Impact of Blade Geometric Parameters on the Specific Cutting Energy of Willow (Salix viminalis) Stems

Abstract

This article presents a model to estimate the specific energy demand for cutting annual willow stems, considering variations in plant moisture content and sliding-cutting angles. The study involved laboratory tests and statistical analyses. Key parameters were measured for 50 randomly selected annual willow shoots, including total plant weight, leaf weight, stem weight, centre of gravity of the shoot, shoot length, and stem diameter at specified heights: 0, 150, 500, 750, 1000, 1250, 1500, and 2000 mm. Five levels of willow shoot moisture content were evaluated. The study established a cutting force-deformation relationship through strength tests with an accuracy of 1 N, which was subsequently used to calculate shear stress and specific cutting energy. Steel blades with an angle of 30° and sliding-cutting angles of 0°, 15°, 30°, and 45° were used in the study. Ten repetitions were performed for each combination of variable parameters: shoot moisture content and blade sliding-cutting angle. Experimental results were evaluated using analysis of variance (ANOVA), while Duncan’s test was applied to identify and classify groups with homogeneous specific energy values. The developed characterisation offers valuable information for designing shredding units and optimising their operational parameters to reduce energy consumption.

1. Introduction

Increasingly stringent legal and environmental regulations, coupled with the depletion of conventional fuel resources, are driving the advancement of renewable energy sources (RES) [1,2,3]. In 2022, primary energy production in the European Union (EU) amounted to 23,566 PJ, with renewable energy sources contributing approximately 40% (a decrease from 43.2% in 2021) [4,5]. In Poland, 13.2% of primary energy is derived from renewable sources, including ambient heat, biofuels, biomass, waste, water, wind, solar and geothermal energy. Among this, 4.7% comes from non-wood renewable sources [6,7].

Renewable energy includes resources such as water, wind, solar, and geothermal energy [8], as well as energy derived from woody biomass, which is produced from tree and shrub residues from forests, agriculture (e.g., orchards), and other sources (e.g., urban greenery) [9]. Fast-growing willow species are the most commonly cultivated energy crops in Poland [10,11,12]. Among these, basket willow, also known as Salix viminalis, has achieved the highest popularity [13]. It is characterised by significant annual woody mass growth (approximately 14 times that of naturally growing forests) [14,15]. As a perennial plant, it can yield for 25–30 years after planting. One hectare of willow cultivation produces approximately 10 tons of dry matter annually, with a calorific value of 19.23 MJ/kg [16,17].

The greatest potential for cost reduction, while adhering to current fuel quality standards, lies in optimising energy inputs at various stages of production technology [18,19,20]. Among these stages, biomass grinding is identified as one of the most energy-intensive processes [21]. The blade is the direct working element in the cutting process, interacting with the plant. Its parameters affect the working resistance of machines and the quality of cutting [22]. Cutting resistance is not only influenced by technical parameters (blade angle and cutting speed) but also by the biological properties of the material, and the conditions under which the plant is stored and seasoned. The energy intensity of this process is heavily impacted by material moisture content, the cutting area, and the length of the chips produced [23].

The energy transition and decarbonisation of the power and heating sectors are driving the need for alternative energy sources to replace traditional fuels and meet increasing energy demands [24,25,26,27,28].

Despite intensified efforts in recent years to promote the widespread use of renewable energy sources, logistical, economic, and technical challenges persist [29,30].

Biomass is a fuel used in commercial power and heating industries [31,32]. Its utilisation enables the achievement of the required energy efficiency levels while maintaining low environmental impact [33,34]. Biomass combustion is the oldest and simplest method of energy conversion. Compared to coal, biomass has a higher volatile content, reduced ash and sulphur content, increased oxygen content, and higher moisture levels, resulting in a significantly lower calorific value than coal [35,36,37,38]. One of the main advantages of biomass is its ability to be stored and pelletised over short time periods. To prepare biomass for combustion in boilers, it must undergo several processing steps, including drying and grinding.

