Linier Research Articles

An analysis of the difficulty of prospective mathematics teachers on algebraic materials

Prospective mathematics teachers experience errors in solving straight-line equations, such as using unorthodox methods, answers that conflict with concepts and wrong calculations. This study aimed to analyze the difficulties of prospective mathematics teachers in algebraic material about straight-line equations. This research is descriptive qualitative research with a case study approach. The subjects in this study were students of the 3rd semester of the Mathematics Education Study Program, Widya Dharma University, Klaten, who had taken field analytic geometry courses. The data collection method in this study used the test method and the interview method. This study uses triangulation techniques to obtain valid data. The triangulation technique used is a triangulation method that compares data or information using different methods. The research instrument includes the main instrument, namely the researcher, whose role is to collect research data and auxiliary instruments in tests and interview guidelines. The data obtained from the interviews were analyzed using the analysis model of Miles, Huberman and Saldana, which includes data condensation, data presentation and drawing conclusions. The results of this study are that prospective mathematics teacher have difficulty in: (1) identifying which equations are straight lines and which ones are not, (2) explaining the concept of gradient, (3) proving the statement that two parallel lines have the same gradient, (4) prove the statement that two lines are perpendicular if the two gradients are multiplied the result is -1, (5) prove the formula for the equation of a straight line with a known gradient and a point through which it passes, and (6) prove the equation for a straight line if two are known the point through which. This study concludes that prospective mathematics teachers have difficulty in the material of straight-line equations.

Six-Dimensional Manifold with Symmetric Signature in a Unified Theory of Gravity and Electromagnetism

A six dimensional manifold of symmetric signature (3,3) is proposed as a space structure for building combined theory of gravity and electromagnetism. Special metric tensor is proposed, yielding the space which combines the properties of Riemann, Weyl and Finsler spaces. Geodesic line equations are constructed where coefficients can be divided into depending on the metric tensor (relating to the gravitational interaction) and depending on the vector field (relating to the electromagnetic interaction). If there is no gravity, the geodesics turn into the equations of charge motion in the electromagnetic field. Furthermore, symmetric six-dimensional electrodynamics can be reduced to traditional four-dimensional Maxwell system, where two additional time dimensions are compactified. A purely geometrical interpretation of the concept of electromagnetic field and point electric charge is proposed.

The influence of wind load on the stress characteristics of dropper for a high-speed railway

In this paper, the influence of wind load on the stress characteristics of dropper for a high-speed railway is studied. The section method is used to obtain the vibration equation of the dropper, and the finite difference method is used to convert the partial differential equation of the dropper vibration into a finite difference equation. Through the force analysis of the contact line section upwind, the vibration equation of the contact line with air damping is obtained. Thus, the partial differential equation of the motion can determine the initial and boundary conditions of each dropper. The MATLAB program is written to obtain the stress change diagram of each dropper, and the influence of wind load on the stress characteristics of the dropper is analyzed. The results show that the maximum tensile and compressive stresses of each dropper are different due to the difference of wind load and dropper location, and the dropper in the middle location is most sensitive to the change of wind load. At a low wind speed, there are immediate rebound and obvious attenuation vibration stages during the stress change of dropper. In addition, with the increasing speed of wind load, the stress amplitude and the maximum tensile stress of dropper do not almost change or decrease except the middle dropper.

A Cable Harness Routing Method Based on the Expected Maximum Crosstalk

With the increasing number of interconnected cables in electronic systems, the crosstalk between interconnected cables has played an important role in the intrasystem interference performance. However, the traditional routing method based on the shortest path cannot solve the problem of cable crosstalk. In this article, a novel cable harness routing method based on the expected maximum crosstalk is proposed. First, the closed-form expression for crosstalk based on the electrically small assumption is derived from the multiconductor transmission line (MTL) equation. According to this expression, the concept of maximum overlap length corresponding to the desired maximum crosstalk is developed. In addition, a conservative strategy is proposed to deal with higher frequency cable routing. The proposed routing method consists of the escape graph and the routing algorithm based on the maximum overlap length. A Dijkstra’s algorithm variant with the maximum overlap length as the constraint condition is proposed. The proposed method is applied to two single-ended and differential signals cable harness routing cases and compared with the traditional method to show that the routing results of the proposed method would keep the crosstalk between cable harness branches below the expected maximum crosstalk.

CARC4: LVAD Use in Minorities: Are We Making Progress?

