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Dynamic stability of under hoist transmission jacks
Safety Science 68 (2014) 34–40
Contents lists available at ScienceDirect
Safety Science journal homepage: www.elsevier.com/locate/ssci
Dynamic stability of under hoist transmission jacks Elisabetta M. Zanetti a,⇑, Giordano Franceschini a, Alberto L. Audenino b a b
DI– University of Perugia, Via Duranti 1, 06125 Perugia, Italy DIMEAS – Politecnico di Torino, Cso Duca degli Abruzzi 24, 10129 Torino, Italy
a r t i c l e
i n f o
Article history: Received 27 September 2013 Received in revised form 16 January 2014 Accepted 21 February 2014
Keywords: Transmission jack Dynamic instability Overturning Handle position Vehicle maintenance
a b s t r a c t Under hoist transmission jacks are indispensable tools for vehicle service and maintenance. They are critical due to their high height/base width ratio, large carried weights and size, poor visibility. This work moves from the analysis of an actual accident where a trans-jack overturned; this event is one of manual handling injuries, usually classified as being struck by an object and or equipment in statistical reports. Requirements to achieve a good stability are here studied and defined; more in detail, the dynamic stability of a traveling transmission jack changing its speed has been studied as well as the stability of a transmission jack suddenly stopped due to wheel impingement since, up to now, there is not specific directive addressing these conditions. Results have demonstrated that the instability while translating is not likely to take place for usual geometries; it could become more critical for higher center of mass positions, lower points of application of the force (for example when using feet instead of hands), and for lower carried weights. On the contrary, the instability due to a sudden stop represents a real possibility; it becomes more critical for higher center of mass heights, higher pushing forces, or higher points of application of the force. The introduction of a translation speed limit is therefore strongly recommended. Other operative advice are that higher points of application of the pushing/pulling force are convenient when changing the traveling speed of a transmission jack, while lower handles position should be used while moving at constant speed. Ó 2014 Published by Elsevier Ltd.
1. Introduction Manual vehicles such as carts and mobile equipment are used in nearly every industry; allowing greater flexibility and efficiency, they become necessary whenever the distance of the push or pull, the load to be moved or the respective task frequency exceeds safety limits (ISO, 2007; Snook and Ciriello, 1991). Considering vehicle service and maintenance, transmission jacks are no doubt an indispensable tool (Fig. 1); these devices follow the same regulations as trolleys or other 4-wheel vehicles, nonetheless they have some specificity: they are more prone to instability, due to a less favorable height/base width ratio and to the high inertia of moved objects (motors, or gears, or vehicle parts); secondly, they often leave poor visibility due to the large size of the moved objects; finally, the transported weight can be very high (up to 10,000 kg), therefore the eventual overturning represents a very serious hazard because of human beings may be crushed by the falling weight. Considering BS EN 1494 directive (BSI, 2008), the ⇑ Corresponding author. Tel.: +39 075 5853700; fax: +39 075 5853703. E-mail addresses: [email protected] (E.M. Zanetti), giordano.franceschini@ unipg.it (G. Franceschini), [email protected] (A.L. Audenino). http://dx.doi.org/10.1016/j.ssci.2014.02.016 0925-7535/Ó 2014 Published by Elsevier Ltd.
only prescriptions concerning transmission jacks specifically, concern the necessity of a load carrying device (cradle), able to safely secure the load, and load descent speed limits in case of leakage. This work moves from the analysis of an actual accident where a trans-jack overturned: two operators were involved since one operator on the back was pushing the transmission jack, while another operator on the front was driving it (the large size of the transported object left poor visibility to the first operator); the falling weight hurt the back of the operator on the front, resulting in the fractures of L1 vertebra, and of the eight and nineth ribs; the other operator reported the fracture of the third finger which was crushed in the accident. This work is aimed to define what conditions are to be fulfilled for balance to be maintained, and how good the balance is, in given situations. The standard answer to the first question is, of course, that the moment produced by the pushing force must be counterbalanced by the moment produced by the weight load, even in the case of an uneven ground, as regulated by existing directives (BSI, 2008), where apposite tests are also prescribed to be performed in order to guarantee that the designed tool complies with static stability. However, also operative conditions must be regulated and specific directives are still missing: in dynamical conditions, the velocity of the Centre of Mass
E.M. Zanetti et al. / Safety Science 68 (2014) 34–40
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specifically, the wheel which is carrying the greatest load (P in Fig. 2). Three situations can lead to instability: – Static instability: the moment arm of the pushing force exceeds the stabilizing moment produced by the gravitational force. Actually this condition should never verify if the afore mentioned directives have been followed, even considering an uneven surface (BSI, 2008); – the transmission jack is subjected to an acceleration or deceleration with the respective inertial forces (dynamics instability while translating); – the transmission jack is traveling, and it is suddenly stopped due to one wheel impingement, or to an obstacle on the ground: considering the carried weight can reach 10,000 kg, even small ground unevenness can lead to this circumstance (dynamic instability when suddenly stopped). 2.1. Analysis of static stability
Fig. 1. Under hoist transmission jack carrying a truck gear.
(CoM) needs to be taken into account because, even if the CoM projection is within the base, balance may be impossible if CoM velocity is directed outward. Various aspects need therefore to be taken into account: height/width ratio, the mass of the moved object, the applied pushing force, the height of its point of application, the movement speed. This work sets up apposite graphs, in order to be able to give recommendations for the proper use of these tools.