In scientific literature and reports on decarbonisation, researchers commonly use the terms “sustainable biomass” and “modern solid biomass” [39,40]. Sustainable biomass refers to biomass produced with minimal environmental impact, ensuring support for local communities. This concept includes resource management practices that prevent deforestation, land degradation, biodiversity loss, and excessive water consumption [41,42]. Modern solid biomass encompasses advanced processing technologies such as pelletisation and briquetting, along with the implementation of high-efficiency, low-emission solid biofuel furnaces and boilers [43,44].

The production of renewable energy through the co-combustion of biomass and coal (referred to as classic co-combustion), which has been pursued for many years, is technologically straightforward and economically viable, provided that sufficient quantities of low-cost (resource cost + resource transportation cost) biomass are available near the energy producer [45,46,47,48]. It is estimated that, with a high conversion rate, a 100-hectare biomass plantation can produce enough dry plant matter annually to power a plant with a capacity of less than 300 kW [49,50].

However, direct co-combustion in power boilers presents several challenges [51,52]. Increasing the share of biomass with a moisture content of 40–60% in co-combustion with coal by 1% leads to a 0.5–1% reduction in boiler efficiency [53,54]. Transitioning from coal to mixtures of coal and alternative fuels increases the deposition of particulate residues on heat exchanger surfaces, accelerates low- and high-temperature corrosion, and raises the emission of undesirable by-products in flue gases and ash [55,56]. In order to remove moisture from fuel and enhance its energy density, an autothermal valorisation process is conducted through thermolysis [57]. Biomass subjected to valorisation can serve as a valuable fuel for highly efficient renewable energy production technologies. Thermolysis produces biochar, also known as biocarbon, with physicochemical properties that allow its immediate use in power boilers. The properties of torrefied biomass are significantly determined by the fuel type and the thermal treatment conditions [58,59,60].

In the process of obtaining biomass from willow trees, the stems are subjected to many loads related to bending, cutting and crushing. Obtaining the lowest possible energy expenditure in these processes involves knowing the properties of the plants. Knowing them makes it possible to understand the behaviour of the material in relation to different operations. Therefore, determining the effect of humidity and sampling location on the amount of cutting energy for willow stems is extremely important [61].

This study aimed to analyse the specific energy demand for cutting annual willow stems, considering variations in plant moisture content and sliding-cutting angles. The laboratory results discussed in this article were subjected to statistical analysis.

2. Materials and Methods

2.1. Study Materials

Shoots of annual willow were sourced from the plantation of the Experimental Station of the Institute of Agriculture, Warsaw University of Life Sciences located in Skierniewice, Poland. The plantation is located on soil classified as IVa valuation class. Characterisation of the collected willow shoots was conducted by measuring 50 randomly selected samples. The parameters assessed included whole plant weight, leaf weight, stem weight, centre of gravity of the shoot, shoot length, and stem diameter at heights of 0, 150, 500, 750, 1000, 1250, 1500 and 2000 mm. The measurements were performed using an electronic balance WLC 6/A2 with an accuracy of 0.1 g, a digital calliper, type MAUa-E24F, with a range of 0–150 mm and an accuracy of 0.01 mm, and a 3 m tape measure with an accuracy of 1 mm. The results are summarised in

Table 1. Parameters of the willow shoots analysed in the study.

Plant No.	Unit	Geometric Mean	Median	Min *	Max *	Deviation	CV *
Whole plant weight	g	254.45	237.6	119.7	448.8	80.99	31.83
Leaf weight	g	60.99	54.65	4.80	132.6	29.09	47.69
Stem weight	g	80.34	72.70	7.10	210.6	49.34	61.41
Basal shoot weight	g	152.89	142.75	89.50	248.0	36.16	23.65
Centre of gravity of the shoot	mm	1159.1	1155.0	770.0	1380.0	133.52	11.52
Shoot length	mm	2301.0	2295.0	1900.0	2670.0	237.44	10.32

* CV—Coefficient of variation; Min—Minimum value; Max—Maximum value.

and

Table 2. Parameters of the willow shoots analysed in the study—stem diameter.

