ThermalExpantion说明书

Thermal Stress

A change in length is associated with a stress. Temperature change causes a change in length.
F L Y A L0
L TaL0
F TaYL0 aYT A L0
Microscopic Spacing

Atoms are in constant motion.
• Vibration increases with temperature • Spacing increases with temperature
Change in Volume

The volume of matter expands when the atomic spacing increases.
Coefficient 1 x 10-6 C-1 9 x 10-6 C-1 27 x 10-6 C-1 35 x 10-6 C-1 75 x 10-6 C-1 180 x 10-6 C-1 210 x 10-6 C-1 950 x 10-6 C-1 1100 x 10-6 C-1 3400 x 10-6 C-1
• Increase temperature → increase volume.
T V

A volume increase is the same as a density decrease.
T + T V + V
V V0T
Coefficient of Volume Expansion


Use linear expansion. Solve for L = aL0 T. First in winter,

热应力英语一、单词1. thermal- 英语释义：of, relating to, or caused by heat.- 用法：可作形容词，修饰名词。

例如：thermal energy（热能）。

- 双语例句：Thermal expansion is amon phenomenon in materials.（热膨胀是材料中的一种常见现象。

）2. stress- 英语释义：force or pressure exerted on a material object.- 用法：可作名词，也可作动词（表示强调，给……加压力等）。

作名词时，例如：The bridge can't bear the stress.（这座桥无法承受压力。

）作动词时，如：Don't stress yourself too much.（不要给自己太大压力。

）- 双语例句：High - stress situations can affect people's mental health.（高压力的情况会影响人们的心理健康。

）3. strain- 英语释义：the deformation of a material body under the action of applied forces.- 用法：可作名词或动词。