2. Material and methods Usually, when a transmission jack overturns, it starts rotating around one of its points of contact to the ground, and, more
The static stability problem has been widely considered by the existing directives; it is here summarized as an introduction to the following paragraphs. As well known, the stabilizing moment produced by the weight load should be higher than the moment produced by the pushing force, both considering rotation about O wheel or about P wheel:
Mg ðl sin hÞ F p f P 0
ð1Þ
Mg ðl sin hÞ þ F p f P 0
ð2Þ
where (Fig. 2): M is the mass of the transported object; l is the distance between the center of mass C and the center of rotation (O or P); h is the angle between a line perpendicular to the ground and OC segment (h = arctan (b/h);Fig. 2); Fp is the applied pushing force and f is its lever arm.
Fig. 2. Transmission jack rotation: O is the center of rotation (point of contact between a wheel and the ground); F is the applied pushing force with its lever arm f; l is the distance between the center of mass C and the center of rotation O; h is the angle between OC segment and a line perpendicular to the ground. The pushing/pulling force can be applied through the apposite handles (lower position) or may be applied on the carried mass (higher position).
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E.M. Zanetti et al. / Safety Science 68 (2014) 34–40
Consequently:
Fp 6
Mg ðl sin hÞ f
Fp P
ð1bisÞ
Mg ðl sin hÞ f
ð2bisÞ
If the transmission jack is free to move, it should be taken into account that whenever the pushing force overcomes the rolling resistance (equal to the product of the weight load and the rolling friction coefficient r), movement takes place and the solution given in Section 2.2 should be followed; a more correct expression is therefore:
Fp 6
Mg ðl sin hÞ f
Fp P
and F p 6 Mg r
Mg ðl sin hÞ f
and F p P Mg r
ð1terÞ
ð2terÞ
Considering usual transmission jack designs, the most restrictive conditions are the second ones, in both inequalities; therefore, static instability may take place only if the wheels are not free to move, and a constant force is applied. 2.2. Analysis of the dynamic stability while translating The dynamic stability problem can be studied considering the following equilibrium equations (Fig. 2): – horizontal equilibrium
R F p þ M€x ¼ 0
ð3Þ
– moment equilibrium about point O (Fig. 2), supposing P reaction is null: 2 Mg ðl sin hÞ F p f þ M €h l þ M€x ðl cos hÞ ¼ 0
ð4Þ
moment equilibrium about point P (Fig. 2), supposing O reaction is null: 2
Mg ðl sin hÞ þ F p f M €h l M€x ðl cos hÞ ¼ 0
ð5Þ
where R represents the rolling resistance; x is the horizontal position. In this case, we are mostly interested in assessing if an overturn hazard exists ð€ h > 0Þ; this condition can be verified with the following inequalities referring, respectively, to the rotation about O or to the rotation about P:
Mg b F p f þ M€x h P 0
ð6Þ
Mg b þ F p f M€x h P 0
ð7Þ
h ¼ l cos h;
b ¼ l sin h
where h is the height of the center of mass when the transmission jack is in upright position, and b is the horizontal distance between the center of mass and the wheel acting as a pivot (Fig. 2). Calculating the horizontal inertial term from Eq. (3):
This inequalities lead to a conservative approach: they define which conditions can produce the beginning of overturning (this conditions can be called ’incipient overturning’), however, overturning really takes place when the applied forces are maintained up to reaching a vertical position of OC segment (dashed lines, Fig. 2): this condition will be called ’no return overturning’ in the following. 2.3. Analysis of the dynamic stability when suddenly stopped Inequalities (6) and (7) would establish that a sudden stop (due, for example to dirt on the ground or to one wheel impingement) would always produce overturning because a theoretically infinite deceleration takes place; this approach would lead to the paradox that the manual translation of transmission jack should be always forbidden, for safety reasons. A less conservative approach should therefore be followed in order to analyze the ‘sudden stop’ case: Eqs. (4) and (5) would need to be solved in order to establish if ‘no return overturning’ condition takes place. As well known, the solution of Eqs. (4) and (5) is dependent on the system geometry, the applied forces and inertias, and, finally, on the initial conditions which are: the initial transmission jack orientation (which is supposed to be with its base parallel to the ground) and its initial speed. This equation is often linearized in order to give an analytic solution; however this approach would not hold in this case because h angle can be very large; therefore, whenever the whole body kinematics is being inquired, numerical solutions need to be implemented through apposite software: for example, Matlab Simulink or multi-body codes such as MSC Adams (see online material). However, the major interest of this inquiry is not defining the transmission jack kinematics, but is to establish if ‘no return overturning’ takes place. An energetic approach can therefore be followed: transmission jack overturning requires the increase of its potential energy (point C in Fig. 2 rises); this energy can be taken from kinetic energy or from the work of the applied forces, in equations:
X 1 M m2 þ F i si ¼ Mg l ð1 cos hÞ 2
where v is the transmission jack velocity immediately before overturning; Fi are the applied forces; si are the displacements of the points of application of forces, along their respective directions. In the following paragraph, recommendable operative conditions will be calculated for an existing transmission jack, whose specifications have been taken from existing ones, and have been summarized in Table 1. CoM height range has been chosen considering that the minimum height of transmission jacks should be used when translating, according to manuals prescription, and this height is usually between 0.85 and 1.2 m, while the transported
Table 1 Transmission jacks Specifications.
