Cutting mechanisms and the cutting force are the focus of this article. The cutting force can be determined theoretically or mathematically by statistical analysis. In this work, the cutting speed was compared when changing the diameter of the test wood and when using the three types of angular geometry of delimbing knives. Experimental measurements were conducted on a self-designed experimental pneumatic stand. Empirical relationships and values from the scientific literature were used to determine the input parameters. Based on a regression analysis, conclusions were drawn relative to factors affecting the process of delimbing. The angular geometry of the delimbing knife plays a significant role in the delimbing process. The thicker the knife, the higher the energy consumption in the cutting process and the poorer the quality of the cutting surface of the wood. The quality of chipless separation timber was found to depend on the cutting speed, and the optimal speed was 2.0 m s-1.
Influence of Knife Geometry on Selected Factors Pertaining to the Delimbing Process
Ján Melicherčík,* Jozef Krilek, Ján Kováč, and Pavol Harvánek
Cutting mechanisms and the cutting force are the focus of this article.
The cutting force can be determined theoretically or mathematically by statistical analysis. In this work, the cutting speed was compared when changing the diameter of the test wood and when using the three types of angular geometry of delimbing knives. Experimental measurements were conducted on a self-designed experimental pneumatic stand. Empirical relationships and values from the scientific literature were used to determine the input parameters. Based on a regression analysis, conclusions were drawn relative to factors affecting the process of delimbing. The angular geometry of the delimbing knife plays a significant role in the delimbing process. The thicker the knife, the higher the energy consumption in the cutting process and the poorer the quality of the cutting surface of the wood. The quality of chipless separation timber was found to depend on the cutting speed, and the optimal speed was 2.0 m s-1.
Keywords: Cutting force; Cutting speed; Delimbing knife; Branch diameter
Contact information: The Technical University in Zvolen, The Faculty of Technology, The Department of Environmental and Forestry Machinery, T. G. Masaryka 24, Zvolen 960 53 Slovakia; * Corresponding author: firstname.lastname@example.org
The chipless wood cutting process, as the object of investigation, is characterized by a number of parameters found to be in close correlation with one another. The geometry of the knife and the cutting force have a significant influence in the delimbing process of wood; they affect a large number of factors, as shown in previous studies (Mikleš and Mikleš 2012; Krilek et al. 2018). Delimbing is the technological process in which the tool penetrates the material (wood) and interferes with the interconnection of wood fibers in order to divide it into 2 or more parts (Siklienka et al. 2017). The feeding mechanism of the device consists of a pneumatic cylinder, the primary delimbing knife with different geometric shapes, and a different cutting edge angle. Delimbing is a process that is used to cut branches from the trunk during the tree harvesting process. This process can be described as the chipless cutting of green wood (Spinelli et al. 2010; Hatton et al. 2016). The chipless wood cutting process is a forestry process that is used primarily in machines for delimbing trees. It is a technological process in which a product is produced without the formation of chips (Siklienka et al. 2017). This method of cutting is applied to the cutting heads of multi-operation machines (USA, Canada). The free-body diagram of the work of the wedge knife is shown in Fig. 1. The process of chipless wood cutting, with the help of a branching knife, is carried out across the fibers in the wood. This condition causes an increase in the cutting force acting on the pruning knife. Somewhere it is possible to define this process as force cutting. (Marko 1997).
Fig. 1. (a) wood cutting with a wedge knife; and (b) wood cutting with a flat knife (Krilek et al. 2018)
A delimbing knife is a cutting tool whose design may have different profiles, i.e., the cutting edge shape and the cutting edge. The cutting edge is the part of the cutting wedge that is to be cut and is the intersection of the face and back of the tool with a knife thickness “s”. With the cutting edge angle β and the back angle α = 0, the cutting angle is δ = β. The results of chipless wood cutting research showed that the cutting force at the entrance of the knife into the wood initially increased linearly and then dropped to zero. The maximum force Fmax corresponds to a knife penetration depth of 55% to 80% at the cross sectional area. When chipless cutting wood via a wedge knife in a direction that does not correspond to the direction of the wood fibers, considerable cutting forces arise. This results in considerable energy intensity of the cutting process. One of the specific cases of this method is the power cutting of branches, in which knives with a complicated structure are used. The special feature of the knives designed for cutting branches via the force method is a combination of effective cutting with copying ability of knives in the process. The magnitude of the cutting force acting in the direction of the velocity vector is the result of all the components of the force of resistance acting on the different parts of the knife, which forms its cutting profile (forehead, back, and cutting edge), (Kováč 2006; Mikleš and Mikleš 2015).
