Doctoral dissertation summary: Research on dynamic parameters of circular saw in bamboo crosscutting process

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Building a model, setting up a system of dynamic equations of the circular saw cutting bamboo, solving the dynamic equations, from which to calculate and determine some reasonable kinetic and dynamic parameters of the circular saw to improve productivity and cutting surface quality

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Nội dung Text: Doctoral dissertation summary: Research on dynamic parameters of circular saw in bamboo crosscutting process

MINISTRY OF EDUCATION AND TRAINING MINISTRY OF AGRICULTURE AND RURALDEVELOPMENT VIETNAM NATIONAL UNIVERSITY OF FORESTRY HOANG HA RESEARCH ON DYNAMIC PARAMETERS OF CIRCULAR SAW IN BAMBOO CROSSCUTTING PROCESS DOCTORAL DISSERTATION SUMMARY HA NOI, 2021
The dissertation is conducted at Vietnam National University of Forestry Supervisors: 1. Assoc.Prof.Dr. Duong Van Tai 2. Dr. Nguyen Van Bi PhD dissertation Reviewer 1: PhD dissertation Reviewer 2: PhD dissertation Reviewer 3: The dissertation is defended in front of the scientific committee at the Vietnam National University of Forestry Date of doctoral dissertation defence: The dissertation can be found at the National Library and the Library of Vietnam National University of Forestry Ha Noi, 2021
1 INTRODUCTION 1. The problem statement According to a report by the Department of Agro-Forestry Processing and Markets under the Ministry of Agriculture and Rural Development, Vietnam has about 1,000 bamboo processing enterprises and thousands of households producing handicrafts from bamboo. Export turnover of bamboo products in 2020 will reach about 500 million USD, thereby creating a significant source of income for businesses and households. Currently, processing bamboo products has been mechanized, since then productivity and product quality have been increased, meeting export requirements. However, the equipment used in bamboo processing technology still has some shortcomings that need to be overcome to create higher-quality products, thereby enhancing the added value of the products. The survey results of bamboo processing plants show that the bamboo cutting equipment is mainly used a circular saw, there are still many problems in the cutting process, which is a large cutting surface roughness, when cutting parts. The pointed end is often scratched and unsmooth, in order to create a smooth surface, it must go through a grinding device. Besides, The circular saw used in bamboo processing is the one used in woodworking, because the structure of bamboo has different characteristics compared to another types of wood, requiring more appropriate cutting equipment. This is the aim of research. Currently, the research works on the equipment in bamboo processing are still limited, there is not alot of deeper studies on the dynamics of the bamboo cross- cutting circular saw. In order to have a theoretical basis for perfecting the bamboo circular saw, it is necessary to study the dynamics in order to determine the optimal parameters of the bamboo circular saw when cutting. With the reasons stated above, the thesis finds that it is very necessary to study the process of cutting and cutting bamboo with a circular saw. Eventually, I chose and conducted the research topic: "Study on some dynamic parameters of circular saws during bamboo cross cutting". 2. Research objectives of the dissertation Building a model, setting up a system of dynamic equations of the circular saw cutting bamboo, solving the dynamic equations, from which to calculate and determine some reasonable kinetic and dynamic parameters of the circular saw to improve productivity and cutting surface quality. 3. New findings of the dissertation 1. The dynamic model has been built, the system of differential equations for the motion of the saw blade in the process of cutting bamboo has been established, the stiffness of the saw blade has been calculated, and the results of the investigation of the system of differential equations have been established. The motion of the saw
2 blade shows that at the rotational speed of the saw blade varying in the range of 3500-4500 rpm, with the angular momentum of the saw blade is the largest. 2. The vibration calculation model of the saw blade has been built, the system's vibration differential equation has been established along with its solution, and the horizontal vibration amplitude of the saw blade has been investigated in the time domain. Using Matlab-simulink software, a solution has been proposed to reduce the vibration of the saw blade. 3. A model of experimental study of the dynamics of a circular saw blade has been built, and some dynamic parameters of the circular saw have been determined to solve problems and verify the computational models. Theoretical approach, and experimental model also can be used to study on cutting bamboo. The experimental formula has been developed to determine the specific shear resistance and the surface roughness of the cutting section, and the reasonable parameters of the bamboo cross-section saw have been determined including; cutting angle δ = 48.50; grinding angle of main cutting edge β = 29.50; Rotating speed of saw blade v = 4150.8 rpm, pushing speed U=0.12m/s and motor power N=1.854 kw with the above reasonable parameters for minimum cutting resistance, quality cutting surface is improved. 