M €x ¼ ðF p r M gÞ ðr h bÞ ðh f Þ
ð6bisÞ
ðr h þ bÞ ðh f Þ
ð7bisÞ
Fp P M g
Fp < M g
ð8Þ
Base width, b (m) Nominal load (kg) Shipping weight (kg) CoM height (nominal load) (m) CoM height (no load) (m) Friction coefficient, r Maximum pushing force, Fp (N)
Analyzed jack
Actual accident data
0.256 500 60 0.85–1.2 0.3–0.65 0.054–0.540 300
0.256 6000 94 1.62 / 0.054 300
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Fig. 3. Non-dimensional graph reporting the limit pushing/pulling force per unit weight towards the center of mass height. Different rolling resistance coefficients have been considered (r = 0.54, black curves; R = 0.054, grey curves) and different force application heights (h = 0.9 m, solid lines; h = 0.5 m, dashed lines).
mass can be very large, and a cradle is often used as an interface. The pushing force for sustained movement has been maximized to 300 N, according to the maximum allowed force by BS EN1494 (BSI, 2008). Two different application points have been considered for the pushing force (Fig. 2): on the jack axis, at f = 0.5 m, which is the usual position of carrying handles, or f = 0.9 m and 2b horizontal distance from O wheel, supposing the pushing action is exerted against the transported component (this is very common, due to the large size of the transported mass, but it is against manual prescriptions).
generic point (A), belonging to the transmission jack itself (Fig. 2). If A point has s and t coordinates, its distance from O is d = (s^2 + t^2)^0.5; its angle from the vertical is c = arctan(s/t); after the rotation, A goes in A0 , its distance from O has not changed, while its angle from the vertical becomes c0 = ch; A0 coordinates s0 and t0 are now d sin(c0 ) and d cos(c0 ), respectively.
3. Results The following cases will be analyzed:
2.4. Geometrical considerations Considering h angle rotation of the transmission jack around its wheel O, it is useful to be able to calculate the new coordinates of a
– Case 1 – The transmission jack is translating with a given acceleration/deceleration. – Case 2 – The transmission jack is suddenly stopped.
Fig. 4. Limit pushing/pulling force towards the center of mass height for an unloaded transmission jack. In this case, the x axis ranges from 0.3 to 0.64 m. Different rolling resistance coefficients have been considered (r = 0.54, black curves; R = 0.054, grey curves) while the force application height has been kept equal to 0.5 m.
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Fig. 5. Limit pushing/pulling force towards the center of mass height for a full-load transmission jack. Different rolling resistance coefficients have been considered (r = 0.54, black curves; R = 0.054, grey curves) and different force application heights (h = 0.9 m, solid lines; h = 0.5 m, dashed lines). Circular marks represent operative conditions relative to the case study.
3.1. Case 1 Inequalities (6bis) and (7bis) can be here applied; the pushing force can be scaled by the weight load in order to obtain non-dimensional results; different heights of the center of mass, and different pushing force application points have been considered, however the application point height f has been supposed to be always lower than CoM, therefore the denominators of both inequalities are positive. Inequality (6bis) might produce a negative result; in this case, the inequality is automatically verified whenever the force has the same directions as displacement; on the contrary, when, for example, a pulling force is applied in order to decelerate the transmission jack, a more detailed evaluation needs to be performed. Results can be observed in Fig. 3. Overturning hazard is higher when the transmission jack is less loaded (results have been showed in a non-dimensional form with reference to the transported mass weight), when CoM is higher, and when a lower pushing force application point is being used; Figs. 4 and 5 analyze more in detail the transmission jack carrying no load or carrying its nominal load (500 kg), respectively. Referring to Fig. 4, a pushing/pulling force greater than 700 N would be required to produce overturning hazard. According to Fig. 5, when the transmission jack is loaded at its nominal capability, a minimum 500 N pulling force and a minimum 950 N pushing force are required to produce overturning hazard, while traveling. 3.2. Case 2 In this case the rolling resistance R is null because the transmission jack is not moving; Eq. (8) can be applied; the pushing force has been set equal to 0 (supposing the operator immediately senses the transmission jack is overturning and therefore he stops pushing it), to 300 N (supposing the operator is intensely pushing), or to 30 N which can be assumed to be a realistic estimate of rolling resistance at nominal weight; the displacement of the point of application of the pushing force has been calculated according to Section 2.4, and assuming s = b and t = 0.5 m (the force is applied on the apposite handles which are symmetric about the jack
central axis) or s = 2b and t = 0.9 m (the force is applied on the carried mass). The maximum recommendable transmission jack translating speed has been calculated as a function of CoM height, inverting Eq. (8):
m¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2½Mg l ð1 sin hÞ F p sp
ð9Þ
It has been here assumed that the only external force is the pushing force, and sp is its traveled distance (the force is assumed to keep parallel to the ground). Results can be observed in Fig. 6: a moderate speed such as 0.5 m/s can be kept safely only if the apposite handles are used to apply the pushing force or if CoM height is sufficiently small (h < 1.5 m) or supposing the rolling resistance is kept low (well lubricated wheels, clean surfaces); even considering the last condition, a translating speed over 0.65 m/s is not recommendable, unless the center of mass height is kept lower than 1.5 m. 3.3. Case study of an actual accident Actual accident data are now input to the previously described model in order to assess its causes; operative details are reported in Table 1, the carried weight was equal to 470 kg. The first assessment has concerned the static stability; the required pushing/pulling force can be calculated from equations (1bis) and (2bis)and it results to be equal to 920 N. The second assessment has concerned stability while traveling (Fig. 5): a pushing/pulling force above 1 kN would be required to produce overturn in this condition. The third assessment has concerned stability when suddenly stopped (Fig. 6): overturning could take place at a translating speed above 0.62 m/s, or an even lower speed could be sufficient, assuming that the rolling resistance is equal to 300 N, the limit fixed by BS EN 1494 directive (BSI, 2008): in this case the maximum allowed speed would be 0.555 m/s. In the worst scenario, the pushing force reaches 300 N, and the operator does not use the apposite handles and applies the pushing force on the transported mass: this scenario would result in a maximum allowed speed equal to 0.485 m/s.
