Predicting cavitation desinence in automotive torque converters

Predicting cavitation desinence in automotive torque converters
C. Walber1, J. Blough2, C. Anderson2, M. Johnson2, J, Schweitzer3 1 PCB Piezotronics 3425 Walden Ave, Depew, NY, USA e-mail: [email protected]
2 Michigan Technological University, Department of Mechanical Engineering 1400 Townsend Dr. Houghton, Michigan, USA
3 General Motors Powertrain Pontiac, Michigan, USA
Abstract
Cavitation is a concern in automotive torque converters because it can cause operation to be altered from design intent, generate unacceptable noise in the passenger compartment of a vehicle, and damage torque converter components in extreme situations. Previous cavitation experiments have determined the onset of cavitation in stall mode. During actual operating conditions, however, torque converter stall occurs for a short duration. Thus characterization of cavitation in speed ratio operation is needed. Torque converter speed, torque, and hydraulic parameters at cavitation desinence were determined experimentally using a dynamometer test cell in concert with nearfield acoustic measurements. These experimentally determined operating conditions along with design parameters were used to create a set of dimensionless parameters, which were used to develop non-dimensional predictive models of the cessation of cavitation during simulated vehicle takeoff. Models were developed for several populations of torque converters with varying degrees of similitude.
1 Introduction
The automotive torque converter is the powertrain component that multiplies engine torque to overcome the poor low speed torque characteristics of an internal combustion engine. It regulates engine speed to evenly increase during vehicle acceleration. Modern automotive torque converters are made up of three elements, a mixed flow pump and turbine, and an axial flow stator. Figure 1 is a basic schematic of a torque converter, including arrows showing the direction of the toroidal flow induced during operation. Maximum efficiency is achieved during high speed ratio operation while maximum torque multiplication is attained at stall, or turbine speed equal to zero. Speed ratio (SR) is defined as the ratio of the turbine speed over the pump speed. In the basic operation of a torque converter, the pump is driven by the engine through connection of the engine crankshaft and flexplate to the cover of the torque converter. Rotation of the pump imparts angular momentum onto the automatic transmission fluid (ATF). The fluid flows from the inner radius of the pump flow path to the outer radius, and is directed into the turbine. The angular momentum of the fluid acts on the turbine, imparting a torque onto the turbine shaft which is the input shaft to the automatic transmission. The fluid exits the turbine and is redirected by the stator toward the pump at a favorable angle with respect to pump operation. The change in angular momentum by the stator is what creates torque multiplication. The torque multiplication factor, called torque ratio (TR), is the performance characteristic that helps the vehicle accelerate from a stop.
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Figure 1: Cross section of an automotive torque converter, toroidal flow is indicated by the direction of the black arrows. Maroon arrows indicate the normal cooling flow
Maximum torque multiplication occurs at stall. As turbine speed and speed ratio increase, torque ratio decreases. This is due in part to the change in flow incidence angle into the stator. The angle of flow exiting the turbine relative to the stator blade inlet angle decreases with increasing turbine speed such that the change in angular momentum across the stator decreases, and stator torque decreases. At a high speed ratio, the incidence angle lines up with the stator blade inlet angle, and torque multiplication becomes one. Up to this point of operation, the stator is grounded to the stator shaft and does not rotate. As turbine speed further increases, incidence angle rotates around the nose of the stator blade such that flow impacts the stator blades on the opposite side. To prevent torque ratio from becoming less than one, the stator assembly has a one-way clutch that allows it to overrun, effectively getting out of the way of the flow. At the point when the stator overruns, the converter is acting as a fluid coupling. The speed ratio at which the stator overruns is called the coupling speed ratio. Progression of incidence angle with speed ratio is depicted in Figure 2.
Torque converters need temperature control to prevent overheating of the ATF. Under practical operation, a converter functions at less than unit efficiency, and all power loss is converted to heat within the working fluid. The automatic transmission pump forces a continuous flow of cooling fluid through the torque converter. ATF flows into the converter between the cover and the clutch, and then into the outer torus region between the pump and the turbine where it is integrated into the toroidal flow. The direction of this flow is indicated in Figure 1 by the maroon arrows. The hotter fluid is evacuated from the converter to the vehicle cooling system. A second function of the transmission pump is to control the level of pressure in the torque converter to suppress cavitation. The flow into the converter is called charge pressure, and the flow out is called back pressure.

