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Design of an active vibration dummy of sitting man
Clinical Biomechanics 16 Supplement No. 1 (2001) S64±S72
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Design of an active vibration dummy of sitting man lfel Alexander Cullmann *, H.P. Wo Department of Dynamics of Structures, Darmstadt University of Technology, Petersenstr. 30, D-64287, Darmstadt, Germany
Abstract Objective. The determination of vibration transmission through vehicle seats today is still performed with small groups of test subjects. This method suers from several severe disadvantages, in particular poor repeatability and objectivity due to varying test conditions and limited group sizes. Replacing test persons with a vibration dummy helps to solve this problem. Design. The active vibration dummy simulates the dynamic behaviour of sitting man expressed in terms of the driving point impedance for arbitrary body masses and excitation signals. Methods. The dummy is realized as a mechatronic system basing on a single degree of freedom setup. A real-time control loop of mass accelerations (and thus acting forces) ®ts the active dummy to the desired driving point impedance data set. Model and controller parameters are determined by a parameter-identi®cation technique giving meaningful results for arbitrary impedance data sets. Results. The prototype shows excellent agreement with the target data under laboratory conditions. Body mass and excitation level can be varied over the full range of car seat test requirements. Relevance The determination of vibration transmission through vehicle seats should be possible without human experiments. An active vibration dummy with adjustable vibration behaviour expressed by the vertical driving point impedance covering the entire scope of car seat tests (masses/excitation intensities) is presented. With the dummy, improved seat test procedures could be established, leading to design improvements and therefore to prevention of whole-body vibration injuries. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Whole-body vibration; Experimental simulation; Seat tests; Impedance; (Active) Vibration dummy
1. Introduction The determination of vibration transmission through vehicle seats today is still performed with small groups of test subjects. This method suers from several severe disadvantages, especially: · A poor repeatability of test results, even for single test subjects, in subsequent tests repeated after a longer time span. · Poor objectivity, as the choice of a small group of test persons cannot be regarded as being representative and test results can be in¯uenced by even slightly different test conditions. Both factors result in either unsatisfactory results or in expensive tests with large groups of subjects to obtain statistically signi®cant results. Due to these restrictions,
*
Corresponding author. E-mail address: [email protected] (A. Cullmann).
technically relevant test procedures in accordance with international quality norms like ISO 9000/9001 can rarely be established. It is therefore desirable to develop a test device in the form of a vibration dummy representing the same mechanical behaviour as the simulated population. Several passive constructions presented in the literature deal with this development task, and all suer from certain limitations: · Several dummies [2±5,9,10], constructed as passive single degree of freedom (SDOF) systems, have been presented. The limitation to a SDOF results in a neglect of higher resonance frequencies and thus in a simpli®cation of the human vibration behaviour which may not be acceptable for frequencies above the ®rst resonance at about 5±6 Hz. · Passive dummies with several degrees of freedom [1,6±8] usually require extensive constructive eorts. Both groups of dummies often suer from unwanted nonlinearities, due to friction or nonlinear damping,
0268-0033/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 8 - 0 0 3 3 ( 0 0 ) 0 0 1 0 7 - 8
A. Cullmann, H.P. Wolfel / Clinical Biomechanics 16 Suppl. No. 1 (2001) S64±S72
thus preventing the use of the dummy at low excitation levels. The representation of varying body masses is dicult, the representation of dierent vibration characteristics caused by varying excitation intensity or postural changes seems to be impossible. We have designed a vibration dummy, based on the approach of active vibration control, which satis®es the following requirements: · Adjustable to dierent body masses. · Adjustable to dierent prescribed vibration characteristics. · Useful at low excitation levels relevant for car seat tests with respect to comfort judgement. 2. Model approach The seated human subject shown in Fig. 1 is excited at several body parts (back, pelvis, feet), which interact with the seat by the driving forces, f , leading to displacements q and z . The index * refers to the dierent measurement points. The most important and therefore best documented interaction takes place between the vertical displacement on the seat surface, zs , and the corresponding vertical driving force, fzs .