E.M. Zanetti et al. / Safety Science 68 (2014) 34–40
39
Fig. 6. Limit translating speed towards the center of mass height. Different pushing force intensities have been considered (Fp = 300 N, black curves; Fp = 30 N, grey curves) and different force application heights (h = 0.9 m, solid lines; h = 0.5 m, dashed lines). Circular marks represent operative conditions relative to the case study.
4. Discussion and conclusions This work has been focused on the dynamic stability of transmission jacks; it has individuated two critical conditions: the transmission jack is accelerating or decelerating, while traveling; the transmission jack suddenly stops due to a wheel impingement. The first condition is thresholded by the applied pushing/pulling force, while instability due to a sudden stop is thresholded by the translating speed. Anthropometric information are needed in order to be able to discuss the obtained results; they can be found in literature concerning carts: according to a reference work by Resnick and Chaffin (1995), the peak pushing force can reach 500 N for male subjects and 200 N for female subjects; stronger operators can move a 450 kg cart at velocities of 0.8 m/s, while weaker subjects can barely reach 0.4 m/s. In those same years, Kumar (1995) pointed out how the maximal strengths depend on performing isometric or isokinetic exercises; in the second case, he asserted the maximum pulling force could reach 438 N, while the maximum pushing force was up to 553 N. A more recent work on Taiwanese males assumes both pushing and pulling forces cannot overcome 300 N (Chen et al., 2011). Considering all these results, and choosing to adopt a conservative approach, it can be assumed that the pushing/pulling forces never exceed 560 N, while the translating speed never overcomes 1 m/s. Considering this information, dynamic instability while translating is not likely to take place for geometries close to the one here considered; it becomes more critical for higher center of mass position, lower position of the point of application of the force (for example when the feet are used instead of the hands), and for lower carried weights. On the contrary, the instability due to a sudden stop can take place for the geometry here considered; it becomes more critical for higher center of mass height, higher pushing forces, or higher point of application of the force. It is the most plausible cause of the accident described in Section 3.3, and, up to now, existing directives regulate the only static stability. In the industry where the reported actual accident has taken place, its incidence rate has resulted to be equal to 1.94 per one
thousand operations, and to 0.6 over seven day injuries per year (referring to 2005–2013). More generally, the incidence of injuries due to mobile equipment overturning, can be inferred from recent work accident reports, and referring to injury cause ‘struck by a falling object’, to the activity ‘manual handling’, and to ‘maintenance’ or ‘vehicle assistance’ industrial activities; some data are reported in the following. Handling has resulted to be the most frequent cause of over seven day injury, and workers injured handling, lifting or carrying have an incidence rate of 210/100,000 workers, according to HSE, 2013a information, licensed under the Open Government Licence v1.0. Another survey reports that maintenance fitters account for 4% major handling injury and 2% total handling injury in the United Kingdom (HSE, 2013b). More generally, according to a previous report (HSE, 2012) pushing/pulling loads accounts for 17% of non-fatal total handling injuries together with ‘handling, lifting or carrying in unknown or unspecified ways’ which accounts for 19% on non-fatal injuries. As reported by USA Bureau of Labour Statistics (BLS, 2013a), workers being struck by object or equipment have represented 12% of fatal injuries in 2012. More specifically, vehicle and mobile equipment mechanics, installers, and repairers account for 2% of fatal injuries, whose cause is being struck by object or equipment in 46% cases. The same institution has analyzed 2012 non-fatal injuries (BLS, 2013b): maintenance and repair workers show a total incidence rate equal to 285.3 per 10,000 full-time workers; among these, injuries related to ‘contact with object’ have an incidence rate equal to 78.3. In order to limit the incidence of this kind of accidents, some preventive measures can be hypothesized from the outcomes of the present work: a translation speed limit could be reported in the operative manual accompanying each transmission jack: consider that 0.5 m/s is the reference speed for rolling force assessment by BS EN 1494 directive (BSI, 2008), and it can be reached both by ‘average’ and a ‘strong’ man when pushing a 450 kg weight (Resnick and Chaffin 1995), while this work has demonstrated that a slightly higher speed (0.555 m/s) is sufficient to produce trans jack overturning, even with proper handle use. The adoption of such measures would eliminate the possibility of trans-jack overturning due to a sudden stop, with a benefit of minus 0.6 over
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seven day injuries per year in the industry where the reported accident has taken place. Other operative advice are that higher points of application of the pushing/pulling force are convenient when accelerating or decelerating the transmission jack (start/stop of the movement), while a low handles position should be used while traveling at constant speed. Considering design issues, the actual handles position (0.5 m height) bears some contraindications: – it is not ergonomic: it is lower than prescribed by ISO 11228-2 (ISO, 2007); – this position forces the operator to work under the heavy weight he is carrying, increasing crushing hazard; – it induces the operator to apply his pushing force on less convenient places, typically on the transported mass: this behavior significantly reduces the dynamic stability in case of a sudden stop. Therefore a different design of pushing/pulling handles is recommended. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.ssci.2014.02.016.
