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Novel compensation of axial thermal expansion in ball screw drives

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Abstract

Novel functional materials in the field of machine tools such as shape memory alloys are capable to convert thermal energy into mechanical energy by generating work. Besides, their self-sensing properties and high energy density make them suitable to compensate thermal deformations. Manufacturing requirements concerning machine tools and machining centers can be summarized in a high productivity, a high reliability (low-maintenance) and a high accuracy/precision. The latter machine design parameter depends almost on linear drive systems, which are responsible for the relative distance between workpiece and tool center point. Their positioning performance is limited, among others, to changes in thermal conditions; even with cooling systems that represent about 90 % of the overall energy consumption of the machine. Therefore, thermal errors in machine tools are currently an issue to overcome. Within the scope of this work, shape memory alloys have been integrated in ball screw drives in order to achieve a thermal stable machine transmission component.

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Abbreviations

AgCd:

Silver cadmium

BSD:

Ball screw drive

CuAlNi:

Copper aluminium nickel

ISO:

International Organization for Standardization

NiAl:

Nickel aluminium

NiTi:

Nickel titanium

OWSME:

One-way shape memory effect

PTT:

Phase transformation temperature

SIM:

Stress-induced martensite

SMA:

Shape memory alloy

SME:

Shape memory effect

TIM:

Temperature-induced martensite

TWSME:

Two-way shape memory effect

α :

Nominal contact angle between ball and groove

α th,n :

Coefficient of thermal expansion of the nuts

α th,s :

Coefficient of thermal expansion of the shaft

α th,w :

Coefficient of thermal expansion of the balls

\(\varDelta L_{\sum _{PR}}\) :

SMA pushrods recovery stroke

\(\varDelta l_{b/t,pr}\) :

Elastic axial deflection due to preload

\(\varDelta l_{b/t}\) :

Deflection backlash

\(\varDelta l_{th}\) :

Thermal backlash

δ :

Displacement

δ PSMA :

Displacement due to the initial prestress

ε :

Strain

σ :

Stress

σ f :

Stress at which the detwinning of martensite finishes

σ sl :

Stress at which the dislocation glide begins

σ s :

Stress at which the detwinning of martensite starts

φ :

Shaft lead angle

A :

Constant

A f :

Austenitic finish temperature at zero stress

A p :

Austenitic peak temperature at zero stress

A st :

Stable austenitic phase

A s :

Austenitic start temperature at zero stress

A ust :

Unstable austenitic phase

B :

Constant

b :

Nut length

b m :

Length of a half nut

C :

Constant

C a :

Basic dynamic rated load

D 0 :

Nominal NiTi wire diameter

d 0 :

Nominal shaft diameter

D pw :

Pitch circle diameter

D w :

Ball diameter

E :

Elastic modulus

F :

Force

F P :

Nominal preload

\(F_{{\sum}_{PR}}\) :

SMA pushrods recovery force

F pr/th :

Preload variation due to thermal changes

F PSMA :

Initial prestress of the SMA element

i :

Number of active threads

k :

Stiffness ratio

L 0 :

Length of a SMA pushrod

l 1 :

Shaft thread length

L T :

Length of the NiTi wire

M dtw :

Detwinned martensite

M d :

Temp. at which martensite is not longer stress-induced

M f :

Martensitic finish temperature at zero stress

M s :

Martensitic start temperature at zero stress

M tw :

Twinned martensite

N :

Number of SMA pushrods

n cr :

Critical speed

P h :

Shaft Lead

R b/t :

Ball contact zone stiffness

\(R_{{\sum}_{SMA}}\) :

Total stiffness of SMA pushrods

R BSD :

Ball screw drive overal axial stiffness

R SMA :

Shape memory alloy stiffness

R SPRING :

Spring stiffness

S a :

Inherent clearance backlash

T :

Temperature

T n :

Average temperature in the nuts

T s :

Average temperature in the shaft

T w :

Average temperature in the balls

v max :

Maximum linear speed

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Acknowledgments

The Cluster of Excellence “Energy-Efficient Product and Process Innovations in Production Engineering” (eniPROD®) is funded by the European Union (European Regional Development Fund) and the Free State of Saxony.

Conflict of interest

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. Institut für Werkzeugmaschinen und Produktionsprozesse, Technische Universität Chemnitz, Reichenhainer Straße 70, 09126, Chemnitz, Germany

    Iñaki Navarro y de Sosa

  2. Fraunhofer Institute for Machine Tools and Forming Technology, Nöthnitzer Straße 44, 01187, Dresden, Germany

    André Bucht, Tom Junker, Kenny Pagel & Welf-Guntram Drossel

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  1. Iñaki Navarro y de Sosa
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Correspondence to Iñaki Navarro y de Sosa or André Bucht.

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Navarro y de Sosa, I., Bucht, A., Junker, T. et al. Novel compensation of axial thermal expansion in ball screw drives. Prod. Eng. Res. Devel. 8, 397–406 (2014). https://doi.org/10.1007/s11740-014-0528-0

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