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A linearization leads to the driving point impedance, the complex quotient of driving force and corresponding velocity in the frequency domain Iz
F zs : jXZ s
1
The model approach presented here is to replace the test person with the SDOF structure presented in Fig. 2, which consists of a base mass, m0 , rigidly connected to an anatomically formed seat interface and a moving mass, m, with a vertical degree of freedom. The back is connected to the base with linear bearings, allowing displacements parallel to the backrest surface. Both masses are interacting via: · Spring forces, fc . · Bearing forces, fb , representing coulomb friction and arbitrary damping forces depending on the relative velocity. · Actuator forces, fa . It is now possible to write the frequency domain driving force F zs jX2 m0 Z s mZ 2 in terms of the acting forces F zs jX2 m0 Z s F c F b F a :
3
While the terms F b and F c are state-dependent, the actuator force F a allows a direct control of the driving
Fig. 1. Seated subject under vibration excitation.
Fig. 2. SDOF model-approach.
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A. Cullmann, H.P. Wolfel / Clinical Biomechanics 16 Suppl. No. 1 (2001) S64±S72
force and therefore the resulting driving point impedance F zs Z 0 Iz jX m m : 4 jXZ s Zs Control of the actuator forces therefore enables this SDOF-structure to behave like any structure with several degrees of freedom providing the same driving point impedance. Calculating the actuator forces requires determination of the masses m0 , m and a mathematical description of the transfer function H z jX Z=Z s .
3. Impedance data parameter-identi®cation The identi®cation algorithm follows the subsequent steps: · De®nition of the transfer function, H z in terms of the desired identi®cation parameters masses, natural frequencies and damping ratios. The number of natural frequencies contributing to the impedance ± and thus to H z ± can be chosen as appropriate. · Formulation of error functions expressed in terms of impedance magnitude errors, if only magnitude information is given X I par X I data X 2 err 5 X
or based on complex magnitude errors X I par X I data X 2 err:
6
X
· Minimization of error values err by a common leastsquare optimization technique.
Table 1. Fig. 3 compares the identi®cation results with the target data. The identi®cation results show good agreement with the target data and meaningful masses even for a small number of given target data points. Additional tests with 20 male and 20 female subjects in car-typical postures were performed in corporation with Audi, DaimlerChrysler, Ford, Johnson Controls, Keiper, Lear, Opel and Volkswagen at the FIOSH Berlin [14], covering the 5th (3 subj.), 33rd (4 subj.), 50th (6 subj.), 67th (4 subj.), 95th (3 subj.) male and female percentile group. Three broad-band excitation signals with 0.3/0.7/ 1.4 m/s2 rms (excitation signals e1±e2±e3) in the frequency range 1±30 Hz were generated. The excitation signals covered timespans of 64 s with a sample rate of 512 Hz. A hydraulic SCHENCK shaker with displacement control input allowing maximum displacements of 200 mm was used. The acceleration signals measured on the seat platform were checked to meet the desired power spectral densities as presented in Fig. 4. Identi®cation results under varying number of poles were obtained. Best results were obtained for 5 pairs of conjugate complex poles based on complex magnitude errors (cf. Eq. (6)). The results are presented in Figs. 5(a) and (b) and Table 2 for the 5th female (f05), 50th male (m50) and 95th male (m95) percentile groups. The results reported in abridged form in Table 2 show · Base masses m0 between 6.1 and 8.0 kg. · Masses m between 28 and 52 kg. · Decreases of the natural frequencies of about 1 Hz for increase of excitation magnitude from 0.3 to 1.4 m/s2 rms.
4. Results
5. Simulation model
Identi®cation results for some exemplary impedance data sets [9,11,12] and for DIN data scaled by the factor 55/75 to obtain comparable dynamic masses [6,13] ± all based on the assumption of three resonance frequencies and real-magnitude errors (cf. Eq. (5)) ± are presented in
The identi®cation results obtained for car-typical posture and excitation signals allow a unique dummy setup with: · Base mass m0 8 kg. · Moving mass m adjusted between 28 and 52 kg.