Forces Acting on the Forehead of a Knife Cutting Branch
Chipless cutting is characterized in particular by the fact that, up to the moment of removal of the branch from the forehead knife, it penetrates the wood only via the compressing the wood and pushing it out of the cutting zone in a volume equal to that of the protruding portion of the knife. This is illustrated by the fact that a branch that has a long enough length is characterized by major resistance to shearing along the fibers, and therefore the vertical force FQ1 is not able to overcome this resistance. Therefore, chips are not formed, and the branch subsequently observed a characteristic decrease in cutting resistance. The cutting resistance is constantly increasing, reaching the maximum at the moment when the over-cut branch begins to separate from the forehead knife, after which the opposite process takes place. The nature of the growth and decrease of the cutting resistance must ideally be the same. It follows that the maximum force acting from the wood on the forehead of the knife must be counted out based on the condition of energy consumption for pressing the wood. Here the authors assume that the relative pressure, caused by the cut-off branch on the forehead of the knife is in direct dependence of the volume of the wood extruded by the forehead in the cutting process.
The measuring pressure on the entire area in contact with the forehead knife being evenly distributed is most likely to cause chipless cutting. The principle is that in the given method, the over-cut part of the branch does not leave the forehead knife but is attached to it until the conditions are maintained and the relationship applies, as shown in Eq. 1,
where FQ1 is the pressure of the wood (N), a is the longer axis slit branch (mm), z is the depth of the knife penetration (mm), b is the shorter axis slit branch (mm), and OH is the timber strength of the branch along the fibers (MPa).
Fig. 2. Forces acting on the front of the knife (Mikleš and Mikleš 2015)
When calculating the forces FS1, FQ1, and FP1, the deformation is caused by the pressing of the front edge of the knife into the wood. When this occurs, the normal force FN1, acting on the forehead of the knife, can be determined from the following relationship, as shown in Eq. 2,
where q is the specific compression force, per unit of volume of the compressed wood (N·mm-3), and V1 is the volume of the wood, knife – crush out (mm3).
The resultant force FS1 is obtained as the geometric sum of the forces FN and F1 as shown in Eq. 3,
where V1 is the volume of the wood, knife – crush out (mm3), f1 is the coefficient of friction between the knife and the tree trunk, and FS1 is the resultant force (N).
These values can be applied to Eqs. 4 and 5,
where FP1 is the pressure force (N).
The maximum value of the FRmax cutting force, according to Mikleš (2009) and Hatton et al. (2015), is directly proportional to the square diameter of the “dc” of the cut branch in the bark, as shown in Eq. 6,
where a1 is the coefficient of proportionality, which is dependent on the parameters of the knife, the wood, and the angle of the ingrowth of the branches. This relationship shows that FRmax is directly proportional to the cutting surface of branch S, as shown in Eq. 7,
where k equals FspMAX, which is the proportionality ratio corresponding to the maximum nominal cutting force, which includes the influence of the geometric characteristics of the knife (N·mm-2), and S is the cutting surface of the branch (mm-2).
This study deals with the comparison of various cutting speeds with respect to the cutting resistance of different delimbing knife geometries. To analyze these different geometries, a special device was built to allow the cutting process to be monitored in laboratory conditions and to measure the cutting forces, which results in recording the energy intensity of the delimbing process. The authors experimented with a pneumatic cylinder. For evaluating the delimbing process, knives with different geometric parameters were used (Table 1). The geometry of the cutting wedge delimbing knife is shown in Fig. 3. The purpose of this paper was to determine the optimal geometry of the knife. Under the same cutting conditions (a delimbing speed of 4 cm·s-1), the maximum cutting force was determined (or measured cutting force).
The experimental measurements were carried out by professional employees of the school forestry company. Wood sampling took place in the course of a logging operation in the forest. The samples were always brought on the day of the experimental measurement, and during the measurement they were stored in an open hangar to maintain the necessary conditions and properties of the wood. The moisture content of the samples was measured by the gravimetric method, always before the start of the experimental measurements. The diameters of the sampling woods used in the experiment were from 10 to 55 mm. A larger diameter sample was inserted into the experimental stand, from which the delimbing branch is based. When measuring a change in the type debranching blade, 27 specimens were studied. The number of specimens was determined by a basic statistical set.
For chipless wood cutting applications in woodland harvesting, further refinement of the cutting tool was necessary. The incompleteness of the design of the cutting tool and the cutting mechanism did not allow for a good cutting surface, especially when cutting frozen wood (in the splitting process wood is shredded and longitudinal cracks emerge from the forehead), and also causes large cutting forces, which cause considerable load on the whole mechanism.
