Load-cell Sensor
Fig. 8.4
Fig. 8.4 Experimental set-up Experimental set-up for macro-model for macro-model verification.verification.
mechanism connected to the load cell, the voltage readings were taken at 0 lb (before mechanism connected to the load cell, the voltage readings were taken at 0 lb (before loading), during loading, and 0 lb (after unloading). This process was repeated until loading), during loading, and 0 lb (after unloading). This process was repeated until
consistent voltage readings were obtained. A series of weights, ¼, ½, ¾ and 1 lb, were consistent voltage readings were obtained. A series of weights, ¼, ½, ¾ and 1 lb, were symmetrically applied to the input ends
symmetrically applied to the input ends of two second-stage lever arms.of two second-stage lever arms.
Two lever configurations, one 1S-2S type and one 1S-2D type, were tested and Two lever configurations, one 1S-2S type and one 1S-2D type, were tested and the results are shown in Fig. 8.5. The 1S-2S configuration had a force amplification the results are shown in Fig. 8.5. The 1S-2S configuration had a force amplification factor of ~50 with a slight decrease at heavier weights. In comparison, the 1S-2D type factor of ~50 with a slight decrease at heavier weights. In comparison, the 1S-2D type had a force-amplification factor of ~22, but with a slight increase at heavier weights.
had a force-amplification factor of ~22, but with a slight increase at heavier weights.
These measured amplification factors are much lower than the ideal amplification factor These measured amplification factors are much lower than the ideal amplification factor of 120 as calculated below:
of 120 as calculated below: L L11 = 221 mm,= 221 mm, ll11 = 22.8 mm,= 22.8 mm, A A11 == L L11 // ll11 = 9.67,= 9.67, L L22 = 257= 257 mm,
mm,ll22 = 19 mm,= 19 mm, A A22== L L22// ll22= 13.5, the ideal total amplification factor = 13.5, the ideal total amplification factor A A== A A11 A A22= 130.= 130.
The analytical equation (4.8) predicts a value of 90. The amplification factor of The analytical equation (4.8) predicts a value of 90. The amplification factor of the first stage,
the first stage, A A11, is calculated by first substituting beam dimensions and , is calculated by first substituting beam dimensions and E E = 70GPa (for = 70GPa (for aluminum alloy) into equation (4.23) to calculate all the spring constants (e.g,
aluminum alloy) into equation (4.23) to calculate all the spring constants (e.g, k k vvpvvp,1,1 == EW
EW p,1 p,1 t t / / ll p,1 p,1 = 6.9 x 10= 6.9 x 1022 N/m) and then substituting the calculated spring constants intoN/m) and then substituting the calculated spring constants into equation (4.8). The amplification factor of the second stage,
equation (4.8). The amplification factor of the second stage, A A22, is calculated by first, is calculated by first substituting beam dimensions and
substituting beam dimensions and E E = 70GPa (for aluminum alloy) into e= 70GPa (for aluminum alloy) into equations (5.4) toquations (5.4) to (5.7) to calculate all the spring constants and then substituting the calculated spring (5.7) to calculate all the spring constants and then substituting the calculated spring constants into equation (4.8).
constants into equation (4.8).
With respect to SUGAR simulation of 1S-2S type, the netlist file is given in With respect to SUGAR simulation of 1S-2S type, the netlist file is given in Attachment I and the node information is the same as in Figure 5.5(c). The amplification Attachment I and the node information is the same as in Figure 5.5(c). The amplification factor by SUGAR simulation is 80. For the 1S-2D type, the netlist file is given in factor by SUGAR simulation is 80. For the 1S-2D type, the netlist file is given in Attachment H and the node information is the same as in Figure 5.5 (b). The Attachment H and the node information is the same as in Figure 5.5 (b). The
amplification factor of 1S-2D type by SUGAR simulation becomes 63, which is slightly amplification factor of 1S-2D type by SUGAR simulation becomes 63, which is slightly lower than that of the 1S-2S type. The experiment results shown in Fig.8.5 has a lower lower than that of the 1S-2S type. The experiment results shown in Fig.8.5 has a lower amplification factor than those predicted by the first order analytical results as above amplification factor than those predicted by the first order analytical results as above (using equation 4.8). This is qualitatively similar to the SUGAR results which also show (using equation 4.8). This is qualitatively similar to the SUGAR results which also show a lower amplification factor than the 1
a lower amplification factor than the 1stst order analytical results (e.g., Fig. 5.9). However,order analytical results (e.g., Fig. 5.9). However, the experimentally measured difference in the amplification factor between 1S-2S and the experimentally measured difference in the amplification factor between 1S-2S and 1S-2D macrolevers was much greater than that predicted by SUGAR simulation. For the 1S-2D macrolevers was much greater than that predicted by SUGAR simulation. For the dimension used at the macro-level experiment, the quantitative difference is much larger.
dimension used at the macro-level experiment, the quantitative difference is much larger.
Although there is a negligible variation with the input load, the structure weight Although there is a negligible variation with the input load, the structure weight contributes to a great amount of the elastic deformation as described in the next contributes to a great amount of the elastic deformation as described in the next paragraph.
paragraph.
In all, the measured amplification factors of the macro-levers are much lower than In all, the measured amplification factors of the macro-levers are much lower than the predicted values, and the difference in the measured amplification factors between the the predicted values, and the difference in the measured amplification factors between the 1S-2S and 1S-2D types is much greater than that predicted by SUGAR. All these are 1S-2S and 1S-2D types is much greater than that predicted by SUGAR. All these are most likely due to the large displacements (even under lever arm gravity only, without most likely due to the large displacements (even under lever arm gravity only, without any input force) at the second-stage lever arm input. As the dimensions of a microlever any input force) at the second-stage lever arm input. As the dimensions of a microlever are scaled up with a scaling factor
are scaled up with a scaling factor R R to a macrolever, the surface area of the macrolever to a macrolever, the surface area of the macrolever arm is enlarged by a factor equaling the square of
arm is enlarged by a factor equaling the square of R R. Consequently, the weight of the. Consequently, the weight of the lever arm is scaled as the cubic of R and may no longer be ignored as in the micro-scale.
lever arm is scaled as the cubic of R and may no longer be ignored as in the micro-scale.
If the macrolever is positioned horizontally, the weight of the lever arm may bring the If the macrolever is positioned horizontally, the weight of the lever arm may bring the structure into contact with the “substrate”. On the other hand, if the macrolever is structure into contact with the “substrate”. On the other hand, if the macrolever is positioned
positioned vertically, vertically, the the weight weight of of the the lever lever arm arm which which is is in in the the same same direction direction as as thethe input force may by itself cause significant displacement of the structure and hence affect input force may by itself cause significant displacement of the structure and hence affect
the amplification of the input force. Since the weight is also shrunk while at micro level, the amplification of the input force. Since the weight is also shrunk while at micro level, making device at micro-scale has many advantages verse the same device in macro level.
making device at micro-scale has many advantages verse the same device in macro level.
Fig. 8.5 Measured amplification factors as a function of the input load for Fig. 8.5 Measured amplification factors as a function of the input load for
1S-2S and 1S-2D two-stage aluminum levers.
1S-2S and 1S-2D two-stage aluminum levers.
0 0 20 20 40 40 60 60 80 80
M M e e a a s s u u r r e e d d A A m m p p l l i i f f i i c c a a t t i i o o n n F F a a c c t t o o r r
0.5 1.0 1.5 2.0
0.5 1.0 1.5 2.0
To
Tottal al InInpput ut LoaLoad d (w(weieighghtts)s), , lblbss
1
1SS--22SS 11SS--22DD