作名词时，例如：The strain on the rope was too much.（绳子上的拉力太大了。

）作动词时，如：The material will strain under heavy load.（这种材料在重负荷下会变形。

） - 双语例句：Excessive strain can cause the structure to fail.（过度的变形会导致结构失效。

）二、短语1. thermal stress analysis- 释义：对热应力进行分析。

- 用法：在工程、材料科学等领域使用。

The Q400EM is a high-performance, research-grade thermomechanical analyzer (TMA), with unmatched flexibility in operating modes, test probes, fixtures, and available signals. For standard TMA applications, the Q400 delivers the same performance and reliability. It is ideal f or research, teaching, and quality control applications, with perf ormance equivalent to competitive research models.Temperature Range (max)-150 to 1,000°C-150 to 1,000°CTemperature Precision + /- 1°C+ /- 1°CFurnace Cool Down Time <10 min from 600°C to 50°C <10 min from 600°C to 50°C (air cooling)Maximum Sample Size - solid 26 mm (L) x 10 mm (D)26 mm (L) x 10 mm (D)Maximum Sample Size - film/fiber 26 mm (L) x 0.5 mm (T)26 mm (L) x 0.5 mm (T)x 4.7 mm (W)x 4.7 mm (W)Measurement Precision +/- 0.1 %+/- 0.1 %Sensitivity15 nm15 nmDynamic Baseline Drift <1 µm (-100 to 500°C)<1 µm (-100 to 500°C)Force Range 0.001 to 1 N 0.001 to 1 N Force Resolution 0.001 N 0.001 N Frequency 0.01 to 2 Hz Not Available Mass Flow Control Optional Optional AtmosphereInert, Oxidizing, Inert, Oxidizing, (static or controlled flow)or Reactive Gasesor Reactive GasesNote: The Q400 can be field upgraded to the Q400EM.Operational Modes Standard Included Included Stress/Strain Included Not Available CreepIncluded Not Available Stress Relaxation Included Not Available Dynamic TMA (DTMA)IncludedNot AvailableModulated TMA ™(MTMA ™) Included Not Available1The Q400 features a rugged and reliable furnace. Its customized electronics provide excellent heating rate control and rapid response over a wide temperature range. Furnace raising and lowering is soft-ware controlled. The design ensures long life and performance consistency. The excellent heating rate control provides for superior baseline stability and improved sensitivity, while the rapid response permits Modulated TMA™operation. Furnace movementprovides operational convenience, and easy access to the sample chamber.2Located in the furnace core, the easily accessed chamber provides complete temperature and atmosphere control for sample analysis. Purge gas regulation is provided by an optional digital mass flow controller. These include enhanced data quality, ease-of-use, and productivity. The open design simplifies installation of available probes (see Modes of Deformation), sample mounting, and thermocouple placement. Data precision is enhanced by mass flow control of the purge gas.2 13Force Motor A non-contact motor provides aprecisely controlled, friction-free, calibrated force to the sample via the measurement probe or fixture. The force is programmable from 0.001 to 1 N, and can be increased to 2 N by addition of weights to a special tray. A precision sine wave generator provides a set of ten individual frequencies for use in dynamic experiments. Benefits:The motor smoothly generates the accurate and precise static, ramped, or oscillatory dynamic force necessary for quality measurementsin all modes of operation. The choice of frequencies allows optimization of dynamic TMA (DTMA) experiments in compression, 3-point bending, or tension modes of deformation.4Linear Variable Differential Transducer The heart of the Q400TMA sample measurement system is the precision, moveable-core, linear variable differential transducer (LVDT). Benefits:It generates an accurate output signal that is directly proportional to a sample dimension change. Its precise and reliable response over a wide temperature range (–150 to 1,000°C) makes for reproducible TMA results. Its location below the furnace protects it from unwanted temperature effects and ensures stable baseline performance.3421Expansion measurements determine a material’scoefficient of thermal expansion (CTE), glass transi-tion temperature (Tg), and compression modulus.A flat-tipped standard expansion probe (Figure 1)is placed on the sample (a small static force may be applied), and the sample is subjected to a temperature program. Probe movement records sample expansion or contraction. This mode is used with most solid samples. The larger surface area of the macro-expansion probe (Figure 2)better facilitates analysis of soft or irregular samples, powders, and filmsP ENETRATIONPenetration measurements use an extended tip probeto focus the drive force on a small area of the samplesurface (Figure 3). This provides precise measurementof Tg, softening, and melting behavior. It is valuablefor characterizing coatings without their removal froma substrate. The probe operates like the expansionprobe, but under a larger applied force. The hemi-spherical probe (Figure 4)is an alternate penetrationprobe for softening point measurements in solids.C OMPRESSIONIn this mode, the sample is subjected to either a static, linear ramp, or dynamic oscillatory force, while under a defined