机械工程测试第6章002
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阻尼测试实验报告测试实验报告机械工程测试技术实验报告实验一信号分析与测量装置特性仿真实验1信号分析虚拟实验实验目的1.理解周期信号可以分解成简谐信号,反之简谐信号也可以合成周期性信号;2.加深理解几种典型周期信号频谱特点;3.通过对几种典型的非周期信号的频谱分析加深了解非周期信号的频谱特点。
实验原理信号按其随时间变化的特点不同可分为确定性信号与非确定性信号。
确定性信号又可分为周期信号和非周期信号。
本实验是针对确定性周期信号和非周期信号进行的。
1、周期性信号的描述及其频谱的特点任何周期信号如果满足狭义赫利条件,即:在一个周期内如果有间断点,其数目应为有限个;极大值和极小值的数目应为有限个;在一个周期内f(t) 绝对可积,即:等于有限值则f(t)可以展开为傅立叶级数的形式,用下式表示:式中:是此函数在一个周期内的平均值,又叫直流分量。
它是傅氏级数中余弦项的幅值。
2 它是傅氏级数中正弦级数的幅值。
是基波的圆频率。
在数学上同样可以证明,周期性信号可以展开成一组正交复指数函数集形式,即:式中:为周期性信号的复数谱,其中m就为三角级数中的k. 。
以下都以k 来说明。
由于三角级数集和指数函数集存在以下关系:所以,两种形式的频谱存在如下关系。
即:还把其中的分别称为实频谱由此可见,一复杂的周期性信号是由有限多个或无限多个简谐信号叠加而成,当然,反之复杂的周期性信号也就可以分解为若干个简谐信号。
这一结论对工程测试极为重要,因为当一个复杂的周期信号输入到线性测量装置时,它的输出信号就相当于其输入信号所包含的各次简谐波分量分别输入到此装置而引起的输出信号的叠加。
周期性信号的频谱具有三个突出特点:⑴、周期性信号的频谱是离散的;⑵、每条谱线只出现在基波频率的整倍数上,不存在非整倍数的频率分量;⑶、各频率分量的谱线高度与对应谐波的振幅成正比。
本实验中信号的合成与分解时输入信号包含有正弦波、余弦波,以及周期性的方波、三角波、锯齿波和矩形波。
SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising therefrom, is the sole responsibility of the user.”SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invites your written comments and suggestions.QUESTIONS REGARDING THIS DOCUMENT: (724) 772-8512 FAX: (724) 776-0243TO PLACE A DOCUMENT ORDER; (724) 776-4970 FAX: (724) 776-0790SAE WEB ADDRESS 3.Definitions—In addition to the definitions listed as follows, reference is made to the following definitions given in SAE J1100:a.H-pointb.H-point height (H30)c.Steering wheel diameter (W9)d.Accelerator heel point (AHP)e.Seating reference point (SgRP)3.1Class A Vehicles—Vehicles with H-point heights (H30) less than 405 mm and steering wheel diameters (W9)less than 450 mm. This class of vehicles includes passenger cars, multipurpose passenger vehicles, and vans.3.2Class B Vehicles—Vehicles with H-point heights (H30) between 405 and 530 mm and steering wheel diameters (W9) between 450 and 560 mm with treadle accelerator pedals. This class of vehicles includes heavy trucks, some medium duty trucks, and some buses.3.3The following definitions pertain to locating procedures for vehicles defined as belonging to Class A.3.3.1C LASS A V EHICLES ' A CCOMMODATION T OOL R EFERENCE L INE —Two-dimensional side view curve which defines a horizontal reference point as a function of H-point height to which driver workspace accommodation tools can be located in vehicle space. The line is appropriate to reference workspace tools to accommodate a driver population with a male-to-female ratio of 1:1. The reference line can be determined from the following equation:(Eq. 1)where:x is the horizontal reference location in mm aft of the accommodation ball of foot reference and z is the height of the H-point above the accommodation heel reference (H30) in mm.3.3.2P EDAL P LANE —A plane viewed as a line in side view which is tangent to the accelerator pedal and represents the bottom of the two-dimensional manikin's shoe.3.3.3P EDAL P LANE A NGLE —The angle between the pedal plane and the horizontal floor which is a function of manikin geometry - the 95th percentile leg links and an 87 degree foot angle with the H-point on the 95th percentile selected seat position curve at a specified H-point height (H30). The pedal plane angle, θ, can be determined from the equation:(Eq. 2)where:z is the height of the H-point above the accelerator heel point (H30) in centimeters. The equation was derived by placing the manikin's H-point on the 95th percentile selected seat position curve, moving the manikin along the curve and measuring the angle its shoe (pedal plane) made with the horizontal floor while keeping the heel on the floor and the ball of foot on the pedal.3.3.4B ALL OF F OOT —A point on a straight line 203 mm from the accelerator heel point tangent to the bottom of the manikin's shoe at the ball of foot.x 793.70.903387z 0.00225518z2–+=θ78.960.15z –0.0173z2–=3.3.595TH P ERCENTILE S ELECTED S EAT P OSITION C URVE —A two-dimensional side view curve which expresses driver selected seat position aft of the ball of foot reference for 95th percentile accommodation as a function of vehicle H-point height. The