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畢業(yè)設計(論文)外文資料翻譯
學 院
?！ I(yè)
機械設計制造及其自動化
學生姓名
班級學號
外文出處
International Journal of Industrial Ergonomics 38 (2008) 715–725
外文資料
Modeling of the hand–arm system for impact loading
in shear fastener installation
Department of Mechanical and Aerospace Engineering, Room No. 330, Engineering Research Laboratory, 1870 Miner Circle,
University of Missouri-Rolla, Rolla, MO 65401, USA
Department of Engineering Management and Systems Engineering, University of Missouri-Rolla, Rolla, MO 65401, USA
Received 2 October 2007; accepted 3 October 2007
Available online 26 November 2007
Abstract
The aim of this study is to model the hand–arm system during fastening operation using shear fasteners. This fastening operation has considerable dynamic forces caused by the impact delivered to the hand–arm at the end of the operation because of fastener shear-off.The hand–arm is modeled as a rotational single-degree-of-freedom system. The values of the model parameters are obtained using the magnitude of compliance spectrum calculated from the measured torque and angular displacement data, which are obtained while installing fasteners on a fixtured experimental setup, and by a non-linear least-square curve fitting technique. The experimental setupfacilitates transferring the torque from a torque driver to a fastening tool handle held by the subject. The identified parameter values arefound consistent for the trials conducted under same test conditions. Strong agreements are seen between the predicted responses usingthe model and the measured responses.
Relevance to industry
This study is useful in tool selection and workplace design for assembly shop floors where hand-held power tools are commonly used.It demonstrates a systematic approach in predicting the motion of an operator’s hand–arm for a given torque impulse produced by afastening tool. The predicted motion can be used for further analysis to determine the detrimental effect it may have in causing cumulative trauma disorders.
2007 Published by Elsevier B.V.
Keywords:Biomechanics; Compliance; Hand–arm model; Fastening operation
1. Introduction
Powered hand tools such as nut-runners, screwdrivers and drills require the operator to react to the tool’s dynamic forces. For many types of power tools, both electric and pneumatic, the greatest source of dynamic force is a sudden change in the applied torque of the tool.
This could be the result of a fastener reaching the end of its travel or a part of the fastener shearing-off at the end of the operation. The reaction of the hand–arm to a torque impulse is dependent upon the condition of the hand–arm immediately before and after the impulse. The muscles of the hand–arm system holding the tool generate appropriate reaction to the torque at the end of the operation. In reacting to the impulsive torque, the operator contracts the muscles of the hand–arm system and positions the body in such a manner so as to maintain the dynamic
equilibrium.This muscle contraction is generally non-isometric in nature. The nature of such muscle contractions is believed to have potential of causing injuries like reduction in strength and onset of muscle soreness (Komi and Buskirk, 1972; Komi and Rusko, 1974).
Biomechanical studies of the hand–arm system in response to continuous excitation forces have used dynamic-system models with one to four degrees of freedom for calculating the response of the hand–arm based on mechanical properties like impedance and ARTICLE IN PRESS www.elsevier.com/locate/ergon 0169-8141/$ - see front matterr2007 Published by Elsevier B.V.
doi:10.1016/j.ergon.2007.10.012
Corresponding author. Tel.: +1 573 341 6557. E-mail address:asjdkd@umr.edu (A. Joshi).
compliance (Gurram et al., 1995, 1996; Reynolds and Soedel, 1972; Reynolds and Keith, 1977; Reynolds and Falkenberg, 1982; Suggs, 1972; Suggs and Mishoe, 1975).