Table 1 Impedance data identi®cation results Data set
fi (Hz)
Boileau 70 kg [12] DIN/FMD 75 kg [6] Fairley 75 kg [11] FIOSH 75 kg [9] FIOSH 55 kg [9] FIOSH 98 kg [9]
4.8 5.2 4.9 5.0 5.8 4.8
Di (%) 10.9 10.8 9.4 9.2 11.8 8.6
22.3 23.2 24.7 19.1 24.6 19.6
39 29 35 35 42 25
33 17 43 48 89 40
22 32 54 61 11 52
m (kg)
m0 (kg)
47.2 52.9 54.0 54.4 47.6 70.5
6.6 0.0 4.0 0.0 1.1 0.0
A. Cullmann, H.P. Wolfel / Clinical Biomechanics 16 Suppl. No. 1 (2001) S64±S72
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Fig. 3. Impedance data identi®cation results; amplitude values, identi®cation results in continuous lines compared with reported data points (symbols).
· Stiness c of about 70,000 N/m chosen to minimize resulting actuator forces. · Actuator speci®cation of 8 mm stroke and 200 N peak power to allow seat tests under conditions similar to [14]. A M A T L A B / S I M U L I N K simulation model is presented in Fig. 6. A digital signal processor evaluates a time discrete ®lter representation of the transfer function H z with the input seat acceleration measured at the base mass, leading to the required mass acceleration. The required acceleration is compared to the actually measured value. The acceleration dierence is then evaluated by the discrete-time ®lter {NDu, DDu} which determines the necessary actuator forces to close the acceleration control loop. A separate position controller to prevent lowfrequent oscillations, as formerly proposed in [15], is not necessary for an appropriately chosen band-pass characteristic of the ®lter {NDu, DDu} in order to eliminate quasi-static output. The control voltage signal fed out by the ®lter {NDu, DDu}serves as input for the linear ampli®er which operates the voice coil type electrodynamic actuator in voltage control mode. In this mode, any dierential velocity in the vibration dummy causes inductive current, leading to energy dissipation in the
form of damping forces, thus minimizing the required ampli®er power output. The simulation model presented above includes · A state-space representation of seat and passive dummy components. · Coulomb friction modelling fb 1 N. · Acceleration quantization in the analog to digital converters covering a range of 10 V, respectively, 10 m/s2 with 16 bit resolution. · Voltage quantization in the digital to analog converter covering a range of 10 V with 16 bit resolution. · Broad-band acceleration sensor noise input of 4 mV rms (15 mV peak). · Time discretization with a sample rate of 2048 Hz for the acceleration control loop. · Unsynchronous external data logging with a sample rate of 256 Hz. This features make it possible to design and verify the active vibration dummy behaviour under control theory aspects. 6. Prototype realization Fig. 7 presents the data processing equipment installed in a portable 1900 rack and the prototype with
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A. Cullmann, H.P. Wolfel / Clinical Biomechanics 16 Suppl. No. 1 (2001) S64±S72
Fig. 4. Impedance measurement for car-typical posture and excitation signals power spectral densities.
mass con®gurations chosen to represent groups f05, m50 and m95. The actuator is realized using a moving coil motor with permanent-magnetic stator contributed to the moving mass m. Piezoelectric acceleration sensors are placed on both masses m and m0 . The actuator is driven by a linear power ampli®er, the force signal is provided by a digital signal processor which evaluates the acceleration signals from the B&K charge ampli®er. System setup and data storage is done by a standard laptop PC. All components are driven by a 12 V DC power supply. The total power consumption of less than 10 A for ampli®er and data processing units meets onboard test requirements. The dummy was positioned in a car seat, the excitation signals were measured at the connection between
seat and the vibrator platform. Further acceleration sensors providing control inputs were placed at the interface between dummy and seat cushion and at the moving mass. The following test results show the driving point impedance derived by Eq. (4) from the measured acceleration signals: ! 2 jX Z 0 I z jX m m : jX2 Z s The excitation signal with the characteristic of the power spectral density distribution of e2 (0.7 m/s2 rms) was varied between 0.1 and 1.7 m/s2 rms to examine control performance for very low and high excitation levels. The test results are presented in Fig. 8.