References BLS, 2013a. National Census of Fatal Occupational Injuries in 2012 (Preliminary Results). BLS, USA, pp. 1–14. (accessed 15.01.14). BLS, 2013b. Nonfatal Occupational Injuries and Illnesses Requiring Days Away from Work, 2012. BLS, USA, pp. 1–32. (accessed 15.01.14). BSI, 2008. BS EN 1494:2000 + A1:2008. Mobile or Movable Jacks and Associated Lifting Equipment. Chen, Y.L., Lee, Y.C., Hsu, T.C., 2011. Isometric push and pull strengths of young Taiwanese males. Ind. Health. 49, 696–702. HSE, 2012. Handling Injuries in Great Britain (2001–2002 to 2010–2011). HSE, UK, pp. 1–6. (accessed 15.01.14). HSE, 2013a. Table INJKIND1 – 2012/13. HSE, UK. (accessed 15.01.14). HSE, 2013b. Handling Injuries in Great Britain. HSE, UK, pp. 1–9. (accessed 15.01.14). ISO, 2007. 11228-2:2007. Ergonomics – Manual Handling – Part 2: Pushing and Pulling. Kumar, S., 1995. Upper body push–pull strength of normal young adults in sagittal plane at three heights. Int. J. Ind. Ergonom. 15, 427–436. Resnick, M.L., Chaffin, D.B., 1995. An ergonomic evaluation of handle height and load in maximal and submaximal cart pushing. Appl. Ergon. 26, 173–178. Snook, S.H., Ciriello, V.M., 1991. The design of manual handling tasks: revised tables of maximum acceptable weights and forces. Ergonomics 34, 1197–1213.
Contents lists available at ScienceDirect
Safety Science journal homepage: www.elsevier.com/locate/ssci
Dynamic stability of under hoist transmission jacks Elisabetta M. Zanetti a,⇑, Giordano Franceschini a, Alberto L. Audenino b a b
DI– University of Perugia, Via Duranti 1, 06125 Perugia, Italy DIMEAS – Politecnico di Torino, Cso Duca degli Abruzzi 24, 10129 Torino, Italy
a r t i c l e
i n f o
Article history: Received 27 September 2013 Received in revised form 16 January 2014 Accepted 21 February 2014
Keywords: Transmission jack Dynamic instability Overturning Handle position Vehicle maintenance
a b s t r a c t Under hoist transmission jacks are indispensable tools for vehicle service and maintenance. They are critical due to their high height/base width ratio, large carried weights and size, poor visibility. This work moves from the analysis of an actual accident where a trans-jack overturned; this event is one of manual handling injuries, usually classified as being struck by an object and or equipment in statistical reports. Requirements to achieve a good stability are here studied and defined; more in detail, the dynamic stability of a traveling transmission jack changing its speed has been studied as well as the stability of a transmission jack suddenly stopped due to wheel impingement since, up to now, there is not specific directive addressing these conditions. Results have demonstrated that the instability while translating is not likely to take place for usual geometries; it could become more critical for higher center of mass positions, lower points of application of the force (for example when using feet instead of hands), and for lower carried weights. On the contrary, the instability due to a sudden stop represents a real possibility; it becomes more critical for higher center of mass heights, higher pushing forces, or higher points of application of the force. The introduction of a translation speed limit is therefore strongly recommended. Other operative advice are that higher points of application of the pushing/pulling force are convenient when changing the traveling speed of a transmission jack, while lower handles position should be used while moving at constant speed. Ó 2014 Published by Elsevier Ltd.
1. Introduction Manual vehicles such as carts and mobile equipment are used in nearly every industry; allowing greater flexibility and efficiency, they become necessary whenever the distance of the push or pull, the load to be moved or the respective task frequency exceeds safety limits (ISO, 2007; Snook and Ciriello, 1991). Considering vehicle service and maintenance, transmission jacks are no doubt an indispensable tool (Fig. 1); these devices follow the same regulations as trolleys or other 4-wheel vehicles, nonetheless they have some specificity: they are more prone to instability, due to a less favorable height/base width ratio and to the high inertia of moved objects (motors, or gears, or vehicle parts); secondly, they often leave poor visibility due to the large size of the moved objects; finally, the transported weight can be very high (up to 10,000 kg), therefore the eventual overturning represents a very serious hazard because of human beings may be crushed by the falling weight. Considering BS EN 1494 directive (BSI, 2008), the ⇑ Corresponding author. Tel.: +39 075 5853700; fax: +39 075 5853703. E-mail addresses: [email protected] (E.M. Zanetti), giordano.franceschini@ unipg.it (G. Franceschini), [email protected] (A.L. Audenino). http://dx.doi.org/10.1016/j.ssci.2014.02.016 0925-7535/Ó 2014 Published by Elsevier Ltd.
only prescriptions concerning transmission jacks specifically, concern the necessity of a load carrying device (cradle), able to safely secure the load, and load descent speed limits in case of leakage. This work moves from the analysis of an actual accident where a trans-jack overturned: two operators were involved since one operator on the back was pushing the transmission jack, while another operator on the front was driving it (the large size of the transported object left poor visibility to the first operator); the falling weight hurt the back of the operator on the front, resulting in the fractures of L1 vertebra, and of the eight and nineth ribs; the other operator reported the fracture of the third finger which was crushed in the accident. This work is aimed to define what conditions are to be fulfilled for balance to be maintained, and how good the balance is, in given situations. The standard answer to the first question is, of course, that the moment produced by the pushing force must be counterbalanced by the moment produced by the weight load, even in the case of an uneven ground, as regulated by existing directives (BSI, 2008), where apposite tests are also prescribed to be performed in order to guarantee that the designed tool complies with static stability. However, also operative conditions must be regulated and specific directives are still missing: in dynamical conditions, the velocity of the Centre of Mass
E.M. Zanetti et al. / Safety Science 68 (2014) 34–40
35
specifically, the wheel which is carrying the greatest load (P in Fig. 2). Three situations can lead to instability: – Static instability: the moment arm of the pushing force exceeds the stabilizing moment produced by the gravitational force. Actually this condition should never verify if the afore mentioned directives have been followed, even considering an uneven surface (BSI, 2008); – the transmission jack is subjected to an acceleration or deceleration with the respective inertial forces (dynamics instability while translating); – the transmission jack is traveling, and it is suddenly stopped due to one wheel impingement, or to an obstacle on the ground: considering the carried weight can reach 10,000 kg, even small ground unevenness can lead to this circumstance (dynamic instability when suddenly stopped). 2.1. Analysis of static stability
Fig. 1. Under hoist transmission jack carrying a truck gear.
