Instantaneous Cutting Force Variability in Chainsaws - MDPI

Article

Instantaneous Cutting Force Variability in Chainsaws Adam Maciak 1 , Magda Kubu´ska 1 and Tadeusz Moskalik 2, * 1

2

*

Department of Agricultural and Forestry Machinery, Faculty of Production Engineering, Warsaw University of Life Sciences-SGGW, Nowoursynowska 164, 02-787 Warsaw, Poland; [email protected] (A.M.); [email protected] (M.K.) Department of Forest Utilization, Faculty of Forestry, Warsaw University of Life Sciences-SGGW, Nowoursynowska 159, 02-776 Warsaw, Poland Correspondence: [email protected]; Tel.: +48-22-5938121

Received: 12 September 2018; Accepted: 17 October 2018; Published: 22 October 2018







Abstract: Chainsaws with chipper-type chains are widely used in timber harvesting. While existing research on such saws assumes a continuous cutting process, the objectives of the present study were to determine whether or not that is true, as well as to measure instantaneous cutting forces and active cutting time (the time during which the chainsaw cutters are actually engaged with the wood sample). Tests were conducted on a special experimental stand enabling cutting force measurement with a frequency of 60 kHz. The test material was air-dry pine wood. The feed force range was 51–118 N. The chain was tensioned. The study revealed considerable variability in instantaneous cutting force, which was correlated with the rotational speed of the chainsaw engine, as indicated by frequency analysis. Furthermore, the process of cutting with chainsaws was shown to be discontinuous, and a cutter engagement time ratio was defined as the proportion of active cutting time to the overall time of chainsaw operation when making the cut. It was also found that active cutting time was directly proportionate to the applied feed force and inversely proportionate to the rotational speed of the chainsaw engine. The results may be practically applied to establish an optimum range of rotational speed that should be maintained by the operator to maximize cutting efficiency. Keywords: timber harvesting; chainsaw; wood cutting; cutting rate; cutting force

1. Introduction Despite the increasing presence of high-performance multi-function machines in forestry [1], chainsaws are still widely used in the process of timber harvesting and preliminary processing in many places around the world. This is mostly due to economic factors associated with small harvesting sites, high prices of timber harvesters and other multi-function machines, and terrain conditions preventing the access of large machines [2–5]. Unfortunately, working with chainsaws entails certain risks and hazards [5,6] and places a considerable physical strain on the operators [7–10], who are exposed to excessive noise and vibrations [11–13]. Also the sawdust produced during cutting, whose amount largely depends on the geometry of cutters (teeth), is detrimental to health [14]. In a chainsaw, individual chain links are connected by means of rivets subjected to tensile force. The fact that those links may deviate from the kerf plane during operation makes the process of chainsaw cutting different from, for example, cutting with circular saws and bandsaws. Moreover, chainsaws are typically powered by one-cylinder two-stroke gasoline engines, which are characterized by variable piston speed during the work cycle. Piston speed is accelerated by the ignition of the fuel mixture in the combustion chamber and slowed down during the compression phase, which translates into variable rotational speed of the crankshaft [15]. This in turn leads to high acceleration forces and the related inertial forces, which are often many times greater than the active cutting forces [16].

Forests 2018, 9, 660; doi:10.3390/f9100660

www.mdpi.com/journal/forests

Forests 2018, 9, 660

2 of 13

This property is a crucial difference in the operation of chainsaws as compared to those powered with electric or hydraulic motors. According to the classification proposed by Kaczmarek, cutting processes may be divided into continuous and discontinuous [17]. In discontinuous cutting, the cutters periodically engage with and disengage from the material being cut, either removing it or skipping over its surface. Researchers dealing with this problem assumed that if kerf height is greater than the chainsaw pitch then cutting is continuous and each cutter produces continuous shavings [18–21]. Obliwin et al. [22] reported that variation in cutting resistance was significantly affected by the angular speed of the engine shaft, the number of teeth on the drive sprocket, and chainsaw weight. Reynolds and Soedel [23] developed a dynamic operator-chainsaw model, which they applied to analyze the forced vibrations of chainsaws attributable to the fact that the slider-crank mechanism of the chainsaw engine is not in a state of mechanical balance. Using that model, Górski [24] found that variability in the instantaneous cutting force of electric chainsaws is attributable to changes in cutting depth caused by chainsaw vibrations. In turn, in Coermann’s model of the human operator was replaced with a spring and damper system of masses with many degrees of freedom and many free vibration frequencies [25]. Indeed, a human–machine system has a complex dynamic structure, being non-linear, stochastic, and non-stationary with parameters changing over time. Researchers agree that the free vibration frequencies of the operator–machine system depend on the physical characteristics of the operator, posture at work, fatigue, and so on. Therefore, to eliminate these highly changeable and dynamic variables, the chainsaw should be mounted on an experimental stand with known parameters [25,26]. Some researchers claim that the high variability of cutting force arises from the chainsaw cutters passing through successive annual rings [27,28]. However, Gendek [15] found that the frequency of changes in chainsaw cutting resistance corresponded to the engine work cycle. He concluded that the inertial forces resulting from the combustion cycle affected chain tension, thus changing the angle of cutters with respect to the kerf plane, which translated into varied instantaneous cutting force. An important parameter in wood cutting is the feed force applied by the operator, as it has been found to be significantly positively correlated with the cutting rate. According to Wi˛esik [27], the maximum feed force should not exceed the force that is needed to obtain shavings with the thickness permitted by the depth gauge, as greater feed forces lead to an abrupt increase in energy losses in the process of wood cutting. The objective of the presented study was do elucidate the characteristics of cutting force variability over time to determine whether chainsaws enable a continuous cutting process, or perhaps that process is discontinuous due to cutters disengaging from (losing contact with) the workpiece. 2. Materials and Methods During tests, the chainsaw was mounted on a special experimental stand shown in Figure 1. The chainsaw used in the study (7) was rigidly mounted on the experimental stand. The wood sample (8) was clamped in a vise (9), horizontally with respect to the chainsaw. Vertical movement of the wood sample was provided by weights of different sizes (13) acting on the vise via a steel rope running through the guiling rollers (10). The feed force could be changed by applying different weight sizes.