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Low Pressure Side

High Pressure Side

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Figure 2: Flow incidence angle across the blades of the stator
When the torque converter is operating at high speed ratios, a clutch can be engaged to create a direct shaft connection between the engine and transmission to bypass the hydrodynamic inefficiency of the torque converter. The clutch is engaged by reversing this cooling flow, pushing the pressure plate of the clutch toward the cover of the converter. Pressure is regulated to create a full lock between the cover and clutch, or a controlled speed slip.
In torque converter mode, individual element torques are created from the change in angular momentum flux across an element from inlet to outlet. The torque is a function of the local static pressure times the radius integrated over the entire surface of each blade. A greater pressure differential across a blade proportionally increases the individual element torque. Consequently, at some large element torque, the pressure on the low pressure side of a blade can drop to below the vapor pressure of the fluid, and the nucleation of cavitation bubbles may occur.
The effect of cavitation on performance is dependent on whether sustained cavitation is reached. Incipient cavitation can occur at stall and dissipate before it is of any consequence. But if a high level of element torque is sustained for a long duration, the heavy cavitation will result in large vapor regions that displace the working fluid, affect performance, and possibly cause damage when cavitation bubbles collapse. Furthermore, collapsing bubbles cause a broadband noise that may affect the overall sound quality of the vehicle. Advanced cavitation can cause a decrease in individual element torques, which alters the relationship between speed and torque for the converter.
2 General Considerations
2.1 Torque Converter Cavitation at Stall
In previous research, Robinette et al. [1] and Kowalski et al. [2] studied torque converter cavitation in depth with the converter operating at stall. This is the condition at which a torque converter is most susceptible to cavitation due in part to the high element torques. Toroidal flow within a converter is highly three dimensional with large element flow incidence angles. The high angle of flow into the stator at stall creates regions of separated flow on the low pressure side of the blade. Research by Mekkes et al. [3] confirmed that cavitation initiates in the separated flow region at the stator inlet. As speed ratio increases, stator torque decreases, and flow incidence angle becomes less severe. Regions of separated flow are reduced, and the pressure differential across a stator blade drops, reducing the likelihood of cavitation bubbles forming at the inlet of the stator.

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Mekkes [3] used wireless microwave telemetry to measure pressure at the stator inlet. The telemetry was placed on the stator, and pressure measurements were made at the inlet region of the blades. Wireless telemetry was required due to the difficulty in running wires from inside a rotating torque converter to the data acquisition equipment. The telemetry was used to acquire pressure measurements from taps on stator blades and to transmit readings to an antenna through the pump via a series of RTV filled slits milled out of the pump/stator interface. This antenna carried the signal to a receiver which converted it back to the raw data for a data acquisition system. A method was developed by Kowalski [2] that uses nearfield acoustic measurements to accurately detect cavitation without requiring wireless telemetry. In this way, a large population of torque converters can be tested for cavitation without the time and expense needed to create microwave instrumented torque converters for each blade design of interest. Robinette et al. [4] used the acoustic method to determine incipient cavitation at stall for a population of torque converters with a wide range of sizes and blade geometries. A correlation was formulated based on operating conditions and converter geometry to estimate the point of incipient cavitation during stall.
2.2 Speed Ratio Operation
A torque converter remains in stall only so long as there is not sufficient torque to create vehicle motion. If cavitation is present at stall, it will cease at some higher speed ratio as stator torque and turbine torque decrease. If cavitation at stall is at a low level, and cavitation desinence occurs shortly into the vehicle launch, then noise from cavitation will not be noticed, and its effect on performance will be of no consequence. If, however, torque levels are high enough to sustain cavitation to a high vehicle speed, then cavitation noise could be objectionable to the vehicle operator. Therefore, it is important to characterize the duration of cavitation versus speed ratio with respect to torque converter design parameters and operating conditions. This project utilized the previously developed acoustic method that was used to identify incipient cavitation, but applied it to speed ratio testing to identify cavitation desinence.
3 Experiment
A dynamometer test fixture was constructed for taking acoustic data with torque converters during the previous stall cavitation project. The fixture is much larger than typically used for torque converter testing so that it can be filled with acoustic foam to assist in absorbing and insulating noise. Figure 3 shows pictures of both a typical torque converter test fixture and the acoustically treated fixture used for the cavitation experiments. On the right is a picture of the fixture opened to reveal a torque converter and acoustic foam.

