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1o ensure that the Denetit of INpuUl SNaping Is not limited to this particular set of parameters, re peatability tests were conducted with several probe approach and gross motion distances. Figure § shows the repeatability as a function of probe ap proach distance for measurements with a 20-mm gross motion. Each datapoint in Figure 9 repre sents the range of measurements obtained from ;

Figure 9 1o ensure that the Denetit of INpuUl SNaping Is not limited to this particular set of parameters, re peatability tests were conducted with several probe approach and gross motion distances. Figure § shows the repeatability as a function of probe ap proach distance for measurements with a 20-mm gross motion. Each datapoint in Figure 9 repre sents the range of measurements obtained from ;

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Soiving Equations (1) and (2) yields the three- impulse, zero vibration and zero derivative {ZVD) shaper, which can be expressed as: > Returning to the simple input shaper shown ir Figure 4, the second impulse must have the prope amplitude if it is to cancel the vibration from the first impulse. The amplitude can be determined by florming an expression for the residual vibratior paused by an impulse sequence and then setting the expression equal to zero. The residual vibratior amplitude can be expressed as the ratio of residua vibration with shaping to that without shaping Ihis percentage vibration can be determined by us- ing the expression for residual vibration of a sec. ond-order harmonic osciltator of frequency w Fadi. ans/s and damping ratio ¢, which is given in the references.° The vibration from a series of im- julses is divided by the vibration from a single im bulse to get the percentage vibration [Equation (1}]
Soiving Equations (1) and (2) yields the three- impulse, zero vibration and zero derivative {ZVD) shaper, which can be expressed as: > Returning to the simple input shaper shown ir Figure 4, the second impulse must have the prope amplitude if it is to cancel the vibration from the first impulse. The amplitude can be determined by florming an expression for the residual vibratior paused by an impulse sequence and then setting the expression equal to zero. The residual vibratior amplitude can be expressed as the ratio of residua vibration with shaping to that without shaping Ihis percentage vibration can be determined by us- ing the expression for residual vibration of a sec. ond-order harmonic osciltator of frequency w Fadi. ans/s and damping ratio ¢, which is given in the references.° The vibration from a series of im- julses is divided by the vibration from a single im bulse to get the percentage vibration [Equation (1}]
An alternate procedure for increasing insensi- tivity uses extra-insensitive (El) constraints.® In- stead of forcing the residual vibration to zero at the nominal frequency, the residual vibration is only reduced to a Jow level V. The width of the notch in the sensitivity curve is then maximized by forcing the vibration to zero at two frequencies, one lower Figure 6 shows that the ZVD shaper is much mor insensitive to frequency shifts than the ZV shaper However, the 2VD shaper has a time duration eque to one period of the vibration frequency, as op posed to the one-haif period length of the Z' shaper. This means that the shaped command ob tained with a ZVD shaper will be one-half periox jonger than the ZV shaped command and one pe riod longer than the unshaped command. Thi: trade-off is typical of the input shaper design pro cess—increasing robustness usually requires in creasing the length of the Input Shaper. wm ._ dep. ye
An alternate procedure for increasing insensi- tivity uses extra-insensitive (El) constraints.® In- stead of forcing the residual vibration to zero at the nominal frequency, the residual vibration is only reduced to a Jow level V. The width of the notch in the sensitivity curve is then maximized by forcing the vibration to zero at two frequencies, one lower Figure 6 shows that the ZVD shaper is much mor insensitive to frequency shifts than the ZV shaper However, the 2VD shaper has a time duration eque to one period of the vibration frequency, as op posed to the one-haif period length of the Z' shaper. This means that the shaped command ob tained with a ZVD shaper will be one-half periox jonger than the ZV shaped command and one pe riod longer than the unshaped command. Thi: trade-off is typical of the input shaper design pro cess—increasing robustness usually requires in creasing the length of the Input Shaper. wm ._ dep. ye
For equations that describe the El shaper as a func tion of damping ratio see the references.?
For equations that describe the El shaper as a func tion of damping ratio see the references.?
The performance of a CMM is generally measurec with an array of tests described in an ANSI/ASME standard.’ The standard includes tests for repeat: ability, linear displacement accuracy, streamlined
The performance of a CMM is generally measurec with an array of tests described in an ANSI/ASME standard.’ The standard includes tests for repeat: ability, linear displacement accuracy, streamlined
‘igure&S Measurements during a 50-point repeat. ibility test (1-mm probe approach distance, 20-mrr yross motion)
‘igure&S Measurements during a 50-point repeat. ibility test (1-mm probe approach distance, 20-mrr yross motion)
in the repeatability tests summarized in Figure 70 the probe approach distance and gross motion were held constant throughout the 50 measure- ments. These types of repeatability tests are very valuable for evaluating CMM performance when parts are fixtured in the workspace consistently and when part geometries do not vary greatly. How- ever, if consistent part fixturing is not used, then probe approach distances could vary from part te part. Also, “Many machines/probe systems exhibit vastly different characteristics depending on the
in the repeatability tests summarized in Figure 70 the probe approach distance and gross motion were held constant throughout the 50 measure- ments. These types of repeatability tests are very valuable for evaluating CMM performance when parts are fixtured in the workspace consistently and when part geometries do not vary greatly. How- ever, if consistent part fixturing is not used, then probe approach distances could vary from part te part. Also, “Many machines/probe systems exhibit vastly different characteristics depending on the
JU-DOINE repeatabuity test WIN the given probe ap- proach distance and a 20-mm gross motion. {n gen- eral, repeatability improves with increasing probe approach distance. Figure 9 also demonstrates that input shaping improves repeatability over a wide range of probe approach distances. Figure 10 shows that input shaping also improves repeatabil- ity when a 10- or 15-mm gross motion is used. Note that as the probe approach distance increases, the benefit of input shaping over the standard control- ler decreases.
JU-DOINE repeatabuity test WIN the given probe ap- proach distance and a 20-mm gross motion. {n gen- eral, repeatability improves with increasing probe approach distance. Figure 9 also demonstrates that input shaping improves repeatability over a wide range of probe approach distances. Figure 10 shows that input shaping also improves repeatabil- ity when a 10- or 15-mm gross motion is used. Note that as the probe approach distance increases, the benefit of input shaping over the standard control- ler decreases.
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