Forests 2018, 9, 660 Forests 2018, 9, x FOR PEER REVIEW

3 of 13 3 of 13

Figure 1. 1. Scheme Scheme of of experimental experimental stand stand for for measuring measuring chainsaw chainsaw cutting cutting parameters parameters (1—cutting (1—cutting force force Figure sensor, 2—feed measuring sensor, 2—feed force force sensor, sensor, 3—sensor 3—sensor measuring measuring crankshaft crankshaft rotational rotational speed, speed, 4—sensor 4—sensor measuring clutch drum rotational speed, 5—computer, 6—measurement amplifier, 7—chainsaw, 8—wood sample, clutch drum rotational speed, 5—computer, 6—measurement amplifier, 7—chainsaw, 8—wood 9—vise, 10—guide rollers, 11—slider, 12—base, 13—weight, 14—detachable sensor measuring static sample, 9—vise, 10—guide rollers, 11—slider, 12—base, 13—weight, 14—detachable sensor feed force, 15—guide bar temperature sensor). measuring static feed force, 15—guide bar temperature sensor).

Following each cut, the chainsaw was turned off to prepare the wood sample for another test. Following each cut, the chainsaw was turned off to prepare the wood sample for another test. The following parameters were measured: cutting and feed forces (using piezoelectric sensors) and the The following parameters were measured: cutting and feed forces (using piezoelectric sensors) and rotational speeds of the clutch drum and crankshaft (using induction sensors). The obtained cutting the rotational speeds of the clutch drum and crankshaft (using induction sensors). The obtained force plots also enabled the determination of actual (active) cutting time. cutting force plots also enabled the determination of actual (active) cutting time. Measurement accuracy for the parameters was as follows: Measurement accuracy for the parameters was as follows:

•• •• •• ••

rotational speed ±1rpm rpm rotational speed ±1 feed force P ± 3% (measured withaadynamometer dynamometerprior priortotocutting) cutting) feed force Ppp ± 3% (measured with cutting force force P 3% cutting Pss ±±3% 0.0001ss cutting time as read from the force plots plots ± ± 0.0001

Cutting force force was was measured measuredatat60 60kHz. kHz.Such Suchaahigh highfrequency frequencywas wasnecessary necessary enable analysis toto enable analysis of of instantaneous cutting force variability. Real view of the experimental stand is shown in Figure instantaneous cutting force variability. Real view of the experimental stand is shown in Figure 2. 2. Data from the sensors were sent to an Esam Traveller Plus measurement bridge. The data were recorded on a computer disc, processed, and analyzed using ESAM 3 software (ESA Messtechnik GmbH, toto each experiment, thethe feedfeed force waswas adjusted using weights. Ten GmbH, Olching, Olching,Germany). Germany).Prior Prior each experiment, force adjusted using weights. test werewere carried out,out, each consisting of of 1818measurements, Ten series test series carried each consisting measurements,with withthe thefeed feed force force gradually increased within total of of 180180 measurement trials were made, which was was shown to beto a withineach eachseries. series.AA total measurement trials were made, which shown sufficient number by analysis of preliminary results. TheThe feed force be a sufficient number by analysis of preliminary results. feed forcerange rangewas wasadopted adopted on on an experimental experimental basis. basis. Prior Prior to to measurements measurements proper, proper, itit was was determined determined below below what what feed feed force the chainsaw lower threshold. threshold. Also the chainsaw could could no longer cut wood (51 N), which was then used as the lower upper threshold thresholdwas wasestablished established experimentally as force the force the chainsaw engine experimentally as the aboveabove whichwhich the chainsaw engine choked choked N).toPrior each test series, the measurement entire measurement was calibrated, and prior to (118 N).(118 Prior each to test series, the entire setup setup was calibrated, and prior to each each measurement it was reset. If the cross-section of a wood sample revealed a knot, the measurement it was reset. If the cross-section of a wood sample revealed a knot, the measurement was measurement was repeated on a of knot-free segment of the sample. repeated on a knot-free segment the sample. In order order to toensure ensuresufficient sufficientaccuracy, accuracy, measurement system turned on an half an prior hour thethe measurement system waswas turned on half hour prior the beginning of measurements (in accordance with the manufacturer’s instruction to to theto beginning of measurements (in accordance with the manufacturer’s instruction [29]) to[29]) warm warm the electronic elements and stabilize their parameters. up theup electronic elements and stabilize their parameters. Five identical identical brand-new brand-newchainsaws chainsawswere were used during study. They sharpened used during thethe study. They werewere sharpened after after each each measurement The saws were alternately used alternately to prevent a situation in which the cutters measurement series.series. The saws were used to prevent a situation in which the cutters (teeth) (teeth) veryout worn outend at the endstudy of theasstudy as aofresult of excessive sharpening. would would be verybe worn at the of the a result excessive sharpening.

Forests 2018, 9, 660

4 of 13

Forests 2018, 9, x FOR PEER REVIEW

4 of 13

Figure 2. 2. Real Real view view of of experimental experimental stand stand for for measuring measuring chainsaw chainsaw cutting cutting parameters parameters ((a)—general ((a)—general Figure view, cutting cutting force force sensor, sensor, (b)—sensor (b)—sensor measuring measuring crankshaft crankshaft and and clutch clutch drum drum rotational rotational speed, speed, view, (c)—feed force forcesensor, sensor,1—base, 1—base,2—chainsaw, 2—chainsaw,3—wood 3—woodsample, sample,4—weight). 4—weight). (c)—feed

