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Research Papers

Effect of Compliance and Backlash on the Output Speed of a Mechanical Transmission System

[+] Author and Article Information
Ramamurthy V. Dwivedula

 Ideal Institute of Technology, Kakinada 533 003, Indiaram_dula@yahoo.com

Prabhakar R. Pagilla1

School of Mechanical and Aerospace Engineering,  Oklahoma State University, Stillwater, OK 74078-016pagilla@okstate.edu

1

Corresponding author.

J. Dyn. Sys., Meas., Control 134(3), 031010 (Apr 04, 2012) (9 pages) doi:10.1115/1.4005493 History: Received January 11, 2008; Revised October 14, 2011; Accepted October 17, 2011; Published April 03, 2012; Online April 04, 2012

A dynamic model to describe the effect of compliance in a transmission system is presented. Analysis of this model shows that it is desirable to use feedback from driver-side of the transmission system. This model is extended to include the effects of both compliance and backlash in a mechanical transmission system. The proposed model considers compliance (which may be either due to the elasticity of the shafts or belt in a belt-pulley transmission system) and backlash appearing in series in a drive system. In contrast to the classical backlash model which considers both input and output to the backlash as displacements, the proposed model considers (torque) force as input to the backlash and (angular velocity) velocity of the driven member as the output of the backlash. Thus, the proposed model does not assume that the load is stationary when contact is lost due to backlash width, i.e., momentum of the load is taken into account. Using the proposed model, a bound on the speed error due to the presence of backlash is derived. Experiments were conducted on a rectilinear mass-spring system platform, which has a provision to change the backlash width by a known value. Experiments were conducted with different backlash widths and a velocity error bound was computed. The error bound obtained from the experimental results agrees with the theoretically computed bound.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic of backlash

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Figure 2

Input–output plot for friction-controlled backlash

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Figure 3

Force on the motor

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Figure 4

Input–output plot of backlash with force as input

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Figure 5

Schematic of a belt driven transmission system

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Figure 6

Block diagram of the belt driven transmission system. R is the speed ratio, R = R2 /R1 .

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Figure 7

Two feedback schemes: (a) feedback from load shaft and (b) feedback from motor shaft

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Figure 8

Schematic of a gear drive

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Figure 9

Linear analog: (a) without backlash and (b) with backlash

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Figure 10

Schematic of a belt-pulley transmission system

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Figure 11

Block diagram of a controller for system with backlash

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Figure 12

Rectilinear system

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Figure 13

Backlash gap in experiments

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Figure 14

Closed-loop experiment with backlash of 1.55 mm

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Figure 15

Closed-loop experiment with backlash of 1.55 mm

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Figure 16

Simulation with backlash of 1.55 mm

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