The simple harmonic vibration can be regarded as the uniform circular motion (decomposition) in two directions orthogonal to each other (that is, perpendicular to each other), and the motion in any one direction is a simple harmonic motion. It can be seen that the simple harmonic motion is much more complicated than the uniform circular motion.
The projectile motion can be decomposed into: a uniform linear motion and another uniform linear motion, so the projectile motion is much more complicated than the uniform linear motion.
In the process of orthogonal decomposition [1] of uniform circular motion, the centripetal force of the original size becomes the restoring force of periodic changes in both size and direction. Simple harmonic vibration is already complicated enough. Therefore, the vibration is quantitatively studied until the simple harmonic motion. However, the microscopic conditions of the vibrations we usually encounter are much more complicated than the simple harmonics. Therefore, the study of simple harmonic vibration transition to the study of vibration, thermal vibration, etc., requires insight, imagination and abstract thinking, logical reasoning and other capabilities.
The characteristics of the simple harmonic vibration are: 1. There is an equilibrium position (the only position where the vibrator should be stationary after the mechanical energy is exhausted). 2, there is a magnitude and direction of the cyclical change of the recovery force. 3. The frequency is single and the amplitude is unchanged. The vibrator is an abstraction of a vibrating object: ignoring the shape and size of the object, and using the mass point instead of the object for research. This particle that replaces a vibrating object is called a vibrator. The position of the vibrator at a certain moment is represented by the displacement x. The displacement x is the distance and direction of the "position of the vibrator at a certain moment" with the equilibrium position as the reference (base point - reference point). When we study the uniform shifting linear motion and the projectile motion, the reference point is selected at the starting point of the motion. When we study the uniform circular motion and the simple harmonic motion, the reference point is chosen at the center of the circle or at the equilibrium position (the fixed point).
The reference object should be the point that remains static (or assumed to be stationary) during the research process. Our physical idea is to "study from a certain amount and a constant quantity." There is a fundamental difference between the determined quantity and the constant quantity. When studying the uniform shifting linear motion and the projectile motion, the reference point is selected at the starting point of the motion. This is a certain amount, but not necessarily a constant amount. Especially when we conduct a segmentation study, the end of each phase is the starting point of the next phase.
We choose the starting point of the movement as the benchmark point, which can simplify the research process. This is subject to the principle of “simplification and simplification†in physics research. Therefore, we choose different benchmark points at different research stages. When studying the uniform circular motion and the simple harmonic motion, the problem is very complicated due to the macroscopic periodicity and the microscopic topologicality. Therefore, the starting point of the motion cannot be selected as the reference point for research, but the determination and the constant are selected. The center of the circle or the equilibrium position, as a reference point for research, is also subject to the principle of "simplification and simplification" in physics research.
In the simple harmonic motion, the amplitude A is the maximum value of the displacement x, which is a constant amount. The minimum time required for the vibrator to return to that state from a state (position and velocity) is called a period T. The vibration of the vibrator in one cycle is called a full vibration. The "number of times" of the full vibration of the vibrator in one second is called the frequency f. The period T is the time of one full vibration, and the frequency f is the number of times of full vibration in one second. Therefore, Tf=1 (four-equivalent formula 1), the circular frequency ω (read as [oumiga]) is one second. The center of the circle. The central angle corresponding to one full vibration is 2π (ie, 360 degrees). This is the concept of borrowing a uniform circular motion. In uniform circular motion, ω is called angular velocity. When the uniform circular motion is orthogonally decomposed into a simple harmonic motion, the angular velocity is converted into a circular frequency. (Someone also calls the circular frequency the angular frequency.) Obviously, ω=2πf (four-equivalent formula 3), (the angle corresponding to the total number of vibrations per second)
ωT=2π (four-equivalent formula 2) (the angle corresponding to each full vibration) Finally, the number of times of total vibration per minute is defined as "speed n", obviously, n=60f (four-equivalent formula 4) Among the four quantities of T, f, ω, and n, one is known, and the other three are known, so the four formulas that convert each other are called "four-equivalent". As long as the object reciprocates periodically, it is vibration. For example, the ball is shot, and its v-t diagram corresponds to the sawtooth wave in electrotechnical, so it is also vibration. Some people say: "There is no balance position in the ball, or the balance position is not in the symmetry center of the motion, so it cannot be considered vibration." People who say this, electrotechnical certainly did not learn well. There is a mathematical branch called the Fourier integral, which breaks down any vibration into a number of simple harmonic vibrations. The frequency of these simple harmonic vibrations is an integer multiple of the original vibration, and the main frequency (pitch) of the original vibration is the minimum frequency of these simple harmonic vibrations. Other multipliers (overtones), the amplitude is much smaller than the pitch. Therefore, this constitutes the concept of "sound" of non-harmonic vibration. The process by which the human ear distinguishes the sounding body is the process of using the Fourier integral spontaneously, automatically, and instinctively, which is very clever. Since the frequency of the sound is determined by the sound source, no matter how the sound wave propagates to our ears, we still accurately identify the characteristics of the starting sound.