Throughout monitored by by measuring thethe tip radius of the Throughout the theexperiments, experiments,cutter cuttersharpness sharpnesswas was monitored measuring tip radius of cutting edge ρ, with the mean values ranging from 8 to 12 µm. This means that the chainsaw was the cutting edge ρ, with the mean values ranging from 8 to 12 μm. This means that the chainsaw was sharp sharp during during the the tests. tests. The The sharpness sharpness measurement measurement setup setup consisted consisted of of aa Nikon Nikon Alphaphot-2 Alphaphot-2 microscope microscope (PZO (PZO Polish Polish Optical Optical Factories, Factories, Warsaw, Warsaw,Poland) Poland)equipped equippedwith withan anOH OH11 halogen halogen illuminator illuminator (PZO (PZO Polish Polish Optical Optical Factories, Factories, Warsaw, Warsaw, Poland) Poland) for for reflected reflected light light observations observations and and with with aa digital digitalcamera. camera. The The cutters cutters were a lead plate, which was then on the on microscope table. Images acquired wereimprinted imprintedinin a lead plate, which was placed then placed the microscope table.were Images were under 400under × magnification. Finally, theFinally, recorded wereimages analyzed using MultiScan Base v. 18.03 acquired 400× magnification. theimages recorded were analyzed using MultiScan software (Computer Scanning Systems Ltd, Warsaw, o calculate theotip radius. the tip radius. Base v. 18.03 software (Computer Scanning Systems Poland) Ltd, Warsaw, Poland) calculate The content of ofwood woodsamples sampleswas wasmeasured measured weight loss drying. initial The moisture content byby weight loss on on drying. TheThe initial and and weight determined using a RadwagWPS210S WPS210Slaboratory laboratorybalance balance (Factory (Factory of precision finalfinal weight waswas determined using a Radwag precision mechanics mechanics Radwag, Radwag, Radom, Poland) with an an accuracy accuracy of of 0.001 0.001 g. g. The samples were dried in aa Heraeus laboratory ovenoven (Kendro Laboratory Products, Hanau, Germany) with air circulation. HeraeusUT UT6120 6120 laboratory (Kendro Laboratory Products, Hanau, Germany) with air Hardness was measured bymeasured the Brinell using a [30], universal circulation. Hardness was byprocedure the Brinell[30], procedure usingtester. a universal tester. The The chainsaw chainsaw used used in experiments was a Husqvarna 357 XP (Husqvarna, Huskvarna, Sweden). 3, power—3.2 According its its cylinder displacement is 56.3 cm3 , cm power—3.2 kW, Accordingtotothe themanufacturer’s manufacturer’sspecifications, specifications, cylinder displacement is 56.3 and kg without a bar aorbar chain and with tanks.tanks. The chainsaw was equipped with kW,weight—5.5 and weight—5.5 kg without or chain and empty with empty The chainsaw was equipped a 15long inchguide long guide baranand an Oregon 70 (Blount Inc, Portland, OR, full-chisel USA) full-chisel awith 15 inch bar and Oregon Super Super 70 (Blount Inc, Portland, OR, USA) chain chaina with a 3/8pitch, inch pitch, 1.5gauge, mm gauge, and depth of 0.5The mm.chain The consisted chain consisted of 56 with 3/8 inch 1.5 mm and depth gaugesgauges of 0.5 mm. of 56 drive driveand links 28 (teeth); cutters it(teeth); it had of a weight of 0.28 kg and a length 1066.8 mm. The links 28 and cutters had a weight 0.28 kg and a length of 1066.8 mm.ofThe tensioning of tensioning of monitored the chain was monitored during study in the A following way:was A 20 N weight was the chain was during the study in thethe following way: 20 N weight hanged halfway hanged halfway underside the bar with sag of samples 5 mm. The wood samples underside the guide bar with theguide expected chainthe sagexpected of 5 mm.chain The wood consisted of Scots consisted Scots pine wood moisture with an absolute content 9.7–12.9% and pine (Pinusofsylvestris L.)(Pinus woodsylvestris with an L.) absolute content moisture of 9.7–12.9% and of with a hardness with a hardness of 31.5–36.8 MPa as determined by the Brinell hardness test for the face of the workpiece. The pine wood was obtained from the Chojnów Forest District, from trees felled in winter time. Sample density ranged from 0.48 to 0.51 g/cm3, with 4 to 8 annual rings/cm.

Forests 2018, 9, 660

5 of 13

of 31.5–36.8 MPa as determined by the Brinell hardness test for the face of the workpiece. The pine wood was the Chojnów Forest District, from trees felled in winter time. Sample5density Forests 2018, 9, x obtained FOR PEER from REVIEW of 13 ranged from 0.48 to 0.51 g/cm3 , with 4 to 8 annual rings/cm. The overarchingconcern concernwas wastotouse use homogeneous homogeneous wood took a long The overarching wood samples. samples.The Themeasurements measurements took a time and it would have been very difficult to maintain very moist wood at the same moisture content long time and it would have been very difficult to maintain very moist wood at the same moisture over that wood would also have at been a higher of depreciation. On the other hand, content overtime. that Moist time. Moist wood would alsobeen have at arisk higher risk of depreciation. On the a relatively homogenous moisture content of air-dry wood samples was maintained by storing other hand, a relatively homogenous moisture content of air-dry wood samples was maintained them by in a heated room. Moreover, to the literature the effect of moisture content on cutting storing them in a heated room.according Moreover, according to [31], the literature [31], the effect of moisture resistance is not resistance very large.isInnot thevery caselarge. of cutting wood, the resistance is by 12%islower content on cutting In thedry case of cutting dry wood, theapprox. resistance by than that for freshly felled logs. Moisture content and hardness were determined to ensure that approx. 12% lower than that for freshly felled logs. Moisture content and hardness were determinedthe the study were to wood ensuresamples that theused woodinsamples used in homogeneous. the study were homogeneous. The wood samples a rectangular cross-section a width (B)24ofcm 24and cm aand cut height The wood samples hadhad a rectangular cross-section withwith a width (B) of cutaheight of of 14 cm. The cuts were made across the wood fibers, as is typical of logging. At the adopted kerf 14 cm. The cuts were made across the wood fibers, as is typical of logging. At the adopted kerf height, four cutterssimultaneously simultaneouslyengaged engagedwith with the the wood sample, thethe kerf. height, four cutters sample,removing removingmaterial materialfrom from A preliminary study was conducted to obtain a better understanding of the nature of the cutting kerf. A preliminary study was conducted to obtain a better understanding of the nature of the process and to design the main experimental part of theof investigation. cutting process and to design the main experimental part the investigation. seen, the outsetcutting cuttingresistance resistanceincreases, increases,while whilerotational rotational speed speed decreases decreases due to AsAs cancan bebe seen, at at the outset the higher loading on the chainsaw engine (Figure 3). to

Figure 3. Diagram showing cutting force variability (1) as well as the rotational speed of the engine (2) Figure 3. Diagram cutting variability (1) as well as the rotational speed of the engine and clutch drumshowing (3) during woodforce cutting. (2) and clutch drum (3) during wood cutting.