A. Cullmann, H.P. Wolfel / Clinical Biomechanics 16 Suppl. No. 1 (2001) S64±S72
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Fig. 5. (a) Impedance data identi®cation results for car-typical conditions for dierent percentile groups; identi®cation results as continuous lines, target data as broken lines. (b) Impedance data identi®cation results for car-typical conditions for 5th female percentile group, in¯uence of excitation level, identi®cation results as continuous lines, target data as broken lines. Table 2 Impedance data identi®cation results for car-typical posture Group
f05 m50 m95
f1 (Hz)
m0 (kg)
m (kg)
e1
e2
e3
e1
e2
e3
e1
e2
e3
6.1 6.3 5.8
5.6 6.0 5.5
5.1 5.1 5.0
28.5 42.2 52.1
28.0 41.2 51.6
28.2 41.2 51.6
7.5 6.9 8.0
7.3 6.6 7.8
7.1 6.1 7.4
7. Discussion The excellent results underline the ability of the established control strategy which eliminates in¯uences of friction forces in the bearing mechanism or any other kind of nonlinear damping and stiness terms due to the small air gaps in the actuator. The in¯uence of acceleration signal noise is negligible for the signal conditioning in our experimental setup. Further research should focus on: · Seat interface optimization ful®lling the following requirements:
1. Representation of a typical pressure distribution on a foam seat via an appropriate buttocks and back contour. 2. Correct longitudinal positioning. 3. Optimization of kinematic coupling between active vibration dummy and shells representing buttocks and back contour. The contact area shapes are obtained by coupling nonlinear foam material with the given pressure distribution. Longitudinal positions of the dummy components are chosen to balance the resulting reaction forces at the seat backrest and cushion. Both contact area shapes and
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Fig. 5. (b) Continued.
Fig. 6. SIMULINK model of acceleration control loop.
A. Cullmann, H.P. Wolfel / Clinical Biomechanics 16 Suppl. No. 1 (2001) S64±S72
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Fig. 7. Prototype setup for dierent masses, data processing unit.
longitudinal position are based on pressure distributions measured at the FIOSH Berlin on car-seats and a ¯at experimental foam seat combined with a static posture control. · Dummy evaluation on three reference car seats in order to show the seat transfer functions are determined in [14]. · Interfacing to numerical models. As presented in [16], the vibration dummy is as far as possible compatible with a numerical model of sitting man developed at the Department Dynamics of Structures, Darmstadt University of Technology. Both dummy and numerical model are equipped with the same seat interface. The identi®cation results described above are used to validate the numerical model which will be connected to additional contact points such as pedal pads and steering wheel. As both models refer to the same data base and global vibration characteristic expressed by the driving point impedance, the numerical model can be used for further numerical data processing of experimental data obtained with the vibration dummy, therefore providing
information about interior vibration responses of the body. The vibration dummy again can be used for prototype tests of seats developed with a virtual prototyping process by FE-simulation with the numerical model. 8. Conclusions The performance of common passive anthropodynamic dummies is limited by several restrictions, in particular undesired nonlinearity at low excitation signal levels and the inability to simulate arbitrary vibration characteristics caused by dierent body masses, varying excitation levels or dierent postures. A modern control approach resulting in an active vibration dummy helps to solve these problems. With improved dummy functionality, a higher industrial acceptance of dummy seat tests could be achieved.
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Fig. 8. Prototype test results.
References [1] Suggs CW, Stikeleather LF. Application of a dynamic simulator in seat testing. Purdue University: American Society of Agricultural Engineers; 1969. [2] Mans®eld NJ, Grin, MJ. Vehicle seat dynamics measured with an anthropodynamic dummy and human subjects. In: Proceedings of Internoise, vol. 96. Liverpool; 1996. [3] Huston DR, Johnson CC, Zhao XD. A human analog for testing vibration attenuation seating. J Sound Vib 1998;214(1):195±200. [4] Lewis CH. The implementation of an improved anthropodynamic dummy for testimg the vibration isolation of vehicle seats. In: 33rd United Kingdom Group Meeting on Human Response Vibration; 1998. [5] Gu Y. A new dummy for vibration transmissibility measurement in improving ride comfort. Advanced Technology and Test Center, Lear Corporation. SAE Technical paper 1999, 99B-14. [6] Knoblauch J. Entwicklung und Bau eines physikalischen Schwingungsmodells des sitzenden Menschen. Aachen: Verlag Shaker, 1993. [7] Buck B, Knoblauch J, W olfel HP. Ein Schwingungsdummy zur objektiven und reproduzierbaren Messung der Schwingungseinwirkung auf den sitzenden Menschen. VDI Berichte Nr. 1189;1995:275±84. [8] Cullmann A, W olfel, HP. Komfortbewertung und Sitzpr ufung mittels des Schwingungsdummys MEMOSIK. Fachtagung Fahrzeugsitze: Haus der Technik Essen; 1998.
