Tractor Final Drive Axle Simulation in Inspire Motion

John_Dagg_0
John_Dagg_0
Altair Employee
edited June 27 in Altair Exchange

Overview

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INTRODUCTION

The design of new agricultural equipment can be improved by incorporating simulation. Simulation including structural analysis, multibody dynamics, and soil interactions can be used to predict the performance of equipment and improve the design before manufacturing. In this example, a multibody dynamics simulation is performed on the rear axle assembly of a tractor.

This model contains the rear axle and hitch of a tractor. A locking differential transmits power to planetary gearboxes on each output shaft. The planetary gearboxes transfer torque to the wheels. The locking differential allows the wheels to move at different speeds when the tractor makes turns. When the tractor needs to pull heavy equipment, the axles can be locked together with the hydraulically actuated locking differential to increase traction.

In this model, tractor final drive axle geometry is imported into Altair’s Inspire. Inspire is an integrated simulation environment that enables faster decision making by design engineers and CAE analysts. Foregoing the traditional “pre-process - solve - post-process” cycle prevalent in traditional CAE software, it can perform all 3 functions in a single environment. Inspire’s CAD integration, semi-automated MBD model build, and structural solver integration help considerably flatten the learning curve. A design engineer or non-CAE expert may thus take direct advantage of Altair’s high-performance CAE solvers. 

 

Pre-Requisite

SOFTWARE REQUIREMENTS

Altair Inspire (2024 or newer)

MODEL FILES

Tractor_Transmission.zip (See Attachments)

Usage/Installation Instructions

MODEL SETUP

This model setup assumes a level of familiarity with Inspire Motion. A motion ready model called Tractor_Transmission_Motion_Ready.stmod is available for reference in the attached zip file.

  1. Import the geometry Tractor_Transmission_Geometry.x_b into Inspire.
  2. Create rigid groups.
  3. Ground the transmission housing.
  4. Add joints to the model.
  5. Add motors.
    1. One motor should drive the pinion at a set velocity of 60 rpm.
    2. Two motors should drive the output shafts with a set torque to simulate the resistance from pulling equipment. Ensure the torque opposes the direction of motion.       
      1. Set one motor to apply 3.5e6 N-mm.
      2. Set the second motor to apply 3.55e6 N-mm.
  6. Add actuators.
    1. Create actuators to move the hitch lift mechanism between the actuator cylinders and pistons.
    2. Create an actuator between the right differential output shaft and the plunger. This is possible if a translational joint is created between the two parts. The actuator will be used to emulate the locking mechanism on the differential. Make the actuator move 15 mm to separate the plunger and plunger lock at the 5 second mark.
  7. Create motion contacts between each set of gear teeth, including the plunger and plunger lock.

SIMULATION STEPS

  1. Run an analysis for 10 seconds with active contact iteration on.
  2. Review the results.

Post-Requisite

RESULTS

After setting up the model and running the analysis, the motion of the tractor transmission can be reviewed. During the first three seconds the differential is locked and both output shafts share the same velocity. After three seconds, the differential unlocks and the output shafts spin at different velocities based on the resisting torque. The hitch, which is attached to the transmission, is also demonstrated lifting up and down.

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Tractor Transmission and Hitch Motion

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Transmission Motion without Housing or Hitch

The locking differential features two differential couplers shown in different shades of red. One coupler is bolted to the differential housing and crown wheel. The second coupler is splined onto the output shaft. When the couplers interlock, the differential is locked causing both output shafts and the crown wheel to spin at the same velocity. When the couplers are not interlocked, the differential functions identically to an open differential.

In reality, hydraulic fluid causes the differential to become locked, and a spring returns the coupler to the unlocked position. In this multibody model, an actuator creates the effect of locking and unlocking. A co-simulation between a multibody dynamics model and computational fluid dynamics could be a logical next step if the coupler-hydraulic fluid interaction is of interest. The Inspire Motion model could be exported to Altair’s nanoFluidX to simulate the hydraulic fluid.

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Differential Motion with Locking Mechanism Shown

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Wheel Velocities over Time
Velocities Diverge after Unlocking the Differential

In addition to the motion of the transmission, parts can be analyzed for displacements and stresses. For example, the stresses on the differential housing can be reviewed to determine an appropriate material. With the low resisting torques, the maximum stress on the housing during motion is 1.53 MPa indicating the steel chosen would be adequate for that load case. Real load cases would show more realistic stresses in the housing.

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Von Mises Stresses on the Differential Housing
Maximum of 1.53 MPa

The stresses on the gear teeth can be analyzed by using the analyze part option in Inspire Motion. By reviewing the stresses on the crown wheel, we can see the stresses reach 55 MPa, indicating the steel crown wheel is safe from yielding. A potential next step is to use the stresses for a fatigue analysis.

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Ring Gear Stresses

CONCLUSION

Simulation is a powerful tool that can be used to understand the kinematics of a system, forces on joints, and component stresses. In this model, we set up the motion of a tractor’s rear transmission with a locking differential. We reviewed the motion of the hitch, locking differential, planetary gearsets, and output axles. We also analyzed the stresses on the differential housing to learn the steel chosen would be acceptable for the housing. In the design of new machinery, it is crucial to utilize simulation to understand and improve system performance before manufacturing.

AUTHORS

John Dagg, Systems Engineering Intern

Christopher Fadanelli, Solution Engineer - Systems Integration

Ananth Kamath Kota, Global Technical Manager - Systems Integration

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