(CoM) needs to be taken into account because, even if the CoM projection is within the base, balance may be impossible if CoM velocity is directed outward. Various aspects need therefore to be taken into account: height/width ratio, the mass of the moved object, the applied pushing force, the height of its point of application, the movement speed. This work sets up apposite graphs, in order to be able to give recommendations for the proper use of these tools.
2. Material and methods Usually, when a transmission jack overturns, it starts rotating around one of its points of contact to the ground, and, more
The static stability problem has been widely considered by the existing directives; it is here summarized as an introduction to the following paragraphs. As well known, the stabilizing moment produced by the weight load should be higher than the moment produced by the pushing force, both considering rotation about O wheel or about P wheel:
Mg ðl sin hÞ F p f P 0
ð1Þ
Mg ðl sin hÞ þ F p f P 0
ð2Þ
where (Fig. 2): M is the mass of the transported object; l is the distance between the center of mass C and the center of rotation (O or P); h is the angle between a line perpendicular to the ground and OC segment (h = arctan (b/h);Fig. 2); Fp is the applied pushing force and f is its lever arm.
Fig. 2. Transmission jack rotation: O is the center of rotation (point of contact between a wheel and the ground); F is the applied pushing force with its lever arm f; l is the distance between the center of mass C and the center of rotation O; h is the angle between OC segment and a line perpendicular to the ground. The pushing/pulling force can be applied through the apposite handles (lower position) or may be applied on the carried mass (higher position).
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Consequently:
Fp 6
Mg ðl sin hÞ f
Fp P
ð1bisÞ
Mg ðl sin hÞ f
ð2bisÞ
If the transmission jack is free to move, it should be taken into account that whenever the pushing force overcomes the rolling resistance (equal to the product of the weight load and the rolling friction coefficient r), movement takes place and the solution given in Section 2.2 should be followed; a more correct expression is therefore:
Fp 6
Mg ðl sin hÞ f
Fp P
and F p 6 Mg r
Mg ðl sin hÞ f
and F p P Mg r
ð1terÞ
ð2terÞ
Considering usual transmission jack designs, the most restrictive conditions are the second ones, in both inequalities; therefore, static instability may take place only if the wheels are not free to move, and a constant force is applied. 2.2. Analysis of the dynamic stability while translating The dynamic stability problem can be studied considering the following equilibrium equations (Fig. 2): – horizontal equilibrium
R F p þ M€x ¼ 0
ð3Þ
– moment equilibrium about point O (Fig. 2), supposing P reaction is null: 2 Mg ðl sin hÞ F p f þ M €h l þ M€x ðl cos hÞ ¼ 0
ð4Þ
moment equilibrium about point P (Fig. 2), supposing O reaction is null: 2
Mg ðl sin hÞ þ F p f M €h l M€x ðl cos hÞ ¼ 0
ð5Þ
where R represents the rolling resistance; x is the horizontal position. In this case, we are mostly interested in assessing if an overturn hazard exists ð€ h > 0Þ; this condition can be verified with the following inequalities referring, respectively, to the rotation about O or to the rotation about P:
Mg b F p f þ M€x h P 0
ð6Þ
Mg b þ F p f M€x h P 0
ð7Þ
h ¼ l cos h;
b ¼ l sin h
where h is the height of the center of mass when the transmission jack is in upright position, and b is the horizontal distance between the center of mass and the wheel acting as a pivot (Fig. 2). Calculating the horizontal inertial term from Eq. (3):
This inequalities lead to a conservative approach: they define which conditions can produce the beginning of overturning (this conditions can be called ’incipient overturning’), however, overturning really takes place when the applied forces are maintained up to reaching a vertical position of OC segment (dashed lines, Fig. 2): this condition will be called ’no return overturning’ in the following. 2.3. Analysis of the dynamic stability when suddenly stopped Inequalities (6) and (7) would establish that a sudden stop (due, for example to dirt on the ground or to one wheel impingement) would always produce overturning because a theoretically infinite deceleration takes place; this approach would lead to the paradox that the manual translation of transmission jack should be always forbidden, for safety reasons. A less conservative approach should therefore be followed in order to analyze the ‘sudden stop’ case: Eqs. (4) and (5) would need to be solved in order to establish if ‘no return overturning’ condition takes place. As well known, the solution of Eqs. (4) and (5) is dependent on the system geometry, the applied forces and inertias, and, finally, on the initial conditions which are: the initial transmission jack orientation (which is supposed to be with its base parallel to the ground) and its initial speed. This equation is often linearized in order to give an analytic solution; however this approach would not hold in this case because h angle can be very large; therefore, whenever the whole body kinematics is being inquired, numerical solutions need to be implemented through apposite software: for example, Matlab Simulink or multi-body codes such as MSC Adams (see online material). However, the major interest of this inquiry is not defining the transmission jack kinematics, but is to establish if ‘no return overturning’ takes place. An energetic approach can therefore be followed: transmission jack overturning requires the increase of its potential energy (point C in Fig. 2 rises); this energy can be taken from kinetic energy or from the work of the applied forces, in equations:
X 1 M m2 þ F i si ¼ Mg l ð1 cos hÞ 2
where v is the transmission jack velocity immediately before overturning; Fi are the applied forces; si are the displacements of the points of application of forces, along their respective directions. In the following paragraph, recommendable operative conditions will be calculated for an existing transmission jack, whose specifications have been taken from existing ones, and have been summarized in Table 1. CoM height range has been chosen considering that the minimum height of transmission jacks should be used when translating, according to manuals prescription, and this height is usually between 0.85 and 1.2 m, while the transported
Table 1 Transmission jacks Specifications.