[9] Mechanische Modelle des sitzenden Menschen mit unterschiedlicher Masse f ur die normgerechte Pr ufung von Fahrersitzen, Bundesanstalt f ur Arbeitsschutz und Arbeitsmedizin Abschlubericht F 1171; 1996. [10] Uberarbeitung der Konstruktion und Bau von mechanischen Schwingungsmodellen des sitzenden Menschen, Bundesanstalt f ur Arbeitsschutz und Arbeitsmedizin Abschlubericht F 1687; 1998. [11] Fairley TE, Grin MJ. The apparent mass of the seated human body: vertical vibration. J Biomech 1989;22(2). Wu X, Rakheja S. De®nition of a range of idealized [12] Boileau PE, values to characterize seated body biodynamic response under vertical vibration. J Sound Vib 1998;215(4). [13] DIN 45 676, Mechanische Eingangsimpedanz und Ubertragungsfunktion des menschlichen K orpers; September 1987. [14] Durchf uhrung von Personenmessungen als Grundlage einer zu entwickelnden Pr ufmethode von PKW-Sitzen als Beitrag f ur eine Verbesserung der Gestaltung des Fahrerarbeitsplatzes im PKW, con®dential FIOSH report, Berlin 1998, to be published. [15] Cullmann A, Pankoke S, W olfel HP. Simulation of human wholebody-vibrations ± numerical and experimental approaches. In: 32nd ISATA Conference, Vienna; June 1999. [16] Pankoke S, Cullmann A, W olfel HP. Darstellung des Schwingungsverhaltens von PKW-Insassen-Symbiose aus Experiment und Simulation. Fachtagung Subjektive Fahreindr ucke sichtbar machen. Haus der Technik Essen; November 1998.
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Design of an active vibration dummy of sitting man lfel Alexander Cullmann *, H.P. Wo Department of Dynamics of Structures, Darmstadt University of Technology, Petersenstr. 30, D-64287, Darmstadt, Germany
Abstract Objective. The determination of vibration transmission through vehicle seats today is still performed with small groups of test subjects. This method suers from several severe disadvantages, in particular poor repeatability and objectivity due to varying test conditions and limited group sizes. Replacing test persons with a vibration dummy helps to solve this problem. Design. The active vibration dummy simulates the dynamic behaviour of sitting man expressed in terms of the driving point impedance for arbitrary body masses and excitation signals. Methods. The dummy is realized as a mechatronic system basing on a single degree of freedom setup. A real-time control loop of mass accelerations (and thus acting forces) ®ts the active dummy to the desired driving point impedance data set. Model and controller parameters are determined by a parameter-identi®cation technique giving meaningful results for arbitrary impedance data sets. Results. The prototype shows excellent agreement with the target data under laboratory conditions. Body mass and excitation level can be varied over the full range of car seat test requirements. Relevance The determination of vibration transmission through vehicle seats should be possible without human experiments. An active vibration dummy with adjustable vibration behaviour expressed by the vertical driving point impedance covering the entire scope of car seat tests (masses/excitation intensities) is presented. With the dummy, improved seat test procedures could be established, leading to design improvements and therefore to prevention of whole-body vibration injuries. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Whole-body vibration; Experimental simulation; Seat tests; Impedance; (Active) Vibration dummy
1. Introduction The determination of vibration transmission through vehicle seats today is still performed with small groups of test subjects. This method suers from several severe disadvantages, especially: · A poor repeatability of test results, even for single test subjects, in subsequent tests repeated after a longer time span. · Poor objectivity, as the choice of a small group of test persons cannot be regarded as being representative and test results can be in¯uenced by even slightly different test conditions. Both factors result in either unsatisfactory results or in expensive tests with large groups of subjects to obtain statistically signi®cant results. Due to these restrictions,
*
Corresponding author. E-mail address: [email protected] (A. Cullmann).
