低速载货汽车变速器的设计
摘要：课题来源于生产实际，依据《机动车安全技术条件》和《汽车机械变速器总成技术条件》，针对低速载货汽车的运行特点而设计。参与了汽车的总体设计，确定了汽车的质量参数，选择了合适的发动机，并且计算出汽车的最高速度。
关于变速器的设计，首先选择标准的齿轮模数，在总档位和一档速比确定后，合理分配变速器各档位的速比，接着计算出齿轮参数和中心距，并对齿轮进行强度验算，确定了齿轮的结构与尺寸，绘制出所有齿轮的零件图。根据经验公式初步计算出轴的尺寸，然后对每个档位下轴的刚度和强度进行验算，确定出轴的结构和尺寸，绘制出各根轴的零件图。根据结构布置和参考同类车型的相应轴承后，按国家标准选择合适的轴承，然后对轴承进行使用寿命的验算，最终完成了变速器的零件图和装配图的绘制。
此变速器的齿轮都为标准齿轮，档位数和传动比与发动机参数匹配，保证了汽车具有良好的动力性和经济性。该变速器具有操纵简单、方便、传动效率高、制造容易、成本低廉、维修方便的特点，适合低速载货汽车的使用。

关键词：低速载货汽车；变速器；设计

Design The Transmission of Low-speed Truck
Abstract: The topic comes from the production reality, which is based on the safety specifications for power driven vehicles operating on roads and the specifications for the automobile mechanical transmission. It designs the low-speed truck’s movement characteristic. The automobile quality parameters are determined, according to the automobile system design, choosing the appropriate engine, and calculating the maximum speed.
When design the transmission, first, we choose the standard gear modulus and determine all speed’s proportions after we choose the number of the transmission’s gears and the first gear, then calculate the gear’s parameter and the center distance, and the gear needs the intensity checking calculation. We determine gear’s structure, then complete drawing of the gears’ component. According to the empirical formula, we preliminary carry on the checking calculation to each gear’s rigidity and the intensity to determine the axis’ structure and size, and thus draw up various axis’ component drawing. After arranged structure and compared with the similar type of vehicle’s bearing, according to the national standard, we select the appropriate bearings, and then calculate the service life of the bearings. Finally drawing of the component and the assembly of the transmission are completed.
Because the transmission gear is the standard gear and the number of gears and speed’s proportions match to the engine conditions, which ensure the necessary power and economy. This transmission has many merits of simple operation, efficient, easy manufacturing, low cost, and convenient.

Key words: Low-speed Truck；Transmission；Design目录
1 前言 1
2 低速载货汽车主要参数的确定 3
2.1 质量参数的确定 3
2.2 发动机的选型 3
2.3 车速的确定 4
3 变速器的设计与计算 6
3.1 设计方案的确定 6
3.1.1 两轴式 6
3.1.2 三轴式 6
3.1.3 液力机械式 6
3.1.4 确定方案 6
3.2 零部件的结构分析 7
3.3 基本参数的确定 8
3.3.1 变速器的档位数和传动比 8
3.3.2 中心距 10
3.3.3 变速器的轴向尺寸 11
3.3.4 齿轮参数 11
3.3.5 各档齿轮齿数的分配 14
3.4 齿轮的设计计算 16
3.4.1 几何尺寸计算 16
3.4.2 齿轮的材料及热处理 17
3.4.3 齿轮的弯曲强度 17
3.4.4 齿轮的接触强度 18
3.5 轴的设计与轴承的选择 21
3.5.1 轴的设计 21
3.5.2 轴承的选择 33
4 结论 40
参考文献 41
致谢 42

1 前言
低速载货汽车是一种特殊的货车,特殊在于它以前叫农用运输车，GB7258-2004[1]将“四轮农用运输车”更名为“低速货车”，明确“农用运输车”实质上是汽车的一类。GB18320-2001[2]规定以柴油机为动力装置，中小吨位、中低速度，从事道路运输的机动车辆，包括三轮农用运输车和四轮农用运输车等，但不包括轮式拖拉机车组、手扶拖拉机车组和手扶变型运输机。农用运输车最高设计车速不大于70km/h，最大设计总质量不大于4500kg，长小于6m、宽不大于2m和高不大于2.5m。
我国农用运输车诞生于20世纪80年代初。我国农村运输的特点是运量小、运距短、货物分散、道路条件差。由于同吨位的柴油车较汽油车运载能力强，燃油价格低，且柴油保管无须特殊设备，又为广大农民所熟悉，所以，农用运输车均选用柴油机为动力。农用运输车的载质量一般不超过1.5t。当前四轮农用

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内容简介：: 盐城工学院本科生优秀毕业设计选编1低速载货汽车变速器的设计低速载货汽车变速器的设计机械设计制造及其自动化（0260110101）陈中指导老师：李书伟摘摘要：要：课题来源于生产实际，依据机动车安全技术条件和汽车机械变速器总成技术条件，针对低速载货汽车的运行特点而设计。参与了汽车的总体设计，确定了汽车的质量参数，选择了合适的发动机，并且计算出汽车的最高速度。关于变速器的设计，首先选择标准的齿轮模数，在总档位和一档速比确定后，合理分配变速器各档位的速比，接着计算出齿轮参数和中心距，并对齿轮进行强度验算，确定了齿轮的结构与尺寸，绘制出所有齿轮的零件图。根据经验公式初步计算出轴的尺寸，然后对每个档位下轴的刚度和强度进行验算，确定出轴的结构和尺寸，绘制出各根轴的零件图。根据结构布置和参考同类车型的相应轴承后，按国家标准选择合适的轴承，然后对轴承进行使用寿命的验算，最终完成了变速器的零件图和装配图的绘制。此变速器的齿轮都为标准齿轮，档位数和传动比与发动机参数匹配，保证了汽车具有良好的动力性和经济性。该变速器具有操纵简单、方便、传动效率高、制造容易、成本低廉、维修方便的特点，适合低速载货汽车的使用。