Tractive Force Requirements

FBD Constants and Derived Equations

Application of Equations: Required Tractive Force for Scenarios Defined by Pulling Class Weight, Coefficient of Static Friction, and Load Force

2017 Pull Data Analysis

Gear Set Selections

Constraints and Assumptions for Gear Set Selections:

• Competition governor settings are 3,600 RPM and 1,750 RPM for no-load high idle and low idle respectively.

• Dynamometer data for 3,500 RPM and 3,250 RPM governor settings are currently available for the design team.

  • Due to issues with the team's testing engine, a 3,600 RPM dyno pull issue is not currently possible to obtain.

  • Trends in both sets of available power and torque curves indicate that maximum power is generated at 300 RPM less than the high idle governor setting at a torque of 43.4-44.3 ft-lbs.  Therefore, to simulate the competition settings, an engine speed of 3,300 RPM and averaged torque of 43.85 ft-lbs. were used as the point of maximum power for gear ratio calculations.

• Ideally, the tractor should operate as close to its point of maximum power output throughout most of the pull.  Therefore, gear ratios were selected on the basis of meeting the required tractive force for the initiation of motion at the point of maximum power.

• The transaxle that will be used in the system design has only one option for the differential gear ratio (4.60:1).

• Since the main purpose of the dropbox is to act as a lowering mechanism for the input of the transmission, an internal gear ratio of 1.00:1.00 will be used in order to allow for the most flexibility in input location.

  • Also, the Wildcat Pulling Team has suggested the potential option of doing away with the drop box entirely if an in-line configuration is utilized.  Setting the dropbox gear ratio as 1.00:1.00 prevents that potential change from altering the final drive gear ratios.

• Due to the proven durability of the components, the Wildcat Pulling Team requests that all internal transmission components be sourced from Midwest Super Cub (MWSC) if the Cub Cadet Transaxle is to be used in the design.

• Based on the 2017 pull data and FBD scenario calculations, the required tractive forces for pulling events are as follows:

  • 1100 lb. pulling class: 1740 lbs.

  • 1600 lb. pulling class: 1971 lbs.

• One gear must provide a low enough ground speed at no-load, full throttle in order to comply with the speed requirements of sound testing (4 mph +/- 2 mph)

• In order to be conservative, the stock, uncut diameter of the tractor's tires (26 inches) was used during output tractive force calculations for selected gear sets.

• The conservative assumption was also made to analyze the maximum available tractive force for each gear ratio at the point of maximum torque for the 3,500 RPM dyno pull (48.4 ft-lbs. @ 2,210 RPM).

Instructions and Calculator Preface

Introduction

The 3-speed Cub Cadet transaxle from Midwest Super Cub (MWSC) utilizes four different gear sets that create three forward gears and one reverse gear.  The gear sets are:

·        The Input Gear Set (12 options)

·        1st and Reverse Gear Set (11 options)

·        2nd and 3rd Gear Set (25 options)

·        Differential Ring and Pinion Gear (1 option)

In order to analyze all of the potential options, an Excel-based calculator was developed in order to determine the theoretical land speed, axle torque, and traction force that would be produced by the three forward gears for a user-selected combination of gear sets.  The current version of the calculator outputs theoretical results (100% efficiency) due to a lack of information needed to appropriately calculate theoretical drivetrain efficiency (overall gear sizes, weight of gears, static friction of driven tires, etc.).  

Important Constants and Formulas:

Instructions for Calculator Use:

1.       Refer to the “Key” in to see the color-coding scheme for the calculator.

2.       Input the desired value for Engine Speed (RPM), Engine Torque (ft-lb), and Tire Diameter (in.) in the “Vehicle Inputs” box.

3.       Input the desired gear ratio for the dropbox in the “Additional Gear Reductions/Constants” box (if no dropbox is to be used, set this value to 1).

4.       Select the desired input gear set, reverse and 1st gear set, and 2nd and 3rd gear set from the drop-down lists in the “Gear Selections Box”.

a.       Note: The forward and reverse gear sets are defined by the cluster gear for the gear set.  The cluster gear for these gear sets acts as two input gears for the gear set.  The total number of teeth between the input gear on the cluster gear and the output gear for a particular forward or reverse gear always equals 52 teeth. (Example: a 15/16 gear set for 2nd and 3rd gear will have a cluster gear that has one 15-tooth gear and one 16-tooth gear along with the corresponding 37-tooth and 36-tooth output gears).

5.       Upon completing all gear set selections, the input tooth count and output tooth count for all gear sets are automatically populated below in boxes that correspond to each selected gear set.

a.       Both the input gear tooth count and output gear tooth count for the transmission input gear selection are pulled from gear set database on “sheet 2”.  The gear ratio for the transmission input gear set is calculated using Formula 1.

b.       The input gear tooth count for the forward gear is pulled from the gear set database on “sheet 2”.  The output gear tooth count is calculated using Formula 2.  The gear ratio is calculated using Formula 3.

6.       Then the final gear ratios for all selectable forward gears are calculated using Formula 4.

7.       For each forward gear, the following are calculated and given as the final results:

a.       Land Speed (mph) using Formula 5.

b.       Axle Torque (ft-lb) using Formula 6.

c.       Tractive Force (lb.) using Formula 7.

Flowchart of Selected Gear Ratios within Drivetrain

Gear Set Selections and Rationale:

• Dropbox Gear Ratio: 1.00:1.00

  • Allows for the most flexibility in design (see constrains and assumptions above).  If the component is deemed to be necessary, the internal gears will be selected during the final design of the dropbox subsystem.

• Input Reduction Gear Set: 23% Overdrive

  • Allowed for what the design team considered to be the most flexibility in selecting the Reverse/1st and 2nd/3rd gear sets.

• Reverse/1st Gear Set: 13/15

  • Sets the maximum ground speed for first gear at 4.54 mph which is well within the range competition rules demand for sound testing.

• 2nd/3rd Gear Set: 17/19

  • This gear set results in the theoretical tractive force (at the point of maximum power) for second and third gear being slightly higher than what is required for heavyweight and lightweight pulls, respectively (2nd: 2068 lbs.; 3rd: 1744 lbs.).

• Differential Gear Ratio: 4.60:1.00 (MWSC 46 tooth ring gear with MWSC 10 tooth pinion gear)

  • See constraints and assumptions above for selection rationale.