Figure 3: Left: Comparison of original torque converter dynamometer test fixture (red) and acoustic test fixture (gray). Right: Close up of opened acoustic test stand with acoustic foam

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The SR test procedure was developed to emulate torque converter performance during vehicle takeoff with the engine running at constant torque. During a test, the turbine speed is accelerated at a steady rate while the pump is held at a fixed torque. The first step in the test procedure is to bring the pump up to the torque it will sustain throughout the experiment. A short settling period is needed to allow speed transients due to the control system to settle out. The turbine is then ramped at 50 rpm/s from low speed (100 rpm) to high speed (2500 rpm). An upper speed of 2500 rpm was selected to achieve high enough speed ratio to ensure that cavitation desinence would occur for any of the torque converters planned to be tested. After the test is completed, a torque correction factor which includes dynamic torque losses due to the entire dynamometer system is applied to the measured torques. As with all torque converter testing, speeds, torques, pressures, temperatures, and flow rates are collected via the control system at a 10 Hz sample rate. Nearfield acoustic measurements are taken at a 51.2 kHz sample rate. This frequency was selected as suitable since cavitation noise was known to be detectable acoustically (In frequencies below 22 kHz). Pump and turbine speeds then are also measured at 51.2 kHz so that some reference may be made between the acoustic data and other test parameters.
Speed ratio sweeps were conducted for each torque converter at various input torques and charge pressures. Charge pressures tested were 480, 690, 900, 1030, and 1240 kPa with a pressure delta of -210 kPa for the back pressure. Cooling flow temperature was held constant throughout all of the tests at 70°C. Input torque for each test was selected based on the torque required to initiate cavitation stall in the previous stall testing plus 70 Nm. The extra torque was added to make sure that cavitation occurred during the speed ratio test. The minimum input torque used was 150 Nm and the maximum was 310 Nm for the torque converters in this study.
The goal of the speed ratio testing was to determine the desinence of cavitation, or the point at which the bubbles can no longer be detected within the working fluid. In the stall testing by Robinette [1], incipient cavitation was characterized by a sudden increase in the amplitude of the high pass filtered sound pressure level (SPL) of the noise measurements. This SPL was further processed into a slope2 curve, which was then used as an indicator function to determine the onset of cavitation. A similar approach is taken to determine cavitation desinence. Figure 4 is a colormap from a SR test showing the nearfield noise versus SR and frequency. Overlaid on the plot are the filtered SPL curve and the slope2 curve of SPL normalized to the sound pressure level so that both curves can be plotted on the same graph. The slope2 curve is used to facilitate identifying the key changes in the SPL curve. The region of high broadband noise on the left half side of the colormap corresponds to cavitation. The high magnitude peak in the slope2 curve near 0.4 SR corresponds to the desinence of cavitation.

Figure 4: Example of torque converter speed ratio data plot

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4 Analysis
4.1 Preliminary Data
After data for a torque converter SR test is acquired, the speed ratio at desinence of cavitation, labeled SRd, needs to be identified. During speed ratio operation, however, the noise from the turbine and pump increases as turbine speed increases, and the overall noise content of the converter is complex. This is evidenced by the numerous local peaks and valleys in the SPL curve in Figure 4. SPL drops to a fairly constant level after cavitation stops, but the roughness of the curve and the lack of a sharp transition from the cavitation region to non cavitation necessitated the development of a repeatable and objective procedure for identifying SRd. Figure 5 demonstrates the method that was used.