关键词：关键词：低速载货汽车；变速器；设计Abstract: The topic comes from the production reality, which is based on the safety specifications for power driven vehicles operating on roads and the specifications for the automobile mechanical transmission. It designs the low-speed trucks movement characteristic. The automobile quality parameters are determined, according to the automobile system design, choosing the appropriate engine, and calculating the maximum speed. When design the transmission, first, we choose the standard gear modulus and determine all speeds proportions after we choose the number of the transmissions gears and the first gear, then calculate the gears parameter and the center distance, and the gear needs the intensity checking calculation. We determine gears structure, then complete drawing of the gears component. According to the empirical formula, we preliminary carry on the checking calculation to each gears rigidity and the intensity to determine the axis structure and size, and thus draw up various axis component drawing. After arranged structure and compared with the similar type of vehicles bearing, according to the national standard, we select the appropriate bearings, and then calculate the service life of the bearings. Finally drawing of the component and the assembly of the transmission are completed. Because the transmission gear is the 低速载货汽车变速器的设计2standard gear and the number of gears and speeds proportions match to the engine conditions, which ensure the necessary power and economy. This transmission has many merits of simple operation, efficient, easy manufacturing, low cost, and convenient.Key words: Low-speed Truck；Transmission；Design1 前言本课题为低速载货汽车变速器的设计，该课题来源于结合生产实际。研究的主要内容是：参与汽车的总体设计；变速器结构型式分析和主要参数的确定；变速器结构设计。本说明书以设计低速载货汽车变速器的传动机构为主线。第2 章着重介绍了在参与总体设计当中，如何确定低速载货汽车参数，进而明确变速器应满足的条件及其所受的限制。第 3 章则重点介绍低速载货汽车变速器的传动机构的设计说明。在参与总体设计当中，首先是对低速载货汽车的产品技术规范和标准进行分析，然后确定低速载货汽车的总质量，以此来选择合适的发动机。根据发动机的功率以及汽车的总质量确定该车的最高速度（满足低速载货汽车安全技术条件）。关于变速器的设计，首先选择合适的变速器确定其档位数，接着对工况进行分析，拟订变速器的各档位的传动比和中心距，然后计算出齿轮参数以选择合适的齿轮并且对其进行校核，接着是初选变速器轴与轴承并且完成对轴和轴承的校核，最终完成了变速器的零件图和装配图的绘制。2 低速载货汽车主要参数的确定2.1 质量参数的确定本课题通过计算选用ma=3500kg。2.2 发动机的选型针对本次设计任务选用达到欧排放标准的YD480柴油机。2.3 车速的确定计算出 Vmax62.3km/h,所以该车车速满足要求。盐城工学院本科生优秀毕业设计选编33 变速器的设计与计算3.1 设计方案的确定3.1.13.1.1 两轴式两轴式这种结构适用于发动机前置、前轮驱动或发动机后置、后轮驱动的轿车和微、轻型货车上，其特点是输入轴和输出轴平行，无中间轴。3.1.23.1.2 三轴式三轴式它的第一轴常啮合齿轮与第二轴的各档齿轮分别与中间轴的相应齿轮相啮合，且第一、二轴同心。适用于传统的发动机前置、后轮驱动的布置形式。3.1.33.1.3 液力机械式液力机械式由液力变矩器和齿轮式有级变速器组成,其特点是传动比可在最大值和最小值之间的几个间断范围内作无级变化，但结构复杂，造价高，传动效率低。3.1.43.1.4 确定方案确定方案由于低速载货汽车一般是传统的发动机前置，后轮驱动的布置形式，同时考虑到制造成本以及便于用户维护等因素，现选用三轴式变速器。 3.2 零部件的结构分析通过对齿轮型式、轴的结构、轴承型式的分析，来确定所有零件的结构。3.3 基本参数的确定3.3.13.3.1 变速器的档位数和传动比变速器的档位数和传动比选择最低档传动比时，应根据汽车最大爬坡度、驱动车轮与路面的附着力、汽车的最低稳定车速以及主减速比和驱动车轮的滚动半径等来综合考虑、确定。它可以根据汽车最大爬坡度计算，也可以根据驱动车轮与路面的附着条件计算。3.3.23.3.2 中心距中心距商用车变速器的中心距约在 80170mm 范围内变化,初选 A=100mm。3.3.33.3.3 变速器的轴向尺寸变速器的轴向尺寸初选轴向尺寸:（2.42.8）A=（2.42.8）100=240280mm。3.3.43.3.4 齿轮参数齿轮参数通过计算并参照同类车型选取标准模数 m=3.5，所有齿轮采用标准齿轮。3.3.53.3.5 各档齿轮齿数的分配各档齿轮齿数的分配首先确定档齿轮的齿数，然后修正中心距 A=（3.560）/2=105mm，接着确定常啮合传动齿轮副的齿数，以及其他档位的齿轮齿数，最后确定倒档齿轮副的齿数。低速载货汽车变速器的设计43.4 齿轮的设计计算3.4.13.4.1 几何尺寸计算几何尺寸计算分别根据齿数和模数计算出尺寸。3.4.23.4.2 齿轮的材料及热处理齿轮的材料及热处理本课题变速器齿轮选用材料是 20CrMnTi，采用渗碳处理。3.4.33.4.3 齿轮的弯曲强度齿轮的弯曲强度因为该变速器所有的齿轮采用同一种材料，所以当校核时只要校核受力最大和危险的档位齿轮。分别计算出档、倒档齿轮的弯曲强度且都满足要求。3.4.43.4.4 齿轮的接触强度齿轮的接触强度常啮合齿轮副，档、档、档、倒档的齿轮都满足强度要求。3.5 轴的设计与轴承的选择3.5.13.5.1 轴轴的设计的设计轴的尺寸可按关系式初选。首先校核第二轴在各档位下的强度与刚度，然后校核中间轴在各档位下的强度与刚度，最后校核倒档轴的强度与刚度。3.5.23.5.2 轴承的选择轴承的选择第一轴后轴承为 6209 轴承,第二轴后轴承为 6307 轴承。第二轴前端选用无套圈长圆柱滚子轴承,型号为:KNL20.61233.32535；在中间轴上与中间轴齿轮配合的轴承，也选用该种轴承，型号为：KNL25.441.20860.4。4 结论本课题是针对低速载货汽车而设计的变速器，基于经济实用的考虑，变速器采用手动机械变速，三轴式传动机构布置方案，有四个前进档和一个倒档。典型轻型货车 NJ130 系列的变速器齿轮大多采用非标准齿轮，本次设计的变速器齿轮等零部件贯彻了国家或行业的最新标准，具有较好的加工和使用性能，结构紧凑、使用维修方便，并可附装取力机构供用户的特殊需要。随着城乡路况的好转，以及人们对乘车舒适性的要求越来越高，日后可以考虑采用常啮合斜齿轮传动，同步器换档的变速器，而且可以增加一个超速档，这样可以使汽车的动力性和经济性有更大地提高。主要参考文献主要参考文献1 GB7258-2004，机动车运行安全技术条件S.2 GB18320-2001，农用运输车安全技术条件S.3 王望予.汽车设计M.北京：机械工业出版社，2000.盐城工学院本科生优秀毕业设计选编54 刘惟信.汽车设计M.北京：清华大学出版社,2001.5 陈家瑞.汽车构造.（下册）M.