M €x ¼ ðF p r M gÞ ðr h bÞ ðh f Þ
ð6bisÞ
ðr h þ bÞ ðh f Þ
ð7bisÞ
Fp P M g
Fp < M g
ð8Þ
Base width, b (m) Nominal load (kg) Shipping weight (kg) CoM height (nominal load) (m) CoM height (no load) (m) Friction coefficient, r Maximum pushing force, Fp (N)
Analyzed jack
Actual accident data
0.256 500 60 0.85–1.2 0.3–0.65 0.054–0.540 300
0.256 6000 94 1.62 / 0.054 300
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Fig. 3. Non-dimensional graph reporting the limit pushing/pulling force per unit weight towards the center of mass height. Different rolling resistance coefficients have been considered (r = 0.54, black curves; R = 0.054, grey curves) and different force application heights (h = 0.9 m, solid lines; h = 0.5 m, dashed lines).
mass can be very large, and a cradle is often used as an interface. The pushing force for sustained movement has been maximized to 300 N, according to the maximum allowed force by BS EN1494 (BSI, 2008). Two different application points have been considered for the pushing force (Fig. 2): on the jack axis, at f = 0.5 m, which is the usual position of carrying handles, or f = 0.9 m and 2b horizontal distance from O wheel, supposing the pushing action is exerted against the transported component (this is very common, due to the large size of the transported mass, but it is against manual prescriptions).
generic point (A), belonging to the transmission jack itself (Fig. 2). If A point has s and t coordinates, its distance from O is d = (s^2 + t^2)^0.5; its angle from the vertical is c = arctan(s/t); after the rotation, A goes in A0 , its distance from O has not changed, while its angle from the vertical becomes c0 = ch; A0 coordinates s0 and t0 are now d sin(c0 ) and d cos(c0 ), respectively.
3. Results The following cases will be analyzed:
2.4. Geometrical considerations Considering h angle rotation of the transmission jack around its wheel O, it is useful to be able to calculate the new coordinates of a
– Case 1 – The transmission jack is translating with a given acceleration/deceleration. – Case 2 – The transmission jack is suddenly stopped.
Fig. 4. Limit pushing/pulling force towards the center of mass height for an unloaded transmission jack. In this case, the x axis ranges from 0.3 to 0.64 m. Different rolling resistance coefficients have been considered (r = 0.54, black curves; R = 0.054, grey curves) while the force application height has been kept equal to 0.5 m.
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Fig. 5. Limit pushing/pulling force towards the center of mass height for a full-load transmission jack. Different rolling resistance coefficients have been considered (r = 0.54, black curves; R = 0.054, grey curves) and different force application heights (h = 0.9 m, solid lines; h = 0.5 m, dashed lines). Circular marks represent operative conditions relative to the case study.
3.1. Case 1 Inequalities (6bis) and (7bis) can be here applied; the pushing force can be scaled by the weight load in order to obtain non-dimensional results; different heights of the center of mass, and different pushing force application points have been considered, however the application point height f has been supposed to be always lower than CoM, therefore the denominators of both inequalities are positive. Inequality (6bis) might produce a negative result; in this case, the inequality is automatically verified whenever the force has the same directions as displacement; on the contrary, when, for example, a pulling force is applied in order to decelerate the transmission jack, a more detailed evaluation needs to be performed. Results can be observed in Fig. 3. Overturning hazard is higher when the transmission jack is less loaded (results have been showed in a non-dimensional form with reference to the transported mass weight), when CoM is higher, and when a lower pushing force application point is being used; Figs. 4 and 5 analyze more in detail the transmission jack carrying no load or carrying its nominal load (500 kg), respectively. Referring to Fig. 4, a pushing/pulling force greater than 700 N would be required to produce overturning hazard. According to Fig. 5, when the transmission jack is loaded at its nominal capability, a minimum 500 N pulling force and a minimum 950 N pushing force are required to produce overturning hazard, while traveling. 3.2. Case 2 In this case the rolling resistance R is null because the transmission jack is not moving; Eq. (8) can be applied; the pushing force has been set equal to 0 (supposing the operator immediately senses the transmission jack is overturning and therefore he stops pushing it), to 300 N (supposing the operator is intensely pushing), or to 30 N which can be assumed to be a realistic estimate of rolling resistance at nominal weight; the displacement of the point of application of the pushing force has been calculated according to Section 2.4, and assuming s = b and t = 0.5 m (the force is applied on the apposite handles which are symmetric about the jack
central axis) or s = 2b and t = 0.9 m (the force is applied on the carried mass). The maximum recommendable transmission jack translating speed has been calculated as a function of CoM height, inverting Eq. (8):
m¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2½Mg l ð1 sin hÞ F p sp
ð9Þ
It has been here assumed that the only external force is the pushing force, and sp is its traveled distance (the force is assumed to keep parallel to the ground). Results can be observed in Fig. 6: a moderate speed such as 0.5 m/s can be kept safely only if the apposite handles are used to apply the pushing force or if CoM height is sufficiently small (h < 1.5 m) or supposing the rolling resistance is kept low (well lubricated wheels, clean surfaces); even considering the last condition, a translating speed over 0.65 m/s is not recommendable, unless the center of mass height is kept lower than 1.5 m. 3.3. Case study of an actual accident Actual accident data are now input to the previously described model in order to assess its causes; operative details are reported in Table 1, the carried weight was equal to 470 kg. The first assessment has concerned the static stability; the required pushing/pulling force can be calculated from equations (1bis) and (2bis)and it results to be equal to 920 N. The second assessment has concerned stability while traveling (Fig. 5): a pushing/pulling force above 1 kN would be required to produce overturn in this condition. The third assessment has concerned stability when suddenly stopped (Fig. 6): overturning could take place at a translating speed above 0.62 m/s, or an even lower speed could be sufficient, assuming that the rolling resistance is equal to 300 N, the limit fixed by BS EN 1494 directive (BSI, 2008): in this case the maximum allowed speed would be 0.555 m/s. In the worst scenario, the pushing force reaches 300 N, and the operator does not use the apposite handles and applies the pushing force on the transported mass: this scenario would result in a maximum allowed speed equal to 0.485 m/s.