technically relevant test procedures in accordance with international quality norms like ISO 9000/9001 can rarely be established. It is therefore desirable to develop a test device in the form of a vibration dummy representing the same mechanical behaviour as the simulated population. Several passive constructions presented in the literature deal with this development task, and all suer from certain limitations: · Several dummies [2±5,9,10], constructed as passive single degree of freedom (SDOF) systems, have been presented. The limitation to a SDOF results in a neglect of higher resonance frequencies and thus in a simpli®cation of the human vibration behaviour which may not be acceptable for frequencies above the ®rst resonance at about 5±6 Hz. · Passive dummies with several degrees of freedom [1,6±8] usually require extensive constructive eorts. Both groups of dummies often suer from unwanted nonlinearities, due to friction or nonlinear damping,
0268-0033/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 8 - 0 0 3 3 ( 0 0 ) 0 0 1 0 7 - 8
A. Cullmann, H.P. Wolfel / Clinical Biomechanics 16 Suppl. No. 1 (2001) S64±S72
thus preventing the use of the dummy at low excitation levels. The representation of varying body masses is dicult, the representation of dierent vibration characteristics caused by varying excitation intensity or postural changes seems to be impossible. We have designed a vibration dummy, based on the approach of active vibration control, which satis®es the following requirements: · Adjustable to dierent body masses. · Adjustable to dierent prescribed vibration characteristics. · Useful at low excitation levels relevant for car seat tests with respect to comfort judgement. 2. Model approach The seated human subject shown in Fig. 1 is excited at several body parts (back, pelvis, feet), which interact with the seat by the driving forces, f , leading to displacements q and z . The index * refers to the dierent measurement points. The most important and therefore best documented interaction takes place between the vertical displacement on the seat surface, zs , and the corresponding vertical driving force, fzs .
S65
A linearization leads to the driving point impedance, the complex quotient of driving force and corresponding velocity in the frequency domain Iz
F zs : jXZ s
1
The model approach presented here is to replace the test person with the SDOF structure presented in Fig. 2, which consists of a base mass, m0 , rigidly connected to an anatomically formed seat interface and a moving mass, m, with a vertical degree of freedom. The back is connected to the base with linear bearings, allowing displacements parallel to the backrest surface. Both masses are interacting via: · Spring forces, fc . · Bearing forces, fb , representing coulomb friction and arbitrary damping forces depending on the relative velocity. · Actuator forces, fa . It is now possible to write the frequency domain driving force F zs jX2 m0 Z s mZ 2 in terms of the acting forces F zs jX2 m0 Z s F c F b F a :
3
While the terms F b and F c are state-dependent, the actuator force F a allows a direct control of the driving
Fig. 1. Seated subject under vibration excitation.
Fig. 2. SDOF model-approach.
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A. Cullmann, H.P. Wolfel / Clinical Biomechanics 16 Suppl. No. 1 (2001) S64±S72
force and therefore the resulting driving point impedance F zs Z 0 Iz jX m m : 4 jXZ s Zs Control of the actuator forces therefore enables this SDOF-structure to behave like any structure with several degrees of freedom providing the same driving point impedance. Calculating the actuator forces requires determination of the masses m0 , m and a mathematical description of the transfer function H z jX Z=Z s .
3. Impedance data parameter-identi®cation The identi®cation algorithm follows the subsequent steps: · De®nition of the transfer function, H z in terms of the desired identi®cation parameters masses, natural frequencies and damping ratios. The number of natural frequencies contributing to the impedance ± and thus to H z ± can be chosen as appropriate. · Formulation of error functions expressed in terms of impedance magnitude errors, if only magnitude information is given X I par X I data X 2 err 5 X
or based on complex magnitude errors X I par X I data X 2 err:
6
X
· Minimization of error values err by a common leastsquare optimization technique.
Table 1. Fig. 3 compares the identi®cation results with the target data. The identi®cation results show good agreement with the target data and meaningful masses even for a small number of given target data points. Additional tests with 20 male and 20 female subjects in car-typical postures were performed in corporation with Audi, DaimlerChrysler, Ford, Johnson Controls, Keiper, Lear, Opel and Volkswagen at the FIOSH Berlin [14], covering the 5th (3 subj.), 33rd (4 subj.), 50th (6 subj.), 67th (4 subj.), 95th (3 subj.) male and female percentile group. Three broad-band excitation signals with 0.3/0.7/ 1.4 m/s2 rms (excitation signals e1±e2±e3) in the frequency range 1±30 Hz were generated. The excitation signals covered timespans of 64 s with a sample rate of 512 Hz. A hydraulic SCHENCK shaker with displacement control input allowing maximum displacements of 200 mm was used. The acceleration signals measured on the seat platform were checked to meet the desired power spectral densities as presented in Fig. 4. Identi®cation results under varying number of poles were obtained. Best results were obtained for 5 pairs of conjugate complex poles based on complex magnitude errors (cf. Eq. (6)). The results are presented in Figs. 5(a) and (b) and Table 2 for the 5th female (f05), 50th male (m50) and 95th male (m95) percentile groups. The results reported in abridged form in Table 2 show · Base masses m0 between 6.1 and 8.0 kg. · Masses m between 28 and 52 kg. · Decreases of the natural frequencies of about 1 Hz for increase of excitation magnitude from 0.3 to 1.4 m/s2 rms.
