The team created theoretical models of the continuously variable transmission (CVT) on the Cal Poly Baja car to improve performance. Their Adams model showed that increasing weight on the primary pulley results in faster expansion and quicker response time. Their Simulink model calculated that using the ideal CVT ratio would reduce the 0-100 ft time to under 5 seconds, improving their acceleration time by over 10%. Testing different ramp angles on the primary pulley also showed potential for obtaining the ideal ratio. Experimental validation was recommended over relying solely on analytical models.
1. CVT Project
MATT MYERS, DELANEY BALES, TAYLOR VANDENHOEK, ALEK LINQUIST,
JESS MCCAFFERTY
ME 416, FALL 2014
2. Background
CVT - Continuously Variable Transmission
◦ Transitions between an infinite number of gear ratios
◦ Primary pulley driven by engine RPM
◦ Secondary pulley driven by torque
Baja Team runs a CVT to transfer power from the engine to the gearbox.
4. Purpose
The CVT on the Cal Poly Baja car has several factors leading to inefficiencies and
improper tuning.
◦ Last year we tried tuning the CVT with different weights.
◦ Placed 33rd in the Acceleration Event with 5.023 seconds
◦ 1st place had a time of 4.199 seconds
CVT should be custom tailored for Baja Car.
This model would be used by the Baja Club to predict CVT performance based
on variable inputs.
5. Goals
Our goal as a group was to improve the efficiency of the CVT through theoretical
modeling.
◦ Create dynamic model of CVT
◦ Determine most influential variables
◦ Determine the relationships between variables
◦ Reduce time to distance from 0-100 ft and 0-150 ft
◦ Improve acceleration time by 10%, from 5.023s to 4.58s, which would equal 5th place based on 2014
results.
6. Baja Vehicle Performance
Tractive Effort Curve
◦ Ideal Tractive Effort
◦ Actual Tractive Effort
◦ Road Load
◦ Traction Limit
Ideal CVT Ratio
MOTOR CVT GEARBOX CVJ TIRES
η = 96%
η = 98%10 HP
η = 85%
3.5-0.9:1 6.25:1
Reff = 10in.
9. Theoretical Model
SolidWorks model of CVT primary pulley.
Adams simulation of primary pulley to generate the pulley diameter as a
function of time and belt tension.
Simulink model to calculate time to distance of the vehicle.
SolidWorks Adams Simulink
10. Assumptions
RPM increases steadily (no longer constant)
Asphalt, no slip
Ignore belt stretching
Constant belt length and width
Constant center-to-center distance between pulleys
Constant effective vehicle mass
14. Adams
Import SolidWorks model and run primary pulley to generate
pulley diameter as a function of time and belt side pressure
Can control:
◦ Belt Side Pressure
◦ Engine RPM
◦ Weights
◦ Spring Rate
21. Summary and Findings
◦ Primary does not operate independently from secondary.
◦ Keeps expanding after engine reaches 3400 RPM.
◦ Dynamic belt side pressure
◦ From Adams:
◦ More weight means faster expansion and quicker response time.
◦ Ramp angle has the best chance of obtaining Ideal CVT Ratio
◦ Spring stiffness shifts elongates the displacement vs. rpm graph
◦ Adams is good for finding trends, but not good for giving realistic data
◦ Model the secondary pulley
◦ Experimental results would be better than analytical model results
22. References
Aaen, Olav. Clutch Tuning Handbook. 2007. Print.
Adams Tutorial Kit for Mechanical Engineering Courses. 2nd ed. MSC Software. Print.
Budynas, Richard, and J. Keith Nisbett. Shigley's Mechanical Engineering Design. 9th ed. New York:
McGraw-Hill, 2011. Print.
Cha, S.W., W.S. Lim, and C.H. Zheng. "Performance Optimization of CVT for Two-Wheeled
Vehicles." International Journal of Automotive Technology 12.3 (2010): 461-68. Print.
Chang-song, Jiang, and Wang Cheng. Computer Modeling of CVT Ratio Control System Based on
Matlab. IEEE, 2011. 146-150. Print.
Narita, Yukihito. "Design of Shaft Drive CVT - Calculation of Transmitted Torque and Efficiency." Power
Transmission and Gearing Conference. Vol. 5B. ASME, 2005. 875-881. Print.
Willis, Christopher Ryan. A Kinematic Analysis and Design of a Continuously Variable Transmission.