北京：机械工业出版社，2005.Experimental analysis of a composite automotive suspension arm M. PINFOLD and G. CALVERT (University of Warwick/Rover Group Gaydon, UK) Received 11 November 1992; revised 26 March 1993 In applications where weight saving and parts integration can be achieved, the Rover Group has been investigating the design and manufacture of components from composite materials. The methods used in the different steps in the design- to-manufacture cycle in the high volume automotive industry are relatively well known for a steel component, but are not so well established for a composite component. A design methodology for composites has been emerging in which a principal procedure is design analysis. One of the most established methods of analysisis that using the finite element technique, and this is being supplemented with experimental tests on prototypes using photoelastic analysis and stress pat- tern analysis by thermal emission, coupled with conventional strain gauge moni- toring. Little work has been undertaken to correlate the results obtained from these different test methods and to compare the results with measurements made on an actual component. This paper presents some of the work undertaken concerning the analysis and testing of a composite automotive suspension arm. The results obtained from the three different analysis techniques are compared with experi- mental test results, and their accuracy is discussed. Key words: autmotive suspension arm; stress analysis; finite element method; photoelastic analysis; SPA TE; strain gauges; sheet moulding compound Sol and de Wilde state that composite materials have been used increasingly as structural materials. A reason for this., is that composite materials have high strength to weight and high stiffness to weight ratios which can significantly reduce the weight of a structure. Perhaps the most important feature ofcomposite materials is that their mechanical p:operties can be tailored to meet a specific criterion. However, Johnson et al? suggest that composite design, analysis and fabrication technology must undergo major developments and successful demonstrations before significant structural components will be incorporated in production automobiles and trucks. Composite materials have to compete with steel within the engineering environment. Within the automotive industry this requires a certain amount of technology transfer from places such as the Advanced Technology Centre at the University of Warwick, which work with material manufacturers and automotive engineers to enable understanding about these materials as an alter- native to the traditional materials such as steel. If com- posites are to compete with traditional materials in a real sense, then automotive designers need to be fully aware 0010-4361/94/010059-05 of their strengths and limitations so that they can be one of perhaps many options considered at the concept stage of the design. For this to happen automotive engineers need to catch up on the techniques of designing, testing and manufacturing components from composites. This will include understanding how various methods such as finite element (FE) analysis, stress pattern analysis by thermal emission (SPATE) and photoelastic analysis can be applied to composite components in their design and development. Thus far little work appears to have been undertaken to study whether the results obtained from these different analysis methods correlate with one another or with actual experimental results obtained from testing a real component. In order to study the application and corre- lation of the different analysis methods to composite materials, a composite component - an automotive lower suspension arm - was manufactured. This com- posite component was analysed by the three methods described above and also tested under realistic loading conditions, with experimental results being obtained from strain gauges. 1994 Butterworth-Heinemann ktd COMPOSITES . VOLUME 25 . NUMBER 1 . 