4. Results
5. Simulation model
Identi®cation results for some exemplary impedance data sets [9,11,12] and for DIN data scaled by the factor 55/75 to obtain comparable dynamic masses [6,13] ± all based on the assumption of three resonance frequencies and real-magnitude errors (cf. Eq. (5)) ± are presented in
The identi®cation results obtained for car-typical posture and excitation signals allow a unique dummy setup with: · Base mass m0 8 kg. · Moving mass m adjusted between 28 and 52 kg.
Table 1 Impedance data identi®cation results Data set
fi (Hz)
Boileau 70 kg [12] DIN/FMD 75 kg [6] Fairley 75 kg [11] FIOSH 75 kg [9] FIOSH 55 kg [9] FIOSH 98 kg [9]
4.8 5.2 4.9 5.0 5.8 4.8
Di (%) 10.9 10.8 9.4 9.2 11.8 8.6
22.3 23.2 24.7 19.1 24.6 19.6
39 29 35 35 42 25
33 17 43 48 89 40
22 32 54 61 11 52
m (kg)
m0 (kg)
47.2 52.9 54.0 54.4 47.6 70.5
6.6 0.0 4.0 0.0 1.1 0.0
A. Cullmann, H.P. Wolfel / Clinical Biomechanics 16 Suppl. No. 1 (2001) S64±S72
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Fig. 3. Impedance data identi®cation results; amplitude values, identi®cation results in continuous lines compared with reported data points (symbols).
· Stiness c of about 70,000 N/m chosen to minimize resulting actuator forces. · Actuator speci®cation of 8 mm stroke and 200 N peak power to allow seat tests under conditions similar to [14]. A M A T L A B / S I M U L I N K simulation model is presented in Fig. 6. A digital signal processor evaluates a time discrete ®lter representation of the transfer function H z with the input seat acceleration measured at the base mass, leading to the required mass acceleration. The required acceleration is compared to the actually measured value. The acceleration dierence is then evaluated by the discrete-time ®lter {NDu, DDu} which determines the necessary actuator forces to close the acceleration control loop. A separate position controller to prevent lowfrequent oscillations, as formerly proposed in [15], is not necessary for an appropriately chosen band-pass characteristic of the ®lter {NDu, DDu} in order to eliminate quasi-static output. The control voltage signal fed out by the ®lter {NDu, DDu}serves as input for the linear ampli®er which operates the voice coil type electrodynamic actuator in voltage control mode. In this mode, any dierential velocity in the vibration dummy causes inductive current, leading to energy dissipation in the
form of damping forces, thus minimizing the required ampli®er power output. The simulation model presented above includes · A state-space representation of seat and passive dummy components. · Coulomb friction modelling fb 1 N. · Acceleration quantization in the analog to digital converters covering a range of 10 V, respectively, 10 m/s2 with 16 bit resolution. · Voltage quantization in the digital to analog converter covering a range of 10 V with 16 bit resolution. · Broad-band acceleration sensor noise input of 4 mV rms (15 mV peak). · Time discretization with a sample rate of 2048 Hz for the acceleration control loop. · Unsynchronous external data logging with a sample rate of 256 Hz. This features make it possible to design and verify the active vibration dummy behaviour under control theory aspects. 6. Prototype realization Fig. 7 presents the data processing equipment installed in a portable 1900 rack and the prototype with
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A. Cullmann, H.P. Wolfel / Clinical Biomechanics 16 Suppl. No. 1 (2001) S64±S72
Fig. 4. Impedance measurement for car-typical posture and excitation signals power spectral densities.