Figure 4 shows a fragment of the cutting force plot with a duration of 0.036 s. It reveals a Figure 4 shows a fragment thenumerous cutting force with duration of 0.036 reveals discontinuous cutting process of as at timeplot points thea cutting force dropss.toItzero (thena of discontinuous cutting process as at numerous time points the cutting force drops to zero (then of course no cutting occurs). Those time points are followed by an abrupt increase in cutting force, which course cutting Thosea certain time points followed by an abrupt increase in cutting force, then no again dropsoccurs). to zero after activeare interval. which then again drops to zero aftercutting a certain active interval. Variability in instantaneous resistance is very high; for instance, the duration of the tei Variability in instantaneous cutting resistance is very for to instance, the duration of the interval, from the moment when cutting force begins to high; increase the moment it goes back to zero, interval, from the moment when cutting force begins to during increasewhich to thethe moment goes back to zero, amounts to 0.0025 s, which corresponds to the period cuttersitactually remove some amounts tofrom 0.0025 which corresponds to the period during which some material thes,kerf. Over 0.0013 s, the cutting force surges from the zerocutters to 516 actually N, whichremove signifies actual material from the kerf.Subsequently, Over 0.0013 s, cutting force surges from zero to 516 N, which cutter engagement. thethe cutters disengage causing idle chain movement andsignifies a 0.0024 s actual cutter engagement. Subsequently, cutters disengage causing idle chain movement and break in the cutting process. In the casethe in question, the cutter engagement interval is similar toathe 0.0024 s break in the cutting process. In the case in question, the cutter engagement interval is similar idle interval. to the idle interval. During zero cutting force intervals, no cutter engages with the wood. Thus, it appears that zero cutting intervals, cutter engages with the wood. it appears that all allDuring chain cutters whichforce are at a given no time inside the kerf engage with Thus, the wood simultaneously, chain cutters which are at a given time inside the kerf engage with the wood simultaneously, and and disengage after reaching a certain shaving (chip) thickness h1 in a cyclic process (Figure 4). disengage after reaching a certain shaving (chip) thickness h1 in a cyclic process (Figure 4). The drop in cutting force to less than zero that can be seen in Figure 4 is attributable to the construction of the experimental stand and the force sensors used. As a result of chainsaw vibration in the longitudinal axis, the sensors detected transient pressure applied in the opposite direction. This gives rise to an impression as if the cutting force dropped slightly below zero. This phenomenon is the most pronounced following an abrupt (lasting several ten thousandths of a

Forests 2018, 9, 660

6 of 13

The drop in cutting force to less than zero that can be seen in Figure 4 is attributable to the construction of the experimental stand and the force sensors used. As a result of chainsaw vibration in the longitudinal axis, the sensors detected transient pressure applied in the opposite direction. This gives to PEER an impression Forests 2018, 9,rise x FOR REVIEW as if the cutting force dropped slightly below zero. This phenomenon 6 of 13 is the most pronounced following an abrupt (lasting several ten thousandths of a second) decline in second) decline in cutting force from orderObviously, of 500 N toin zero. Obviously, in reality the cutting force cutting force from an order of 500 N an to zero. reality the cutting force cannot go below cannot below zero, as this imply thatbackwards. the saw moved backwards. zero, asgo this would imply thatwould the saw moved

Figure 4. 4. Cutting Cutting force force plot plot with with aa duration duration of —individual cutter cutter engagement engagement time. time. Figure of 0.036 0.036 s: s: ttii—individual

As it it has has been been mentioned, mentioned, in in the the present present study study it it was was assumed assumed that that when when cutting cutting force force dropped dropped As to zero, no cutting tooth was engaged with the wood sample. The length of time intervals during to zero, no cutting tooth was engaged with the wood sample. The length of time intervals during which the the cutting cutting force force was was greater greater than than zero zero was was read read from from the which the feed feed force force plot plot and and these these intervals intervals were summed up for each measurement trial. were summed up for each measurement trial. Given the the above, above, the the cutter cutter engagement engagement time time ratio ratio ττ can can be be defined defined as as the the sum sum of of all all intervals Given intervals during which the cutters are engaged with the workpiece to the overall time of chainsaw during which the cutters are engaged with the workpiece to the overall time of chainsaw operation operation while making making aa cut, while cut, as as expressed expressed by by the the following following equation: equation: nc 1 τ = 1 ∗∗ ∑ tei T0 i=1

(1) (1)

where: where:

—cutter engagement τ—cutter engagement time time ratio; ratio; —timeover overwhich which chainsaw cutters (teeth) remove material the workpiece an chainsaw cutters (teeth) remove material from thefrom workpiece during an during individual te —time individual cutter engagement interval [s]; cutter engagement interval [s]; [s]; T0—overall —overall time time during during which which aa given given kerf kerf (cut) (cut) area area is is made made [s]; engagement intervals intervals over over time time T .. nc —number —number of of cutter cutter engagement 0 The cutter engagement time ratio may be given as a dimensionless value or a percentage of the The cutter engagement time ratio maywhich be given a dimensionless valueactually or a percentage the overall time of chainsaw operation during the as chainsaw cutters (teeth) engagedofwith overall time of chainsaw operation during which the chainsaw cutters (teeth) actually engaged with the wood. Subsequently, regression analysis was used to determine changes in the cutter the wood. Subsequently, regression analysisofwas to determine in the cutter engagement time ratio, that is, the effects the used applied feed forcechanges on the actual cuttingengagement time. Also time ratio, that is, the effects of the applied feed force on the actual cutting time. Also the average the average individual cutter engagement interval was calculated from the equation: individual cutter engagement interval t av was calculated from the equation: ∑ (2) n ∑i=c 1 tei t av = (2) nc Statistical analysis consisted of regression analysis. The parameters of the regression function were calculated using the least squares method. The fit of the model was evaluated by analyzing the obtained determination and correlation coefficients. Statistical analysis was done using Statistica 12 software (StatSoft Poland, Cracow, Poland), which was also employed to compute the means and standard deviations of the measured parameters. To determine whether cutting force variability was affected by factors other than the rotational