Background: Published demographic data suggest that black and Hispanic patients are less likely to receive a left ventricular assist device (LVAD) in comparison to white patients. However, this conclusion is based on total implant data and may not capture the true utilization of the technology, independent of access to therapy. We therefore sought to describe the utilization rate of LVADs over time stratified by race in an in-patient setting Methods: Utilizing the National Inpatient Sample (NIS) data from 2013 – 2019, we obtained all patients admitted to the hospital with a primary diagnosis of heart failure and a secondary diagnosis of cardiogenic shock, who then went on to receive an LVAD during that hospitalization. We calculated the annual percentages of non-Hispanic white, nonHispanic black, non-Hispanic other, and Hispanic patients who received an LVAD in order to define an LVAD Utilization Rate (LUR). We also calculated the annual percent differences in LVAD use, defined as the LVAD Utilization Rate Gap (LURGAP), across the racial groups using non-Hispanic whites as the reference. Results: LUR were stable across all racial groups during the defined period, with white patients being implanted at a higher rate than any other racial group (Fig 1). The LURGAP is highest when comparing whites to Hispanic and other (non-black/non-Hispanic) patients and has not narrowed across any racial comparison. When plotted as a linear relationship, the LURGAP has widened comparing white to black patients (WB LURGAP Slope-intercept form y=1.9407x + 33.011 Fig 2). Conclusion: LVADs remain under-utilized in racial minorities despite awareness of this potential disparity. In patients admitted with heart failure complicated by cardiogenic shock, there is a growing underutilization of LVADs in black patients. Further studies are needed to examine this trend more closely.

Generation of energy in console piezoelectric energy harvesters

Energy harvesting of mechanical vibrations and their conversion into electrical energy using piezoelectric devices has become widespread. This has been made possible by the creation of high-energy piezoelectric materials and the proliferation of miniature devices with a few milliwatts of power.
 In this work, the oscillations of the rod cantilever bimorph energy harvester under harmonic loads are investigated. A two-layer rod consisting of a brass base and a rectangular piezoelectric element with electroded flat surfaces without and with tip mass is considered. The thickness of the layers is much less than the width and the width is much less than the length, which allows us to use the hypothesis of flat sections and assumptions of the potential difference linearity by thickness of the element, as well as beams bending relations.
 There is derived the characteristic equation for beam bending oscillations, the wave numbers, circular frequencies and natural frequencies are determined. There is carried out The averaging of material characteristics over the cross-sectional area. Eigenforms of oscillations are constructed, the dependence of natural frequencies from body size and tip mass is analyzed.
 The next step is to study the forced oscillations of the energy harvesters with tip mass at the end at given oscillations of the base. The equation of the elastic line of the console is formed, the maximum deflections and angles of rotation are determined. The voltage generated on the piezo element plates is determined taking into account the electrical resistance. Due to the voltage and resistance of the conduct line the power of the energy harvester is determined. Curves of voltage and power dependence from load frequency and external resistance are constructed. It is established that the voltage and power of the element change in proportion to R. The maximum power of the energy collector occurs in the vicinity of resonances, and before the first resonance the power is almost zero. Between the first and second resonance, the power is approximately 1,5 mW. During the transition to the ultrasonic zone, the power of the energy collector increases significantly.Analysis of the harvester operation at resonant frequencies requires consideration of the damping of oscillations in the material.

UV Spectrophotometric Method Development and Validation for Amlodipine Besylate in Bulk and Tablet Dosage Form

Analytical method development and validation is important in development of pharmaceutical preparations. In present study a spectroscopic method for determination of Amlodipine besylate in pharmaceutical dosage form has been developed and validated. The wavelength maxima of Amlodipine besylate was found to be 360nm. Ethanol was used as a solvent. Amlodipine besylate obeys beers law in the concentration range of 5-40μg/ml. The line equation obtained is y = 0.0136x + 0.001 with correlation coefficient (r2) of 0.998. Interday, intraday variations were studied to determine the precision of the proposed method and was found to be with good precision as the %RSD was less than 2%. The assay of 2 different marketed formulation (A and B) has been performed and the % assay of A and B was found to be 98.3% and 99.2% respectively. The sensitivity of the method was determined by LOD and LOQ was found to be 0.08123µg/ml and 0.2461µg/ml respectively. The method employed the parameters like linearity, accuracy, precision, sensitivity, robustness, ruggedness and all the procedures were as per ICH guidelines.