4. Scientific significance of the research results of the thesis topic The research results of the thesis project have built a model, established the equation to calculate the force acting on the elements of the cutting teeth, the system of differential equations of motion of the saw blade, the system of vibration equations of the saw clade to investigate the influence of some parameters of cutting teeth, the rotational speed of the saw blade on dynamics functions of the circular saw when cutting bamboo. Theoretical survey results and experimental research have identified a number of reasonable parameters of the bamboo cross- section saw, which can be the scientific basis for the calculation, design and manufacture of cross-sectional circular saws used for cutting some bamboo species in Vietnam. 5. The practical significance of the thesis The research results of the thesis can be used for the design and manufacture of bamboo circular saws, in addition, they can also be used as references for establishments of and other facilities related to bamboo processing in Vietnam. Chapter 1 STATE OF THE ART 1.1. Overview of researches on bamboo crosscutting saws 1.1.1. Overview of research works on circular saws in the world In the world, there are many research works on circular saws, but only focusing on the vibration of the saw blade, the cutting speed of the saw blade, there only are
3 some studies on the dynamics of the circular saw, but the This work mainly on the circular saw for cutting bamboo. 1.1.2. Overview of research works on circular saws in Vietnam Wood cutting has been studied by many scientists for a long time that has been relatively completed, but research on cutting bamboo is still limited, in which research on cutting bamboo with a circular saw has not yet been published. But bamboo has a vascular structure like in wood, so the principle of cutting bamboo can be based on the principle of cutting wood 1.2. Research contents In order to achieve the research objectives stated above, and based on the limitations and scope of the study, the research content is set out as follows: 1.2.1. Theoretical research The content of theoretical research addresses the following issues: – Building a model to calculate the force acting on the elements of the blade in the process of cutting bamboo; – Formulate the calculation equations for the force acting on the cutting tooth elements in the process of cutting bamboo; – Determine the specific shear resistance, investigate the parameters affecting the cutting force ratio, working as a basis for calculating and designing the elements of the cutting teeth; – Building a dynamical model of the saw blade's motion, setting up the differential equations of motion of the saw blade, examining the set of dynamic differential equations to draw the necessary conclusions; – Build a model, set up the vibration equation of the saw blade, investigate the set of equations to propose solutions for anti-vibration of the saw disc to improve the quality of the cutting surface. 1.2.2. Experimental study Experimental results have been calculated according to the theory and determine the shear force, the specific shear force in the process of cutting bamboo. From the experimental results, some optimal parameters of cutting teeth have been determined, so the content of the experimental research includes the following issues: – Measure the force acting on the cutting teeth when cutting the bamboo to test the results that had already been calculated based on the theory approach; – Measure the vibration of the saw blade when cutting horizontally to verify the theoretical calculation model; – Determine the specific cutting resistance as a basis for calculation to determine the optimal parameters of the cutting edge; – Determine the reasonable pushing speed, cutting speed and motor power for the bamboo cutting cicular saw.
4 Chapter 2 Kinematics and dynamics of the bamboo crosscutting process 2.1. Determination of the forces acting on the cutting teeth during crosscutting bamboo 2.1.1. Modeling the force acting on the cutting elements of the saw tooth The diagram of the force acting on the elements of the cutting teeth is shown in Figure 2.1. Figure 2.1: General diagram of the total forces acting on the elements of the cutting teeth of the saw disc The sum of the forces acting on the cutting elements is determined by the following formula:   P  2 Pm1  Pt1  Ps1  Pb  Pm 2  Pt 2  Ps 2 h )     Q  2 Qm1  Qt1  Qs1  Qm 2  Qt 2  Qs 2 h )  (2.6) Where : Pm1; Qm1 - Cutting force and thrust acting on the cutting tooth tip;; Pt1; Qt1 - Cutting force and thrust acting on the front face of the cutting tooth; Ps1; Qs1 - Cutting force and thrust acting on the back face of the cutting tooth; Pb - Cutting force acting on saw blade;  - Main cutting edge , - rear angle of the main cutting edge,  - Grinding angle of the main cutting edge, γ - front angle of the main cutting edge, 2.1.2. Diagram of the total forces acting on the cutting tooth The diagram of the total forces acting on the cutting teeth, chipless cutting is shown in Figure 2.2.
