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Design Innovation

Load Redistribution on Lead Screw Threads Wearing Under Varying Operating Conditions

[+] Author and Article Information
David J. Murphy

 Bechtel Plant Machinery Inc., Schenectady, NY 12301

Thierry A. Blanchet1

 Rensselaer Polytechnic Institute, Troy, NY 12180blanct@rpi.edu

1

Corresponding author.

J. Tribol 130(4), 045001 (Aug 12, 2008) (13 pages) doi:10.1115/1.2959118 History: Received January 28, 2008; Revised April 24, 2008; Published August 12, 2008

The load applied to a lead screw assembly is distributed amongst the engaged threads of its wearing nut in a manner that can range from highly nonuniform to nearly uniform. Nonuniform load distributions can arise when new or unworn threads are initially placed into service or, alternatively, in worn threads whereupon the operating conditions are changed from pre-existing conditions at steady-state wear. In threads wearing under constant conditions, nonuniform load distributions evolve to uniform load distributions with sufficient continued sliding as the most heavily loaded threads wear most rapidly, causing their loads to be redistributed to those threads less heavily loaded. Using a newly implemented discrete-thread numerical approach, an example lead screw with rigid nut and elastic screw body having flexible meshed thread pairs is modeled here to demonstrate the broad distribution of thread loads on a new lead screw assembly that gradually evolves toward uniformity as the coupled consideration of thread loading and wear depth approaches a steady-state of equal rates of thread wear. Thread load redistributions brought about by linear ramp changes in applied load, or temperature in the case of a nut/screw pair of dissimilar materials, are predicted at various rates of ramp between prior and future steady operating conditions. While showing the expected maintenance of uniform thread loading under slowly ramped conditions, this numerical approach was verified in cases of rapid ramps approaching step changes, for which existing closed-form analytical models provide agreement. At intermediate rates, this numerical model is complemented by newly expanded closed-form analytical models of both discrete- and continuous-thread types that describe asymptotic behavior during extended ramps.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of simplified screw and nut assembly with five engaged threads within a nut having a rigid body. Example case shown with Acme thread form as well as hollow lead screw.

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Figure 2

Schematic of discrete model depicting the displacement x of a node on the screw body corresponding to the base of its ith thread, as well as those of its neighboring threads, to applied external load in the axial direction, which causes tensile force Ps,i in the screw body above each ith thread. Meshing threads modeled as cantilever spring pairs of effective stiffness kt, while screw body segments between nodes modeled as axial springs of stiffness ks.

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Figure 3

Loading and wear behavior of initially unworn threads under an externally applied load of 8.897kN initially, which is doubled to 17.794kN in a step change at a sliding distance s=7m. Temperature remains constant at Tref. kt=4.71×109N∕m, ks=12×109N∕m, At=494mm2, and κ=10−13m3∕Nm. (a) Thread load fraction and (b) nut thread wear depth.

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Figure 4

Loading and wear behavior of initially unworn threads at temperature Tref initially which increases by 5.56°C in a step change at a sliding distance s=7m. Externally applied load remains constant at 8.897kN. αn-αs=5×10−6°C−1, kt=4.71×109N∕m, ks=12×109N∕m, At=494mm2, and κ=10−13m3∕Nm. (a) Thread load fraction and (b) nut thread wear depth.

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Figure 5

Thread load fraction versus sliding distance for various ramp rates of applied load increase dP*∕ds* from a steady-state developed for unworn nut threads in an initial period at Pold*=5.921×10−5 to new load Pnew*=8.881×10−5 after the ramp. kt*=0.4, and constant ambient temperature. (a) rate=dP*∕ds*=9.8×10−8, (b) rate=dP*∕ds*=9.8×10−7, (c) rate=dP*∕ds*=9.8×10−6, and (d) rate=dP*∕ds*=9.8×10−5.

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Figure 6

Thread load fraction versus sliding distance for various ramp rates of applied load decrease dP*∕ds* from a steady-state developed for unworn nut threads in an initial period at Pold*=8.881×10−5 to new load Pnew*=5.921×10−5 after the ramp. kt*=0.4, and constant ambient Temperature. (a) rate=dP*∕ds*=−9.8×10−8, (b) rate=dP*∕ds*=−9.8×10−7, (c) rate=dP*∕ds*=−9.8×10−6, and (d) rate=dP*∕ds*=−9.8×10−5.

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Figure 7

Thread load fraction versus sliding distance for various ramp rates of temperature increase dT*∕ds* from a steady-state developed for unworn nut threads in an initial period at Tref* to new temperature Tnew*=Tref*+0.41×10−4 after the ramp. kt*=0.4, and constant applied load P*=1.184×10−4. (a) rate=dT*∕ds*=4.63×10−7, (b) rate=dT*∕ds*=4.63×10−6, (c) rate=dT*∕ds*=4.63×10−5, and (d) rate=dT*∕ds*=4.9×10−3.

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Figure 8

Thread load fraction versus sliding distance for various ramp rates of temperature decrease dT*∕ds* from a steady-state developed for unworn nut threads in an initial period at Tref* to new temperature Tnew*=Tref*−0.41×10−4 after the ramp. kt*=0.4, and constant applied Load P*=1.184×10−4. (a) rate=dT*∕ds*=−4.63×10−7, (b) rate=dT*∕ds*=−4.63×10−6, (c) rate=dT*∕ds*=−4.63×10−5, and (d) rate=dT*∕ds*=−4.9×10−3.

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Figure 9

Thread load fraction versus sliding distance for an extended ramp of temperature increase at rate dT*∕ds*=9.27×10−6 from an initial steady-state developed for unworn nut threads at Tref*. Threads kt*=0.4, and constant applied load P*=1.184×10−4.

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Figure 10

Thread load function f(Pt) versus sliding distance for an extended ramp of applied load increase at rate dP*∕ds*=9.8×10−5 from an initial steady-state run-in on unworn nut threads at load P*=5.921×10−5. kt*=0.4, and constant ambient temperature.

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