Blacksburg, VA: Virginia Polytechnic Institute and State University, 2006. Print.
Editor's Notes
At the start of our project, we wanted to obtain a complete model of the CVT used in the baja car, with the goal of being able to input various geometric parameters, as well as spring constants and preloads, and output a theoretical time to speed. This time to speed could then be used to either adjust the parameters, or compare to experimental data in order to calculate efficiencies of various parts of the system.
Research shows that the CVT mainly operates as follows:
Power is transferred from the engine to the primary pulley, which starts at a high width, small belt radius. As speed increases, flyweights in the stationary section of the primary are thrown outward, causing a normal force against the ramps mounted on the moving section of the primary. Both sections are constrained to rotate with the same angular velocity, but can move axially. Axial movement is impeded by a linear spring in between the two sections. Force created by the rotation of the flyweights is opposed by the linear spring, both of which determine how quickly the pulley will contract. As speed increases, the primary pulley width decreases, pushing the belt to higher radii.
As the belt is pushed to higher radii by the primary, the radius of the secondary is pulled inward, due to the tension of the belt. This decrease in radius is impeded by a torsional spring in the secondary, which acts through rollers against a helix on the stationary part of the secondary. The main effect of the spring in the secondary is to impeded the axial acceleration of the secondary, which causes a smaller change in gearing.
Overall, the CVT operates from around a 4:1 ratio at low speeds to a .75:1 ratio at high speeds. Continuous changing of the gearing allows for maximum tractive force to be applied at all times, as well as allowing the engine to operate at a constant RPM during acceleration. The tradeoff for this is efficiency, as belt slippage results in a lower overall efficiency.
Goals Recap
We did create a dynamic model.
Not every variable was considered so it was difficult to find the most influential, however the ramp angles (seen later in PPoint) of the CVT has the most promise for improvement of CVT Ratio
Weights are important
Belt tension has a huge effect on how the primary responds, but we weren’t sure how to obtain it or model it.
Relationships were hard to determine, but trends were visible. Power curve fit did model ideal CVT ratio well.
Time to distance was reduced with Ideal CVT Ratio
After many difficulties to obtaining a theoretical model, our focus and goals turned more to finding out how the Primary CVT works and we thought we could make the Secondary a dependent of the Primary, which is untrue and possibly the opposite.
These are the Baja vehicle parameters that we used for all our calculations that were used in the Excel file.
TRACTIVE EFFORT Figure: This figure shows the ideal tractive effort capable with the Baja car and the actual tractive effort using the efficiency values given in the previous slide. The traction limit is also shown and this value was calculated in the accompanying Excel file. As you can see we are traction limited up until about 10 MPH, this has a huge impact on the ideal CVT ratio as you will see in the next slide. Also, no slip was an important assumption in gaining the tractive effort value. The road load is also calculated and that curve is also calculated in the Excel File.
IDEAL CVT RATIO Figure: This plot shows the ideal CVT ratio that we calculated from the data in the Tractive Effort Figure. The CVT Ratio accounts for the tractive effort and sets it around 2.8 so the tires do not slip. After we are no longer traction limited, the ideal ratio begins to decline. The rate at which it declines is determined by the Actual Tractive Effort which we calculated. A sample of the actual CVT ratio was collected from an experimental test run of the Baja vehicle on asphalt. From visual inspection, the tires are slipping below about 12 MPH and overall the CVT ratio is always higher than ideal thus not allowing for maximum acceleration. It should be noted that from experience that either the traction limit is too low or the actual tractive effort is too high as the Baja car does not spin out up to 10 or 12 MPH; there must be some discrepancy, however the general Ideal CVT Ratio curve is valid.
This was the game plan we had for starting the project.
Assumptions:
At first, we used an constant RPM but this gave us no results in Adams as we didn’t have the secondary model to talk to the primary. We had to use a step function for RPM so we could get actual trends.
Asphalt assumption made it simpler to analyze.
No belt stretching and constant length and width helped simplify it and wasn’t important for what we were trying to achieve.
Didn’t want to get involved with changing center to center distance.
Constant effective vehicle mass allowed us to simplify our model even further. Effective mass calculation was performed by the Baja team last year.
Ramps were modeled as linear, with a single break point in the middle. This however, is not a fully accurate representation of the ramps. In reality, the break point divides two non-linear portions of the ramp. As we did not fully understand the functions which determined the ramp angle, a linear model was created to find the relationships between ramp angle and tractive effort.