1994 59 , B a l l J o i nt Housing Fig. 1 The composite suspension arm DESIGN The existing steel lower suspension arm consists of nine pieces welded together whilst the re-designed composite component-which can be seen in Fig. 1-is a single moulded part. The material used to manufacture the suspension arm was a sheet moulding compound (SMC), comprising a polyester resin bonding agent with a 30% content of randomly arranged short glass fibres and cal- cium carbonate fiIler. The weight of the steel suspension arm is 2.53 kg whilst the re-designed SMC suspension arm complete with bushes and ball joint weighs 1.5 kg. The material properties used for the composite suspension arm in these analyses, obtained from tests carried out at Rovers materials laboratory, were Youngs modulus = 10.5 GPa, Poissons ratio = 0.26 and density = 1.8 x 10 -6 kg mm -3. EXPERIMENTAL TECHNIQUES Prior to undertaking experimental analysis of an actual engineering component, some initial validation work was required to gain confidence in the techniques when applied to sheet moulding compound. Therefore, fiat plates, beams and discs constructed from SMC were ana- lysed under various loading conditions before progress- ing on to the designed component. Most validation tests were carried out using strain- gauged specimens to correlate with the finite element analysis results. Although it is recognized that SMC is not an isotropie material due to some fibre orientation during processing, for the purposes of analysis the mater- ial was assumed to be isotropic. Also, when the actual SMC suspension arm was cut up and examined, signifi- cant fibre distribution was observed in the ribs. It is felt that the correlation between the experimental and analy- sis results validated this assumption in the case of this particular component. Strain gauge tests Before undertaking the experimental test work, the com- posite component was mounted via its rubber mounting bushes onto a relatively infinitely stiff structure. It is very difficult to cover all of the loading conditions when con- ducting experimental tests and thus a worst-case scenario is usually assumed. The worst-case loading condition on suspension components is known as pot-hole brake. This attempts to simulate the vehicle falling into a deep pot-hole at 30 mph with the brakes fully applied at the point of impact. The resultant fore/aft and lateral loads are then calculated based on the weight and velocity of the vehicle. Due to the limitations of the test rig the full pot-hole loads could not be applied to the component, and thus reduced loads with the same resultant direction as the pot-hole loads were applied and the results scaled. The loads applied for the full pot-hole brake case were 24.2 kN in X and 8.2 kN in Y, and for the reduced load case were 5.9 kN in X and 2.02 kN in Y - see Fig. 1. The strain gauges used consisted of six three-axis rosette gauges and 13 single-grid gauges, with 2.5 mm grid lengths, chosen to fit into the radii of the component in an attempt to measure the maximum strain, Gauges were situated near the ball joint housing, where the loads were applied, and around the radii of the body mounting bushes, where the component would be mounted to the car subframe. Additional strain gauges were situated on some of the strengthening ribs and close to the anti-roll bar mounting position. SPA TE analysis Stress pattern analysis by thermal emission (SPATE) can be used to determine the surface stresses of components by studying the small changes in temperature due to cyclic loading conditions. SPATE equipment comprises a detector unit with scanning head, an analogue signal processing unit and a digital electronic data unit. The system works by detecting the minute temperature changes which occur when a structure is cyclically loaded. The infra-red detector scans the structure and correlates the measured output with a reference signal from the loading system. An electronic data processing system correlates the detected stress-induced thermal fluctuations with the loading reference signal. A colour contour map of the sum of the principal stresses (cr + 4) is then plotted, together with a bar chart giving actual values. This correlation of signals effectively eliminates all signal frequencies other than those caused by the loading system, i.e., all ambient temperature fluctua- tions. The SPATE system has a temperature resolution of 0.001C, and a spatial resolution of less than I mm. This type of analysis has been shown by a number of authors TM to also be applicable to non-isotropic mater- ials such as