios are preferred

Benefits of Increasing Number of Gear Ratios

A tangible benefit not directly captured in the analysis for this investigation is the drive quality and shift quality enhancements received by smaller and more closely spaced gear ratios. An in depth discussion is beyond the scope of this paper, but the reader is referred to content contained in [22], that objectively quantifies these benefits. Additionally, as considered in [22], an efficiency benefit is derived from shorter shift times afforded by suitable step gear automatic transmission designs with smaller ratio steps and low rotating inertias, principally multi-input clutch layshaft architectures. Figure 14 contains fuel consumption versus number of shifts on the WLTP schedule for the future DSB V6 gasoline engine and all transmission, axle ratios from the L18 orthogonal array. The analysis results shows that the general trend is towards reduced fuel consumption as the shift count increases. Noted in Figure 14 are two regions exhibiting this trend, one with shift pattern constraint 1 and the other with shift pattern constraints 2 and 3. A third smaller region with shift pattern constraints 2 and 3 with low axle ratios for 11 and 12 speed transmissions counter this trend because of suboptimal ratio matching. Increasing shift count and minimizing the disturbance to vehicle occupants is only possible by increasing the number of forward gear ratios with smaller ratio step sizes.

There is potential to reduce fuel consumption through downspeeding the engine with wide overall ratio, OAR, spreads achieved through higher launch and lower top gear ratios. As Figure 15 indicates, the lowest fuel consumption occurs with the widest ratio spread of 10 through 12 speeds. Marginally higher fuel consumption is achieved with narrower OAR spreads of 8.3 with 10 speeds or 6.9 with 11 speeds. This highlights that the fuel consumption benefit of OAR spread can be dependent on matching to the vehicle, engine, and the particulars of the transmission design. The key takeaway being that not much fuel consumption is given up if the widest possible OAR spread is achieved during matching. The same observation as noted in Figure 15 are consistent for the other three engine variants.

The benefit of adding more forward gear ratios to the transmission is the opportunity to downspeed both the engine and transmission to reduce parasitic energy losses as well as put the engine in a more optimal operating point on its BSFC map as examined by [6]. To highlight these benefits the results for the future DSB V6 gasoline engine and all the analysis points from the L18 orthogonal array study are plotted and coded by number of transmission speeds in Figure 16. Fuel consumption versus total powertrain energy losses, which includes engine friction and pumping losses in addition to all transmission and final drive axle ratio, clearly shows the benefit of adding gear ratios to the transmission as described previously. Total powertrain energy loss was reduced when the right combination of final drive axle ratio is selected, operating the powertrain at its most efficient points to minimizing fuel consumption while satisfying the road load power requirements of the WLTP test schedule.


Leveraging the results of the L18 orthogonal array as well as previous research on the subject matter, [1, 2, 3., 4, 5, 6, 7], step gear automatic transmission concepts can be developed for current and future engines. Using insight from the analysis and methodology described in this investigation for the light duty, full-sized truck application and engine variants, the proposed concepts were developed with and simulated for fuel consumption. This section will detail the transmission concepts, highlight key features and compare performance relative to a currently available 6 speed planetary automatic transmission. The objective of these new concepts is to place greater emphasis on a fundamental architecture that facilitates easy adaptability to various engine and vehicle applications.

RWD Dual Clutch Transmissions

Dual clutch transmissions, DCTs, are constructed on layshaft gear architecture with either a single or double countershaft layout. Although DCTs have not entered application in the light duty, full size truck market, but their low rotating inertia, comparatively higher mechanical efficiency and ability to tune individual gear ratios to make the unit match to unique applications make it an ideal candidate for consideration. For this investigation, two unique DCT architecture layouts were converged upon to yield an assortment of gear ratio options to determine impact on fuel consumption. The architecture variants were developed with a focus on fuel consumption performance and modularity of the base design to accommodate additional planes of content such as gears and synchronizers to adapt to multiple engines.