These methods use a frequency range of 10–2000 Hz in the analysis and they apply to the cases of periodic and random vibrations produced by tools like sanders and grinders that continuously generate forces to excite vibrations for a relatively long period of time. However,these models do not apply well to the impulsive-type forces/torques generated by fastening tools. The typical
range of frequencies for dynamic responses in these tools is in the range of 0–25 Hz (Armstrong et al., 1999; Kihlberg, 1995; Kihlberg et al., 1995; Oh and Radwin, 1997, 1998; Oh et al., 1997; Starck and Pyykko, 1986). Other studies have used surface electromyography as a means to study
the effects of reaction forces and torques acting on the hand (Freivalds and Eklund, 1993; Kihlberg et al., 1993; Radwin et al., 1989). However, these studies do not model the hand–arm system and require a large number of experiments to deduce the relationship between the probability of causing injuries and factors such as tool type and hand–arm posture. Previous attempts to model the hand–arm response to impulsive torques are based on the response of the hand–arm under conditions of maximum exertion (Lin et al., 2001, 2003a, b). This resulted in an underestimation of the hand deflection and an overestimation of the contact force between the hand and the tool when using real tools. The aim of the study as described in the present paper is
to develop a biomechanical model to understand the response of the hand–arm system to impulsive torque encountered in fastening operation with shear fasteners.
The study includes the modeling of a simulated fixture as a two-degree-of-freedom system and the response of the hand–arm using a one-degree-of-freedom system. The developed hand–arm system model will be useful in designing and/or selecting power tools to minimize the forces/torques and resultant motions encountered by the operators as well as comparing ergonomic risks associated with different tools. The model can predict the motion of the hand–arm and allow the tool to be designed to minimize the hand movement, thus reducing the associated ergonomic risks.
2. Methods
To model the response of the hand–arm system one naturally thinks of an experiment with the subject using an actual tool performing real operations. However, acquiring data in such a completely free-moving experiment would require modeling the complex tool dynamics as well as the complex hand–tool interactions, which would require collecting a large amount of data including the applied forces/torques and the resultant translational/rotational displacements. This process is not only expensive but it often results in widely varying parameter values from trial to trial under same test conditions. Hence, an experimental setup to simulate the actual working conditions has to be built which would transfer the same forces/torques to the hand–arm system as a real tool would but in a more manageable manner. In this study, an experimental setup has been designed such that the torque from a real tool is transferred directly to the test subject and the system response is determined using a fixtured tool handle. This has the advantage that the subject responds to all torques generated from the securing of a fastener until the fastener shears off.
2.1. Experimental setup
The experimental setup is shown inFig. 1. The source of torque input is the torque driver, which is an actual tool as shown on the left side ofFig. 1, while the fixtured handle of the test tool as shown on the right side ofFig. 1is gripped by the test subject to measure the response.
2.2. Tool modeling
The study starts with modeling of the test tool. The response of the test tool is obtained by manually providing impulsive torques to the test tool without the subject holding the test tool. The measured compliance is used to determine the degree of the system necessary to model the dynamics of the test tool. The magnitude of the frequency spectrum of the compliance as shown inFig. 4is given by the ratio of measured angular displacement to the input torque for the test tool. It shows two distinct natural frequencies below the upper-bound frequency of 20 Hzused in the analysis. Based on the frequency spectrum of the compliance, a two-degree-of-freedom system model is chosen for the test tool. This model is shown schematically inFig. 5, wheretis the torque input.
The dynamic equation of this system is given by
The frequency spectrum of the system’s compliance is
given by
Where
The frequency spectrum of the compliance of the test tool is computed from the Fast Fourier Transforms of the encoder data and the torque sensor data. The unknown parameters of the system shown inFig. 5and Eq. (1) are determined by curve fitting of Eq. (2) to the frequency spectrum of the measured compliance. A non-linear least square curve-fitting algorithm is used to compute the values of the model parameters. Eq. (3) is the objective function that is minimized to determine the model parameters by using the Gauss–Newton method of Optimization.
where ‘F(x,xdata)’ is a vector-valued function and ‘ydata’is associated with the measured data.