composites, and the small errors (6%) demonstrated from such studies when compared with theoretical or FE results are felt to be due to inaccuracies in the material data used 4. It is apparent from the studies undertaken that the use of thermoelastic stress analysis to evaluate stresses and strains in anisotropic composite materials is more complex than for isotropic materials. However, it has been shown that the technique can provide valuable qualitative information on stress distri- bution, effects of surface defects and crack growth predictions. It has also been demonstrated that, given accurate details of material properties including expan- sion coefficients, quantitative results can be obtained depending upon the degree of anisotropy of the material. Prior to undertaking a full SPATE analysis of the suspen- sion arm it was necessary to determine a calibration factor for the material used. This can be achieved in two ways, either by loading a disc of the material in compres- sion and comparing the SPATE output with the theoreti- 60 COMPOSITES. NUMBER 1 . 1994 cal solution, or by strain gauging directly onto the component in an area of even stress distribution, thereby obtaining a direct comparison with the SPATE output. Both methods were used in this case, but direct calib- ration with strain gauges can overcome a lot of the problems, thus allowing significant information to be obtained from the SPATE output. Photoelastic analysis The majority of photoelastic work investigating the mac- romechanical behaviour of composite materials has been undertaken using photoelastic coating techniques. This is done to avoid the complexities of constructing a photo- elastic model with anisotropic properties and thus con- structing a composite like the original which would lose its transparency and could not be analysed. However, for complex fibre lay-ups this would be the only method of conducting photoelastic analysis, and thus some research has been undertaken investigating the use of the actual composites j7-30. Reasonable results have been obtained from such analyses, but with limitations due to the neces- sity for transparency within the composite. However, the composite component considered in this study was manufactured from SMC and the material was assumed to be isotropic, thus simplifying the creation of a photo- elastic model. A three-dimensional epoxy resin model of the suspension arm was constructed for the photoelastic analysis. The model was then loaded in a representative manner, with scaled-down loads, and subjected to a stress freezing cycle. This involves heating the model up to the mater- ials glass transition temperature, at which point the Youngs modulus changes, and the model deforms under the applied loads. The model is then slowly cooled, avoiding any uneven temperature distribution which could result in unwanted thermal stresses. During the cooling cycle the deformations and stresses are locked into the model. When viewed under polarized light the three-dimensional model is a jumble of interference fringes. In order to determine both magnitude and direc- tion of the principal stresses at any point, a slice is removed and observed under polarized light. By count- ing the fringes the stresses in the model can be calculated and converted into actual stress in the component. This is done by means of proportionality, between the model and component materials, and the loading and dimensio- nal parameters. The lower suspension arm is mounted to the rest of the car via rubber mounting bushes. Investigations were carried out as to the possibility of modelling these mounting bushes. However, experiments with silicon and foam rubbers showed that the required scaled-down stiffness of the bushes during stress freezing at elevated temperatures could not be maintained. The photoelastic analysis thus assumed that the suspension arm was solidly mounted. FINITE ELEMENT ANAL YSIS The composite suspension arm was modelled using approximately 1300 of the STIF45 ANSYS