0687 The circadian misalignment is associated with reduced slow-wave sleep in individuals with autism spectrum disorder

Abstract Introduction Sleep disturbances are one of the key features among individuals with autism spectrum disorder (ASD). Many studies have uncovered critical developmental links between cognition, behavior, and sleep. It is suggested that the circadian system desynchronization plays a vital role in the development of ASD. While research on sleep disruption and circadian disturbance has accumulated, only a few studies have investigated a relationship between sleep architecture and circadian rhythm of individuals with ASD to date. We aim to elucidate the relation using the methods of dim light melatonin onset (DLMO) and ambulatory PSG. Methods Eleven individuals with autism (3 females, age: 13.07 ± 4.76 years; age range: 8-23 years) were recruited. After a week of systematic desensitization, an ambulatory overnight PSG was conducted in the participant’s home. Participants collected saliva samples independently at home on two consecutive days. The first evening sample took place 3 hours before the average sleep onset time and continued each 30-minute interval afterward for a total of 5 evening samples. The DLMO was calculated for each day by plotting melatonin levels against the time of saliva sampling. Linear regression was used to determine the best-fit line equation for each plot to calculate when melatonin levels first reached 4 pg/mL and continued to rise. Results The percentage of Stage N3 sleep across the night was significantly negatively associated with phase angle (time between DLMO and sleep onset), revealing that Stage N3 percentage decreases as the phase angle increases. The Phase angle showed a significant positive association with REM percentage across the night. Additionally, a significant difference was found between the mean phase angle for the ASD subjects in this study and the mean phase angle expected from a group of age-matched, typically developing (TD) individuals. Conclusion Our data revealed that circadian misalignment in individuals with ASD is associated with sleep architecture characterized by reduced slow-wave sleep and increased REM sleep. Given the importance of slow-wave sleep for memory and cognitive functions, this finding may contribute to understanding the relationship between sleep alterations and brain development in ASD. Support (If Any)

Study on Strength Theory Effect of Plastic Zone Distribution of Roadway Surrounding Rock

The plastic zone of surrounding rock is an important basis for evaluating the stability of roadway, and the distribution of plastic zone is closely related to the strength theory. The equation of boundary line of plastic zone is derived by using the approximate plastic condition method. According to specific parameters, the plastic zone is calculated. When the lateral pressure coefficient increases from 0.3 to 1, almost all the plastic zones calculated by different strength criteria have four shapes: butterfly, curved rectangle with concave horizontal direction and convex vertical direction, approximate ellipse, and circle, but the butterfly shape based on DP1 is not obvious. There are differences in the maximum plastic radius calculated by different strength criteria with the same lateral pressure coefficient from large to small: DP3 criterion, DP2 criterion, Mohr–Coulomb criterion/UST (b = 0)/DP5 criterion, UST (b = 0.25), DP4 criterion, UST (b = 0.5), UST (b = 0.75), Matsuoka–Nakai criterion, UST (b = 1), Mogi–Coulomb criterion, Lade–Duncan criterion, and DP1 criterion. With the increase in lateral pressure coefficient, the difference between the results calculated by different strength criteria is smaller. When K0 = 0.3, the maximum plastic radius is distributed at 43°∼47°. The results of this paper show that the strength theory effect of plastic zone distribution cannot be ignored, which enriches the theory of approximate plastic condition method and can provide an important reference for roadway stability evaluation and support design.

Mathematical and deep learning analysis based on tissue dielectric properties at low frequencies predict outcome in human breast cancer

BACKGROUND: The early detection of human breast cancer represents a great chance of survival. Malignant tissues have more water content and higher electrolytes concentration while they have lower fat content than the normal. These cancer biochemical characters provide malignant tissue with high electric permittivity (ε´) and conductivity (σ). OBJECTIVE: To examine if the dielectric behavior of normal and malignant tissues at low frequencies (α dispersion) will lead to the threshold (separating) line between them and find the threshold values of capacitance and resistance. These data are used as input for deep learning neural networks, and the outcomes are normal or malignant. METHODS: ε´ and σ in the range of 50 Hz to 100 KHz for 15 human malignant tissues and their corresponding normal ones have been measured. The separating line equation between the two classes is found by mathematical calculations and verified via support vector machine (SVM). Normal range and the threshold value of both normal capacitance and resistance are calculated. RESULTS: Deep learning analysis has an accuracy of 91.7%, 85.7% sensitivity, and 100% specificity for instant and automatic prediction of the type of breast tissue, either normal or malignant. CONCLUSIONS: These data can be used in both cancer diagnosis and prognosis follow-up.

