1 Introduction
1.1 Rotating shaft balance and application
1.2 Design optimization, manufacturing and instrumentation of a conventional RSB
1.3 Benefits of topology optimization and additive manufacturing of an RSB
2 Topology optimization method for a new RSB design
2.1 Finite element model of the RSB
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\({\text{F}}_{{\text{x}}} = { 13}00{\text{ N,}}\)
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\({\text{F}}_{{\text{y}}} = {\text{ F}}_{{\text{z}}} = { 65}0{\text{ N,}}\)
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\({\text{M}}_{{\text{x}}} = { 16}0000{\text{ N}}*{\text{mm,}}\)
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\({\text{F}}_{{\text{c}}} = { 64}0{\text{2 RPM }}\left( {\text{centrifugal load}} \right).\)
2.2 Topology optimization requirements
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The RSB design should be as stiff as possible, mass reduction was not directly of interest for a first prototype.
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In each Wheatstone bridge consisting of four strain gauges, two strain gauges should experience tensile stress and the other two compressive stress.
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Specific stress values are desired at the strain gauge locations of Wheatstone bridges BFx1, BFx2, BMx1 and BMx2 for the single loads Fx and Mx.
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Low stress values are desired at the strain gauge locations of Wheatstone bridges BFx1, BFx2, BMx1 and BMx2 for centrifugal Fc.
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An overhang angle constraint is needed for 3D printing of the RSB.
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The interface holes for bolts and dowel pins should be maintained.
2.3 Topology optimization method
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\({\text{4 mV }} \le {\text{BF}}_{{{\text{x1}}}} \le {\text{ 6 mV for F}}_{{\text{x}}} ,\)
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\({\text{4 mV }} \le {\text{BF}}_{{{\text{x2}}}} \le {\text{ 6 mV for F}}_{{\text{x}}} ,\)
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\({\text{4 mV }} \le {\text{BM}}_{{{\text{x1}}}} \le {\text{ 6 mV for M}}_{{\text{x}}} ,\)
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\({\text{4 mV }} \le {\text{BM}}_{{{\text{x2}}}} \le {\text{ 6 mV for M}}_{{\text{x}}} ,\)
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\({\text{BF}}_{{{\text{x1}}}} \le \, 0.{\text{5 mV for F}}_{{\text{c}}} ,\)
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\({\text{BF}}_{{{\text{x2}}}} \le \, 0.{\text{5 mV for F}}_{{\text{c}}} ,\)
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\({\text{BM}}_{{{\text{x1}}}} \le \, 0.{\text{5 mV for F}}_{{\text{c}}} ,\)
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\({\text{BM}}_{{{\text{x2}}}} \le \, 0.{\text{5 mV for F}}_{{\text{c}}} .\)
3 Topology optimization and detailed design results
3.1 Optimal design results
3.2 Detailed design results
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My = 120,000 N*mm,
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Mz = 120,000 N*mm.
Fx | Fy | Fz | Mx | My | Mz | |
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BFx1 | 5.03 | 0.00 | 0.00 | − 0.01 | 0.00 | 0.00 |
BFy1 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 | − 3.06 |
BFz1 | 0.00 | 0.00 | 1.02 | 0.00 | 3.06 | 0.00 |
BMx1 | − 0.01 | 0.00 | 0.00 | 6.66 | 0.00 | 0.00 |
BMy1 | 0.00 | 0.00 | 1.02 | 0.00 | 3.06 | 0.00 |
BMz1 | 0.00 | − 1.02 | 0.00 | 0.00 | 0.00 | 3.06 |
3.3 Additive manufacturing results
4 Conclusions
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A new design for an RSB can be developed with topology optimization complying with requirements for balance stiffness, bridge outputs and strength.
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The topology optimized RSB can be printed in stainless steel after optimization of L-PBF settings and adding extra supports between the front and aft flexures of the RSB for 3D printing.