The theory of chipless wood cutting processes is based on analysis of works by foreign authors (Gerasimov et al. 2012; Hatton et al. 2015; Orlowski et al. 2018) and the author’s previous research (Kováč and Alexi 2004; Krilek et al. 2018). That work involved an analysis to determine the impact of various parameters on cutting, and found that the parameter with the greatest impact on the cutting resistance upon entering the wood was the thickness of the knife (s). The greater the thickness of the knife, the higher the energy consumption in the delimbing process and the worse the quality of the cutting surface. Therefore, a reduction in the thickness of the knife can cause a significant impact in terms of tool optimization. For the laboratory pruning tests, 3 knives with a constant thickness (s = 15 mm), the geometry of these knives was the most appropriate according to the results of the initial chipless separation measurements. The effective cutting edge width for all knives was 130 mm. The tool steel DIN C45W was used for the production of the test knives. All knives were hardened to a hardness of 52 HRC to 56 HRC and were machined to a surface roughness of Ra = 0.8 µm. The technical parameters of the blades are shown in Table 2.
Fig. 3. Experimental device for testing delimbing knives
The experimental equipment was constructed of profiled steel and shaped elements by means of welded joints. The device had dimensions of 1404 x 500 mm, and the branching knife was 400 mm away from the sample material. The air tank was located on a profile stand, which included a barometer, by which to monitor the air pressure and a pressure reducing valve to adjust the air flow in the system. A pneumatic double-acting cylinder was mounted by screws, with parameters according to ISO 6431. The HBM S9 strain gauge was located on the piston rod of the cylinder by means of the proposed fastening jigs. Starting the double acting cylinder provided movement of the pneumatic actuator, which was provided with a check valve and a silencer. The sensor was powered by connecting cables to the Quantum MX 840 measuring unit, which was an 8-channel measuring control panel. The advantage of the measuring unit is compatibility with HBM devices. The cutting device consisted of a flat delimbing knife, which was located on the piston rod and was detected by a pin. After the piston rod is extended, the knife moves towards the wood sample, while there is a transverse division of the wood – delimbing. The sample material was secured against ejection by a pressure cylinder, which was controlled by a separate pneumatic control unit, which consisted of a pneumatic actuator, a throttle valve, a trigger valve, and an exhaust valve at the outlet of the pressure cylinder.
Spruce (Picea excelsa) was used for the experimental measurements, and the chosen wood samples had the maximum specific cutting resistance that was processed. The delimbing branches of fresh spruce branches had a moisture content of 40% to 70%. Individual measurements were carried out via pneumatic measuring; the primary part the measuring device consisted of a pneumatic cylinder on which the authors fastened the selected delimbing knives, according to Table 2.
Fig. 4. a.) The geometry of the cutting wedge delimbing knife (s is the thickness of the knife; α is the angle of the knife; δ is the cutting angle; h1 is the depth the knife penetrates the wood; and hD is the thickness of the cut layer) b.) Sampling trees with the average groups used in the experiment
Table 2. Technical Parameters of the Knives Intended for Experimental Tests
For the sake of evaluation, the authors compiled a measurement chain from individual sensors. To measure the speed, the authors used a single axis SA I/L acceleration sensor, which measured the acceleration of the knife for a certain time unit, which allows for the calculation of the delimbing speed after conversion. The growth of the HBM Force sensor pressure transducer was within a pressure range of 25 to 60 MPa. The process and the individual measurement results were displayed using Conmes Spider (version8) from HBM. The experimental delimbing measurements investigated the maximum cutting force and speed relative to the cutting resistance. The tested cutting knife speeds were
1.5, 2.0, and 2.5 m.s-1, with three different knives (the knife parameters are shown in Table 2). The relative moisture content of the samples ranged from 21% to 46 %. Basic statistical characteristics were performed in the STATISTICA statistical program (STATISTICA12 software, TIBCO Software Inc., Palo Alto, CA, USA), and the results are shown in Table 3
RESULTS AND DISCUSSION
The primary goal of this experiment was to compare the cutting speed, with consideration to the cutting resistance and the delimbing knife geometry, via changing the parameters that characterized the cutting process. When cutting a branch at the point of its emergence, the character of the cutting force acting in the direction of the knife displacement is a close-up shape of a triangle with a cut off vertex, with the speed of the cutting knife being a mirror image of the action of the cutting force. When the depth of the cut when the knife enters the branch increases, the cutting force increases linearly and the cutting speed decreases linearly; this pattern coincides with the shape of the typical curve of total wood deformation. The linear dependence of the cutting power and cutting speeds usually changes only at a depth of penetration of the tool equal to approximately 0.5 dc (Mikleš and Mikleš 2010), or slightly less than half the branch diameter. The individual laboratory results of the maximum cutting force measurements at different speeds were processed in tabular form with the STATISTICA program.
Statistical Curves of Maximum Cutting Force During the Delimbing Process Using the Delimbing Knives Described in Table 2
Fig. 5. The maximum cutting force when processing the spruce wood branch at a cutting speed of 1.5 m·s-1
Fig. 6. The maximum cutting force when processing the spruce wood branch at a cutting speed of 2.0 m·s-1
Fig. 7. The maximum cutting force when processing the spruce wood branch at a cutting speed of 2.5 m·s-1
Fig. 8. The maximum cutting force when processing the spruce wood branch at a cutting speed of 1.5 m·s-1