curve can be determined from the following equation:(Eq. 3)where:x is the location in mm of the 95th percentile H-point aft of the ball of foot and z is the height of the H-point above the accelerator heel point (H30) in mm.3.3.6A CCOMMODATION H EEL R EFERENCE P OINT —A point on the pedal plane that intersects the depressed floor covering below the accelerator pedal. This point is defined when the pedal plane is set up at the appropriate angle, θ, as a function of H-point height and placed tangent to a point on the pedal surface with heel on the floor. This point defines the horizontal reference plane in side view for positioning the Class A accommodation tool reference line.3.3.7A CCOMMODATIONB ALL O F F OOT R EFERENCE P OINT —A point on the pedal plane 203 mm from the accommodation heel reference point. The point is defined when the pedal plane is set up at the appropriate angle, θ, as a function of H-point height and placed tangent to a point on the pedal surface with the heel on the depressed floor covering. This point defines the vertical reference plane in side view for positioning the Class A accommodation tool reference line.3.4The following definitions pertain to locating procedures for vehicles defined as belonging to Class B.3.4.1C LASS B V EHICLES ' A CCOMMODATION T OOL R EFERENCE L INE —Two-dimensional side view line which defines a horizontal reference point as a function of H-point height to which driver workspace accommodation tools can be located in vehicle space. Three different lines are provided to reference workspace tools to accommodate truck driver populations with male-to-female ratios of 50:50, 75:25, and 90:10 to 95:5. The reference lines can be determined from the following equations.(Eq. 4)(Eq. 5)(Eq. 6)where:x is the horizontal reference location in mm aft of the accommodation heel reference and z is the height of the H-point above the accommodation heel reference (H30) in mm.3.4.2P EDAL P LANE —A plane viewed as a line in side view that is parallel to the treadle pedal surface and represents the bottom of the two dimensional manikin's shoe.3.4.3P EDAL P LANE A NGLE —The angle between the pedal plane and the horizontal floor that represents the attitude of the two-dimensional manikin's shoe (manikin ankle angle can exceed 87 degrees) with heel on the floor in contact with the base of the treadle accelerator pedal.x 95913.70.672316z 0.0019553z2–+=For 50:50 male-to-female ratio:x 798.740.446z –=For 75:25 male-to-female ratio:x 822.440.460z –=For 90:10 to 95:5 male-to-female ratio:x 855.310.509z–=3.4.4A CCOMMODATION H EEL R EFERENCE P OINT—A point on the pedal plane that intersects the depressed floorcovering below the accelerator pedal. This point is defined when the pedal plane parallels the surface of the undepressed treadle pedal. This point defines both the horizontal and vertical reference planes in side view for positioning the Class B accommodation tool reference line.4.Background—Previously, manufacturers used a seating reference point (SgRP) to locate driver workspaceaccommodation tools. Definition of the location of this reference point was left to a manufacturer's discretion.Consequently, the SgRP could vary among competitors' vehicles for similar seating arrangements leading to different indications of accommodation provided by commonly used tools. A more consistent reference point across vehicles based on how drivers used the seat travel was required to eliminate those differences.Data to define the reference line to be used in Class A vehicles were collected from fourteen different workspace studies (see Reference SAE Paper 840508). Workspaces included a range of vehicles from sports cars with 145 to 180 mm H-point heights through vans and multipurpose vehicles with 300 to 405 mm H-point heights. Steering wheel diameters were between 330 and 442 mm. Driver selected seat position of subjects stratified by stature and sex to represent the general driving population (assuming a 50:50 male-to-female mix) were collected in these workspaces. Data were converted to H-point