The first DCT architecture considered produced an 8 and 10 speed variants with OAR spreads of 7.9 and 9.0, respectively. The gear ratios for these two DCTs are contained in Table 6. The particulars of the powerflow is a single countershaft design owing to the relaxed packaging restriction along the transmission axial length due to the longitudinal orientation. This configuration all allows for greater flexibility in tuning individual gear ratios to get the desired progression and OAR spread for a given application.

Common to transverse powertrain applications is the use of two countershafts to reduce packaging length. The same principle was sought for longitudinal, RWD, applications, to condense packaging and mechanization of the DCT. A new family of two countershaft design was created with easy adaptation to add more planes of gear pairs and synchronizers to increase forward gear ratio count. However, the packaging of twin countershafts can become challenging due to the width required to package and shaft center distances. A few examples of DCTs with 9 or more gear ratios can be found in patent documents such as [25, 26, 27, 28, 29], which can be equally applied to either transverse or longitudinal configurations. The two countershaft concept developed based upon this investigation is also depicted with an approximate cross-section diagram in Figure 17. An 11 speed arrangement is easily obtained with the two countershaft layout, facilitating a significant number of clutch-to-clutch, C2C, skip shifts of odd to even or even to odd gears. With this arrangement, multiple gear ratio options exist and are listed in Table 6. Note that four gear options, V1 to V4, were created for the 11 speed variant to demonstrate benefit and alignment with the L18 orthogonal array findings for engine matching.

Table 6 contains the gear ratios and OAR spreads for the DCT layouts depicted in Figure 17. The gear ratios were selected based upon best pairing with the characteristics of the V8 and future DSB V6 engines. Overall ratio spreads ranged from 7:1 to as high as 10.6:1. The fuel consumption performance of these DCT variants for the future DSB V6 engine is shown in Figure 18. Each transmission variant was analyzed with the same four final drive axle ratios listed in Table 4. For this engine pairing, the DCT variants net an average fuel consumption reduction across all axle ratios of 3.75% for the 7 speed and upwards of 5 to 5.1% for 11 speed variants 2 and 3, respectively. The best average fuel consumption is noted with the 11 speed DCT with variant V3 gear ratios. The availability of four overdrive ratios with a moderately highly launch ratio and large initial ratio step sizes make this option the most appealing for applicability to a range of engines based upon the findings of the fraction factorial L18 analysis.

Eight and ten speed DCT fuel consumption performance on the WLTP test schedule is shown in Figure 19 for the V8 and future DSB V6 gasoline engines relative to a current 6 speed planetary automatic as the baseline. The approximate benefit of the 8 and 10 speed DCTs over the 6 speed planetary is between 2.5 and 3.5%, respectively for the V8 engine, while an improvement of 2.9 and 6.8% is noted for the future DSB V6 engine. The benefit of the 8 or 10 speed DCTs is relatively flat in Figure 19 with respect to final drive axle ratio in either engine application. The best fuel consumption occurs though with higher axle ratios of 3.42 or 3.73 as gear mesh losses are minimized and in the case of the V8 engine, more time on the WLTP test schedule is spent in cylinder deactivation mode.

RWD Triple Clutch Transmissions

One drawback of DCT architectures can be the inability to execute even to even or odd to odd gear skip shifts as clutch-to-clutch, C2C. For example, this means a 7-5 shift is not possible without going through neutral or sequencing a 7-6-5 downshift. To overcome this a triple concentric input shaft is added to the base DCT architecture to form a triple clutch transmission, TCT. A diagram cross-section of a TCT is shown in Figure 20, with three concentric input shaft, two counter shafts and a common output shaft. Appendix B contains a truth table describing engagement of clutches and synchronizers to achieve a 10 speed variant as seen in Table B1. The particular arrangement shown in Figure 20 is a derivative the concept reported in [30], moving one of the synchronizer from the middle input shaft to the counter shaft. This re-configuration enables more gear ratios through winding paths. The TCT versus DCT architecture allows for a variety of C2C skip shifts, some even to even or odd to odd. Principally, this becomes a significant benefit getting out of the top gear range as noted by the available C2C ship downshifts available for a 10 speed variant in Figure 20. Such capability will improve transient passing acceleration performance while maintaining positive tractive effort at the drive wheels during the downshift event.