Forests 2018, 9, 660

7 of 13

Statistical analysis consisted of regression analysis. The parameters of the regression function were calculated using the least squares method. The fit of the model was evaluated by analyzing the obtained determination and correlation coefficients. Statistical analysis was done using Statistica 12 software (StatSoft Poland, Cracow, Poland), which was also employed to compute the means and standard deviations of the measured parameters. To determine whether cutting force variability was affected by factors other than the rotational speed of the chainsaw engine (e.g., the number of sprocket teeth), a frequency analysis of the cutting Forests 2018, 9, x FOR PEER REVIEW 7 of 13 force signal was performed using the discrete Fourier transform.

3. Results 3. Results Table 1 presents the mean values and standard deviations of force impulse duration, distance Table 1 presents the mean values and standard deviations of force impulse duration, distance traveled during a single pulse, and the cutter engagement time ratio calculated for the entire range traveled during a single pulse, and the cutter engagement time ratio calculated for the entire range of of feed force. feed force. Table of the the measured measured parameters. parameters. Table 1. 1. Mean Mean values values and and standard standard deviations deviations of

Parameter Parameter Force impulse duration [s] Force impulse duration [s] DistanceDistance [m] [m] Cutter engagement time ratio Cutter engagement time[%] ratio [%]

Mean Mean

SD

0.0042 0.0042 0.081 0.081 63.43 63.43

0.0018 0.036 15.42

SD 0.0018 0.036 15.42

Figure 5 presents a cutting force plot for a relatively low feed force (51 N) and a high rotational Figure 5 presents a cutting force plot for a relatively low feed force (51 N) and a high rotational speed of the engine (12,240–12,320 rpm). The cutter engagement time ratio τ is 0.29 and the average speed of the engine (12,240–12,320 rpm). The cutter engagement time ratio τ is 0.29 and the average individual cutter engagement time is 0.0027 s. In turn, Figure 6 shows a plot for a higher feed force individual cutter engagement time is 0.0027 s. In turn, Figure 6 shows a plot for a higher feed force (81 N). In this case, the rotational speed of the engine is 9620 rpm. The lower engine speed leads to (81 N). In this case, the rotational speed of the engine is 9620 rpm. The lower engine speed leads to an an increased cutter engagement time ratio (0.47). Also the average individual cutter engagement increased cutter engagement time ratio (0.47). Also the average individual cutter engagement time time rose to 0.0031 s. rose to 0.0031 s.

Figure 5. 5. Cutting Cutting force force variability variability at at aa feed feed force force of of 51 51 N. N. Figure

Forests 2018, 9, 660

Figure 5. Cutting force variability at a feed force of 51 N.

8 of 13

Figure 6. 6. Cutting Cuttingforce force variability variability at at aa feed feed force force of of 81 81 N. N. Figure

Figure displays a cutting force plot at a feed force of 89 N and an engine rotational speed of ForestsFigure 2018, 9, 7a x7a FOR PEER REVIEW 8 ofof 13 displays a cutting force plot at a feed force of 89 N and an engine rotational speed

8520 rpm. The cutter engagement time ratio and the average individual engagement interval rose to 8520 rpm. The cutter engagement time ratio and the average individual engagement interval rose to 7b7b presents an an example of frequency analysis for this 0.63 and and 0.0036 0.0036s,s,respectively. respectively.Figure Figure presents example of frequency analysis forfeed this force. feed The strongest signal signal corresponds to the frequency of the engine speed. The same is same true for force. The strongest corresponds to the frequency of the rotational engine rotational speed. The is all the examined cases. true for all the examined cases.

(a)

(b)

Cutting force force variability at a feed feed force force of 89 89 N N (a) (a) and and the the frequency frequency structure structure of the cutting Figure 7. Cutting force signal (b): 1—frequency corresponding to the rotational speed of the engine.

Finally, Figure force of Finally, Figure 88 shows shows aa cutting cutting force force plot plot for for a a feed feed force of 118 118 N. N. In In this this case, case, the the rotational rotational speed of the engine is only 6240–6320 rpm and the idle intervals are very short as compared to the the speed of the engine is only 6240–6320 rpm and the idle intervals are very short as compared to active cutting cutting time time (0.0788 (0.0788 s). The resulting resulting cutter cutter engagement engagement time time ratio ratio is is 0.79 0.79 with with an an average active s). The average individual engagement time of 0.0061 s. individual engagement time of 0.0061 s.

force signal (b): 1—frequency corresponding to the rotational speed of the engine.

Finally, Figure 8 shows a cutting force plot for a feed force of 118 N. In this case, the rotational speed of the engine is only 6240–6320 rpm and the idle intervals are very short as compared to the active cutting Forests 2018, 9, 660time (0.0788 s). The resulting cutter engagement time ratio is 0.79 with an average 9 of 13 individual engagement time of 0.0061 s.

Figure 8. Cutting force variability at a feed force of 118 N. Figure 8. Cutting force variability at a feed force of 118 N.