5 H  Z p1 G N p0-p1   A N  V d I o B p0-p2 N C  d M C1 p2 Figure 2.2: Diagram of the total forces acting on the cutting edge during cutting process 2.1.3. Components of the force acting on the cutting tooth According to the principle of wood cutting [21], there are 3 basic force components acting on the cutting teeth: a) Force acting on the tip of the blade At point B, the deformation is the largest, so the maximum stress causes the bamboo fiber cells to be destroyed. At the point N and M, the deformation is smaller, so the stress is smaller, so the pressure distributed on the cutting edge is zero. Thus, to facilitate the calculation process, the thesis divides pressure into two parts: + The part is evenly distributed in arcs AB and BC with pressure P1 and P2 in figure (2.3); + The part is distributed according to the law of cosine in arcs NI and IM, with pressures (Po - P1) and (Po - P2). b) Force acting on the cutting edge front surface According to the principle of wood cutting, the force acting on the front face is distributed according to the polygonal shape AGHN, to facilitate the calculation is divided into two parts: - The distribution follows the parallelogram AGZN with pressure , (Figure 2.3); - The distribution follows the triangle NZH. c) Force acting on the back of the blade According to the principle of wood cutting, the force acting on the back of the blade is distributed in a triangle CC1d with the largest pressure at C being P2. 2.1.4. Determination of the total force acting on the cutting tooth
6 After determining the impact forces on the nose, front, back, and side of the cutting edge, replace the formulas (into formula (2.6), after calculating the reduced transformation, we get the total force formula cutting P and pushing force Q acting on the cutting teeth when cutting bamboo is as follows:     P  h n (sin(90   )  sin(   ))  f (2  cos(90   )  cos(   ))    ng flb2 sin 1   2 2  2  h( p0  p1 )(90  (   )   cos(90  (   )  f ( sin(90  (   )  2 )   2  2 2  2h ( p0  p2 )(   ) 2        (   ) cos(   )  f  sin(   )    2     2 2 2   2  4(   ) 2 tg  f l2 EB 2  . hE sin 2   .cos 2 1.cot g1.tg (  1 )  1  f  tg ( 1  1 ) 4 L 4 h.E. (2.32)   .sin 2 (90   ) cos(90   ) L  2 B( P0  P2 )(   ) 2      Q  sin(   )  (  2  )  f (   )( cos(   )    2 2 2   4(   ) 2 2 2  cos 2  cot g  Cd  2 B cos  cot g  f   hE EB 2 1   sin 2  l 2  4L 4 1 2   2 f F l1 cot g   cd  B sin   cos   2  f cos   sin     t h B (2.33) From the formula (2.32), (2.33), there are the following conclusions: In the process of cross-cutting bamboo, the blade performs a complex cutting process, many cutting angles and cutting edges simultaneously join to form the cutting chip. The formula for total forces acting on the cutting edge (2.32) is established by taking into account most of the factors involved in the cutting process. In the formula of total force acting on the cutting teeth (2.32), there are many influencing factors, these factors affect the cutting force differently. The law of influence of factors on the shear force is shown in formula (2.32), to find the law of influence of the parameters on the shear force, it is necessary to investigate the formula (2.32), the results are basis to calculate the optimal parameters of the blade and cutting power. 2.2. Kinematics of a circular saw for cutting bamboo 2.2.1. Kinetic relationship between saw blade cutting speed and bamboo push speed a) Calculation model of the circular saw when cutting Calculation model of the kinematic relationship between shear speed and thrust speed is shown in Figure 2.3