MENINGKATKAN KEMAMPUAN KOMUNIKASI MATEMATIS SISWA SMP 1 LEMBANG MELALUI PENDEKATAN KONTEKSTUAL PADA MATERI FUNGSI DAN PERSAMAAN GARIS LURUS

This study aims to examine the achievement and improvement of students' mathematical communication skills of SMP 1 Lembang on the material of straight line functions and equations, as well as examine the interaction between learning and KAM on improving students' mathematical communication skills. This research is a quasi-experimental research with Non-equivalent Control Group Design. The population in this study were all eighth grade students in one of the junior high schools in Lembang. The research sample was determined using purposive sampling. The sample consisted of two classes, the experimental class which received learning with a contextual approach, and the control class which received expository learning. The instrument used is in the form of students' communication ability test questions. The findings of this study are: (1) The achievement and improvement of mathematical communication skills of students who receive learning using a contextual approach is better than students who receive ordinary learning both as a whole and in KAM. (2) There is no interaction between learning and KAM (high, medium, low) on the achievement of students' mathematical communication skills

Calculation of the T – X phase diagram of tetradecane + hexadecane and tetradecane + pentadecane under high pressure by the landau mean field theory

Landau phenomenological model is applied to two binary mixtures (tetradecane + hexadecane and tetradecane + pentadecane) to calculate T−x (temperature - composition) phase diagram under high pressure for their solid – liquid equilibria. The phase line equation derived from the free energy of the solid phase is fitted to the experimental liquidus curve (T−x) from the literature and the parameters in the Landau expansion are determined. As observed experimentally, variation of the temperature with the composition below and above Te (minimum melting temperature) is almost linear at the pressures from 0.1 to 100 MPa in these binary mixtures.Our results indicate that the influence of pressure on liquid – solid equilibria can also be studied for the other binary mixtures or two – components systems by the Landau mean field model, as studied here.

Gender Identification of Embryonic Chicken in the Egg by Heart Beat Modulation Technique

The main goal of this study was to use a heartbeat modulation technique to determine the sex of a chicken embryo five days after incubation and investigate the effect of weight and temperature differences on the sex of the embryo. The embryo's growth after five days of incubation helps to determine the chicken's sex. As the temperature drops, so does the beat rate. In female embryos, the decline is more gradual. Female embryos have a faster rise in heart rate and return to normal after cooling. For the observation process, 200 fertilized eggs were collected and divided into four groups, and another 200 fertilized eggs were collected and divided into four groups for the identification process. Before incubation, the weight of 50 eggs from each group was measured, and five days later, the embryonic growth of each group's embryos was calculated, and samples were collected. The separation constant, embryo weight, and temperature are the essential factors in determining the embryonic chicken's sex. The relationship between heartbeat rate, embryo weight difference, and beat rate as temperature changes can be expressed as a first-order and first-degree differential equation. An integral combination can be determined and is of the form dy + Pydx = Qdx, where P and Q are only functions of x. Using this relationship, the separation constant c is equal to the difference between the heartbeat rate and the sine function of the embryo's weight difference over the cosine function of the embryo's beat difference during cooling. During the five-day incubation period, male chicks have an average beat rate of 62 beats per minute, while females have an average beat rate of 74 beats per minute. Male embryos gain weight faster than female embryos. As the temperature drops, so does the beat rate. In female embryos, the decline is more gradual. Female embryos have a faster rise in heart rate and return to normal after cooling.

Numerical Analysis on the RF Characteristics of the Gyromagnetic Nonlinear Transmission Lines

The gyromagnetic nonlinear transmission line (GNLTL) is a special transmission line loaded with ferrite cores, which can be used as a kind of wideband high-power microwave (HPM) source due to the pulse modulation mechanism. This article carried out a series of simulations and analyses focused on the RF characteristics of GNLTL. Based on the classic transmission line model (TLM) method, a numerical model linking the transmission line equations and the microscopic magnetization dynamics equations was established. The simulations systematically studied the effects of key parameters on the output characteristics especially the RF characteristics, including the effects of transmission line geometry, excitation pulse, magnetic material, and the biasing magnetic field. The simulation results and analyses revealed that almost each parameter has effects on the output, and the effects of different parameters are different. The research introduced in this article preliminarily reveals how the output microwave varies with the parameters and provides a method to find the appropriate parameter values of a GNLTL.