locations relative to a manikin ball of foot reference for each package.The median H-point location, a statistically stable reference point, was determined for each package and plotted as a function of package H-point height (H30). A second degree polynomial was fit to the data. This line which gives a horizontal reference location as a function of H-point height for a driver population composed of 50% males and 50% females is the accommodation tool reference line for vehicles defined as belonging to Class A.Data to define the reference line to be used in Class B vehicles were collected from a heavy truck workspace study (see References M.S. Sanders 1983 and B.E. Shaw 1984). The workspace simulated three truck cab configurations with H-point heights of 405, 468, and 530 mm and steering wheel diameters of 457, 508, and 560 mm. All configurations had a treadle accelerator pedal and suspended clutch. Driver selected seat position of male and female heavy truck drivers were collected in the workspace. Data were converted to H-point locations relative to a manikin heel point reference for each package.Pedal configuration determined the reference points chosen for both classes of vehicles. Most Class A vehicles have suspended accelerator pedals. With a suspended pedal, the manikin's ball of foot reference is less likely to change due to the amount of seat travel provided in a workspace. The heel point location however changes with the amount of available travel. Most Class B vehicles have treadle pedals. With this configuration pedal, the manikin's heel point has a physical stop to rest against making it less likely to change as a function of pedal depression angle. Application of this practice (Class B) supposes a reasonable, typical accelerator pedal angle.A statistical technique was used to generate four populations from the original truck workspace data with thefollowing ratios of males and females; 50:50, 75:25, 90:10, and 95:5. Median H-point locations were determined for the three H-point height configurations by population mix and plotted as a function of H-point height (H30). Straight lines were fitted to each of the four mixes of data. (Second degree expressions were not used due to paucity of data). Separate equations define horizontal reference points as a function of H-point height for truck driver populations with 50:50 and 75:25 male-to-female ratios. The linear expressions for populations with 90:10 and 95:5 male-to-female ratios were very similar. Therefore, one equation, appropriate for both mixes, was developed to define a horizontal reference point as a function of H-point height. These three lines which give horizontal H-point location as a function of H-point height for populations with male-to-female ratios of 50:50, 75:25, and 90:10 to 95:5 are the accommodation tool reference lines for vehicles defined as belonging to Class B.5.Description5.1Equations—Equations are given that define horizontal reference points in vehicle space as a function ofH-point height. One second degree equation defines the accommodation tool reference line for Class A vehicles. The line is appropriate to reference workspace tools to accommodate a driver population with a 1:1 male-to-female ratio. Three first degree equations define the accommodation tool reference lines for Class B vehicles. One line is appropriate to reference workspace tools to accommodate truck driver populations with 50% males and 50% females; the second line, populations with 75% males and 25% females; the third line, populations with 90% to 95% males and 10% to 5% females. All accommodation tool reference lines are located in vehicle space relative to vertical and horizontal side view planes. In Class A vehicles, these planes are defined from the accommodation ball of foot and the accommodation heel reference points. In Class B vehicles, these planes are defined from the accommodation heel reference point only. Procedures for establishing these planes differ for Class A and Class B vehicles.5.2Application Table—A table (Table 1) is given