Frequency analysis revealed that irrespective of the feed force, the strongest signal corresponded Frequency revealed of speed). the feedOnforce, the hand, strongest signal to the frequencyanalysis of the engine workthat cycleirrespective (its rotational the other the signals corresponded thedrive engine work cycle (its rotational Onthe the other the correspondingto tothe thefrequency meshing ofofthe links with the drive sprocket speed). and with bar nosehand, sprocket signals corresponding to the meshing of the drive links with the drive sprocket and with the bar as well as those arising from the effects of annual rings were negligible. nose When sprocket well as those arising from of said annual were theas cutting force value drops to 0the N, effects it can be thatrings during thisnegligible. time, no cutter is cutting When the basis, cutting force valuetodrops to 0 that N, itallcan be said that during this time, the no cutter is wood. On this it is possible conclude cutters in the kerf are penetrating wood at cutting wood. On this basis, it is possible to conclude that all cutters in the kerf are penetrating the the same time, after a certain chip thickness—hmax (Figure 9)—has been attained, they move up; it is a Forests at 2018, x FOR time, PEER REVIEW 9 of 13 wood the9,same after a certain chip thickness—hmax (Figure 9)—has been attained, they move cyclical process. up; it is a cyclical process.

Figure course of the of wood with a saw chain: hmax —maximum chip thickness, Figure9.9.The The course of process the process of cutting wood cutting with a saw chain: hmax—maximum chip l1thickness, —distancel1—distance covered by covered cutter inside the wood, l —distance covered by cutter outside the by cutter inside 2the wood, l2—distance covered by cutter wood. outside the

wood.

Figure 10 shows the relationship between the cutter engagement time ratio and the rotational speed of the chainsaw engine. Figure 10 shows the relationship between the cutter engagement time ratio and the rotational speed of the chainsaw engine.

Figure 9. The course of the process of wood cutting with a saw chain: hmax—maximum chip thickness, l1—distance covered by cutter inside the wood, l2—distance covered by cutter outside the wood.

10 shows ForestsFigure 2018, 9, 660

the relationship between the cutter engagement time ratio and the rotational 10 of 13 speed of the chainsaw engine.

Figure 10. Relationship Relationship between between the the cutter cutter engagement engagement time time ratio ratio and and the rotational speed of the chainsaw engine.

An increase rotational speed of the and the related increaseincrease in chain speed adversely increaseininthethe rotational speed of engine the engine and the related in chain speed affected the cutter engagement time ratio, which in the presented experiments ranged from 6% to 92%. adversely affected the cutter engagement time ratio, which in the presented experiments ranged This thatThis in the worst case the cutters activelythe removed the kerf only fromindicates 6% to 92%. indicates that scenario in the worst case scenario cutters material actively from removed material for 6%the of kerf the overall time. from only forsawing 6% of the overall sawing time. The relationship between the cutter engagement time ratio τ and the rotational speed of the engine n can canbe bedescribed describedby bythe thefollowing followingequation: equation:

0.0087∗∗n [% [%] (3) τ = 141.0395 141.0395 − 0.0087 (3) ] The high regression coefficient, amounting to 0.82, indicates a significant correlation between Theparameters. high regression coefficient, amounting to 0.82, indicates a significant correlation between the the two two parameters. Statistical analysis revealed that the higher the rotational speed of the engine, the shorter the Statistical revealed that thethe higher speed of duration the engine, the shorter the average cuttinganalysis force impulse time and lowerthe therotational variability in the of force impulses, average cutting force impulse time and the lower the variability in the duration of force impulses, which is reflected in the decrease of standard deviation with rotational speed. Figure 11 shows the which is reflected the decrease standard deviation with rotationaldeviation speed. Figure 11 shows the relationship of thein average cuttingofforce impulse time and its standard with the rotational relationship of the average cutting force impulse time and its standard deviation with the rotational speed of the engine. At a low rotational speed of 5000 rpm the average individual cutter engagement speed of the engine. At at a low rotational speed of 5000 rpm s. the average individual cutter engagement time was 0.006 s, while 10,000 rpm it decreased to 0.003 time was 0.006 s, while at 10,000 rpm it decreased to 0.003 s. The rotational speed of the chainsaw engine decreased at it produced increasingly higher cutting force, which rose with feed force. In other words, in can be concluded that lower engine speeds are caused by higher feed forces applied by the operator. Statistical analysis showed that the cutter engagement time ratio τ increased linearly with feed force Pp , in a statistically significant manner. For the studied chainsaw the relationship between the two parameters can expressed by the following equation: τ = 0.0068 ∗ Pp − 0.0838

(4)

Again, the high determination coefficient value (0.84) confirms that the correlation between the two variables is significant.

Forests 2018, 9, 660

11 of 13

Forests 2018, 9, x FOR PEER REVIEW

10 of 13

11. Relationship of the average cutter engagement time and its standard deviation with the the Figure 11. rotational speed speed of of the the chainsaw chainsaw engine. engine. rotational