Vibration in a Broad Sense In a broad sense, vibration refers to the process of describing the parameters of a system state (such as displacement, voltage) alternating between its reference value. In a narrow sense, it refers to mechanical vibration, that is, vibration in a mechanical system. Electromagnetic vibration is customarily called oscillation. The mechanical system maintains vibration and must have elasticity and inertia. Due to the elasticity, when the system deviates from its equilibrium position, a restoring force is generated to cause the system to return to its original position; due to inertia, the system accumulates kinetic energy during the return to the equilibrium position, thereby causing the system to move over the equilibrium position to the other side. It is because of the interaction between elasticity and inertia that the vibration of the system is caused. According to the degree of freedom of motion of the system, there are single degree of freedom system vibration (such as the vibration of the pendulum) and multi-degree of freedom system vibration. The finite multi-degree-of-freedom system corresponds to the discrete system, and the vibration is described by the ordinary differential equation; the infinite multi-degree-of-freedom system corresponds to the continuous system (such as rod, beam, plate, shell, etc.), and the vibration is described by the partial differential equation. A system that does not contain time in the equation is called an autonomous system; a time-independent system is called a non-autonomous system. According to the force of the system, there are free vibration, damped vibration and forced vibration. According to the elastic force and damping force properties, there are linear vibration and nonlinear vibration. Vibration can be divided into deterministic vibration and random vibration. The latter has no deterministic law, such as bumps in the vehicle's travel. Vibration is a common phenomenon in nature and engineering. The negative aspects of vibration are: affecting the function of instruments and equipment, reducing the working accuracy of mechanical equipment, aggravating the wear of components, and even causing structural fatigue damage; the positive aspect of vibration is that there are many equipments and processes that need to use vibration (such as vibration transmission, vibration grinding). , vibration sinking piles, etc.). The basic task of vibration analysis is to discuss the excitation of the system (ie, input, external disturbance of the system, also known as interference), response (ie, output, the response of the system after excitation) and system dynamic characteristics (or physical parameters). Relationship between. After the 1960s, major advances in computer and vibration testing techniques opened up broad prospects for comprehensive use of analytical, experimental, and computational methods to solve vibration problems.
Mechanical vibration is the reciprocating motion of an object (or a part of an object) near the equilibrium position (the position at which the object is stationary). Can be divided into free vibration, forced vibration. It can be divided into undamped vibration and damped vibration. Common simple harmonic motions include spring oscillator models, single pendulum models, and so on. Vibration in the machinery industry
The application of vibration in machinery is very common. For example, in the vibrating screening industry, the basic principle is to convert the rotary motion of the motor into horizontal, vertical and inclined three times by the weight (unbalanced weight) installed on the upper and lower ends of the motor shaft. Yuan movement, and then convey this movement to the screen surface. Changing the phase angle of the upper and lower weights can change the direction of travel of the material.
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Label: Interaction of vibrating discs in mechanical equipment
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Natural Graphite , as its name implies, is naturally formed by natural Graphite , which is generally found in graphite schist, graphite-gneiss, graphite-bearing schist and metamorphic shale.