Stem Diameter at Height of:	Unit	Geometric Mean	Median	Min *	Max *	Deviation	CV *
0	mm	14.82	14.67	11.86	19.25	1.74	11.77
150	mm	14.14	13.79	11.59	18.5	1.71	12.06
500	mm	12.98	12.745	10.19	16.64	1.53	11.77
750	mm	12.20	12.09	9.84	15.52	1.38	11.30
1000	mm	11.29	11.25	8.61	14.84	1.49	13.21
1250	mm	9.76	9.71	6.55	13.36	1.66	17.01
1500	mm	8.13	8.195	4.64	12.02	1.87	23.05
2000	mm	6.04	6.16	2.28	10.19	1.59	26.39

* CV—Coefficient of variation; Min—Minimum value; Max—Maximum value.

.

Five levels of willow shoot moisture content were evaluated. The average moisture content of the fresh sample was determined using the oven-drying method in accordance with ASABE Standard S358 [62,63]. The samples were dried in an SLW 115 TOP laboratory drying oven at a temperature of 103 ± 0.4 °C for 24 h. They were weighed on a WLC 0.6/A1 electronic balance with an accuracy of 0.01 g. The moisture content was calculated using the following formula:

$$MC={\displaystyle \frac{m_w-m_s}{m_w}}\times 100\%$$

(1)

where:

• MC—moisture content of the fresh sample, %;
• m_w—weight of the fresh sample, g;
• m_s—weight of the sample after drying, g.

The highest moisture content was observed in samples collected immediately after harvesting. The next three levels of moisture were obtained through natural drying of the stems, while the lowest level was achieved by forced semi-drying. This process resulted in five moisture levels: 46.30 ± 0.55%, 37.05 ± 0.61%, 25.43 ± 1.07%, 15.21 ± 0.16%, and 1.35 ± 0.64%, which were used for subsequent analyses.

2.2. Test Stand

The test stand utilised for the study comprised the TIRAtest 2803 universal testing machine, operated using MATEST H009N software (Figure 1a), with an accuracy of 1 N [64,65,66]. The machine used in the research is built on a frame structure. The working beam is driven by a screw transmission, which in turn is connected via a toothed belt to a worm transmission. The machine is equipped with a modern servo drive [67,68]. The software allowed the determination of the cutting force-deformation relationship through strength tests with an accuracy of 1 N, which was subsequently used to calculate shear stress and specific cutting energy. Shoot sections, each 200 mm in length, were mounted on a special head, perpendicular to the blade plane. Cutting measurements were taken at a constant speed of 10 mm/min. The basket willow shoots analysed in the study are shown in Figure 1b.

Steel blades with an angle of 30° and sliding-cutting angles (A) of 0°, 15°, 30°, and 45° were used in the study (Figure 2).

Ten repetitions were performed for each combination of variable parameters: shoot moisture content and blade sliding-cutting angle.

The shear stress τ_t was calculated for the maximum cutting force:

$${\tau }_t={\displaystyle \frac{F_{tmax}}{S_t}}$$

(2)

where:

• τ_t—shear stress, MPa;
• F_tmax—maximum cutting force, N;
• S_t—cross-sectional area of the sample at the cutting point, mm²;

The specific cutting energy was calculated as the ratio of the total deformation energy to the cross-sectional area of the willow stem, using the following formula:

$$E_{jt}={\displaystyle \frac{1}{S_t}}{\displaystyle \int F_{t}dx}$$

(3)

where:

• E_jt—specific cutting energy, mJ⋅mm⁻²;
• F_t—cutting force, N;
• S_t—cross-sectional area of the sample at the cutting point, mm²;
• x—deformation (blade displacement), mm.

Experimental results were evaluated using analysis of variance (ANOVA), while Duncan’s test was applied to identify and classify groups with homogeneous specific energy values. The analysis was performed using the STATISTICA software package, version 13.3.