An additional benefit of the TCT architecture seen in Figure 20 is that the transmission can be programmed to have a variable number of forward gear ratios without having to change any mechanical components. For the TCT architecture in Figure 20, a maximum of 12 forward gear ratios are possible with 4 achieved through a winding path. To lower the gear ratio count, certain gears are simply skipped while still maintaining all sequential shifts as C2C. Anywhere from a 12 speed to fewer speed transmission is thus possible with one transmission design. The fixed gear ratios possible for a given set of tooth counts for all gear pairs are summarized in Table 7, showing between 7 speeds and the maximum of 12 speeds with sequential C2C shifting. The tooth counts for the gear pairs were selected to optimize for efficiency and for broad applicability to a range of engine applications. The ability of the transmission concept to have a variable number of fixed gear ratios facilitates adaptability to gasoline or diesel engine applications in the pursuit of minimizing fuel consumption or maximizing acceleration by introducing various mode selections to match driving conditions or engine characteristics without having to have unique tooling or many transmission hardware variants. A clear outcome of the L18 study was that no single step gear automatic transmission optimizes all engine variants, but the mechanization of the TCT concept is a potential concept that can bridge the gap. The TCT variant of Figure 20 with the gear ratio options shown in Table 7 can cover all the engines simulated in the L18 for optimal fuel consumption or acceleration performance with only calibration changes. For current or future gasoline engines, 9 and 10 speed variants of the TCT in Table 7 have sufficient OAR spread with the desirable ratio progression and gear ratios identified by the L18 study for minimizing C[O.sub.2] emissions or acceleration times.

Similarly, for diesel engines, best fuel consumption occurs with a numerically low top gear ratio, achieved through gear ratio 0.534:1 in Table 7. This optional, super overdrive gear ratio eliminates any trade off that once existed in selecting the axle ratio for performance capability.

The improvement in fuel consumption for 9 and 10 speed TCT's paired with the V8 and future DSB V6 gasoline engines relative to a currently available 6 speed planetary is shown in Figure 21. Overall, WLTP fuel consumption is reduced by approximately the same amount regardless if 9 or 10 speeds are utilized for the same final drive axle ratio. For the V8 gasoline engine a reduction of 2 to 2.5% in g C[O.sub.2]/km is realized depending on axle ratio. As noted in Figure 21. the amount of C[O.sub.2] reduction increases with axle ratio for the V8 engine as the time spent on the WLTP schedule in cylinder deactivation mode increases by roughly 10% from lowest to highest axle ratio. This result of best fuel consumption with high axle ratio brings performance harmony with the objectives of a light duty truck, namely towing capability. When paired with the future DSB V6 gasoline engine, the TCT 9 or 10 speed yield a 4 to 4.6% reduction in C02 relative to the 6 speed planetary. Conversely, as axle ratio increases the absolute value of fuel consumption represented by C[O.sub.2] emissions increases. The higher top gear ratio of the 9 and 10 speed reported in Table 7 when combined with a high axle ratio results in higher powertrain speeds and parasitic losses with this configuration. For the future DSB V6 gasoline engine, lower axle ratios are favored unless an additional, lower top gear ratio is provided as part of the shift pattern as with the 11 or 12 speeds noted in Table 7.

The fuel consumption reduction benefit of all variants of number of forward gear ratios for the TCT reported in Table 7 are contained in Figure 22 for the future DSB V6 gasoline engine and all 4 final drive axle ratios listed in Table 4. The analysis shows that the fundamental powerflow results in lower powertrain parasitic losses and in conjunction with improved engine operating points reduces fuel consumption as reported in g C[O.sub.2]/km emissions on the WLTP. For this particular engine, optimal fuel consumption becomes independent of the number of forward gear ratios specified by the TCT shift pattern and is dependent on axle ratio selection.

