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Torque and Displacement Measurement with Enhanced Signal Processing for System Lash Estimation of a MDOF Rotating System

Experimental Techniques volume 46, pages 931–944 (2022)Cite this article

Abstract

Experimental testing for system backlash size relies on speed or displacement measurements of an isolated test apparatus but lack reference to engineered lash tolerances and expected values. These methods are prone to error when the measurement speed is not accounted for and hysteresis impacts the measurement. This study measures backlash on an experimental apparatus to update control model parameters. The results are also confirmed by comparing with analytical part tolerances based on CAE modeling. This is done by comparing three different test methods; output displacement only on a fixed-free apparatus, input torque with measured displacement on a fixed-free apparatus, and in-situ testing with torque and estimated displacement from rotating speed. The torque and displacement techniques recognize the influence of hysteresis and propose signal processing techniques to improve accuracy of the results. This signal processing technique was verified with an analytical model like those tested in the study. The three techniques used were all able to measure results within 31% of the CAE predictions when accounting for manufacturing tolerance. The signal processing method to account for hysteresis was analytically shown to have error less than 8.7% and 4.8% using an input frequency of <1 Hz with a sinusoidal and sawtooth forcing function respectively. The in-situ results were within 24% agreement of CAE projections without the need for a controlled laboratory test environment. These results showed that hysteresis should be accounted for when possible with an updated signal processing technique. The analytical model used to confirm backlash estimates with hysteresis also showed the need for controlled input forcing functions to improve the estimate accuracy. The study also confirms that experimental lash measurements can be collected from in-situ data when torque and displacement estimates are available.

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Abbreviations

BLFH:

Bisecting Linear Fit Hysteresis

CAD:

Computer Aided Design

DOF:

Degree(s) of Freedom

EKF:

Extended Kalman Filter

FOM:

Full Order Model

LPF:

Low Pass Filter

LVDT:

Linear Variable Displacement Transducer

POFs:

Polymer Optical Fibers

ROM:

Reduced Order Model

SALI:

Shifted Average Linear Intercept

SDOF:

Single Degree of Freedom

c n :

Negative Contact Damping (N Degree /s)

c p :

Positive Contact Damping (N Degree /s)

G :

Shear Modulus (Pa)

I :

Polar Moment of Inertia (m4)

J :

Mass Moment of Inertia (kg m2)

k n :

Negative Contact Stiffness (N/ Degree)

k p :

Positive Contact Stiffness (N/ Degree)

L :

Length of Shaft (m)

T :

Applied Contact Torque

θ :

Angular Displacement (Degrees)

θ 0 :

Initial Angular Displacement (Degrees)

\(\dot{\theta}\) :

Angular Velocity (Degrees /s)

\(\ddot{\theta}\) :

Angular Acceleration (Degrees /s2).

δ lash :

System Lash (Degrees).

δ measured :

Measured Lash (Degrees).

τ :

Applied Torque (Nm).

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Acknowledgements

The authors of this paper would like to thank their colleagues at Ford Motor Company for their continued financial support and technical expertise. We would like to individually recognize our colleagues Max Gibbs, Natalie Remisoski, Kalyan Addepalli, for their technical guidance, along with Cote Taylor for data collection in the development of this manuscript. The authors also would like to declare no conflict of interest in this manuscript relative to competitive vehicles and declare all processes and techniques to be applicable to most/all rotating machinery with lash coupling elements.

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Authors and Affiliations

  1. Michigan Technological University, Mechanical Engineering, Houghton, MI, USA

    J.E. Furlich, D.L. Robinette & J.R. Blough

  2. Ford Motor Company, Dearborn, MI, USA

    N. Remisoski & C. Taylor

Authors
  1. J.E. Furlich
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  2. D.L. Robinette
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  3. J.R. Blough
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  4. N. Remisoski
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  5. C. Taylor
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Contributions

Jon Furlich was the primary author whom collected data, post processed all data, wrote and edited the manuscript. Jason Blough, Darrell Robinette, and Natalie Remisoski mentored the data processing and manuscript editing. Cote Taylor collected and compiled test data for the manuscript.

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Correspondence to J.E. Furlich.

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Furlich, J., Robinette, D., Blough, J. et al. Torque and Displacement Measurement with Enhanced Signal Processing for System Lash Estimation of a MDOF Rotating System. Exp Tech 46, 931–944 (2022). https://doi.org/10.1007/s40799-021-00524-7

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  • DOI: https://doi.org/10.1007/s40799-021-00524-7

Keywords

  • Lash
  • Experimental verification
  • CAE Validation
  • Rotating dynamics
  • Automotive drivetrain

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