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Fig. 6. Limit translating speed towards the center of mass height. Different pushing force intensities have been considered (Fp = 300 N, black curves; Fp = 30 N, grey curves) and different force application heights (h = 0.9 m, solid lines; h = 0.5 m, dashed lines). Circular marks represent operative conditions relative to the case study.
4. Discussion and conclusions This work has been focused on the dynamic stability of transmission jacks; it has individuated two critical conditions: the transmission jack is accelerating or decelerating, while traveling; the transmission jack suddenly stops due to a wheel impingement. The first condition is thresholded by the applied pushing/pulling force, while instability due to a sudden stop is thresholded by the translating speed. Anthropometric information are needed in order to be able to discuss the obtained results; they can be found in literature concerning carts: according to a reference work by Resnick and Chaffin (1995), the peak pushing force can reach 500 N for male subjects and 200 N for female subjects; stronger operators can move a 450 kg cart at velocities of 0.8 m/s, while weaker subjects can barely reach 0.4 m/s. In those same years, Kumar (1995) pointed out how the maximal strengths depend on performing isometric or isokinetic exercises; in the second case, he asserted the maximum pulling force could reach 438 N, while the maximum pushing force was up to 553 N. A more recent work on Taiwanese males assumes both pushing and pulling forces cannot overcome 300 N (Chen et al., 2011). Considering all these results, and choosing to adopt a conservative approach, it can be assumed that the pushing/pulling forces never exceed 560 N, while the translating speed never overcomes 1 m/s. Considering this information, dynamic instability while translating is not likely to take place for geometries close to the one here considered; it becomes more critical for higher center of mass position, lower position of the point of application of the force (for example when the feet are used instead of the hands), and for lower carried weights. On the contrary, the instability due to a sudden stop can take place for the geometry here considered; it becomes more critical for higher center of mass height, higher pushing forces, or higher point of application of the force. It is the most plausible cause of the accident described in Section 3.3, and, up to now, existing directives regulate the only static stability. In the industry where the reported actual accident has taken place, its incidence rate has resulted to be equal to 1.94 per one
thousand operations, and to 0.6 over seven day injuries per year (referring to 2005–2013). More generally, the incidence of injuries due to mobile equipment overturning, can be inferred from recent work accident reports, and referring to injury cause ‘struck by a falling object’, to the activity ‘manual handling’, and to ‘maintenance’ or ‘vehicle assistance’ industrial activities; some data are reported in the following. Handling has resulted to be the most frequent cause of over seven day injury, and workers injured handling, lifting or carrying have an incidence rate of 210/100,000 workers, according to HSE, 2013a information, licensed under the Open Government Licence v1.0. Another survey reports that maintenance fitters account for 4% major handling injury and 2% total handling injury in the United Kingdom (HSE, 2013b). More generally, according to a previous report (HSE, 2012) pushing/pulling loads accounts for 17% of non-fatal total handling injuries together with ‘handling, lifting or carrying in unknown or unspecified ways’ which accounts for 19% on non-fatal injuries. As reported by USA Bureau of Labour Statistics (BLS, 2013a), workers being struck by object or equipment have represented 12% of fatal injuries in 2012. More specifically, vehicle and mobile equipment mechanics, installers, and repairers account for 2% of fatal injuries, whose cause is being struck by object or equipment in 46% cases. The same institution has analyzed 2012 non-fatal injuries (BLS, 2013b): maintenance and repair workers show a total incidence rate equal to 285.3 per 10,000 full-time workers; among these, injuries related to ‘contact with object’ have an incidence rate equal to 78.3. In order to limit the incidence of this kind of accidents, some preventive measures can be hypothesized from the outcomes of the present work: a translation speed limit could be reported in the operative manual accompanying each transmission jack: consider that 0.5 m/s is the reference speed for rolling force assessment by BS EN 1494 directive (BSI, 2008), and it can be reached both by ‘average’ and a ‘strong’ man when pushing a 450 kg weight (Resnick and Chaffin 1995), while this work has demonstrated that a slightly higher speed (0.555 m/s) is sufficient to produce trans jack overturning, even with proper handle use. The adoption of such measures would eliminate the possibility of trans-jack overturning due to a sudden stop, with a benefit of minus 0.6 over
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seven day injuries per year in the industry where the reported accident has taken place. Other operative advice are that higher points of application of the pushing/pulling force are convenient when accelerating or decelerating the transmission jack (start/stop of the movement), while a low handles position should be used while traveling at constant speed. Considering design issues, the actual handles position (0.5 m height) bears some contraindications: – it is not ergonomic: it is lower than prescribed by ISO 11228-2 (ISO, 2007); – this position forces the operator to work under the heavy weight he is carrying, increasing crushing hazard; – it induces the operator to apply his pushing force on less convenient places, typically on the transported mass: this behavior significantly reduces the dynamic stability in case of a sudden stop. Therefore a different design of pushing/pulling handles is recommended. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.ssci.2014.02.016.
References BLS, 2013a. National Census of Fatal Occupational Injuries in 2012 (Preliminary Results). BLS, USA, pp. 1–14.