mass con®gurations chosen to represent groups f05, m50 and m95. The actuator is realized using a moving coil motor with permanent-magnetic stator contributed to the moving mass m. Piezoelectric acceleration sensors are placed on both masses m and m0 . The actuator is driven by a linear power ampli®er, the force signal is provided by a digital signal processor which evaluates the acceleration signals from the B&K charge ampli®er. System setup and data storage is done by a standard laptop PC. All components are driven by a 12 V DC power supply. The total power consumption of less than 10 A for ampli®er and data processing units meets onboard test requirements. The dummy was positioned in a car seat, the excitation signals were measured at the connection between
seat and the vibrator platform. Further acceleration sensors providing control inputs were placed at the interface between dummy and seat cushion and at the moving mass. The following test results show the driving point impedance derived by Eq. (4) from the measured acceleration signals: ! 2 jX Z 0 I z jX m m : jX2 Z s The excitation signal with the characteristic of the power spectral density distribution of e2 (0.7 m/s2 rms) was varied between 0.1 and 1.7 m/s2 rms to examine control performance for very low and high excitation levels. The test results are presented in Fig. 8.
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Fig. 5. (a) Impedance data identi®cation results for car-typical conditions for dierent percentile groups; identi®cation results as continuous lines, target data as broken lines. (b) Impedance data identi®cation results for car-typical conditions for 5th female percentile group, in¯uence of excitation level, identi®cation results as continuous lines, target data as broken lines. Table 2 Impedance data identi®cation results for car-typical posture Group
f05 m50 m95
f1 (Hz)
m0 (kg)
m (kg)
e1
e2
e3
e1
e2
e3
e1
e2
e3
6.1 6.3 5.8
5.6 6.0 5.5
5.1 5.1 5.0
28.5 42.2 52.1
28.0 41.2 51.6
28.2 41.2 51.6
7.5 6.9 8.0
7.3 6.6 7.8
7.1 6.1 7.4
7. Discussion The excellent results underline the ability of the established control strategy which eliminates in¯uences of friction forces in the bearing mechanism or any other kind of nonlinear damping and stiness terms due to the small air gaps in the actuator. The in¯uence of acceleration signal noise is negligible for the signal conditioning in our experimental setup. Further research should focus on: · Seat interface optimization ful®lling the following requirements:
1. Representation of a typical pressure distribution on a foam seat via an appropriate buttocks and back contour. 2. Correct longitudinal positioning. 3. Optimization of kinematic coupling between active vibration dummy and shells representing buttocks and back contour. The contact area shapes are obtained by coupling nonlinear foam material with the given pressure distribution. Longitudinal positions of the dummy components are chosen to balance the resulting reaction forces at the seat backrest and cushion. Both contact area shapes and
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Fig. 5. (b) Continued.
Fig. 6. SIMULINK model of acceleration control loop.
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Fig. 7. Prototype setup for dierent masses, data processing unit.
longitudinal position are based on pressure distributions measured at the FIOSH Berlin on car-seats and a ¯at experimental foam seat combined with a static posture control. · Dummy evaluation on three reference car seats in order to show the seat transfer functions are determined in [14]. · Interfacing to numerical models. As presented in [16], the vibration dummy is as far as possible compatible with a numerical model of sitting man developed at the Department Dynamics of Structures, Darmstadt University of Technology. Both dummy and numerical model are equipped with the same seat interface. The identi®cation results described above are used to validate the numerical model which will be connected to additional contact points such as pedal pads and steering wheel. As both models refer to the same data base and global vibration characteristic expressed by the driving point impedance, the numerical model can be used for further numerical data processing of experimental data obtained with the vibration dummy, therefore providing
information about interior vibration responses of the body. The vibration dummy again can be used for prototype tests of seats developed with a virtual prototyping process by FE-simulation with the numerical model. 8. Conclusions The performance of common passive anthropodynamic dummies is limited by several restrictions, in particular undesired nonlinearity at low excitation signal levels and the inability to simulate arbitrary vibration characteristics caused by dierent body masses, varying excitation levels or dierent postures. A modern control approach resulting in an active vibration dummy helps to solve these problems. With improved dummy functionality, a higher industrial acceptance of dummy seat tests could be achieved.
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Fig. 8. Prototype test results.
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