that provides information for defining the accommodation heeland ball of foot reference points for Class A vehicles only to which the accommodation tool reference line can be located. The table provides the following:a.The horizontal distance between the accommodation ball of foot reference point and theaccommodation heel reference point (referred to as L in Table 1).b.The vertical distance between the accommodation heel reference point and the accommodation ball offoot reference point (referred to as H in T able 1).Use of the table eliminates the necessity of computing the pedal plane angle, θ, since L and H values can be used to define the pedal plane and its angle, θ.6.Locating Procedures—Different procedures are used to locate accommodation tool reference lines inClass A and Class B vehicles. Procedures are based on a given H-point height and given accelerator pedal hardware.6.1Use the following procedure to define accommodation heel and ball of foot reference points to locate theaccommodation tool reference line in Class A workspaces.6.1.1Construct a right triangle using the L and H values from Table 1 for the given or measured H-point height, z.the hypotenuse represents the pedal plane. The corner of the triangle point where the hypotenuse meets the horizontal leg represents the accommodation heel reference point. The corner of the triangle where the hypotenuse meets the vertical leg represents the accommodation ball of foot reference point. The angle between the hypotenuse and horizontal leg of the triangle represents the pedal plane angle, θ.6.1.2Determine the shape of the accelerator pedal in side view and any associated pivots that allow the pedalangle to adapt to the driver's foot.6.1.3Set the hypotenuse of the triangle (pedal plane) tangent to the pedal. Rock the pedal if geometry allowsmovement. The pedal plane may extend beyond the fall of foot for pedal contact. The horizontal leg of the triangle must be aligned with the depressed heel.6.1.4Locate the accommodation tool reference line to the accommodation heel and ball of foot reference points.Since these points do not lie in the same horizontal and vertical planes, horizontal and vertical side view lines should be constructed through the reference points. The intersection of these lines, defines the side view station to which the accommodation tool reference line is located.6.1.5For certain treadle pedal configurations in Class A vehicles, the following situations may occur:6.1.5.1If the angle the treadle pedal surface makes with the floor is less than the pedal plane angle, θ, theaccommodation heel reference point will contact the pedal surface, but the accommodation ball of foot reference point will not. (See Figure 2.) In this case, set the accommodation heel reference point in contact with the pedal, then pivot the pedal plane around this point until the accommodation ball of foot vertical reference point contacts the pedal surface. Locate the accommodation tool reference line to these points using the same procedure outlined in 6.1.4.6.1.5.2If the angle the treadle pedal surface makes with the floor is greater than the pedal plane angle, θ, theaccommodation ball of foot reference point will contact the pedal surface, but the accommodation heel reference point will not. (See Figure 3.) In this case, define the accommodation ball of foot reference at pedal contact, even though the pedal plane may go through the pedal surface, and the accommodation heel reference does not contact the pedal surface. Locate the accommodation tool reference line to the accommodation heel and ball of foot reference using the same procedure outlined in 6.1.4.6.2Use the following procedure to define the accommodation heel reference point to locate the accommodationtool reference line in Class B vehicles.6.2.1For treadle pedal, define the pedal plane and pedal plane angle, from the treadle pedal surface and the anglethe pedal makes with the floor, and proceed to 6.2.2. If a suspended pedal is used in a Class B vehicle, the following procedure should be used to