4. Discussion The rotational speed of the chainsaw engine decreased at it produced increasingly higher cutting force, which rose with on feed force. Incutting other assumed words, inthat canthebecutting concluded that lower engine Most of the existing studies chainsaw process was continuous, speeds caused byexperiments higher feed forces applied by the operator. but theare presented have not shown that to be true. Indeed, the current results Statistical analysis showed that the cutter engagement time ratio τ increased linearly with feed indicate that the process is discontinuous. Researchers investigating the efficiency of chainsaw force , in[12,19,21,27], a statisticallywho significant manner. the studied chainsaw thefeed relationship betweenthat the operations reported that theFor cutting rate increased with force, attributed two parameters can expressed by the following equation: finding to greater thickness of the shavings (chips) produced. However, the present study indicates that this may also be partially explained by the fact increasing feed force leads to a longer active 0.0068 ∗ that0.0838 (4) cutting time. Again, the high determination coefficient value speed (0.84) confirms that theengine correlation the The present results show that a higher rotational of the chainsaw ω (andbetween the related two variables is significant. higher saw chain speed) adversely affects cutting continuity expressed as the cutter engagement time ratio τ. On the other hand, the study does not corroborate reports that the number of teeth on the 4. Discussion drive sprocket or annual ring characteristics affect cutting discontinuity [17]. It has been found that discontinuity with studies the rotational speed of cutting the chainsaw engine. Most of increases the existing on chainsaw assumed that the cutting process was This phenomenon may be caused by thehave increasing variability in be thetrue. instantaneous rotational continuous, but the presented experiments not shown that to Indeed, the current speed of chainsaw engines with increasing average rotational speed as reported by Gendek results indicate that the process is discontinuous. Researchers investigating the efficiency[15], of who defined this factor[12,19,21,27], in terms of differences in the that maximum and minimum rotational speed chainsaw operations who reported the cutting rate increased with feedrelative force, to the average According and Wajand [32], increasing variability engine attributed thatrotational finding tospeed. greater thicknesstoofWajand the shavings (chips) produced. However, theinpresent instantaneous rotational speed adversely affects the durability of mechanical elements and causes study indicates that this may also be partially explained by the fact that increasing feed force leads to vibrations during operation. a longer active cutting time. In his study of electric chainsaws, Górski [24] found that the assumption aboutThe cutting continuity true only heights, up to 40ofmm greaterengine kerf heights giving present resultsis show thatfor a small higherkerf rotational speed thewith chainsaw ω (and the rise to dynamic phenomena hindering the cutting process. Górski concluded that cutting discontinuity related higher saw chain speed) adversely affects cutting continuity expressed as the cutter is attributabletime to the self-oscillation of hand, the chainsaw caused by the unfavorable arrangement of the engagement ratio τ. On the other the study does not corroborate reports that the number main rigidity axes in the mass-elastic-dampening system formed by an operator holding a chainsaw. of teeth on the drive sprocket or annual ring characteristics affect cutting discontinuity [17]. It has The this oscillation remainswith within range of the free vibrations ofengine. the human upper beenfrequency found thatofdiscontinuity increases the the rotational speed of the chainsaw limbs. Thus, a study of cutting which a chainsaw would held by a humanrotational operator This phenomenon may becontinuity caused byin the increasing variability inbe the instantaneous could produce divergent results depending on the operator, his posture, and fatigue. speed of chainsaw engines with increasing average rotational speed as reported by Gendek [15], has beenthis reported operators typically exert a feed force of 110–160 N duringrotational normal work to who Itdefined factor that in terms of differences in the maximum and minimum speed ensure optimum cutting efficiency [33]. In the experiments described in the study this corresponds to relative to the average rotational speed. According to Wajand and Wajand [32], increasing variability the upper instantaneous range of the applied feedspeed force, adversely which wasaffects characterized by the of lowest cutting elements discontinuity. in engine rotational the durability mechanical and Indeed, low discontinuity may be oneInofhis thestudy reasons cutting performance maximized at high causes vibrations during operation. of why electric chainsaws, Górskiis [24] found that the feed force values. Obviously, under such circumstances another factor contributing to cutting efficiency assumption about cutting continuity is true only for small kerf heights, up to 40 mm with greater is theheights fact of giving removing woodphenomena shavings [31]. kerf risethicker to dynamic hindering the cutting process. Górski concluded that

cutting discontinuity is attributable to the self-oscillation of the chainsaw caused by the unfavorable arrangement of the main rigidity axes in the mass-elastic-dampening system formed by an operator

Forests 2018, 9, 660

12 of 13

The presented tests were carried out on an experimental stand in which the chainsaw was immobilized. Therefore, the obtained results cannot be directly extrapolated to real-life conditions as the vibration characteristics of the experimental setup differ from those of the chainsaw-operator system. It should be remembered, that the described measurements could not be reliably performed and compared for the chainsaw-operator system, which has a very complex dynamic structure and is non-linear, stochastic, and non-stationary, with parameters changing over time. Indeed, there is a consensus among researchers [25,26], that the frequency of free vibrations of the chainsaw-operator system depends on the individual physical characteristics of the operator, work posture, fatigue, and so on. (which means that it will vary over time even for an individual operator). 5. Conclusions In all wood cutting tests with a chainsaw the cutting process was discontinuous. The ratio of active cutting time to overall chainsaw operation time ranged from 6% to 92% and increased with feed force, which in turn decreased the rotational speed of the chainsaw engine. The positive correlation between feed force and the cutting rate (efficiency) observed by other researchers may be explained by the fact that an increase in feed force decreases cutting discontinuity and increases active cutting time (during which the cutters actually engage with the wood). Conversely, the lower the feed force the higher the idle time, when the cutters are disengaged from the material. This is a new finding as previous research indicated that the only way in which higher feed force values improve the cutting rate is by increasing the thickness of the wood shavings being removed. Author Contributions: Concept and research idea, A.M. and T.M.; Bibliography, A.M., M.K., and T.M.; Methodology, A.M. and M.K.; Measurements at the cutting stand, A.M. and M.K.; Compilation of data, preparation of results, and statistical elaboration, A.M., M.K. and T.M.; Writing—original draft preparation, review and editing A.M. and T.M. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest

References 1. 2. 3.

4.

5.

6. 7. 8. 9.

Moskalik, T.; Borz, S.A.; Dvoˇrák, J.; Ferencik, M.; Glushkov, S.; Muiste, P.; Lazdin, š, A.; Styranivsky, O. Timber Harvesting Methods in Eastern European Countries: A Review. Croat. J. For. Eng. 2017, 38, 231–241. Spinelli, R.; Magagnotti, N.; Nati, C. Options for the mechanized processing of hardwood trees forests. Int. J. For. Eng. 2009, 20, 39–44. [CrossRef] Montorselli, N.B.; Lombardin, C.; Magagnotti, N.; Marchi, E.; Neri, F.; Picchi, G.; Spinelli, R. Relating safety, productivity and company type for motor-manual logging operations in the Italian Alps. Accid. Anal. Prev. 2010, 42, 2013–2017. [CrossRef] [PubMed] Vusi´c, D.; Šušnjar, M.; Marchi, E.; Spina, R.; Zeˇci´c, Ž.; Picchio, R. Skidding operations in thinning and shelterwood cut of mixed stands—Work productivity, energy inputs and emissions. Ecol. Eng. 2013, 61, 216–223. [CrossRef] Karjalainen, T.; Zimmer, B.; Berg, S.; Welling, J.; Schwaiger, H.; Finér, L.; Cortijo, P. Energy, Carbon and other Material Flows in the Life Cycle Assessment in Forestry and Forest Products; European Forest Institute: Joensuu, Finland, 2001; p. 68, ISBN 952-9844-92-1. Lindroos, O.; Burström, L. Accident rates and types among self-employed private forest owners. Accid. Anal. Prev. 2010, 42, 1729–1735. [CrossRef] [PubMed] Poje, A.; Potoˇcnik, I.; Košir, B.; Krˇc, J. Cutting patterns as a predictor of the odds of accident among professional fellers. Saf. Sci. 2016, 89, 158–166. [CrossRef] Melemez, K.; Tunay, M. Determining physical workload of chainsaw operators working in forest harvesting. Technology 2010, 13, 237–243. Parker, R.J.; Bentley, T.A.; Ashby, L.J. Human factors testing in forest industry. In Handbook of Human Factors Testing and Evaluation, 2nd ed.; Charlton, S.G., O’Brien, T.G., Eds.; Lawrence Erlbaum Associates: Mahwah, NJ, USA, 2008; pp. 319–340, ISBN 0-8058-3290-4.