Duncan’s multiple range test is a statistical test used to compare the means of multiple groups. It is a post-hoc test that is used after a significant difference has been found in an analysis of variance (ANOVA) test. The test determines which group means are significantly different from each other and groups them into subsets based on their similarities [69,70].

The test works by comparing the differences between the means of all possible pairs of groups. It calculates a critical value based on the number of groups and the number of observations in each group. If the difference between two means is greater than the critical value, then the means are considered significantly different from each other.

To perform the Duncan test, the first step is to perform the ANOVA test (to determine if there is a significant difference between the means groups), then calculate the means for each group and the standard deviation of each group. The next step is to sort the groups in descending order based on their mean values and calculate the Duncan critical range (Q) based on the number of groups and the number of observations in each group. This will allow you to compare the differences between the means of all possible pairs of groups. If the difference is greater than Q, then the means are significantly different from each other. In the last step necessary to perform the Duncan test, the means should be grouped into subsets based on their similarities.

3. Results

Representative waveforms depicting the relationship between cutting force and deformation for willow stems at a constant moisture content (25.43%) and varying cutting angles (0, 15, 30, 60°) are shown in Figure 3. Figure 4 presents the relationships observed when cutting willow stem samples with varying moisture content at a fixed cutting angle (45°).

The relationships obtained were used to calculate shear stress and specific cutting energy, as summarised in

Table 3. Shear stress values τ_t obtained.

MC, %	Angle, °	Shear Stress τt, MPa				CV *
		Mean	Min *	Max *	SD *
46.30	0	9.29	8.18	10.47	0.78	8.38
	15	9.79	8.29	11.37	1.05	10.74
	30	8.15	6.80	9.59	0.93	11.37
	45	8.81	7.73	9.72	0.62	7.07
37.05	0	13.79	12.31	15.65	1.04	7.53
	15	13.54	12.35	15.51	0.94	6.94
	30	11.11	8.61	16.08	2.25	20.29
	45	6.84	6.42	7.32	0.31	4.55
25.43	0	10.41	8.76	11.92	0.95	9.13
	15	16.52	14.87	18.09	1.02	6.18
	30	11.17	9.94	12.21	0.63	5.65
	45	7.37	5.81	8.45	0.93	12.61
15.21	0	13.51	10.84	15.34	1.28	9.51
	15	13.93	11.39	16.89	1.77	12.70
	30	12.57	10.85	15.82	1.65	13.13
	45	9.58	8.20	11.88	1.11	11.62
1.35	0	10.77	9.21	12.71	1.19	11.09
	15	10.21	9.45	11.69	0.70	6.88
	30	12.20	10.39	15.08	1.48	12.13
	45	6.96	5.54	7.84	0.71	10.22

* CV—Coefficient of variation; SD—Standard definition; Min—Minimum value; Max—Maximum value.

and

Table 4. Specific cutting energy E_jt values obtained.

MC, %	Angle, °	Specific Cutting Energy Ejt, mJ⋅mm−2				CV *
		Mean	Min *	Max *	SD *
46.30	0	35.70	26.54	53.33	7.95	22.21
	15	31.68	22.80	41.45	6.22	19.62
	30	35.64	22.87	46.37	8.03	22.53
	45	41.05	22.62	58.63	12.25	29.84
37.05	0	69.89	59.17	90.84	11.85	16.95
	15	75.51	62.66	89.60	7.40	9.80
	30	76.37	56.72	107.02	16.58	21.70
	45	63.05	54.74	67.81	3.82	6.06
25.43	0	70.77	62.72	80.57	6.01	8.49
	15	76.72	70.19	89.66	6.49	8.46
	30	63.56	55.07	76.92	7.57	11.91
	45	62.27	48.77	76.07	8.04	12.91
15.21	0	80.05	58.46	95.34	13.40	16.74
	15	76.63	66.31	85.09	5.33	6.95
	30	92.33	77.89	106.54	10.03	10.86
	45	81.82	66.38	97.52	11.40	13.93
1.35	0	61.85	56.09	72.70	5.74	9.28
	15	72.30	64.27	83.47	5.73	7.92
	30	99.88	85.14	110.92	8.68	8.69
	45	78.11	73.07	85.46	3.77	4.83

* CV—Coefficient of variation; SD—Standard definition; Min—Minimum value; Max—Maximum value.