The TCT architecture of Figure 20 contains winding path gear ratios which are highlighted by red cells in Table 7. As the number of forward gear ratios is reduced from 12 the winding path gear ratios are eventually removed entirely from the shift pattern. Fundamentally, a performance degradation will result for the TCT architecture vs a conventional DCT as the winding path gear ratios will result in lower mesh efficiency as four meshes are required to create the gear state versus a typical layshaft gear state requiring only two. For the TCT, winding path gear states are created by going through input shaft C1 or C3 to either countershaft, then selectively engagement of a synchronizer positions A and E to allow torque flow from one countershaft to the other. The additional mesh lowers the overall gear mesh efficiency. This can increase fuel consumption as transmission parasitic loss will increase. Having winding paths as top gear ratios for the 11 and 12 speed configurations is not detrimental to the concept, but is less than ideal. The additional losses of the gear mesh can be offset by improved engine BSFC operation by downspeeding into this particular gear.

Figure 23 summarizes the transmission energy utilization/parasitic losses for the DCT and TCT concepts paired with the future DSB V6 gasoline engine operating on the WLTP test schedule. As expected, all loss categories decrease from the current 6 speed planetary design. Due to the tooth count selection of the TCT, no penalty in gear mesh efficiency is noted between 8 or 11 speed DCTs and 9 or 10 TCTs as the energy associated with this parasitic is within 8 kJ. As the number of TCT speeds increases to 11 and 12 though, an increase in gear mesh losses is accompanied with a decrease in launch devices losses from the utilization of a higher axle ratio noted in Table 8. The gap in overall transmission losses between DCT and TCT concepts is marginal. The adaptability of the TCT to change the number of gears of the transmission with only calibration changes to match characteristics of the engine and vehicle application is a distinct advantage. However, the TCT comes at the addition of another input clutch relative to a traditional DCT, and will necessarily require additional package space and require additional content.

The objective of the DCT and TCT analysis was to demonstrate how their attributes synergize with the findings of the L18 orthogonal array for current and future engines and that they provide some level of performance improvements. Both model sets for the DCT and TCT concepts can be fine-tuned with detail cross sections developed and spinloss assess to include in the energy analysis to demonstrate potential further reductions in fuel consumption.


This investigation sought two primary objectives; 1.) investigate the design requirements of step gear automatic transmission with the foresight of future engine design and operating characteristics to answer the question on how many gear ratios are required for low fuel consumption, wide BSFC island engines and 2.) present transmission concepts that fulfill the requirements identified to match future engines. The fractional factorial design undertaken as an L18 orthogonal array with multiple engines, current and future designs, and final drive axle ratios allowed quick determination of the transmission design requirements with respect to fuel consumption on the WLTP test schedule and 0 to 100 kph acceleration time. Irrespective of the magnitude of fuel consumption or the size and shape of the minimum BSFC contour for an engine, the optimal number of forward gear ratios came out to at least 9. At approximately 9 forward gear ratios, an asymptote on the benefit to fuel consumption was reached. More gears enables reduced operating speeds of both the engine and transmission to minimize losses, but also to operate the engine more frequently in regions of low BSFC. The conclusion regarding number of forward gear ratios is drawn based upon all the underlying assumptions for the hypothetical transmission designs simulated, but yields results consistent with those already reported in the literature. The other strong contributors to reducing fuel consumption are technologies that reduce parasitic losses, increase torque transfer efficiency and enable shift pattern constraints/operating point to aggressively downspeed the powertrain, lock the launch device quickly and shift as frequently as possible. The parameters of ratio progression, top and launch gear ratios were found to be design parameters that contribute a minor amount to reducing fuel consumption compared to the other parameters included in the L18 array. The maximum torque characteristics of the engine strongly dictate the gearing selection of the step gear automatic transmission, particularly near the maximum speed of the engine. Depending on these characteristics of the engine, it could either dictate more or less gears with larger or smaller ratio step sizes. Other transmission parameters leading to best acceleration performance are high launch gear ratio, low inertia gear architecture and low parasitic losses.