7 Figure 2.3: Calculation model of a circular saw when cutting bamboo b) Kinetic relationship between the cutting speed of the saw blade and the pushing speed of the bamboo Assuming that the shear rate vector V has the same direction as the line connecting the tooth vertices, the vector →𝒖 forms an angle . with the vector V. During the cutting process with time interval t0, point A moves to B with a travel distance t (tooth step), and at the same time B also moves to point D, the displacement distance is BD=C called is the displacement of a tooth or the amount of chip intake of a tooth. 𝐶 𝑡 𝑢 𝐶 𝑢 From formular t 0= and t0= , leading to =  C = t 𝑢 𝑉 𝑉 𝑡 𝑉 (2.34) The chip thickness is the distance between the two orbits of the two saw teeth. In Figure 2.9, that distance is MB = h (chip thickness) h=C.sin1 In which: 1- Angle formed by the orbit of the tooth tip with the direction of the vector →𝑢. Since u is much smaller than v, then 1=. Therefore: 𝑢⋅𝑠𝑖𝑛 𝜑 ℎ = 𝐶. 𝑠𝑖𝑛 𝜑 = 𝑡 𝑉 𝑉⋅ℎ Relation of thrust speed and pitch: 𝑢 = (2.35) 𝑡⋅𝑠𝑖𝑛 𝜑 From the kinematic relationship of the bamboo cross-section, the following observations are made: - The push speed of bamboo into the saw is proportional to the cutting speed, inversely proportional to the tooth pitch, when the cutting speed is large, the pushing speed is high, thereby increasing the cutting productivity, when the tooth pitch is large, making the thickness of cutting chip larger, and pushing speed smaller
8 2.2.2. Building a kinematic model to calculate the arc length and cutting area at a bamboo cross-section First formula problem: Given two circles with centers O and O1 with radius R and d, respectively (R > d). Let L be the OO1 distance (Figure 2.4). . Let's calculate the length L: Figure 2.4: Diagram of calculating the arc length of the saw blade with bamboo So in this case we get S = α.R2 + β.d2- R.L.sinα. (2.44) Second problem: The saw blade is a circle with center O and radius R. The donut shape is limited by two circles of bamboo with the same center O1 with radius d1 and d2 (with d2 < d1 < R). The donut moves on a straight line with a distance of h from O, with constant speed v, it is necessary to calculate the length of the circumference of the circle with center O inside the donut shape and the area of the donut inside the circle with center O by time t . v ≤ Figure 2.5: Diagram to calculate the contact area of the saw blade with bamboo We consider only the time during which the donut shape is at the starting position (a) of the cutting process and at the end (b). Thus, the donut shape travels d   R  d1  h  d1   R  d1   h  d1  2 2 2 2 the distance: So the time is considered in the range: 0  t  Vd  T . At the specific time t: x = V.t Then, OI   R  d12  h  d12  V .t (2.47)
9 Thus, OO1  L  2V .t  R  d1   R  d1  h  d1   ( R  d  Vt )2 2 2   1 (2.48) 2.3. Dynamics of circular saws for crosscutting bamboo 2.3.1. Building a dynamic model of the circular saw during crosscutting The system has 3 links, including 2 rotating joints and one translational, the dynamic model of the bamboo cross-section saw is shown in Figure 2.6. Figure 2.6: Dynamic model of a circular saw for cutting Symbols on figure 2.6: M 1 - Active torque of shaft I (motor shaft); M 2 - Active torque of shaft II M 2  M1 , in which  -belt drive efficiency M c - The shear resistance moment caused by the bamboo cutting force M c  Fc R where, R is the radius of the saw blade Fd - Pushing force of bamboo in to saw blade; Fms - The friction force of the table pushing the bamboo into the saw ); ( Fms  m3 gf3 ); f 3 - Coefficient of friction of the table pushing force of the bamboo into the saw blade Fc - Shear resistance of bamboo (value depends on the type of bamboo). 2.3.2. The differential equation of motion of the saw blade The motor drives the saw disc with a power of W0 and transmits it through the belt to create a rotational torque M for the saw disc and the maximum angular speed for the blade.