solid ele- ments. The suspension arm is mounted to the subframe via rubber mounting bushes; these were modelled with spring elements to represent the stiffness of the bushes and to create a realistic load distribution throughout the component. Loads were applied to the FE model via beam elements at the ball joint. Three load cases were analysed using the ANSYS FE software. The first load case simulated the full pot-hole brake loads. The second simulated the reduced load used in the tests due to the limitations of the test rig, to enable comparisons with the results from the experimental strain gauge analysis. These two load cases used spring elements to simulate the stiffness of the rubber mounting bushes. The third load case again used the reduced loads but this time omitted the spring elements; i.e., the suspen- sion arm was modelled as being solidly mounted. This third load case was required to correlate with the SPATE and photoelastic analyses. RESUL TS Finite element analysis Analysis of the suspension arm showed that the maxi- mum equivalent stress in the component for the load case considered is very close to the ultimate tensile strength of the proposed material for the pot-hole loading condition, which is the worst loading condition. This means that the component may need to be manufactured from a differ- ent material, or that other materials need to be posit- ioned in areas of high stress to strengthen the component locally. Due to constraints upon the amount of computer disc space available, the number of elements used within the FE model was relatively low and thus the size of the elements within the area of the radii around the body mounting bushes was too large to detect any large stress concentrations. Also, the types of element used around these areas, due to the geometry of the component, were a mixture of brick, wedge and tetrahedral. The latter shape tends to be too stiff to give good results and is not recommended. If more detailed results were required in these areas, then these radii would have to be modelled in greater detail with more and smaller elements in the areas of high stress gradient. Photoelastic analysis The analysis of the photoelastic model of the suspension arm was undertaken assuming that the directions of the maximum principal stresses lay in a horizontal plane through the model in the direction of the fore/aft load. Whilst this is not strictly true in practice due to local geometry effects in certain areas, the assumption gave sufficiently accurate results. If obvious discrepancies were found in particular areas then it was possible to take slices from different planes. Maximum stresses were seen to occur in the vicinity of the ball joint housing and the body mounts. Due to the ability of photoelastic analysis to pinpoint very small areas of high stress, the maximum stress values given by photoelasticity tended to be higher than the strain gauge results. For example, maximum stress levels in the internal radius of the leading body mount were found to be 43 MPa compared with a SPATE value of 26 MPa. This difference can be explained by examin- ing the slice taken through the photoelastic model which shows that the maximum stress only occurs at a position COMPOSITES. NUMBER 1 . 1994 61 Table 1. Stress results (MPa) for full load con- ditions Position Strain gauges FE Photoelastic Ball joint housing 176 165 176 spanning 3 mm and that the stress values either side of the maximum are around 25 MPa. SPA TE analysis The initial SPATE scan showed large bands of stress running across the mounting areas and some confusion as to whether these areas were in tension or compression. The problem was identified as excessive movement in the suspension arm body mounting positions due to distor- tion of the rubber bushes as experienced in the strain gauge tests. SPATE is equipped with a motion compen- sator device if required, which deflects the scanning mirrors inside the detector in time with the oscillations of the test-piece, thereby