Figure 5: Visualization of the algorithm used to determine desinent cavitation in a torque converter
The top portion of Figure 5 shows the filtered SPL curve. A high pass filter with a cutoff of 10 kHz is used to filter out the background noise, rotational orders, and blade pass frequencies that occur below 10 kHz. The resulting filtered SPL curve displays the wideband noise from cavitation. As expected, cavitation noise is highest near stall, and gradually decreases to a relatively constant level when cavitation bubbles cease to form. A lower high pass filter of 6 kHz was used in the analysis by Robinette [1] due to less background noise being present in stall testing. Due to the jagged nature of the SPL curve, it is smoothed using a three point running average filter. This curve is then used to generate a slope2 curve plotted as a percentage as shown in the bottom portion of Figure 5. The resulting curve is examined to find the maximum speed ratio less than 0.65 where the slope2 curve is greater than 22.5 percent of its maximum. The 0.65 SR limit was determined after examining data from all the tests and finding that cavitation always ends at a lower speed ratio. The 22.5 percent slope2 threshold was selected after studying the data from all the tested converters and selecting a level that correlated with the perceived change in the SPL over the entire population. These criteria were entered into an algorithm to search for the points of cavitation desinence from all the test runs. Figure 5 shows the resulting slope2 curve from the colormap in Figure 4 with the excluded areas shaded out in the lower plot, and the determined point of desinent on both plots. The fluid parameters required for further analysis are taken at the speed ratio of cavitation desinence.

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4.2 Dimensional Analysis
Dimensional analysis was used to develop models for predicting torque converter cavitation desinence using torque converter design parameters and operating parameters measured or controlled in the speed ratio tests. In the stall cavitation research done by Robinette [4], a set of dimensionless parameters that incorporated torque converter design variables, performance parameters and operating conditions was derived and used to develop dimensionless models to predict the emergence of cavitation at stall. Similar parameters were used in this study to develop models for cavitation desinence, but are modified somewhat to accommodate speed ratio operation. These are listed in Table 1.

Unit Input Speed

Based on overall torque converter design

Stall Torque Ratio

Based on overall torque converter design

Torus Aspect Ratio

Based on torque converter geometry

Stator Blade Based on torque converter Thickness Ratio geometry

Number of Stator Blades

Based on torque converter geometry

Dimensionless Operating Point Parameter Pressure Ratio

Prandtl Number Operating Point Parameter

Dimensionless Rotational Power

Combination of Operating Point Parameter and Measured Response

Table 1: Dimensionless Parameters used in Speed Ratio Correlation

A much more exhaustive list of dimensionless parameters could have been used and was discussed in previous research. The major variable contributing to torque converter operation are input and output speed and torque; transmission fluid input and output pressure, flow, and temperature (temperature within the converter can not be ascertained); transmission fluid mechanical parameters of density and viscosity; and lastly the torque converter geometry. It is believed that all of these variables are incorporated in the list of dimensionless parameters in Table 1.
Unit input speed at stall, U, shown in Equation 1, is a parameter that describes torque converter performance and is used to select the best torque converter for a given engine and vehicle application. It contains the relationship between the working fluid (density), the size of the converter (diameter), the input speed, and the input torque.
(1)
Unit input speed describes what the pump speed would be if the other quantities were adjusted to a value of one. It is used to compare torque converter designs of different sizes and under varying operating conditions. The value of U is a function of the blade designs for the pump, turbine, and stator. It is used in the dimensional analysis instead of using a longer list of blade design parameters.

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Torque Ratio was described earlier as the ratio of output torque over input torque. Note that since both U and TR have a dependence on speed ratio, the values of these variables at stall were used for this correlation to improve equation conditioning.
Torus aspect ratio is a definition of the roundness of a torque converter. The measurements used for this along with stator blade thickness ratio are shown in Figure 6. The number of stator blades is a design variable that is a function of stator blade angles and the axial length of the stator.

Figure 6: Left: Schematic of torque converter showing diameter (D) and torus length (Lt) Right: Profile of stator blade depicting maximum thickness (tmax) and chord length (lc)
The dimensionless pressure ratio and the Prandtl number are calculated from the values of the measured charge and back pressures, flows, and temperature taken due to the cooling flow mentioned in the introduction. The formulations of these parameters are shown in Equations 2 and 3. In Equation 2, pcharge and pback are the charge and back pressures applied to the test stand during operation respectively. The term, cp, in Equation 3, is the specific heat of the working fluid, k is the thermal conductivity, and µ is the dynamic viscosity. All of these values are measured or calculated based on the temperature at the point of cavitation desinence.
(2)
(3)
The last dimensionless variable, Dimensionless Rotational Power, is the product of the speed ratio at desinent cavitation, SRd, (selected by the algorithm detailed in Section 3) and the dimensionless input torque. This combination of dimensionless parameters was selected as the dimensionless response in the correlation development because it is defined by quantities that can be used to assess the potential for cavitation in a new torque converter design or a new application of an existing design.
The dimensionless parameters are applied to a Response Surface Model (RS) using a stepwise regression procedure to predict the dimensionless rotational power. The general form of the response surface model is outlined in the research of Madsen et al. [6], and is given here by Equation 4.
(4)
The response, ŷ, is calculated dimensionless rotational power. This will be used later to compare the calculated dimensionless rotational power to measurements taken when the experimentation was performed. The linear, quadratic, and interaction terms are generated from the other dimensionless regressors listed in Table 1. These are used to solve for the β0, βii, and βij terms using a least squares method. The residual error, symbolized in Equation 4 as ε, is the difference between the experimentally measured quantity of the dimensionless rotational power and the predicted value. The variables (xi and xj) are the dimensionless parameters, with k being the number of the parameter.