10 h Figure 2.7: Calculation diagram of motion kinematics of saw discs cutting through bamboo a) Kinetic energy of the saw blade Kinetic energy of volume element dm at coordinate (x,y,z) can be calculated: (x  y z ) (x  y ) 2 2 2 2 2 2 dTm  dm.  dm.  dm. z 2 2 2 Integrate over the entire volume of the saw blade 0  x  y  R1 thì z = 0 2 2 2 Kinetic energy will be: T   dTm   ( x 2 y ) dm   z2 dm 2 2 2 V V V (x  y ) r   2 2 2 2 2 2  dm   dm   r dm  J 2 - 2 2 2 2 (2.49) V V V In which J is the pole moment of inertia of the blade axis with respect to the center O. - 2 2  2 .(1   ) ( 3   )  J  2 R 3 z 2 dm    2 2 0 R    2 2 d ( r R1 ) rdr J 2 . 2 3 0 2 (2.50) V 1 where J2 moment of inertia about the center of a disc of uniform thickness, radius R2, mass density  (kg/m2), with   RR1 2 Therefore, The kinetic energy of the system is: T  J 2  J 0 2 2 2 (2.51) (1   ) ( 3   ) 3 where J0  3 .J 2 and   RR1 (2.52) 2 b) The potential energy of the blade:  C  C 2 2 (2.53) - The centrifugal force of the volume element dm at coordinates (x,y,z) is: dN  dm.r. 2 (2.54) where r  x 2  y 2 and R1 ≤ r ≤ R2 .
11 Figure 2.8: The calculation diagram potential energy of the circular disc The force component perpendicular to the disc surface of centrifugal force vector dN is dN with dN  dN.sin  dN. , the force component causes a moment with: dM LT  ( r  R1 ).dN. (2.55) From (2.54) and (2.55), Integrate both sides of the equation (2.55) on on the part of volume V satisfying R1 ≤ r ≤ R2. Since the saw disc has the same thickness in about R1 ≤ r ≤ R2 so dm   .r.dr.d . The component perpendicular to the blade surface of the centrifugal force dN is dN ,with dN  dN.sin   dN. , this force component causes a moment: dM LT  ( r  R1 ).dN. (2.55) Substitute (2.54) into (2.55) and integrate both sides (2.55) over the part of volume V according to R1 ≤ r ≤ R2. Since the saw blade has the same thickness in the range R1 ≤ r ≤ R2, so . Result is investigated: 2 1   1   4  2 1   1 4  R2 M LT     d  r 2( r  R1 )dr  2 2 .R24 .  2     . 12   3 12  4J 2 0 R1  3  or M LT  CLT . (2.56) 2 1   1  4 with CLT  4J 2    , (N.m/rad) (2.57)  3 12   LT  CLT .  2 Leading to the potential energy MLT : 2 (2.58) Thus, potential energy of the system:    c   LT  C   CLT . 2 2 2 2 (2.59) c) Work of the external force - Work generated by the bamboo cutting resistance and the friction force between the saw blade and the bamboo: Ac If the ratio of the bamboo cross-sectional force is K (N/mm2), the bamboo shear force will now be: Fc  K.hc .hcua .nrc , (N) (2.61) With : hcưa - saw circuit thickness, (mm). Force Fc and momentum Mc Mc = R2. Fc (2.63) With R2 - Radius of saw blade, (m)
12 Figure 2.10. Graph of shear force Figure 2.9. The process of Fc cross-cutting bamboo of saw of the saw blade blade d) The differential equation of motion of the saw blade Using Lagrang's equation II: 2  J 0    C   CLT .   2 2 2 L T    J (2.70) 2 2  2 2    and A  Ac  Add  An   ( M c  M ms ).  M dd .  M 2 0  (2.71) 0 Thus,  d  L  L A       dt       (2.72)  d  L   L  A     dt         J   M 2 .  M 2  ( M c  M ms ) Or  0 (2.73) J   (C  C ).  M  0 LT dd M dm Where : M2  , N.m  1  dm 0 Comment: Formula (2.73) is the differential equation of motion of the saw disc. The quantities in equation (2.73) depend on the geometrical and mechanical parameters of the saw blade, and the physical and mechanical properties of bamboo. There are also: Mc , Mms , Mdđ as a function of the time factor (t) , (due to dependence v(t)). CLT , Mc also depends on  . . In order to determine the law of influence of saw-disc speed on the kinematic characteristics of saw blade in the process of cutting bamboo, it is necessary to investigate the system of differential equations (2.73).