eliminating the movement. How- ever, in this particular case, the geometry and direction of movement could not be eliminated over the entire area at the same time, and thus it was necessary to remove the rubber bushes and to replace them with aluminium ones. The SPATE analysis was repeated with the solid bushes and showed areas of high tensile stress (26 MPa) along the leading edge and around the inner radius of the leading body mounting position. Unfortunately, no SPATE analysis could be undertaken at the ball joint end of the component as it was obscured by the large loading adaptor required to fit the hydraulic actuator supplying the cyclic loading. COMPARISON OF RESULTS It should be clarified that the stress values quoted in the tables from the strain gauge results were calculated from the rosette gauges to give a value of maximum principal stress. The photoelastic analysis also gives maximum principal stresses unless the values are taken inboard of a free edge in which case they are differences in principal stresses (o.- o-,). SPATE analysis gives an output in the form of the summation of the principal stresses (or. + a2) whereas the FE output can be in any form required (in this case yon Mises). Due to the geometry of the compo- nent and the way in which the loads were applied, the values of or2 and cr 3 were always small, and thus direct comparisons could be made between the different analy- sis methods without further conversion. Table l compares the results obtained for the maximum pot-hole load conditions. The maximum stress values all occur at the ball joint area and correlate very well. These resultant stresses for the strain gauges and photoelasti- city were calculated from the results obtained for the reduced load. The model stress was multiplied by a load- ing factor as the ratio between the fore/aft and lateral loading remained constant and in the same proportion as the full pot-hole brake load applied to the suspension arlTI. The results of the analyses undertaken with reduced Table 2. Stress results (MPa) for redTJced loads with mounting bushes Position Strain gauges FE Inner radius of body 25 20 mount Ball joint housing 49 40 Table 3. Stress results (MPa) for reduced loads without mounting bushes Position FE SPATE Photoelastic Inner radius of body 22 mount Ball joint housing 30 26 43 (25) 42 (25) loading but with the mounting bushes included can be seen in Table 2. Table 3 presents the results of the analyses undertaken with reduced loading and without the mounting bushes being used. The stress given by the photoelastic analysis is concentrated at a very small point whereas the stress given by FE analysis is averaged over a relatively large area. In the case of the photoelastic results, an average of the nominal stresses on both sides of the concen- tration point is also quoted in brackets to give a fairer comparison. Compared with the strain gauge results, the values given by SPATE are very similar for the maximum stress. In theory SPATE should be more effective than strain gauges when investigating stress concentration effects, as it is measuring values over a smaller area depending upon its distance from the object during scanning. In this case the measurement point of SPATE was set at I mm diameter compared with a 2.5 mm grid length on the strain gauges. However, in this instance the differences were small and movement of the component during load cycling inevi- tably blurred the image to some extent, thus the differ- ence in resolution was probably negligible. CONCLUSIONS All the analysis techniques used-i.e., SPATE, photoelas- tic, finite element and strain gauge analyses-showed that the area of highest stress was in the vicinity of the ball joint housing. All of the methods also showed signi- ficant stresses in the areas of the body mounting bushes. However, the FE analysis did not always accurately identify these high stresses due to the size of the elements within these areas being too large. If more detailed results were required for these areas from the FE analysis, then they would have to be modelled in more detail with a greater number of elements in the areas of high stress gradient. The overall pattern of stress distribution was the same for each analysis technique. The differences 62 COMPOSITES. NUMBER 1 . 