.

The results of multivariate analysis of variance revealed that both moisture content and sliding-cutting angle had highly statistically significant effects on shear stress and specific cutting energy values (

Table 5. Results of analysis of variation of shear stresses τ_t and specific cutting unit energy E_j for willow plant stems.

Parameter	Factor	Sum of Square	Degree of Freedom	Mean Square	Femp; F-Ratio	p-Value
Shear stress τt	MC: moisture content	277.53	4	69.38	52.02	<0.0001
	A: angle	647.11	3	215.70	161.73	<0.0001
	MC × A	375.73	12	31.31	23.48	<0.0001
	Error	240.07	180	1.33
Specific cutting energy Ej	MC: moisture content	53,842.1	4	13,460.5	168.80	<0.0001
	A: angle	2850.5	3	950.2	11.92	<0.0001
	MC × A	9176.9	12	764.7	9.59	<0.0001
	Error	14,353.8	180	79.7

and

Table 6. Division of shear stress τ_t and specific cutting energy (E_jt) values into homogeneous groups based on moisture content (MC) and sliding-cutting angle (A).

Shear Stress τt
Moisture Content MC, %	Sample Size	Mean, %	Homogeneous Groups
			Group I	Group II	Group III	Group IV
1.35	40	9.008	×
46.30	40	10.036		×
15.21	40	11.320			×
25.43	40	11.368			×
37.05	40	12.398				×
Angle A, °	Sample size	Mean, %	Homogeneous groups
			Group I	Group II	Group III	Group IV
45	50	7.913	×
30	50	11.041		×
0	50	11.553			×
15	50	12.797				×
Specific cutting energy Ejt
Moisture content MC, %	Sample size	Mean, %	Homogeneous groups
			Group I	Group II	Group III	Group IV
1.35	40	36.041	×
25.43	40	68.330		×
15.21	40	71.204		×
46.30	40	78.035			×
37.05	40	82.707				×
Angle A, °	Sample size	Mean, %	Homogeneous groups
			Group I	Group II
0	50	63.668	×
15	50	66.568	×
45	50	65.262	×
30	50	73.556		×

, Figure 5 and Figure 6). The analysis included bivariate interactions between the studied parameters, which were also found to be significant. A comprehensive evaluation of the test results suggests that shear stress values vary more significantly with changes in the sliding-cutting angle than specific cutting energy values. For specific cutting energy, plant moisture content exerts a stronger influence on the observed values.

The method of comparing the averages allowed us to clarify the differences detected by the analysis of variance [71,72,73]. It made it possible to group the obtained mean values and to isolate homogeneous groups, i.e., those for which there are no statistical differences [74,75]. The confidence intervals do not overlap, and the difference between the means is significant. For greater readability of the results, presented in Table 6, they have been arranged in a continuous sequence. On this basis, it can be concluded that the change in the moisture content of willow shoots from 15.21% to 25.43% does not result in a significant change in the shear stress τ_t and the specific cutting energy E_j; they form one homogeneous group. In the case of a change in the sliding-cutting angle for the specific cutting energy E_j, the analysis identified only two groups. Group I contains cutting angles 0°, 15° and 45°, while Group II has angles of 30°.

The findings indicate that the specific cutting energy values for willow stems vary significantly depending on their moisture content and the sliding-cutting angle. To provide a generalised understanding of the factors affecting specific cutting energy in willow stems and to enable its prediction, it was necessary to develop a mathematical relationship.