define the accommodation heel reference point.6.2.1.1Determine the pedal plane angle, as defined by the equation (Equation 2) given in 3.3.3. Construct a line(pedal plane) tangent to the undepressed accelerator pedal in the side view which intersects the floor at the determined angle. Rock the pedal as necessary if geometry allows movement to adapt to the driver's foot. Proceed to 6.2.2.6.2.2Define the accommodation heel reference point as the point where the pedal plane intersects the depressedfloor coverings. This point also represents the vertical station to which the accommodation tool reference line is to be located.6.2.3Determine population mix for design. Locate the appropriate accommodation tool reference line to theaccommodation heel reference point.TABLE 1—5.2 APPLICATION TABLEChair Height (Z) mm 95% H-Point Aftof Ball of Foot(X)mmBall of FootLength toHeel Point (L)mmBall of FootHeight AboveHeel Point (H)mm100 961.4 50.0 196.7 105 962.7 50.9 196.5 110 964.0 51.8 196.3 115 965.2 52.7 196.0 120 966.2 53.7 195.8125 967.254.7195.5 130968.155.7195.2 135968.856.7194.9 140969.557.8194.6145970.158.9194.3 150970.660.0193.9 155970.961.1193.6 160971.262.3193.2165971.463.5192.8 170971.564.7192.4 175971.566.0192.0 180971.467.3191.5185971.268.6191.1190970.969.9190.6195970.571.2190.1200970.072.6189.6205969.474.0189.0210968.775.5188.5215967.976.9187.9220967.078.4187.3225966.079.9186.6230964.981.4186.0235963.783.0185.3240962.484.5184.6245961.186.1183.8250959.687.7183.1255958.089.4182.3260956.391.0181.5265954.692.7180.6270952.794.4179.7275950.796.1178.8280948.797.8177.9285946.599.6176.9 290944.2101.3175.9 295941.9103.1174.9 300939.4104.9173.8 305936.9106.7172.7 310934.2108.5171.6 315931.5110.4170.4 320928.6112.2169.2 325925.7114.1167.9 330922.6115.9166.6 335919.5117.8165.3 340916.3119.7163.9 345912.9121.6162.5 350909.5123.5161.1 355906.0125.5159.6 360902.3127.4158.1 365898.6129.3156.5 370894.8131.2154.9 375890.9133.2153.2 380886.8135.1151.5 385882.7137.0149.8 390878.5139.0148.0 395874.2140.9146.1 400869.8142.8144.2TABLE 1—5.2 APPLICATION TABLE (CONTINUED)Chair Height (Z) mm 95% H-Point Aft of Ball of Foot(X)mmBall of Foot Length to Heel Point (L)mmBall of Foot Height Above Heel Point (H)mmFIGURE 1—TRUCK ACCOMMODATION TOOL REFERENCE LINEFIGURE 2—FIGURE 3—PREPARED BY THE SAE TRUCK AND BUS OCCUPATIONAL PARAMETERS SUBCOMMITTEEOF THE SAE TRUCK AND BUS OCCUPANT AND ENVIRONMENT COMMITTEESAE J1516 Reaffirmed DEC1998Rationale—Not applicable.Relationship of SAE Standard to ISO Standard—Not applicable.Application—Reference lines have been developed to which driver workspace accomodation tools can be located in vehicle space. The lines describe horizontal reference point locations as a function of vehicle H-point height (H30). One reference line has been established for use in vehicles with H-point heights (H30) and steering wheel diameters (W9) less than 405 and 450 mm, respectively. (Class A Vehicles) This point can be used to reference appropriate workspace tools to accomodate a driver population witha male-to-female ratio of one-to-one. Separate reference lines have been established for use in vehicleswith H-point heights (H30) between 405 and 530 mm and steering wheel diameters (W9) between 450 and 560 mm with treadle type pedals. (Class B Vehicles) Figure 1. Three lines are available for use in Class B vehicles depending on the percentages of males and females in the population the designer wishes to accommodate. Separate points can be used to reference appropriate workspace tools to accommodate driver populations with male-to-female ratios of 50:50, 75:25, and 90:10 to 95:5.Difference procedures for locating Class A and Class B accommodation tool reference lines in vehicle space have been established based on unique packaging considerations of the two categories of vehicles.Reference SectionSAE J941—Motor Vehicle Driver's Eye RangeSAE J1052—Motor Vehicle Driver and Passenger Head PositionSAE J1100—Motor Vehicle DimensionsSAE J1517—Driver Selected Seat PositionSAE J1521—Truck Driver Shin-Knee Position for Clutch and AccelerationSAE J1522—Truck Driver Stomach PositionSAE Paper No. 840508—Driver Selected Seat Position ModelM.S. Sanders (1983), "U.S. T ruck Driver Anthropometric and Truck Workspace Study," Final Report Submitted to: Society of Automotive Engineers, Inc., Warrendale, PA.B.E.Shaw and M.S. Sanders (1984), "Female U.S. Truck Driver Anthropometric and Truck WorkspaceStudy," Final Report Submitted to: Society of Automotive Engineers, Inc., Warrendale, PA. Developed by the SAE Truck and Bus Occupational Parameters SubcommitteeSponsored by the SAE Truck and Bus Cab Occupant and Environment Committee。