temperature program, and atmosphere. Sample displacement (strain) is recorded by either expansion / penetration experiments to measure intrinsic material properties, or dynamic tests to determine viscoelastic parameters (DTMA), to detect thermal events, and to separate overlapping transitions (MTMA™).Figure 2Figure 43-P OINT B ENDINGIn this bending deformation (also known as flexure), the sample is supported at both ends on a two-point, quartz anvil atop the stage (Figure 7). A fixed static force is applied vertically to the sample at its center, via a wedge-shaped, quartz probe. Material properties are determined from the force and the measured probe deflection. This mode is considered to represent “pure” deformation, since clamp-ing effects are eliminated. It is primarily used to determine bending properties of stiff materials (e.g., composites), and for distortion temperature measurements.Dynamic (DTMA) measurements are also available with the Q400EM, where aspecial low-friction metallic anvil replaces the quartz version.S PECIALTY P ROBE / F IXTURE K ITSAdditional sample measurement probes and fixtures are available for use with both the Q400 and Q400EM in specialty TMA applications. These include:Dilatometer Probe Kit –for use in volume expansion coefficient measurementsParallel Plate Rheometer –for the measurement of low shear viscosity of materials (10 to 107Pa.s range)under a fixed static force.The expansion, macro-expansion, and penetration probes are supplied with the Q400. These probes, plus the flexure probe, and the low-friction bending fixture, are included with the Q400EM module. Data analysis programs relevant to each of the measurements described are provided in our Thermal Advantage ™for Q Series ™software.T ENSIONTension studies of the stress/strain properties of films and fibers are performed using a Film/Fiber probe assembly (Figure 5). An alignment fixture (Figure 6)permits secure, and reproducible, sample positioning in the clamps. The clamped sample is placed in tension between the fixed and moveable sections of the probe assembly. Application of a fixed force is used to generate stress/strainand modulus information. Additionalmeasurements include Tg, softening temperatures, cure, and cross-link density. Dynamic tests (e.g. DTMA,MTMA™) in tension can be performed to determine viscoelastic parameters (e.g., E |, E ||, tan δ), and to separate overlapping transitions.Figure 6Figure 7TMA measures material deformation under controlled conditions of force, atmosphere, time, and temperature. Force can be applied in compression, flexure, or tension modes using probes previously described. TMA measures intrinsic material properties (e.g., expansion coefficient, glass transition temperature,Young’s modulus), plus processing / product performance parameters (e.g., softening points). These measure-ments have wide applicability, and can be performed by the Q400/Q400EM.TMA can also measure polymer viscoelastic properties using transient (e.g., creep, stress relaxation)or dynamic tests. These require the Q400EM module. In creep, a known stress is applied to the sample, and its deformation is monitored. After a period, the stress is removed, and strain recovery is recorded. In stress relaxation, a fixed strain is applied, and stress decay is monitored.In Dynamic TMA (DTMA), a known sinusoidal stress and linear temperature ramp are applied to the sample, and the resulting sinusoidal strain, and sine wave phase difference (δ), are measured . From this data, storage modulus (E |), loss modulus (E ||), and tan δ(E ||/E |) are calculated as functions of temperature, time, or stress.In Modulated TMA ™(MTMA ™), the sample experiences the combined effects of a linear ramp, and a sinusoidal temperature of fixed amplitude and period . The net signals, after Fourier transformation of the raw data, are total displacement and change in thermal expansion coefficient. Both can be resolved into their reversing and non-reversing component signals.The reversing signals contain events attributable to dimension changes, and are useful in detecting related events (e.g., Tg). The non-reversing signals contain events that relate to time dependent kinetic processes (e.g., stress relaxation).The Q400 and 400EM operating modes permit multiple material property measurements.The Q400 features the Standard mode, while the Q400EM additionally offers Stress/Strain,Creep, Stress Relaxation, Dynamic TMA, and Modulated ™TMA modes.Temperature (Time)Force StrainT(F o r c e )Force (Time)TFS TANDARD M ODE (Q400/Q400EM)Force is constant, and displacement is monitored undera linear temperature ramp. Provides intrinsic property measurements.Strain is constant, and the force required to maintain it ismonitored under a temperature ramp. Permits assessment of shrinkage forces in films/fibers.Force is ramped, and strain measured at constant temperature togenerate force/displacement plots, and modulus information.S TRESS /S TRAIN M ODE (Q400EM)Stress or strain is ramped, and the resulting