In the case of this study, the vector-valued function ‘F’is the compliance of the tool model given by Eq. (2). This function is optimized through an iteration process about the vector ‘x’ starting from a set of initial guesses ‘x0’of values for the model parameters to minimize the objective
function. The ‘data’ is the compliance in Eq. (2) calculated from the measured rotation and torque data. The vector of parameters used for the model given by Eq. where T designates the transpose. The algorithm starts with ‘x0’ as the starting point for optimization of the function ‘F’ and iteratively searches for the global minimum of function ‘G’ using the Gauss–Newton optimization technique to determine the best curve fit in a least-square sense.
2.3. Design of experiment for hand–arm modeling
After acquiring the dynamic model of the test tool,subjects are tested to determine the model of the hand–arm system. They were instructed to grip the test tool handle as needed to simply maintain the position of the handle. For this study, two male subjects participated in the experiment. Both were students and free from any kind of health problems related to the hand, arm, or shoulder that could affect the results of this study. The same two subjects were used to perform additional sets of experiments to validate the model and to test the repeatability of the model results. Prior to the tests, the subjects had installed numerous fasteners with the actual tool in a variety of postures so that they became familiar with the grip and push forces necessary to operate the torque driver. For the experiments, the subject held the test tool handle in neutral posture while a researcher secured a fastener using the torque driver. The model parameters for the hand–arm
system of the subject were determined by measuring the subject’s hand–arm response to the torque input provided by the torque driver. Five trials were conducted for each subject.
The fastening operation lasts for about one second. The operation consists of three parts during which the response of the subject’s hand–arm to the imposed torque alternates between active (voluntary) and passive (involuntary) components as shown in Fig. 6(a). Fig. 6(b)shows the
corresponding response. The portion of data when the fastener is running down and reaches the end of its travel is the torque build-up period, i.e. period (I) inFig. 6(a). This portion of data is an active component because the subject is fighting the torque to prevent the test tool from rotating.
The second portion of data, i.e. period (II), corresponds to the fastener shearing off, resulting in sudden rise in the torque. This period is of very short duration (approximately 0.15 s) in which the excessive torque overpowers the resistance offered by the subject’s hand and the hand rotates in the direction of the imposed torque. In this period of 0.15 s from the peak torque, the response of the subject can be considered involuntary and hence be modeled as a passive dynamic system (Boff and Lincoln,1988). Followed by this period is an active component, i.e.period (III) inFig. 6(a), during which the subject forces the test tool back to its original position while the tool shuts
off, reducing the torque to zero. The analysis is based on modeling the hand–arm system as a passive system during period (II) and determines the values of model parameters using the passive component of the measured data.
To select the data for analysis the following procedure is adopted: the starting point of the torque curve is determined by the slope of the ramp from the torque profile shown inFig. 6(a). A line is constructed using the slope of the ramp and is projected on the time axis to determine the starting point of time for the torque and the response data used for modeling. The transient oscillation seen in the torque plot after the end of operationin Fig. 6(a)is due to the dynamic characteristics of the torque sensor. It is removed from the torque data in the analysis, and the torque in the tool shut-off period is considered zero. The torque and response data used in the analysis are shown inFig7.
3. Results
This section provides the results for modeling the system and verification of the modeling technique.
3.1. Tool modeling
The values of the tool model parameters obtained from each of five trials along with the average values of the identified parameters of the test tool are shown in Table 1.
The magnitude plot of the frequency spectrum of the measured compliance and the fitted curve based on the model for one of the trials is shown inFig. 11.
3.2. Hand–arm modeling
There were five trials of the experiment conducted for each subject in neutral posture. The values of the hand–arm model parameters for the five trials and their averages for each subject performing fastening operation in neutral posture with a pistol-grip tool are listed inTable 2.
Based on these values, the natural frequency calculated for subject 1 is 3.25 Hz and the natural frequency calculated for subject 2 is 3.85 Hz.