Based upon the results in this investigation, depending on the engine torque characteristics, step gear automatic transmission design requirements could vary drastically across applications. To minimize C[O.sub.2] footprint across a range of engine and vehicle applications, point solutions are required. This point is evidenced in powertrain engineering today as unique engine variants are created for certain vehicle applications but the same step gear automatic transmission are applied with tuning only the final drive axle ratio. The lay shaft DCT and TCT transmission concepts presented provide the ability to adapt the transmission gearing for a specific application while only changing gear pair tooth counts. The TCT concept further enhances adaptability and performance to a given application, allowing the number of gear ratios to be calibrated to vary based upon driving conditions. Depending on the details of the engine and the desired performance focus, fuel consumption or acceleration, multiple transmission modes can be calibrated setting the number of gear ratios and ratio progression accordingly without hardware changes. The TCT concept is a fitting step gear automatic transmission solution to evolving engine characteristics without having to tradeoff fuel consumption or acceleration. The DCT and TCT layshaft, step gear automatic transmissions on resulted in fuel consumption reductions on the order of 2 to 6% from a current 6 speed planetary automatic transmission across a range of engines and axles ratios for a light duty, full size truck vehicle.


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BMEP - Brake mean effective pressure, kPa

BSFC - Brake specific fuel consumption, g/kW-hr

C2C - Clutch-to-clutch shift

DCT - Dual clutch transmission

DSB - Downsized boosted (turbocharged)

FTP - Federal Test Procedure

GHG - Greenhouse gas

L18 - Orthogonal array design with 18 runs and 7 design parameters

OAR - Overall ratio spread of transmission

TCT - Triple clutch transmission

US06 - Supplemental Federal Test Procedure

WLTP - Worldwide Light Duty Test Procedure


This appendix contains the fractional factorial orthogonal array selected to create a unique set of step gear automatic transmission designs to minimize the number of simulations required to determine the relative importance of each design parameter on fuel consumption and acceleration performance. Table A1 contains the full L18 orthogonal array with Table A2 containing the details of the shift pattern parameters numbered 1 through 3.
Table A1. Fractional factorial orthogonal array for transmission design

Run  Forward      Ratio        Top Gear  Launch      Spinloss
     Gear Ratios  Progression  Ratio     Gear Ratio  Scaling

 1    7           Geometric    0.55      4.5         -30%
 2    7           Linear       0.6       5           Nom
 3    7           Logarithmic  0.65      5.5         +30%
 4    8           Geometric    0.55      5           Nom
 5    8           Linear       0.6       5.5         +30%
 6    8           Logarithmic  0.65      4.5         -30%
 7    9           Geometric    0.6       4.5         +30%
 8    9           Linear       0.65      5           -30%
 9    9           Logarithmic  0.55      5.5         Nom
10   10           Geometric    0.65      5.5         Nom
11   10           Linear       0.55      4.5         +30%
12   10           Logarithmic  0.6       5           -30%
13   11           Geometric    0.6       5.5         -30%
14   11           Linear       0.65      4.5         Nom
15   11           Logarithmic  0.55      5           +30%
16   12           Geometric    0.65      5           +30%
17   12           Linear       0.55      5.5         -30%
18   12           Logarithmic  0.6       4.5         Nom

Run  Gear Architecture            Shift

 1   Planetary                    1
 2   Layshaft                     2
 3   Layshaft with Winding Paths  3
 4   Layshaft with Winding Paths  3
 5   Planetary                    1
 6   Layshaft                     2
 7   Layshaft                     3
 8   Layshaft with Winding Paths  1
 9   Planetary                    2
10   Layshaft                     1
11   Layshaft with Winding Paths  2
12   Planetary                    3
13   Layshaft with Winding Paths  2
14   Planetary                    3
15   Layshaft                     1
16   Planetary                    2
17   Layshaft                     3
18   Layshaft with Winding Paths  1

Table A2. Details for shift pattern constraints for fraction factorial
orthogonal array parameter.