To make the cutting energy model as reliable as possible, variables were introduced that were strongly correlated with the dependent variable, i.e., moisture content and the sliding-cutting angle, and at the same time as little correlated with each other as possible. The selection of these parameters was dictated by the fact that parameters related to the physico-mechanical properties of the plant and the cutting process are taken into account in the process of crushing plants [76,77,78,79,80]. The physico-mechanical properties of the plants are as follows: type, diameter (thickness) of the stem, moisture content, phase of development, stiffness or where the sample is taken for testing [81,82,83]. The key element of the cutting process is the knife, which divides the material under the action of an external force that exceeds the resistance of the intermolecular material. The variables that will characterize the knife are as follows: blade shape, sharpening and roughness, sliding-cutting angle or knife setting angle. Changing the angle of the sliding cut causes the cutting under the action of the normal force and the lateral force associated with the sliding of the knife relative to the cut stem and facilitates its cutting. Three phases of the cutting process can be distinguished. In the first phase, the knife comes into contact with the stem and with the further movement of the knife the stresses increase and the stem is crushed. Further movement of the knife causes sequences of deformation and elementary cuts. In the third phase, during the continuous movement of the knife, the compression force and stress increase until the strength conditions of the stem are exceeded and it is cut or gradually reaches full separation. These phases can be clearly seen in Figure 3 and Figure 4, but they are different in nature, depending on the moisture content and the sliding-cutting angles. The working conditions of the cutting team, such as the degree of compression of the material or the working speed of the knife, are also important [84,85,86,87]. However, these were not taken into account in this study, as model studies were carried out on individual stems.

Using the obtained set of measurement results and conclusions from the analysis of variance, the search for multiple regression was carried out by a step method. The decisive parameters for the adoption of the final form of the equation were the value of the coefficient of determination and the values of the significant coefficient of regression. The final form of the regression equation was adopted for the maximum value of the multiple correlation coefficient, taking into account the values of the relevant regression coefficients.

The results obtained enabled a multiple regression analysis. The variables used in the model were evaluated using the Student’s t-test and the significance levels of the model coefficients (

Table 7. Analysis of the significance of regression coefficients for the empirical model of changes in the specific cutting energy Ejt of the willow stem.

Independent Variable	RC	SE	T-Statistic	p-Value
Const	34.61	1.886727	18.3445	<0.0001
MC	2.895	0.197582	14.6505	<0.0001
MC2	−50.23 × 10−3	0.004453	−11.2795	<0.0001
MC2 A	0.7832 × 10−3	0.000110	7.0961	<0.0001
MC A2	−0.5694 × 10−3	0.000093	−6.0919	<0.0001

). The overall model accuracy was assessed based on the coefficient of determination. An empirical polynomial model was developed to describe changes in specific cutting energy (Ejt) for willow stems as a function of moisture content (MC) and sliding-cutting angle (A):

$$E_{jt}=34.61+2.895MC-50.23\times {10}^{-3}{MC}^2+0.7832\times {10}^{-3}{MC}^{2}A-0.5694\times {10}^{-3}MC{A}^2$$

(4)

where:

• E_jt—specific cutting energy, mJ⋅mm⁻²;
• MC—moisture content of the fresh sample, %;
• A—sliding-cutting angle, °, with a correlation coefficient R of 0.8350.

Therefore, it may be concluded that the presented model accurately represents the variations in specific cutting energy for willow stems in relation to moisture content MC ∈ <1.35–46.3%> and sliding-cutting angle A ∈ <0–45°>. The changes in specific cutting energy Ejt as a function of moisture content (MC) and sliding-cutting angle (A) for willow stems, as derived from the proposed model, are presented in Figure 7.

4. Conclusions

The analysis of variance and Duncan’s test revealed that the shear stress and specific cutting energy of willow shoots were significantly influenced by variations in sliding-cutting angle and plant moisture content. Additionally, a statistically significant interaction between these two factors was observed.

From the obtained results, it may be concluded that changes in the sliding-cutting angle have a more pronounced impact on shear stress values than on specific cutting energy. Conversely, plant moisture content was found to have a greater effect on specific cutting energy values than on shear stress. Understanding the mechanical properties of willow shoots is essential due to their significance at all stages, from harvesting to plant processing.

The developed model of specific cutting energy demand, which accounts for variations in plant moisture content and sliding-cutting angles for willow stems, provides valuable data for designing shredding units and optimising their operational parameters to minimise energy consumption.