The most important takeaway here is the weight-link angle, which will be defined as the angle between the radial axis of revolution and the line drawn between the weight and the pin connecting the link to the main body. Here it is shown at ~90°.
MODELED WITH CONSTANT BELT SIDE PRESSURE
This model incorporated an overly stiff opposing spring force between the pulley faces to simulate the belt, in order to delay pulley expansion. As mass goes up, more force is generated due to centripetal acceleration, causing a quicker pulley expansion.
Changing the mass also changes the pulley displacement at a given RPM, with more mass causing more pulley displacement for a given RPM.
This concurs with research on clutch tuning, which indicated that the primary weight and spring system mainly effect on the engagement speed of the engine.
MODELED WITH CONSTANT BELT SIDE PRESSURE
Changing the ramp angle involved a larger amount of complexity in modeling, as it was a geometry consideration only. Research on clutch tuning indicates that the changing ramp angle should be a last resort, as is makes tuning the primary much more difficult.
Ramp angle was tested in ADAMS at three different configurations:
The 66° ramp had a 68° angle to begin, and a 66° angle after the break point.
The 68° ramp had no break point, and continued at a 68° angle.
The 70° ramp had a 68° angle before the break point, and continued after at 70°.
The graphs shown here give a relationship between ramp angle steepness and pulley displacement. Due to the nature of the geometry construction of the ramps in solid works, changing the post-breakpoint angle also changed the geometry of the pre-breakpoint ramp, resulting in a small change in the engagement times and slopes the displacement curve. Since the actual time to displacement was not being calculated, this can be disregarded. It does, however, give us insight into what changing the initial weight-link angle affects in terms of pulley response. For the 66° ramp, initial distance was higher, causing a lower weigh-link angle, which caused less effective side force on the pulley, delaying expansion. With a higher weight-link angle, a larger component of the centripetal acceleration is in the direction of expansion, leading to a quicker response time.
The main purpose of these tests, however, was to understand the relationship of the post-breakpoint angle to expansion. As can be seen, higher ramp angles cause a slower expansion with respect to engine speed.
Out of these graphs, the main takeaway is that the ramp geometry primarily determines the weight-link-to-ramp contact angle, which is the most important variable in determining pulley expansion. This variable determines how force will be distributed(radially or axially). Since only axial force contributes to the expansion of the primary, the greater this angle, the more quickly expansion will occur. Unfortunately, this angle is extremely difficult to calculate dynamically, leading to our reliance on ADAMS.
Ideal SIMULINK LOOP
The Simulink model is a basic dynamic model working from a constant engine output torque. The torque is altered through the CVT and drive train components in order to supply the tractive effort at the ground. This tractive effort, minus the road load, accelerates the car. The acceleration is then integrated twice, resulting in the car position as a function of time. During acceleration, the CVT ratio will ideally be changing. The model simulates this change in ratio by using relationships obtained from the Adams model simulation. For the primary pulley, the effective diameter is a function of the belt tension, and the rotational speed. For the secondary, the effective diameter is a function of the belt tension and the transmitted torque. Since we did not get relationships for the secondary pulley, we assumed that the secondary diameter is a function of the primary pulley diameter and the belt length. This assumption would be helpful, but since a second assumption was that the transmitted torque was constant, the primary pulley effective diameter remained constant and in turn the ratio remained constant.
This SIMULINK program uses the ideal CVT ratio, calculated to exactly produce the maximum possible tractive effort at each time.
Inputs are Engine Speed and Ideal CVT ratio. Outputs a time to distance graph. In order to check the Simulink model and ensure that the concept of making the ideal CVT ratio happen would improve our time to distance, we replaced the varying CVT ratio with a calculated ideal ratio function. Using this function for the ratio gave results of a 4.5 second time to reach 100 ft. This time is over 10% better than the results of the current baja car.
Ideal Time to Speed and Distance Graph from SIMULINK Model
This gives a baseline to measure efficiency off, showing a theoretical ~4.5 Seconds to 100 Ft.
Without the secondary spring, the secondary would essentially be a slave to the primary.
With a torsional spring, the side force operating on the belt due to the primary is opposed by the secondary, causing fluctuations in belt tension, as well as a time delay in acceleration, and thus expansion, of the pulley.
General relationships can be drawn from ADAMS, and used to experimentally tune the clutch.
The next step would be to model the secondary pulley in ADAMS, and find a way to connect the two.
The best results would come experimentally.
