Experimental Mechanics

, Volume 30, Issue 1, pp 40–48 | Cite as

Optimal design of an uncoupled six degree of freedom dynamometer

  • T. P. Quinn
  • C. D. MoteJr.
Article

Abstract

A design analysis of a class of six degree of freedom strain-gage dynamometers which are virtually uncoupled in each force and moment component is presented. The method of design is detailed and an optimal design algorithm is implemented. The dynamometer is made of six or more T-sections with thin webs and flanges called shear panel elements (SPE). Complete stress and buckling analyses are carried out for the SPE, and experiments confirm the predictions of the analyses. The optimal design method is illustrated with several case studies. A dynamometer has been built and used in laboratory and field experiments.

Keywords

Mechanical Engineer Fluid Dynamics Field Experiment Optimal Design Flange 

List of Symbols

b, c

dimensions of the cantilever plate in the ξ and ζ directions

d, fw,ff,tw,tf

geometry of the SPE; see Fig. 1

D

flexural rigidity

E, ν

Young's modulus and Poisson's ratio

\(\bar e\)

shear strain in (ξ, ζ) coordinates at the center of the cantilever plate (b/2,c/2)

\(\bar e_w \)

shear strain at the center of the web\(\bar e_w = \bar e\) withL=P, b=f w ,c=d, andt=t w

fij,gij

coefficients in the approximation ofu andv

Fx,Fy,Fz

external force components applied to the cage

Fy

external force applied to the cage in the Y′ direction (e.g.,Fy′=F x if Y′ is aligned with X)

Kx′, Ky′, Kz

stiffness of a SPE for forces applied to the ends of the flange in the X′, Y′, Z′, directions, respectively

K1

torsional stiffness of the web

K2

bending stiffness of one arm of the flange

Kmin

minimum allowable design stiffness of the SPE in the Y′ direction

Kt

torsional stiffness of the SPE about the X′ axis

l

distance from the moment axis of the reference coordinates to the flange of the SPE; see Fig. 1

L

force applied at the end of the cantilever plate; see Fig. 5

\(\bar L\)

the forceL at the onset of buckling

\(\bar L_f \)

the buckling force in the flange;\(\bar L_f = \bar L\) withb=f f /2,c=d, andt=t f

\(\bar L_w \)

the buckling force in the web;\(\bar L_w = \bar L\) withb=f w ,c=d, andt=t w

Mx,My,Mz

external moment components applied to the cage

Mz

external moment applied to cage in the Z′ direction (e.g.,M z ′=M y if Z′ is aligned with Y)

pij,qij

coefficients in the approximation ofw

P

total external force applied to a SPE

r1-r3

minimum allowable stiffness ratios

S

the set of all possibleX

S1–S7

SPE's of the dynamometer in Fig. 3

Sy

yield strength

t

thickness of the cantilever plate

T

shear traction applied at the end of the cantilever plate; see Fig. 5

T1–T6

SPE in a six degree of freedom dynamometer

u, v

displacements of the cantilever plate along ξ and ζ

\(\bar v\)

v(c,b/2)

\(\bar v_f \)

\(\bar v\) withL=1/2, b=f f /2,c=d, andt=t f

\(\bar v_w \)

\(\bar v\) withL=1, b=f w ,c=d, andt=t w

w

transverse displacement of the cantilever plate

X-Y-Z

coordinates at the center of the dynamometer

X′-Y′-Z′

coordinates at the base of an SPE

X

[l,d,f w ,f f ,t w ,t f ]

σζξξζ

stresses in the cantilever plate

\(\sigma '_\zeta ,\sigma '_\xi ,\sigma '_{\xi \zeta } \)

nondimensional stresses in the cantilever plate

\(\bar \sigma \)

maximum von Mises stress in the cantilever plate;\(\begin{gathered} \bar \sigma = 0 \leqslant \mathop \xi \limits^{\max } \leqslant b(\sigma _{^\xi }^2 + \sigma _\zeta ^2 - \sigma _\xi \sigma _\zeta + 3\sigma _{\xi \zeta }^2 )^{1/2} \hfill \\ 0 \leqslant \zeta \leqslant c \hfill \\ \end{gathered} \)

\(\bar \sigma _f \)

maximum von Mises stress in the flange;\(\bar \sigma _f = \sigma \) withL=P/2, b=f f/2 ,c=d andt=t f

\(\bar \sigma _w \)

maximum von Mises stress in the web\(\bar \sigma _w = \bar \sigma \) withL=P, b=f w ,c=d andt=t w

Π

potential energy functional for the cantilever plate

ξ,ζ

local coordinate system for the cantilever plate

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Copyright information

© Society for Experimental Mechanics, Inc. 1990

Authors and Affiliations

  • T. P. Quinn
    • 1
  • C. D. MoteJr.
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaBerkeley

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