4. Discussion
This study has provided a method of dynamic modeling, experimental design, and data analysis for the human hand–arm, which is considered as a dynamic system, in response to the torque generated due to the shear-off of a fastener at the end of the fastening operation. In this study, the hand–arm model is identified as a single-degree-offreedom system.It can be observed from Table 2, that the identified values of model parameters are fairly consistent for all thetrials for both subjects tested. The subjects tested in this study are similar in height and weight. This may explain
why no large variations in the predicted values of the parameters are found. More trials need to be conducted with subjects that vary more substantially in height and weight, in order to determine variations in the model parameters between subjects. The grip force is not considered in this study, and the subjects are asked to grip the handle just hard enough to maintain the position of the test tool. The natural frequencies of the hand–arm system for the two subjects determined by using the derived model parameters are slightly less than that reported in a previous study (Lin et al., 2001), which shows the natural frequency of a hand–arm to be around 4 Hz. This may be due to the fact that the subjects are holding the test tool with anominal grip force just enough to maintain the position,which in turn results in reduction of the stiffness of the hand–arm system.The derived model parameters are used to predict the response of the subject by using Eq. (6) and measuring the torque using the same testing conditions. In reacting to the impulsive torque which arises due to the fastener shearoff, the subject tends to respond passively for a small time duration of about 0.15 s, i.e. period (II) inFig. 6(a), from the peak torque value when the torque overpowers the subject’s resistance to imposed torque. That period is followed by an active response, which is period (III) in Fig. 6(a), when the subject forces the test tool back to the starting position. Previous studies have indicated that it is safe to assume that within a period of 0.15 s the human response can be considered passive (Boff and Lincoln,1988). Hence, for predicting the response of the subject using the identified model parameter values only the passive portion of response is used. However, this period can vary between subjects and even within a subject depending upon the number of repetitions of the operation.
There is a tendency for subjects to anticipate the forcing and brace actively as is observed by Armstrong et al.(1999).Previous studies analyzing the hand–arm response for impulsive torques measured the response under the condition of maximum grip with the use of a simulated physical tool instead of a real tool (Lin et al., 2001, 2003a, b).It resulted in an underestimation of the hand–arm deflection and an overestimation of the interface forcebetween the tool and the hand when using a real tool. The method of data acquisition and analysis in the present study allows for identification of the hand–arm system parameters under conditions more representative of the real-world practice. As the torque driver in this study is an actual tool, the torque exerted on the test tool is also more representative of the real world. Thus, the method closely resembles the real-world working conditions experienced by an operator on the shop floor. By changing the torque drivers and test tools in Fig. 1, different tools can be compared for their dynamic and ergonomic effects on the operator hand–arm system. Currently, the relation between the causes of cumulative trauma disorders and mechanical model parameters is not well understood. The relative contribution of force/torque,deflection, and operation repetition to the occurrence of injuries is not yet quantified. This is a three-part problem.First, it is difficult to quantify the system parametersassociated with changing posture, tool, fixture, etc. Second,due to the cumulative nature of hand–arm disorders it takes months or even years to detect resulting injuries.
Third, it is not yet possible to quantify specific risk factor(s)that cause ergonomic injuries. NIOSH has publishedseveral studies attempting to categorize the risk factor(s).
It divides the risk factors into four categories: high force, high repetition; high force, low repetition; low force,high repetition; and low force, low repetition (NIOSH,1997). However, the range of each of these four categories is not clearly defined. If correlations between the force/repetition and the resulting injury are to be determined,it is imperative that the modeling and analysis techniques used to measure and predict the deflections and hand–tool interface forces be accurate and repeatable. The techniques discussed in this paper provide good correlations between the predicted and the measured angular rotation as shown inTable 3. The tests conducted to check
its repeatability also yield strong correlations between the predicted and the measured angular rotation. This proves that the developed techniques can be used effectively to model the hand–arm system. The derived model can be used to compare different tools, postures, fasteners, etc.
using the predicted angular rotation as a metric of comparison.
ARTICLE IN PRESS
The modeling technique presented in the paper can effectively predict the response of the subject to impulsive torque produced by a fastening tool used for fastening of shear-type fasteners. The angular rotation of the hand–arm system can be used as an objective indicator of the discomfort of the operators as shown in previous studies (Kihlberg et al., 1993; Lindqvist, 1993). Hence, the method discussed