13 2.4. Calculation of the stiffness of the bamboo cross saw blade 2.4.1. Building a model to calculate the stiffness of the bamboo crosscutting saw blade The rim is clamped on the inner rim, the outer rim is subjected to a uniformly distributed cutting force q0, the model for calculating the stiffness of a bamboo cross-section saw disc is shown in Figure 2.11. Figure 2.11. The rim model is clamped at r = b, uniformly loaded with q0 at r = a 2.4.2. Calculating the stiffness of the saw blade for crosscutting bamboo Calculation results, we get the formula for calculating the hardness of the saw blade as follows: ( a  b )2 Với C , (Nm/rad) (2.94)  a 2  b2 A1 2 2  A2 a 2  ln a   8 D  ( a  b )      4   8 D  b  Thus, according to the definition of the stiffness of an elastic body, C is the stiffness of the annular disc that is mounted at the inner boundary r = b, subjected to a uniformly distributed load perpendicular to the blade’s surface on the boundary r = a and has intensity q0 . 2.5. Vibration of saw blade during operation 2.5.1. Sources of agitation causing vibration To determine the law of shear resistance causing vibration for the saw blade, the thesis conducts an experiment to determine the intensity and the law of shear resistance. The results of shearing resistance acting on the saw blade are cyclical and have the form that shown in Figure 2.12. 100 80 60 Lực cắt (N) 40 20 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Thời gian (s) Figure 2.12: Graph of shear force variation over time
14 2.5.2. Vibration of saw blade during crosscutting The vibration model of the saw blade is shown in Figure 2.13 as follows: Figure 2.13: Vibration model of saw disc when operating 1- Engine catch rack; 2- Electric motor; 3- Saw blade support shaft ; 4- Saw disc ; 5- The backing plate holds the saw disc. ω - Angular velocity of the saw disc ; θ – The angle of swing of the saw disc relative to the plane of the saw disc At no load, the saw disc rotates with high angular speed ω, the saw disc rotates and vibrates freely with a command angle relative to the plane direction of the angle saw blade θ is determined by the system of equations as follows: J   M .   M 2  ( M c  M ms )  2 0  (2.102) J 0  (C  CLT ).  0 Where: J - the unique moment of inertia of the saw blade with respect to the center O; k - torque transfer coefficient from the motor to the saw blade. The coefficient k has (1   ) ( 3   ) 3 R units of N.m. J0  3 and   R1 ; .J 2 2 J2 - moment of inertia about the center of a disc of uniform thickness, radius R2, mass density  (kg/m2); C – is the hardness of the saw disc according to formular (2.94); CLT – The centrifugal stiffness of the saw disc due to the centrifugal force of the disc when the saw disc rotates is calculated by the formula (2.57). C  CLT The frequency of free oscillation at no load is   . J0 Note that the stiffness component of the saw disc produced by the centrifugal force, CLT, depends on the rotational speed of the saw blade  . When there is a load, the saw blade is subjected to the shear resistance moment Mc calculated according to (2.48), the frictional resistance Mms and the excitation force acting perpendicularly to the blade face is P(t). The force P(t).
15 evenly distributed on the saw blade produces a bending moment Mdđ that causes the saw blade to vibrate (shown in the second equation in (2.103);    J   M 2 .  M 2  ( M c  M ms ) (a)  0 (2.103)  J 0  ( C  CLT ).  M dd (b ) Trong đó: M dđ = R2 .P(t) với R 2 bán kính lưỡi cưa và P(t) có dạng  2 P( t )  a0   a j .cos( j. .t ) j 1 T 2.6. Investigating the influence of some parameters on the specific shear resistance of the cutting teeth during crosscutting bamboo 2.6.1 Effect of cutting angle δ and chip thickness h on specific shear force The results of investigation on the influence of cutting angle and thickness of cutting chips on specific shear resistance are shown in Figure 2.14 . Figure 2.14: Effect of cutting angle () and chip thickness (h) to the specific shear force K From the survey results received above, there are some comments as follows: - The law of influence of cutting angle  and chip thickness on specific shear resistance is a nonlinear function, when the cutting angle increases from 300500, the specific shear resistance decreases, when the cutting angle increases from 500  700, the shear resistance increased separately, this law is consistent with the theory of wood cutting. From the survey results, it is found that the specific shear resistance is most beneficial when the cutting angle is between 450 and 550. 2..6.2. Effect of grinding angle  of main cutting edge and cutting angle  on the specific shear force The survey results of the influence of the main cutting edge grinding angle, the cutting angle to the specific shear resistance are shown in Figure 2.15.