strain or stress is measured at constant temperature. Both provide stress / strain plots and related modulus information.Strain (Stress)TStrain Stress(S t r a i n )D YNAMIC TMA M ODE (Q400EM):A sinusoidal force (stress) is applied during a temperature ramp. Analysis of the resulting strain and phase data provides viscoelastic property parameters (e.g., E |, E ||tan δ).Timet 2t 1S t r a i n / S t r e s sTemperature (time)STTemperatureTM o d u l a t e d L e n g t hM o d u l a t e d T e m p e r a t u r eC REEP /S TRESS R ELAXATION M ODES (Q400EM)In Creep, stress is held constant, and strain is monitored. In Stress Relaxation,strain is held constant, and stress decay is monitored. Both are transient tests used to assess material deformation and recovery properties.M ODULATED TMA M ODE (Q400EM):Temperature is programmed linearly, and simultaneously modulated at constant stress to generate signals relating to total displacement, CTE, and their reversing and non-reversing components. These permit detection of thermal transitions,and separation of overlapping events (e.g., Tg and stress relaxation).804020090-40-80-12050402030-1001080At a Point 127.3˚C α=25.8µm/m˚CPoint-to-Point Method α=27.6µm/m˚C Average Method α=26.8µm/m˚C230.0˚C45.0˚CAluminumExpansion Probe Size: 7.62mm Prog.: 5˚C/min Atm.: N26040140120100240220200180160260Temperature (˚C)60-20-4071.24˚C -17.48µmSize: 0.492 x 5.41 x 5.08 mm Force: 78.48 mNDeflection: -17.48 µm70605040302080Temperature (˚C)FIGURE 12D i m e n s i o n C h a n g e (µm )I NTRINSIC AND P RODUCT P ROPERTY M EASUREMENTSshows expansion and penetration probe measurements of Tg, and softening point of a synthetic rubber using a temperature ramp at constant force. The large CTE changes in the expan-sion plot indicate the transition temperatures. In penetration, they may be detected by the sharp movement of the loaded probe into the changing material structure.A CCURATE C OEFFICIENT OF T HERMAL E XPANSION (CTE) M EASUREMENTSFigure 11demonstrates the use of the expansion probe to accurately measure small CTE changes in an aluminum sample over a 200˚C temperature range. Advantage ™software permits analysis of the curve slope using an “at point”, “straight line” or “best fit” method to compute the CTE (α) at a selected temperature, or over a range.M ATERIAL P ERFORMANCE ANDS ELECTIONis an example of a 3-point bending mode (flexure probe) experiment on a polyvinyl chloride (PVC) sample, using the ASTM International T est Method E2092 to determine the distortion temper-ature. This test specifies the temperature at which a sample of defined dimensions produces a certain deflection under a given force. It has long been used for predicting material performance.-140-120-100-80-60-40-200102.54˚C-93.22 µm257.71˚C-108.0 µm50100150200250300-50350Temperature (˚C)FIGURE 13D i m e n s i o n C h a n g e (µm )202005202520202015201075250.20.10.30.0-251020304050Time (min)FIGURE 14D i m e n s i o n C h a n g e (µm )T e m p e r a t u r e (˚C )F o r c e (N )20300.0000.0150.0100.005510Slope = Modulus1520Strain (%)FIGURE 15S t r e s s (M P a )0.020M ULTILAYER F ILM A NALYSISFigure 13shows a compression mode analysis, using a penetration probe, of a double layer PE / PET film sample, supported on a metal substrate. The sample temperature was linearly ramped from ambient to 275 ˚C at 5 ˚C/min. The plot shows probe penetra-tions of the PE layer (93.22 µm) at 102 ˚C, and the PET layer (14.78 µm) at 257 ˚C respectively.F ILM P ROPERTY T ESTINGillustrates a classic isostrain experiment, in the tension mode, on a food wrapping film. The film was strained to 20% at room temperature for 5 minutes, cooled to -50 ˚C and held for 5 more minutes, then heated at 5 ˚C/min to 40 ˚C. The plot shows the force variation required to maintain a set strain in the film. The test simulates its use from the freezer to the microwave.F ILM T ENSILE T ESTINGFigure 15displays a strain ramp experiment, at a constant temperature, on a proprietary film in tension. The plot shows an extensive region where stress and strain are linearly related, and over which a tensile modulus can be directly determined. The results show the ability of the Q400EM to function as a mini tensile tester for films and fibers.01230.050.100.150.200.250.300.350.40Force (N)Yield RegionElastic Region40.40.20.60.020406080100120140160180200Temperature (˚C)As ReceivedCold Drawn0.00.20.40.60.81.0-1123456789101112Time (min)FIGURE 18CreepRecoveryS t r a i n (%)1.2F IBER S TRESS /S TRAIN M EASUREMENTSStress/strain measurements are widely used to assess,and compare, materials. shows the different regions of stress/strain behavior in a polyamide fiber (25 µm) in tension, when subjected to a force ramp at a constant temperature. The fiber undergoes instantaneous deformation, retardation,linear stress/strain response, and yield elongation.Other parameters (e.g., yield stress; Young’s modulus) can be determined.T HERMAL S TRESS A NALYSISOFF IBERSdisplays a tension mode experiment,using a temperature ramp at a constant strain (1%), to perform a stress analysis on a polyolefin fiber, as received, and after cold drawing. The plot shows the forces needed to maintain the set strain as a func-tion of temperature. The data has been correlated with key fiber industry, processing parameters, such as shrink force, draw temperature, draw ratio,elongation at break, and knot strength.C REEP A NALYSISCreep tests help in materials selection for end-uses where stress changes are anticipated. Figure 18illustrates an ambient temperature creep study on a polyethylene film in tension. It reveals the instantaneous deformation, retardation, and linear regions of strain response to the set stress, plus its recovery with time on stress removal. The data can also be plotted as compliance, and recoverable compliance, versus time.1301351401450.010.110.00110Time (min)FIGURE 19R e l a x a t i o n M o d u l u s (M P a )150050010001500200025000.100.080.060.040.02200050100150406080100120140160Temperature (˚C)FIGURE 20S t o r a g e M o d u l u s (M P a )T a n D e l t aL o s s M o d u l u s (M P a )3000-20202004000206080100120131.68˚C140160180200Temperature (˚C)FIGURE 21D i m e n s i o n C h a n g e (µm )N o n -R e v D i m e n s i o n C h a n g e (µm )R e v D i m e n s i o n C h a n g e (µm )40S TRESS R ELAXATION A NALYSISshows a stress relaxation test in tension on the same polyolefin film used for the creep study. A known strain is applied to the film, and maintained,while its change in stress is monitored. The plot shows a typical decay in the stress relaxation modulus. Such tests also help engineers design materials for end uses where changes in deformation can be expected.V ISCOELASTIC P ROPERTYD ETERMINATION – D YNAMIC TMAillustrates a dynamic test, in which a semi-crystalline polyethylene terephthate (PET) film in tension is subjected to a fixed sinusoidal stress during a linear temperature ramp. The resulting strain and phase data are used to calculate the material’s viscoelastic properties (E |, E ||, and tan δ). The plotted data shows dramatic modulus changes as the film is heated through its glass transition temperature.S EPARATING O VERLAPPINGT RANSITIONS - M ODULATED ™ TMAFigure 21shows a MTMA™ study to determine the Tg of a printed circuit board (PCB). The signals plotted are the total dimension change, plus its reversing, and non-reversing components. The total signal is identical to that from standard TMA, but does not uniquely define the Tg. The component signals, however, clearly separate the actual Tg from the stress relaxation event induced by non-optimum processing of the PCB.•conduct experiments and simultaneously analyzes data•operates up to 8 modules simultaneously•Wizards – guides and prompts in setting up experiments•provides a real-time display of the progress of the experiment •Autoqueuing– permits pre-programmed set-up of planned experiments •Autoanalysis– permits pre-programmed data analysis of planned experiments•– provides extensive, context sensitive, assistance•– terminates a test upon attaining a specified value (e.g., CTE)UNIVERSAL A NALYSIS ATA A NALYSIS•analyzes data from all TA Instruments modules•provides easy one plot analysis of large and small events•–analyzes data “as it arrives”••within UA 2000 using Microsoft Word™& Excel™templates •– for quick retrieval of previously analyzed data filesI NNOVATIVE E NGINEERINGTA Instruments is the recognized leader for supplying innovative technology,investing twice the industry average in research and development. Our new Q Series™ Thermal Analysis modules are the industry standard. The Q400TMA provides innovative technology suitable for research as well as QC laboratories. The Q400EM includes Dynamic TMA and also Modulated TMA ™, a technique unavailable from other manufacturers.T ECHNICAL S UPPORTCustomers prefer TA Instruments because of our reputation for after-sales support. Our worldwide technical support staff is the largest and most experienced in the industry. They are accessible daily by telephone, email, or via our website. Multiple training opportunities are available including on-site training, seminars in our application labs around the world, and convenient web-based courses.ALESANDERVICEWe pride ourselves in the technical competence and professionalism of our sales force, whose only business is thermal analysis and rheology. TA Instruments is recognized worldwide for its prompt, courteous, and knowledgeable service staff. Their specialized knowledge and experience are major reasons why current customers increasingly endorse our company and products to their worldwide colleagues.Q UALITY P RODUCTSAll thermal analyzers and rheometers are manufactured to ISO 9002 procedures in our New Castle, DE (USA) or our Leatherhead, UK facilities. Innovative flow manufacturing procedures and a motivated, highly skilled, work force ensure high quality products with industry leading delivery times.130******** 33130489460 3227060080 441372360363 31765087270 49602396470 390227421283 81354798418 34936009300 61395530813 46859469200。