Knowledge of changes in unit cutting energy allows the cutting unit to be properly designed and also allows the power demand to be predicted.

5. Discussion

The process of biofuel production is highly complex and encompasses a series of operations, including raw material harvesting and seasoning, transportation and handling, grinding, semi-drying (if necessary), and removal of mineral impurities, followed by densification (briquetting, pelleting) and cooling. Among these biomass processing steps, grinding is one of the most critical stages, as it significantly influences the energy intensity of solid biofuel production. This step is especially crucial from the perspective of enhancing the competitiveness of solid biofuels and optimising subsequent production stages (by minimising energy consumption and maximising the quality of the produced chips). The findings of this study are intended to provide valuable insights for designers and operators of biomass grinding equipment. The results also aim to facilitate optimisation of the chipping process, ensuring high-quality chip production while minimising energy inputs.

Quality requirements for fuel chips vary depending on their intended application (direct combustion or processing into densified fuels).

Biomass for energy applications is subject to standardisation. It must comply with the quality standards defined by national legislation [88]. Legal provisions address various aspects, including the content of halogenated compounds or heavy metals in biomass, contamination with peat and carbonised fractions, the presence of non-biodegradable substances, and fractions derived from hardwood.

However, Poland lacks uniform quality requirements for specific biomass types used in commercial power generation. Typically, quality requirements are determined by the respective energy group (buyer), which adheres to company-specific quality standards. These standards depend on the requirements and parameters defined by manufacturers of biomass combustion systems, biomass feeding systems, and the available biomass storage capacity at power plant facilities. Company-specific quality standards for solid biomass are typically based on the PN-EN ISO 17225-4:2014-07 standard [89]. For biomass in the form of wood chips, size parameters, including both minimum and maximum dimensions, are crucial. This applies to chips from wood, forestry, and energy willow, as well as residues from agricultural and orchard production.

The authors have been publishing the results of studies on energy plant parameters for many years. In previous studies, the lowest energy demand was observed at high humidity and in the upper stem zones where shoots are least woody.

In the process of obtaining biomass from willow trees, the stems are subjected to many loads related to bending, cutting and crushing. Obtaining the lowest possible energy expenditure in these processes involves knowing the properties of the plants. Knowing them makes it possible to understand the behaviour of the material in relation to different operations. Therefore, determining the effect of humidity and sampling location on the amount of cutting energy for willow stems is extremely important [90].

In the authors’ previous studies, the results of a multifactor analysis of variance showed that both the plant species and the height zone from which the stem samples were taken had a highly statistically significant impact on the values of cutting stresses and unit cutting energy. The interactions of these main factors also proved important [91].

The results of the authors’ previous research on the strength of Virginia Mallow show that in the shearing zone, at an altitude of about 0.10 m from the ground, the stalks had the greatest susceptibility to bending, with the greatest resistance to cutting and compression, because they were the most wooden. The lower sections of the Pennsylvania stalk had the lowest elasticity, with the lowest modulus of elasticity for cutting, compression and bending, and they had the most favourable values of the strength parameters at a humidity of about 20% [92].

The results of the studies available in the literature show that, in the process of cutting willow stems, two characteristic courses of cutting forces can be distinguished, depending on the movement of the blade of the knife. The first is characterized by a mild course, and the second by visible decreases in force (reaching up to 40% of the value). It was found that the decrease in cutting forces is determined by the formation of longitudinal cracks of the obtained cuttings.

In addition, the analysis of the cutting process showed that the occurrence of chip cracks is dependent on the physical properties of the thrust and its dimensions. The stresses permissible for cutting (depending on the moisture of the material) and the size of the slip plane (depending on the length of the chip and its diameter) are the parameters determining the occurrence of chip cracks [93].

The time of the willow cutting process affects the knife blade (sharpness). Of course, this depends on the parameters of the material being cut and affects the actual energy of the cut. That is why modern power plant machines are equipped with built-in knife sharpening systems [94]. These issues will be the subject of further work by the authors.