Features
The chemical composition of graphite is carbon (C). Naturally produced graphite is rarely pure and often contains impurities, including SiO2, Al2O3, MgO, CaO, P2O5, CuO, V2O5, H2O, S, FeO and H, N, CO2, CH4, NH3, etc. Natural graphite minerals are black, steel gray, striated black; Metallic luster, crypto, dull, opaque; The hardness is isotropic, the vertical cleavage surface is 3 ~ 5, the parallel cleavage surface is 1 ~ 2; Qualitative soft, density is 2.09 ~ 2.23 g/cm3, have the feeling of greasy, easy to contaminate finger. Mineral chip under the transmitted light is generally not transparent, extremely thin can pervious to light, the light green gray, refractive index of 1.93 ~ 2.07, under the reflected light is light gray, reflective pleochroism, Ro gray with brown, Re dark blue gray, reflectivity Ro23 (red), Re5.5 (red), the reflected color, double reflection were significantly, strong heterogeneity, polarization color for straw yellow.
Graphite is a complex six-party double cone, assumes the six-party tabular crystal, common simplex are parallel double, six-party double cone, hexagonal prism, but in good condition with rare crystal forms, the generally show scaly or platy, aggregate density lump, earthy or globular.
Type
The process performance and usage of graphite is mainly depends on the degree of crystallization, in accordance with its natural Graphite Crystal morphology can be divided into crystalline graphite, Flake Graphite ) and aphanitic graphite (earthy graphite) two types of industry.
Crystalline graphite
In the crystalline (scale) graphite ore, the diameter of graphite crystals is greater than 1 mu m. Ore grade is low, but optional; The mineral associated with graphite is usually mica, feldspar, quartz, diopathic stone, diabase, garnet and a small amount of pyrite, calcite, etc., some of which have some useful components, such as rutile and vanadium. The ore is scales, grainy scales or granulocyte structures, flaky, flaky, or blocky structures.
Crystalline (scale) graphite is divided into High Purity Graphite, High Carbon Graphite, Medium Carbon Graphite and low Carbon Graphite according to the fixed carbon content.
The high purity graphite (fixed carbon content is greater than or equal to 99.9%) is mainly used for flexible graphite sealing material, nuclear graphite, instead of platinum crucible for chemical reagent melting and lubricant base material, etc.
High carbon graphite (fixed carbon content 94.0% ~ 99.9%) is mainly used for refractory materials, lubricant substrate, brush raw materials, carbon products, battery raw materials, pencil materials, filling materials and coatings, etc.
Carbon graphite (80% ~ 94% fixed carbon content) is mainly used for crucible, refractories, casting materials, foundry coatings, pencil raw materials, battery materials and dyes, etc.
Low carbon graphite (fixed carbon content 50.0% ~ 80.0%) is mainly used for foundry coatings.
Cryptocrystalline graphite
Cryptocrystalline graphite is also called soil graphite or amorphous graphite. In cryptocrystalline graphite ore, graphite crystals are less than 1 mu m in diameter, which are microcrystalline and can only be seen in the electron microscope. High grade of ore, but poor selectable; The mineral associated with graphite is often quartz and calcite; The ore is microscaly - cryptocrystalline structure, block or soil structure.
Cryptocrystalline graphite ore is mainly distributed in contact metamorphic deposits. Actually the diameter graphite flake graphite ore is uneven, the so-called crystalline graphite ore, may also contain the aphanitic graphite, are too many content is often referred to as the mixed type graphite ore, may also contain a small amount of aphanitic graphite quality mineral crystalline flake graphite piece diameter slightly larger than 1 microns.
Cryptocrystalline graphite ore is mainly used in pencil, battery, electrode, graphite emulsion, graphite bearing ingredients and the raw materials of battery carbon rod. The non-ferrous graphite is mainly used for casting materials, refractory materials, dyes and electrode paste.
Natural Graphite
Natural Graphite,Expanded Graphite,Colloidal Graphite,Special Graphite
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