Implementasi Pendekatan Saintifik untuk meningkatkan Kemampuan Pemecahan Masalah Matematika Pada Materi Persamaan Garis Lurus di MTs Negeri 3 Cilacap

This study aims to determine the effectiveness of the scientific approach in improving mathematical problem-solving skills in straight line equations. This research is a classroom action research with 22 students as research subjects. This study consisted of two cycles with each cycle consisting of 2 meetings. The instruments used are in the form of questionnaires, interview sheets, and observation sheets. The data analysis technique used descriptive qualitative. The results of the analysis show that: 1) the scientific approach is effective to improve students' mathematical problem-solving abilities; 2) The problem-solving ability in the first cycle showed a fairly good category with an average score of 56.37 with the completeness of 49.99%; 3) The problem-solving ability in the second cycle showed a very good category with an average score of 81.81 with the completeness of 93.17%.

Analysis of Transient Response of ZPW-2000A Jointless Track Circuit Considering Frequency Variation.

In order to accurately analyze the influence of electromagnetic transient signals on the jointless track circuit when the electromagnetic transient signal propagates in the rail, it is necessary to consider the frequency-variable load terminated in the ZPW-2000A jointless track circuit and the frequency-variable loss inside the rail. A method is proposed for calculating the transient response of transmission lines system with frequency-variable end load of jointless track circuit. Firstly, the transmission lines model of jointless track circuit is established, based on multiconductor transmission lines theory, the model equation is deduced and discretized by finite difference time domain (FDTD). The vector fitting method is used to express the admittance of the tuning region in the track circuit, and the rational approximation function of the tuning region is derived from the poles, residues, and constants. The voltage and current at nodes in the tuning region are calculated by piecewise linear recursive convolution algorithm. Combined with the discrete transmission line equation, the current and voltage expression of the transient electromagnetic signal at the receiving end of the track circuit in time domain is obtained. Compared with state variable method, the error is less than 6%, which verifies the correctness of the proposed method. Finally, this paper studies the influence laws of different factors on the overvoltage at the receiving end of jointless track circuit and the weak links of jointless track circuit under the influence of transient electromagnetic signal. It provides theoretical reference for fault research and anti-interference analysis of ZPW-2000A jointless track circuit.

Studies to Explain Further, Why Percentages of Eicosanoid Precursor Fatty Acids Associate Positively in Chicken Muscle

Background: Polyunsaturated fatty acids with 20 or 22 carbon atoms are precursors of eicosanoids and docosanoids, which are important regulatory molecules in cell physiology. In breast muscle of chickens, we recently reported that percentages of these precursors were positively associated. Subsequently, we observed that the concentration ranges of the fatty acids seemed to cause the positive associations, e.g. between %EPA (eicosapentaenoic acid, 20:5: n3) and %AA (arachidonic acid, 20:4 n6). Aim: To explain further correlations between relative amounts of eicosanoid and docosanoid precursors. Methods: Typically, the precursors had low numbers and low variability, as compared with the predominant fatty acids, such as oleic acid (18:1 c9). We first present considerations concerning associations in general between relative amounts of three positive scale variables, two of which (A, B) having narrow ranges relative to the third one (C). Next, we show results of computer experiments to test the reasoning. Results and Discussions: We made S = A + B + C, i.e. %A + %B + %C = 100. %A correlated positively with %B, whereas %A (%B) related negatively to %C. The particular ranges of A, B, and C seemed to explain these associations. We found that slope of %A (abscissa) vs. %B approached B/A. Furthermore, slope of %A (abscissa) vs. %C approached –(1 +B/A), and that of %B (abscissa) vs. %C was near –(1+ A/B). We also show equations of regression lines concerning associations between A (B, C) percentages of S, when ranges of A and B are narrow relative to C. Finally, we compare slope values obtained by the formulas, and by linear regression. Conclusions: We suggest that Intended Ranges of eicosanoid precursor fatty acids might have arisen through evolutionary selection, thereby causing Distribution Dependent Correlations, mathematically. Possibly, this selection could improve the balance between eicosanoids (docosanoids). Definitions and Abbreviations: Variability: the width or spread of a distribution, measured e.g. by the range and standard deviation. Distribution: graph showing the frequency distribution of a variable within a particular range. In this article, we also use distribution when referring to a particular range, a – b, on the scale. Uniform distribution: every value within the range is equally likely. In this article, we may write “Distributions of A, B, and C were a - b, c - d, and e - f, respectively”. OA = Oleic Acid (18:1 c9); LA = Linoleic Acid (18:2 n6); ALA = Alpha Linolenic Acid (18:3 n3); AA = Arachidonic Acid (20:4 n6); EPA = EicosaPentaenoic Acid (20:5 n3); DPA = DocosaPentaenoic Acid (22:5 n3); DHA = Docosa Hexaenoic Acid (22:6 n3); DGLA= Dihomo Gamma Linolenic Acid (20:3 n6); EDA = Eicosa Dienoic Acid (20:2 n6); ETA = Eicosa Trienoic acid (20:3 n3).