Friction Analysis for Piston Ring of Seal Device in the Stirling EngineHou Shunqiang1, a,Zhang Lili2,b and Zhang Xiaoyan 3,c1 Qingdao Binhai University, Qingdao China2Shandong University of Science and Technology, Qingdao China3SAIC-GM-Wuling Automobile Co.Ltd SGMW , Liuzhou Chinaa b cKeywords: Stirling Piston ring; Dynamic seal; Friction and wear.Abstract. The friction pair of piston ring-cylinder liner for the piston ring seal device of Stirling Engine is plastic-metal friction pair, its working conditions for dry friction. So the wear resistance of the piston ring is poor, its service life is short. This paper regard integral non-backpressure piston rings group as the research object in order to reduce wear: First, establishes auto-free lubricating mechanical model to piston rings group； Then, set up the mathematical model, which to meet the requirements of the sealing performance, for friction analysis； At last, Experimental analysis in the Piston Ring Seal Device of Stirling Engine to prove that this model is correct and available. IntroductionThe opening with back pressure free lubricating piston rings is used in most piston ring seal device of Stirling Engine in domestic at present. During the working process of piston rings with opening back pressure free lubricating, the compressed medium pressure will press on the surface of piston ring’s inner column to make adhered pressure between piston ring and cylinder surface, which produce friction consumption in the process of piston rings’ reciprocating movement. However, as the piston ring of Stirling Piston works in the dry friction condition, it is easy to wear and its service life is short, besides, the sealing performance of Stirling Engine is affected by the friction character directly. This paper mainly bases on the operation condition of Stirling Engine to analyze the elements that affect the wear of piston ring and propose some measures to lengthen piston ring’s service life.Improved Sealing Structure of Stirling Engine Piston RingThe improved sealing structure of Stirling Engine piston ring is as Fig. 1. Two piston rings and two guide rings are designed on the piston. The piston ring has a slot and double loop with an inside and outside structure. Two pieces are included in the outside ring and one is the upper ring the anther one is the lower ring. The upper one is the open type one with straight incision structure. The lower one is an integrated ring with a convex at the corresponded point with upper incision. Those two rings form the ring group and make two ends adhere. The inside ring is a spring lamination made by a stainless steel belt piece and it is 10～15mm longer than inside ring’s perimeter. Curve it into a lap round to be a elastic ring when install it and then embed it into piston ring to form interference fit. The guide ring has a slot and a ring with an uninstall hole, which can help guide ring without gas pressure and only play the role of oriented support. The piston ring and guide ring are produced by the Chinese Academy of Sciences Lanzhou Institute of Chemical Physics and the compound design is made by 40% Cu+ 60% F4 filled PTFE with self lubrication and good thermal conduction. With the force analysis as Fig.2 and ignoring the affection that produced by surface roughness （W＝0）betweenApiston ring and cylinder wall, the upper ring end adhered tightly with the lower ring end with influence of gas pressure. Both of the two rings have incision and convex to make these rings into a set without mutual turning. The inner perimeter and metal elastic ring of upper and lower rings hasformed interference fit and the elastic ring’s inner perimeter adheres tightly with piston ring’s slot which also forms interference fit. The inner perimeters of upper and lower rings adhere tightly with metal-made elastic ring, which forms an integrated structure and make these two ends adhere tightly, and so does the elastic ring and metal ring’s slot. In this way, the leakage path and leakage path ①①will be filled it; because of the thermal expansion effect for the upper ring’s opening, the upper