16 Figure 2.15: Effect of main cutting edge grinding angle  and cutting angle  on specific shear resistance Comments: - When the grinding angle is small, the specific shear resistance is small, when the grinding angle is large, the specific shear resistance is large. The specific shear resistance is covariant with the main cutting edge grinding angle, the smaller the grinding angle, the smaller the specific shear resistance, when the grinding angle decreases from 300 to 200, the specific cutting resistance decreases slowly, when the grinding angle increases from 300 to 400the specific shear resistance increases very rapidly. 2.7. Investigating the dynamics of saw discs during crosscutting bamboo 2.7.1. The results of the survey on the dynamics of the saw blade The thesis investigates the influence of the rotational speed of the saw disc on the angular momentum on the shaft mounted with the saw disc. The study conducted a survey with 5 rotational speeds of the saw disc, v=2500rpm; v=3000rpm; v=3500rpm; v=4000rpm; and v=4500rpm. The theoretical survey results are shown in Figure 2.16. Figure 2.16: Graph of the angular momentum of the saw blade when changing the rotational speed Comment: Through the survey, we see that when the speed increases from 2500 rpm to 4000 rpm, the impulse increases, when the speed increases from 4000 rpm to 4500 rpm, the impulse decreases. When the rotation speed of the saw blade is 4000 rpm, the maximum torque. From the results, we can draw a graph of the relationship between the rotational speed of the saw blade and the torque on the saw blade shaft as shown in Figure 2.16.
17 2.7.2. Vibration of the saw blade The thesis conducts a survey in four cases with the rotational speeds of the saw disc: v1=2000v/min; v2= 3000 v/min; v3= 4000v/min; v4= 5500v/min The results of the vibration investigation of the saw blade are shown in Figure 2.17. v= 2000v/ph amax= 1,7mm v= 3000v/ph amax= 0,9mm v=4000v/ph amax=0,43mm v=5000v/ph amax=0,26mm Figure 2.17: Graph of the horizontal vibration amplitude of the saw blade when cutting across the bamboo tube with different revolutions of the saw disc Comment: If only considering the effect of the number of revolutions of the saw blade, when the number of revolutions of the saw blade increases, the amplitude of vibration of the saw blade decreases (inversely varies with the rotation speed of the saw blade), when the number of revolutions of the saw blade increases to above 4000 rpm, the amplitude of vibration decreases slowly. As the number of revolutions of the saw blade increases, the frequency of the oscillation increases. Therefore, The large amplitude of vibration affects the quality of the cutting surface. Chapter 3 EXPERIENCE RESEARCH FOR THE CONFIRMATION OF THEORY MODEL 3.1. Organization and conduction of the experiments 3.1.1. Measuring the torque on the saw-blade axis during crosscutting bamboo The results of the torque measurement experiment are shown in Figure 3.1 .
18 Figure 3.1: Torque diagram of saw blade shaft against cutting time 3.1.2. Measuring the horizontal vibration of the circular saw during crosscutting The results of the oscillation measurement are shown in Figure 3.2 . Figure 3.2: Diagram of horizontal vibration amplitude of saw blade when cutting bamboo with time corresponding to the rotational speed of the saw blade at 4000 rpm 3.2. Verifying the calculation model of the cutting force of saw teeth during crosscutting bamboo The results of the verification of the shear force calculation model are shown in Table 3.1 Table 3.1. Separate shear force with different cutting angles  cutting Specific shear resistance K (N/mm2) angles  Experimental Error (%) Theoretical result (0) result 30 13,32 15,23 11,1 40 11,72 13,17 11,1 50 10,37 12,37 13,9 60 12,61 14,24 11,4 70 16,54 18,52 8,1