PENGARUH PENDIDIKAN DAN LATIHAN (DIKLAT) TERHADAP KINERJA GURU DI SMP NEGERI 1 KECAMATAN SUNGGAL KABUPATEN DELI SERDANG

The purpose of this study was to determine how much influence education and training had on teacher performance at SMP Negeri 1 Sunggal. This type of research was quantitative with the total population in this study was 43 people. The method used in sampling in this study is total sampling. The data collection method used a questionnaire, the data analysis method used description analysis, requirements analysis test, and hypothesis testing. The results of this study stated that the distribution of Education and Training scores (X) was 13 people (30.2%) below the interval class average, 14 people (32.6%) were in the interval class average and 16 people ( 37.2%) above the average. This condition illustrates that the education and training at SMP Negeri 1 Sunggal based on the data above is above the interval class average. This shows that the training carried out at SMP Negeri 1 Sunggal shows an increase in teacher performance. The distribution of Teacher Performance scores (Y) as many as 29 people (67.5%) is below the interval class average, 11 people (25, 6%) were in the average class interval and as many as 3 people (7%) were above the average. Based on the data above, it can be seen that in general the teacher's performance is above the average. There is a positive influence between the training variables on teacher performance at SMP Negeri 1 Sunggal seen by the regression line equation = 138,089+0.724X with a constant of 138,089 stating that if there is no training value, the teacher's performance value is 138,089. While the regression coefficient X of 0.724 means that for every addition of 1 teacher performance value, the value of education and training increases by 0.724 or 72.4%. and the significance can be seen through the t-test obtained tcount of 3.317 while the value of ttable with a value of N = 43, then the significance of 0.05 is 2.01954. Therefore, tcount (3.317) > ttable (2.01954) with a significance level of 0.003 <0.05. This means that there is a significant relationship between the training variables on teacher performance at SMP Negeri 1 Sunggal.

Tuned-Mass-Damper-Inerter Performance Evaluation and Optimal Design for Transmission Line under Harmonic Excitation

To investigate vibration control and optimal design of transmission lines with tuned-mass-damper-inerter (TMDI), the motion equation of transmission lines with TMDI is established in the paper, and the closed-form solutions of the response spectrum of transmission line displacement are derived by the frequency domain analysis method. The design parameters of TMDI are optimized by fixed-point theory, and the vibration control performance of TMDI is discussed. The results show that the increase in apparent mass ratio has a positive effect on the vibration control performance of TMDI; the vibration control performance is greatly affected by frequency ratio and limited by damping ratio; the increase in both mass ratio and apparent mass ratio reduces the peak values of the displacement response spectra of transmission line with TMDI; however, blindly increasing the apparent mass and mass ratio (β > 0.2 or μ > 0.4) has a limited effect on improving the vibration control performance of TMDI; compared with conventional TMD, the peak values of the controlled displacement response spectrum of the transmission line with TMDI can be reduced by about 12%, and TMDI has a better vibration suppression effect on the transmission lines.

Bucket structure optimization of backhoe hydraulic excavator based on compound digging trajectory and limit digging force

A bucket structure optimization method based on compound digging trajectory and limit digging force was proposed for the problem that the real digging resistance of excavators is difficult to measure and difficult to use as bucket load for structure optimization. The uncertainty of the digging resistance in the actual digging process of the excavator was analyzed, and a digging trajectory was obtained by active digging using the compound digging action. Based on the limit digging force model, the digging force and its variation law were calculated, and analyzed for different hydraulic cylinder’s active digging in the trajectory. Based on the bucket shape line equation, a parametric model of the bucket was established using APDL language, and the bucket stress variation under different digging actions was analyzed. The bucket stress and mass were reduced by 4.59% and 5.84% respectively after optimization.