1994 obtained between the strain gauge and the FE results can be explained by the accuracy of the gauges. As noted by Autio el al. 3t, the accuracy of strain gauge measurement depends upon many factors. An error of 5-10% is usually caused by the strain gauge itself and the measure- ment system, whilst further inaccuracies may be caused by orientation, location and gluing of the gauge. Strain gauges need a reasonably large area of uniform stress to obtain accurate results. In the case of the suspension arm this requirement was not always met due to the many changes in geometry, resulting in either steep stress gradients or areas of relatively very low or insignificant stresses. All the experimental techniques used presented similar pictures of stress distribution within the composite sus- pension arm. The methods all highlight the high tensile stress at the ball joint area (except for SPATE for the reasons already mentioned), as well as the high stresses around the body mounting bushes. If the areas of high stress are examined, they are all concentrated around geometry changes as would be expected. The photoelas- tic analysis effectively demonstrates how concentrated these stresses are and the small area that they cover. In contrast, the FE analysis consists of elements spanning several millimetres, thus averaging the stress intensity over that length and consequently presenting a signifi- cantly smaller value. Overall the experimental techniques give a good degree of correlation The patterns of stresses generated by photoelastic, SPATE and finite element analysis for the suspension arm were observed to be all very similar. It can also be concluded that the SPATE technique provides a valuable, non-contacting method for the determination of stresses within composite materials. REFERENCES 1 Sol, H. and de Wilde, W.P. Identification of elastic properties of composite materials using resonant frequencies Proc hit Confon Computer Aided Design in Composite Material Technology. South- anrptot, UK. 1988 (Computational Mechanics Publications, 1988) pp 273 280 2 Johnson, C.F., Chavka, N.G., Jeryan, R.A., Morris, C.J. and Babh- ington, D.A. Design and fabrication of a HSRTM crossmember module Proe Third Advanced Composites Conference. Detroit. M. USA (ASM International. September 1987) pp 197-217 3 Machin, A.S. Sparro,% J.G. and Stimson, M.G. The thermoelas- tic constant SPIE 731 (1987) pp 26-31 4 Stanley, P. and Chan, W.K., The application of thermoelastic stress analysis to composite materials J Strum Anal23 No 3 (1988) pp 137 143 5 Bowles, D.E. and Tompkins, S.S. Prediction of coefficients of thermal expansion for unidirectional composites J Composite Mater 23 (1989) pp 370 388 6 Potter, R.T. Stress analysis in laminated fibre composites by ther- moelastic emission SPIE 731 (1987) pp 110-120 7 Jones, R., Tay, T.E. and Williams, J.F. Thermomechanical behav- iour of composites in Proc US Army Workshop on Composite Materials Response: Constitutive Relations and Damage Mechanks edited by G.C. Sim. G.F. Smith, I.H. Marshall and .J. Wuh (Elsevier, New York, 1988) pp 49 59 8 Potter, R.T. and Greaves, L.J. The application of thermoelastic stress analysis techniques to fibre composites SPIE 817 (1987) pp 134-146 9 Kageyama, K., Ueki, K. and Kikuchi, M. Thermoelastic technique applied to stress analysis of carbon fibre reinforced composite materials Proc Sixth hit Congress on Experimental Mechanics. Portland, OR, USA, 1988 pp 931-936 10 Owens, R.H. Applications of the thermoelastic effect to typical aerospace composite materials SPIE731 (1987) pp 74-85 I 1 Cox, B.N. and Petit, D.E. Non-destructive evaluation of compo- site materials using

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