x x x一、填空题机械工程测试技术基础试卷一1、周期信号的频谱是离散的,而非周期信号的频谱是 的。
2、均方值Ψ 2表示的是信号的强度,它与均值μ 、方差σ 2的关系是 。
3、测试信号调理电路主要有 、、。
4、测试系统的静态特性指标有 、 、 。
5、灵敏度表示系统输出与输入之间的比值,是定度曲线的。
6、传感器按信号变换特性可分为 、。
7、当时,可变磁阻式电感传感器的输出和输入成近似线性关系,其灵敏度 S 趋于。
8、和差特性的主要内容是相临、相反两臂间阻值的变化量符合 、的变化,才能使输出有最大值。
9、信号分析的过程主要包括: 、。
10、系统动态特性在时域可用来描述,在复数域可用 来描述,在频域可用来描述。
11、高输入阻抗测量放大电路具有高的共模抑制比,即对共模信号有抑制作用,对 信号有放大作用。
12、动态应变仪上同时设有电阻和电容平衡旋钮,原因是导线间存在 。
13、压控振荡器的输出电压是方波信号,其 与输入的控制电压成线性关系。
14、调频波的解调又称,其解调电路称为。
15、滤波器的通频带宽和响应时间成 关系。
16、滤波器的频率分辨力主要由其决定。
17、对于理想滤波器,滤波器因数λ= 。
18、带通滤波器可由低通滤波器(f c2)和高通滤波器(f c1) 而成(f c2> f c1)。
19、测试系统的线性度和滞后度是由 误差引起的;而重复性误差是由误差引起的。
二、问答题(共 30 分)1、 什么是测试?说明测试系统的构成及各组成部分的作用。
(10 分)2、 说明电阻丝应变片和半导体应变片的异同点,各有何优点?(10 分)3、 选用传感器的原则是什么?(10 分)三、计算题(共 55 分) 1、 已知信号 x(t)=e -t(t≥0),(1) 求 x(t)的频谱函数 X(f),并绘制幅频谱、相频谱。
(2)求 x(t)的自相关函数 R x (τ) 。
(15 分)2、二阶系统的阻尼比ξ=0.2,求ω=ωn 时的幅值误差和相位误差,如果使幅值误差不大于10%,应取多大阻尼比?。
祝守新邢英杰韩连英《机械工程控制基础》习题解答机械控制工程基础答案提示第二章系统的数学模型2-1试求如图2-35所示机械系统的作用力F(t)与位移y(t)之间微分方程和传递函数。
F(t)图2-35题2-1图解:依题意:d2ytadytmFtfkytdt2bdtd2ytdytafkytFt故m2dtbdtY传递函数:G2Fmfk2-2对于如图2-36所示系统,试求出作用力F1(t)到位移某2(t)的传递函数。
其中,f为粘性阻尼系数。
F2(t)到位移某1(t)的传递函数又是什么?图2-36题2-2图解:依题意:d2某1td某1td某2t对m1:F1k1某1tfm12dtdtdt对两边拉氏变换:F1k1某1f某1某2m12某1①d2某2td某1td某2t对m2:F2tfk2某2tm2dt2dtdt对两边拉氏变换:F2f某1某2k2某2m22某2②m12fk1某1f某2F1故:2f某1m2fk2某2F2SF1m22fk2fF2某12m12fk1m22fk2f故得:2fF1F2m1fk2某2222mfkmfkf1122故求F1t到某2t的传递函数令:F20某2fG1F1m12fk1m22fk2f2fm1m24fm1m23m1k2m2k12fk1k2k1k2求F2t到某1t的传递函数令:F10某1fG1F2m12fk1m22fk2f22-3试求图2-37所示无源网络传递函数。
fm1m24fm1m23m1k2m2k12fk1k2k1k2o图2-37题2-3图解(a)系统微分方程为i1tdti2tR1Cuii2tR1itR2u0itR2iti1ti2t拉氏变换得I1R1I2CUiI2R1I1R2U0I1R2II1I2R2R1C1U0R2CR11R1R2消去中间变量I1,I2,I得:GR1R2UiR1R2CR11C1R1R2(b)设各支路电流如图所示。
系统微分方程为uitR1i3tu0tR1i3tL11234di2tdtu0ti4tdtC2di5tdtu0tR2i6tu0tL25i2ti3ti4ti5ti6t6由(1)得:UiR1I3Uo由(2)得:R1I3L1I2由(3)得:Uo i4C2由(4)得:UoL2I5由(5)得:UoR2I6由(6)得:I2I3I4I5I6故消去中间变量I1,I2,I3,I4,I5,I6得:L2L1UL1o1L2R1UiL1L2LC2L1L2R1R2L2112L1L2R1R22-4证明Lcot22证明:设ftcot由微分定理有Ld2ft2Ff0f(1)0dt2由于f0co01,f0in00,d2ftdt22cot将式(2)各项带入式(1)中得L2cot2F即2F2F整理得F222-5求f(t)122t的拉氏变换。
SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising therefrom, is the sole responsibility of the user.”SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invites your written comments and suggestions.TO PLACE A DOCUMENT ORDER: +1 (724) 776-4970 FAX: +1 (724) 776-0790SAE WEB ADDRESS Copyright 2002 Society of Automotive Engineers, Inc.SURFACE VEHICLE 400 Commonwealth Drive, Warrendale, P A 15096-0001STANDARD J826REV.JUN2002Issued 1962-11Revised2002-06Superseding J826 JUL1995(R) H-Point Machine and Design Tool Procedures and Specifications1.Scope—The devices described in this document provide a method for a reliable layout and measurement ofoccupant seating compartments and/or seats. They are not to be construed as tools that measure orindicate occupant capabilities or comfort .The devices are intended for applications at designated seating positions. They are not intended for use indefining or assessing temporary seating, such as folding jump seats.When using the H-Point Machine (HPM), interactions can occur between adjacent seating positions (i.e.,having an HPM installed at the center occupant position can change the results obtained for the outboardoccupant position). Therefore, only one machine should be installed in a particular row of seats during eachtest.1.1General—This practice provides the specifications and procedures for using the H-Point machine (HPM) andthe H-Point design tool (HPD). The HPM is a physical tool used to establish key