Shift    Minimum Transmission Input Speed for Gears
Pattern  Using Coast Down Fuel Cutoff

1        1200 rpm minimum all gears using coast down
         fuel cutoff, less than 900 rpm for all others
2        Minimum engine speed for coast down fuel cutoff
         + 200 rpm, all other gears idle speed +100 rpm
3        Minimum engine speed for coast down fuel cutoff
         + 200 rpm, all other gears idle speed +100 rpm

Shift    Upshift to Downshift Line
Pattern  Hysteresis

1        3 to 4 kph, shift dependent

2        3 to 4 kph, shift dependent

3        1.5 kph all shifts

Shift    Minimum Transmission Gear Ratio for
Pattern  Engine Refuel During Coast Down

1        Gear ratio nearest 1.5:1

2        Gear ratio nearest 1.5:1

3        Gear ratio between 3:1 to 2.5:1

Appendix B

This appendix contains the truth table for clutch and synchronizer actuation for the triple clutch transmission, TCT, concept presented as a 10 speed variant. The nomenclature and reference to gearsets and synchronizers are contained in Figure 20.
Table B1. Truth table for triple clutch transmission, TCT, 10 speed
variant showing applied clutches and synchronizers required for
sequential upshift and downshift ratio selection. X = engaged, carrying
torque. O = engaged, not carrying torque, e.g. preselection.

Gear   Gear    Ratio      C1      C2      C3      S1_A     S2_B
State  Ratio   Step Size  Clutch  Clutch  Clutch  Synchro  Synchro

Rev    -4.209                             X       O
N              -0.821                             X        X
1st     5.292                     X               X        X
2nd     3.494   1.515                     X                X
3rd     2.826   1.236             X
4th     2.293   1.232     X                       O
5th     1.865   1.229                     X       X
6th     1.515   1.231             X               X
7th     1.229   1.232     X                       X
8th     1.000   1.229                     X
9th     0.809   1.236             X
10th    0.656   1.232     X                       O

Gear   S2_C     SR3_D    SR3_E    SR4_F    SR4_G
State  Synchro  Synchro  Synchro  Synchro  Synchro

Rev             X                 X
N                                 O
1st                               O
2nd                      O        O
3rd    O                 X        X
4th    O                          X
5th                      X        X
6th    X                                   O
7th    X                 X
8th    X                 O                 O
9th    O                 X                 X
10th                     O                 X

Darrell Robinette and Tejinder Singh

General Motors Co.

Table 1. Step gear automatic transmission parameters included in the
L18 orthogonal array.

Parameter                           Level
Number of Gears    7          8     9         10  11  12

Ratio Progression  Geometric        Linear        Logarithmic
Top Gear Ratio     0.55       0.60  0.65
Launch Gear Ratio  4.50       5.00  5.50
Spinloss Scaling   -30%       Nom   +30%
Gear Architecture  Planetary        Layshaft      Layshaft
                                                  w/Winding Path
Shift Pattern      1          2     3

Table 2. Overall ratio spreads for transmission in the L18 orthogonal

                Launch Gear Ratio

Top Gear Ratio  4.50  5.00   5.50
0.55            8.18  9.09  10.00
0.60            7.50  8.33   9.17
0.65            6.92  7.69   8.46

Table 3. Major shift pattern constraints and operating strategy assumed
for this investigation.

Constraint                 Description

Minimum operating speed
for gears using coastdown  Either 1200 rpm or 1100 rpm, see Table Al for
fuel cutoff
Minimum operating speed    800 to 900 or idle speed plus 100 rpm, see
                           Table Al
for gears not using
coastdown fuel cutoff      for details
Minimum gear ratio         For non-aggressive pattern gearratio closest
                           to 1.5:1,
before engine refuel on    for aggressive shift pattern between 3:1 and
Upshift-downshift          For non-aggressive pattern 3 to 4 kph, for
hysteresis                 shift pattern 1.5 kph
Torque converter lockup    Applied right at 1-2 upshift, fully locked
                           for all higher
clutch apply               gears for power on condition
Torque converter lockup    Released on coastdown before downshift in
clutch release             engine is refueled
Upshift shift times        0.65 seconds for 7 speeds, decreasing
                           monotonically to
                           0.35 seconds for 12 speeds
Downshift shift times      0.50 seconds for 7 speeds, decreasing
                           monotonically to
                           0.35 seconds for 12 speeds

Table 4. Final drive axle ratios used in analysis matrix combined with
each engine - transmission combination.