ring’s external diameter adheres with cylinder wall tightly and fill the leakage path . The straight incision ④on the upper ring forms to a clearance fit with the convex on the lower ring, which makes no mutual turning between these two rings. Due to the small clearance between the two ends, some gas thatleaks from the clearance between upper ring’s openingand lower ring’s convex, leak into the clearancebetween lower ring and cylinder wall (gas cell 2and 4)to form the leakage path . The internal and external③diameters of the guide ring form interference fit with theexternal of guide ring’s slot and cylinder’s internaldiameter. However, the load-off hole is equipped on theguide ring and the guide ring does not have sealingfunction, the gas that goes through the clearancebetween guide ring and cylinder wall can not producepressure drop, and the guide ring just play the role ofguide.1-cylinder liner 2- guide ring 3-piston 4-upper piston ring 5-leakage path 6①-elastic ring 7- leakage path 8①-lower piston ring 9- leakage path 10③- leakage path ④Fig.1 the structure diagram of no-back-pressure piston ring setPiston Rings’ Friction AnalysisThe Elastic Specific Pressure Produces by Thermal Expansion.The thermal expansion of piston can produce uniform pressure to the cylinder wall (Fig. 2)Fig. 2 Loaded diagram of no-back-pressure nonmetal pistonSee the metal ring as rigid body when calculate thermal deformation. On the basis of Hooke’s low during the working hours the tensile stress σ of nonmetal ring is [4]: 00)(R R R E E −==εσ (1) The loaded diagram of nonmetal ring during working hours is like drawing 4. It can be known from mechanical equilibrium relation that the resultant force of tensile stress σ on the y axisdirection will equal to the component force that specific pressure P work on the inside of nonmetalring on the y axis. That is to say: ()j j phd d phd ht == ββσπ02sin 2（2）Put the formula （1）into （2）to get the formula between the elastic specific pressure of piston rings, P and the working temperature T 1 :()j d T T Et P 012−=α（i =1,2,3,4） (3) The Effect from Gas Pressure to Piston Rings’ Radial Direction Specific Pressure.The high pressure sealing gas through the leakage path ③ (two places) and other seal surfaces, its pressure reduces from P1 to Pi (i=1,2,3,4) in sequence to corresponding gas cell; −m P is the average radial pressure that beard on the corresponding ring’s external diameter’s cylindrical surface and the pressure’s direction points from external to internal, besides, as the effect of thermal expansion during working hours, the elastic ring produces outward radial specific pressure P to the rings’ internal diameter. Meanwhile, as the compression when first assembling, the guide ring also produces outward radial specific pressure P k to cylinder walls. The algebraic sum of these pressures in radial direction is just the positive pressure that needed to form piston tings’ static friction.The radial elasticspecific pressure of elastic rings P k can be calculated from formula （4）[5] .()108.7−=e e e e k k D D A E P (4) The average radial pressure that beard by each external diameter’s cylindrical surface will be seenas formula （5）[6].()121+−+=m m m P P P )4,3,2,1(=m (5) The relation between average radial pressure and the sealed gas pressure 1P will be seen as formula (6)[6]. 14131211034.0,076.0,20.0,76.0P P P P P P P P ====−−−− (6) The radial specific pressure from gas to piston rings is like the following:14107.1P P P m m m ==∑=− (7)The Effect from Pistons’ Pace to Force of Sliding Friction.F f means the static friction when piston rings in the station of static and sealed, it can be calculated from formula (8).()()()11101,07.1177.1··8P T F P t D D A E d T T t E F f e e e e k j f =⎥⎥⎦⎤⎢⎢⎣⎡−−+−=αμ (8) The piston rings’ round surface and the cylinder walls form the relative sliding to produce sliding friction at sealed surface. We know that the size of sliding friction is related with the speed of relative movement of the things; therefore, the pace of pistons will affect the sliding friction (9)directly. When the system is sealed, the sliding friction can be expressed by the following function among working temperature T 1, sealing medium pressure P 1, piston pace v .