Forests 2018, 9, 660

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

13 of 13

Eroglu, H.; Yilmaz, R.; Kayacan, Y. A Study on Determining the Physical Workload of the Forest Harvesting and Nursery-Afforestation Workers. Anthropologist 2015, 21, 168–181. [CrossRef] Minetti, L.J.; de Souza, A.P.; Machado, C.C.; Fiedler, N.C.; Baêta, F.d.C. Evaluation of noise and vibration effects of forest cutting on chainsaw operators. Rev. Árvore 1998, 22, 325–330. Fonseca, A.; Aghazadeh, F.; de Hoop, C.; Ikuma, L.; Al-Qaisi, S. Effect of noise emitted by forestry equipment on workers’ hearing capacity. Int. J. Ind. Ergon. 2015, 46, 105–112. [CrossRef] Rottensteiner, C.; Tsioras, P.; Stampfer, K. Wood density impact on hand-arm vibration. Croat. J. For. Eng. 2012, 33, 303–331. Marenˇce, J.; Miheliˇc, M.; Poje, A. Influence of Chain Filing, Tree Species and Chain Type on Cross Cutting Efficiency and Health Risk. Forests 2017, 8, 464. [CrossRef] Gendek, A. The Influence of Clutch Parameters on the Wood Cutting Efficiency with a Chainsaw. Ph.D Thesis, Warsaw University of Life Sciences-SGGW, Warsaw, Poland, July 2005. (In Polish) Wi˛esik, J. The load of clutch of portable chain saw driven by internal combustion engine. Przeg. Tech. Roln. Lesn. 2007, 2, 16–19. (In Polish) Kaczmarek, J. The Basics of Turning, Abrasive, and Erosive Machining; WNT: Warsaw, Poland, 1971; p. 848, ISBN 83-7365-029-6. (In Polish) Kuvik, T.; Krilek, J.; Kováˇc, J.; Štefánek, M.; Dvoˇrák, J. Impact of the selected factors on the cutting force when using a chainsaw. Wood Res. 2017, 62, 807–814. Otto, A.; Parmigiani, J. Saw chain cutting. BioResources 2015, 10, 7273–7291. Douda, V. Mechanizaˇcníprostˇredkylesnické a Jejichpoužití; Státní zemˇedˇelské nakladatelství: Prague, Czechoslovakia, 1974; p. 596, ISBN I-04037/74. Maciak, A. Influence of Construction Parameters of Chain Saw Cutters on Wood Cutting Efficiency. Ph.D. Thesis, Warsaw University of Life Sciences-SGGW, Warsaw, Poland, November 2001. (In Polish) Obliwin, W.N.; Sokolow, A.M.; Liejtas, M. Ergonomics in the Forest Supply Industry; Izdatielstwo Liesnaja Promyszliennost: Moscow, Russia, 1988; p. 224, ISBN 5-7120-0019-9. (In Russian) Reynolds, D.D.; Soedel, W. Analytical vibration analysis of non–isolated Chain saws. J. Sound Vib. 1976, 44, 513–523. [CrossRef] Górski, J. Wood Cutting by Means of Electric Chain Saw; Wydawnictwo SGGW: Warsaw, Poland, 2001; p. 114, ISBN 83-7244-205-3. (In Polish) Engel, Z. Protection of the Environment against Vibrations and Noise, 2nd ed; Wydawnictwa Naukowe PWN: Warsaw, Poland, 2001; p. 490, ISBN 83-01-13537-9. (In Polish) ˙ Cie´slikowski, B. Vibration Processes in the Diagnostics of Agricultural Machinery; Polskie Towarzystwo Inzynierii Rolniczej: Kraków, Poland, 2007; p. 150, ISBN 83-917053-5-8. (In Polish) Wi˛esik, J. Energy of cutting of wood with a chainsaw. Roczniki Nauk Rolniczych 1990, 79, 144–156. (In Polish) Wyeth, D.J.; Goli, G.; Atkins, A.G. Fracture toughness, chip types and the mechanics of cutting wood. A review. Holzforschung 2009, 63, 168–180. [CrossRef] Esam Traveller Plus. Data Acquisition System. Technical Manual; Vishay Measurements Group: Heilbronn, Germany, 2005. Kubiak, M.; Laurow, Z. Wodden Raw Material; Fundacja “Rozwój SGGW”: Warsaw, Poland, 1994; p. 493, ISBN 83-86241-33-0. (In Polish) Orlicz, T. Woodworking with Cutting Tools; Wydawnictwo SGGW: Warsaw, Poland, 1988; p. 504, ISBN 83-00-02116-7. (In Polish) Wajand, J.A.; Wajand, J.T. Mid-Speed and High-Speed Piston Engines; Wydawnictwa Naukowo—Techniczne: Warsaw, Poland, 1993; p. 663, ISBN 83-204-1446-6. (In Polish) Maciak, A. The Measurements of Variability of Feed Force during Cross Cutting of Pine Wood. Technika Rolnicza, Ogrodnicza i Le´sna 2010, 5, 15–17. (In Polish) © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).