Axle Ratio 1  Axle Ratio 2  Axle Ratio 3  Axle Ratio 4

3.08          3.23          3.42          3.73

Table 5. Summary of average fuel consumption performance for baseline
and hypothetical, reduced fuel consumption engine variants, averaged
over all step gear transmissions of L18 orthogonal array.

               L18 Average Fuel Consumption g C02/km
Engine         Baseline  Reduced  % Delta

V8             251.0     214.6    14.5
DSB V6         252.2     219.1    13.1
Diesel V6      236.3     231.8     1.9
Future DSB V6  219.1     206.1     6.0

Table 6. Gear ratios for two DCT architecture types depicted in Figure
17. noted four variants of 11 speeds come from same fundamental

Gear#  7 Spd  8 Spd  10 Spd  11 Spd  11 Spd  11 Spd  11 Spd
                             V1      V2      V3      V4

 1     5.100  4.757  4.750   4.450   4.800   4.950    5.600
 2     3.050  3.171  3.167   2.850   3.050   3.250    3.920
 3     1.920  2.114  2.111   2.050   2.250   2.350    2.950
 4     1.350  1.458  1.456   1.700   1.870   1.820    2.250
 5     1.000  1.080  1.103   1.500   1.620   1.500    1.750
 6     0.770  0.864  0.919   1.330   1.410   1.260    1.400
 7     0.600  0.720  0.799   1.160   1.200   1.050    1.150
 8            0.600  0.695   1.000   1.020   0.900    0.950
 9                   0.604   0.870   0.880   0.750    0.790
10                   0.526   0.750   0.725   0.640    0.650
11                           0.635   0.600   0.550    0.530
OAR    8.500  7.928  9.039   7.008   8.000   9.000   10.566

Table 7. Gear ratios for TCT with a given set of gear pair tooth counts
and possible combinations to achieve 7 to 12 speeds all with C2C
shifting. Red cells indicate winding path, 4 gear mesh ratios.

Gear#  7 Spd  8 Spd  9 Spd  10 Spd  11 Spd  12 Spd

 1     5.292  5.292  5.292  5.292   5.292   5.292
 2     3 494  3.494  3.494  3.494   3.494   4.295
 3     2.293  2.293  2.293  2.826   2.826   3.494
 4     1 515  1.515  1.865  2.293   2.293   2.S26
 5     1.000  1.229  1.515  1.865   1.865   2.293
 6     0 809  1.000  1.229  1.515   1.515   1.865
 7     0.656  0.809  1.000  1.229   1.229   1.515
 8            0.656  0.809  1.000   1.000   1.229
 9                   0.656  0.809   0.809   1.000
10                          0.656   0.656   0.809
11                                  1.534   0.656
12                                          0.534
OAR    8.063  8.063  8.063  8.063   9.912   9.912

Table 8. Summary of optimal fuel consumption performance on WLTP test
schedule for future DSB V6 gasoline engine and various step gear
automatic transmissions and axle ratios.

                                WLTP            WLTP Fuel
Transmission  Final Drive Axle  Powertrain      Consumption
              Ratio             Efficiency (%)  g C[O.sub.2]/km

 6 Spd Plnty  3.08              24.56           238.6
 8 Spd DCT    3.42              25.66           228.1
11 Spd DCT    3.42              25.78           226.9
 9 Spd TCT    3.23              25.56           229
10 Spd TCT    3.23              25.52           229.4
11 Spd TCT    3.73              25.52           229.3
12 Spd TCT    3.73              25.52           229.3
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Author:Robinette, Darrell; Singh, Tejinder
Publication:SAE International Journal of Engines
Article Type:Technical report
Date:Sep 1, 2016
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