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A forward selection path of stepwise regression is used to minimize the error in the models. This method starts with a basic equation comprised of only the intercept term, β0. From there, regressors are added until the error of the model is minimized. The dimensionless rotational power is calculated using all of the remaining regressors in addition to those that had previously been added, after which the new regressor is selected by determining which one minimizes the error to the greatest degree. This is repeated until the model error has dropped to less than 15%.
The quality of fit for any RS model is verified by the root mean square error (RMSE) and by determining the linear association between the response (calculated dimensionless rotational power) and the regressors. RMSE estimates the model’s standard deviation and for these correlations are computed as a percentage. Equation 5 shows the calculation for %RMSE. The term yi is the dimensionless rotational power as measured by experimentation, ŷi is the calculated dimensionless rotational power from the model, n is the number of data points, and p is the number of dimensionless regressors in the model.

(5)
The proportionate amount of variation in the response (calculated dimensionless rotational power) explained by a particular set of regressors in the model is measured using the adjusted coefficient of multiple determination, R2a, in Equation 6. This metric calculates to between 0 and 1. Generally, results above .85 signify an accurate model of the data in question. The coefficient of multiple determination, R2, was also calculated. However, it is not preferred as the value of R2 always increases with the addition of regressors. R2a may increase or decrease depending on whether or not the additional terms actually reduce variation in the response.
(6)
Figure 7 shows results from the stepwise regression procedure for the analysis of a population of round torus torque converters to determine the regressors to be added to the model. Each step of the procedure optimizes the %RMSE, the R2a, or both. Only those regressors that have a significant impact on model error or linear association between the response and the regressors are included in the model. This makes the final model for the example population a function of 16 terms, including the intercept term, instead of the 36 possible terms. The value for R2a was brought to above .85 within the first three iterations. Each subsequent iteration was done to improve model error.

Figure 7: Reduction of %RMSE and R2a during stepwise regression for round torus model

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Conditioning of the data matrix also needs to be taken into account. This study was done with a limited number of converters, some of which were somewhat similar. With an ill-conditioned system, if too many regressors are added to the formulation for a particular population of converters, the data matrix becomes close to singular due to the fact that some of the data being used may be similar. The resulting model is unstable in that small changes in the dimensionless regressors will create very large changes with respect to the response.
5 Results
Several RS models based on geometric similitude between torque converters are presented. Each population increases in complexity as the similarity between the converters in the population decreases. The first population shows a correlation using converters of the same unit input speed. The second deals with a specific torus aspect ratio which is common to the converters in that population. As such, that dimensionless regressor is eliminated from the correlation. The third , made up of machined from solid only torque converters, was analyzed to determine if geometric differences that result from the manufacturing process have an effect on formulating a response surface model. The last population correlates all of the converters tested that were made by the same manufacturer. The torque converters in the final population cover a wide range of geometry, but follow similar design rules for torus shapes, blade angles, and for the stator blades, the airfoil shapes. The goal was to develop a general model for predicting dimensionless rotational power at cavitation desinence that can be applied to a wide range of torque converter designs. The predicted value can be used with input torque and operating parameters for a specific application to calculate SRd and estimate the risks for cavitation.
5.1 Constant Unit Input Speed
Three torque converters with close to the same unit input speed, but different diameters were analyzed in this population to model how converters with similar unitized performance characteristics compare with regards to desinent cavitation. The functional form of this RS model is given in Equation 7. Figure 8 is a plot of dimensionless rotational power at cavitation desinence that compares test results (point data) with the predicted curve from the model.

Figure 8: RS model of desinent cavitation in constant unit input speed population (7)