()()υυυ,,,1122111P T F k k P T F F d f d =−+= (9)Experimental AnalysesThe known physical quantity before experiment:Chart 1 part of the certain experimental data The mathematical computation model of friction and friction consumption power can be built according to the above formulas (1)-(9), and then find out the change regulation between the sliding friction F d and other physical quantity. The measured dynamic friction in different operating conditions have been drawn curve graphs as the following Fig.3, Fig.4 and Fig.5.Conclusions(1)It can be seen from Fig.3 that if the sealed gas pressure P 1 and piston pace v are constant, the force of sliding friction F d will increase with the working temperature of piston rings and it will beμ=0.12 E =280MPa t = 1.6mm α=(10～15)×10-5 mmT 0=25℃ dj =55mm E k =193MPa A e =0.2mmD e =51.8mm t e =1.75mm P 1=0～8MPa K 1 =0.28 K 2 =247N·s/msteady at last. It is because when the working temperature increases the heat clearance of pistons’ opening will enlarge and the external diameter of piston will adhere tightly with cylinder wall. Just right now, the radial positive pressure from piston ring to the cylinder wall increase and the static friction F f aggrandizes. When the heat clearance of opening enlarges to limit, the static friction will to be maximum.(2)It can be seen from Fig.4 that if the sealed gas pressures P 1 and the working temperature T 1 are constant; when the pistons start to move its pace v is very low, however, with the increase of v the relative slip on the seal surface are severe and the radial wear quantity h =kpvt of piston ring will increase, and the frictional vibration will be severe and the sliding friction F d will be increased as well. When the radial wear quantity h of piston ring to be the maximum, the contact surface between piston ring’s external diameter and cylinder becomes very smooth and then the friction coefficient μ will decrease, the sliding friction F d will decrease with decrease of static friction. When μ becomes minimum; F f will be steady as well as sliding friction F d .(3)It can be seen from Fig.5 that if the piston pace v and the working temperature T 1 are constant, the force of sliding friction F d will decrease with the increasing of sealed gas pressure and then to be steady. It is because when P 1 increases the positive pressure N will decrease and this can be reflected from formula (8). When the seal gas in cavity became thermal equilibrium state the seal gas pressure P 1 will to be steady. The force of static friction F f will decrease to a steady state value and the sliding friction will be constant as well.F r i c t i o n /K NTemperature/.C F r i c t i o n /K NVelocity/(m/s)Fig.3 curve between sliding friction F d and sealed Fig.4 curve between sliding friction F d and working temperature T 1 when P 1=8MPa,ν=0.57m/s piston pace ν when T 1=150,℃P 1=2MPaF r i c t i o n /K N Pressure/MpaFig.5 curve between sliding friction F d and sealed gas pressure P 1 when ν=0.57m/s,T 1=150℃References [1] Jin Donghan. Technology of Stiring Engine [M]. Harbin: Harbin Engineering University Press. 2009:162-166.[2] Zhu Yufeng. Design & Research of Entirety No-back-pressure Piston Ring on CompressionEngine [J].Lubrication and Sealing. 2006, (12):106-107[3]Li Yanlin. Calculation & Practice of Free Lubrication Piston Rings’ Sealing Parameter and Minimum Opening Clearance [J]. Sinkiang Oil Science and Technology, 1992, (3):84-87.[4]Zhu Yufeng. Design & Calculation of Working Clearance and Relative Interference Fit on No-back-pressure Piston Ring [N].Hebei University of Science and Technology Journal, 2008-03-29(1):53-56.[5]Peng Baocheng, Zhu Yufeng, etc. Affection Research of Elastic Rings to Piston Rings’ Sealing and Service Life [J]. Lubrication and Sealing, 2006, (180):97-98.[6]Chen Geng, Jiao Guilong, Lu Dingji, etc. Tribology Design of Free Lubrication Compression Eengine Piston Ring [J].Shanghai Second Industrial University Journal, 1988,(1):1-8.。