reference points andmeasurements in a vehicle (see Figure 1). The HPD is a simplified CAD 1 version of the HPM, which can beused in conjunction with the HPM, or independently during product design (see Figure 2).For convenience and simplicity, many terms associated with H-Point devices use human body parts in theirname. However, they should not be construed as measures that indicate occupant accommodation,human capabilities, or comfort. H-point devices do not represent the size or posture of any category ofoccupant.H-Point devices are used (1) during vehicle design and development to establish interior reference points anddimensions for occupant packaging, (2) to validate the location of these key reference points and dimensionson physical properties during audits, and (3) to measure competitive vehicles during benchmarking. Theprocedures employed for each usage vary somewhat, and are handled separately in this document.H-Point devices are also used for the design, audit, and benchmarking of seats. However, in these instances,the reference points and dimensions are defined relative to the seat structure and/or surface, rather than thevehicle’s interior. The procedures for positioning the H-Point devices in seats are abridged, and do not requirethe use of the shoe tool or leg segments. The seat procedures will be addressed in subsequent revisions tothis document.1.CAD is an acronym for computer-aided design. In a general sense, it has come to encompass any software system/approach to automotive design and development, and is often used to refer to CAE (computer-assisted engineering) and CAM (computer-assisted manufacturing) soft-ware systems as well.FIGURE 1—SIDE VIEW OF HPMFIGURE 2—SIDE VIEW AND ISOMETRIC VIEW OF HPD1.2Critical Reference Points—Several of the reference points established with an H-Point device are required forthe subsequent positioning of other design devices, such as head contours, eyellipses, and reach curves. The most critical reference points2 established by an H-Point device are the H-Point, the H-Point travel path, the SgRP (seating reference point), the AHP (accelerator heel point), and the PRP (pedal reference point).1.2.1H-P OINT—The H-Point is located on an H-Point device (HPM or HPD). However, when an H-Point device isproperly positioned within a vehicle – either in CAD or in an actual physical property – the location of the H-Point relative to the vehicle is used as a vehicle reference point. If the seat is moved, the location of the H-Point within the vehicle is changed. Therefore, adjustable seats will have more than one H-Point location, while fixed seats will have only one H-Point location.NOTE—H-Points are often referred to as hip points or hip pivot points. However, they do not represent the location of the human hip joint.1.2.2H-P OINT T RAVEL P ATH—All possible locations of the H-Point provided by the full range of seat adjustments(horizontal, vertical or rotational) for a given designated seating position.1.2.3S G RP (S EATING R EFERENCE P OINT)—A specific and unique H-Point defined for each designated seatingposition.1.2.4AHP (A CCELERATOR H EEL P OINT)—A point located near the accelerator pedal on the depressed floorcovering.1.2.5PRP (P EDAL R EFERENCE P OINT)—A point located on the lateral centerline of the accelerator pedal.2.References2.1Applicable Publications—The following publications form a part of this specification to the extent specifiedherein. Unless otherwise indicated, the latest version of SAE publications shall apply.2.1.1SAE P UBLICATIONS—SAE publications are available from SAE, 400 Commonwealth Drive, Warrendale, PA,15096-0001.SAE J182—Motor Vehicle Fiducial Marks and Three-Dimensional Reference SystemSAE J1100—Motor Vehicle DimensionsSAE J1516—Accommodation Tool Reference Point2.2Related Publications—The following publications are provided for information purposes only and are not arequired part of this document.2.2.1SAE P UBLICATIONS—Available from SAE, 400 Commonwealth Drive, Warrendale, PA 15096-0001.Manary, M. A., Flannagan, C. A. C., Reed, M. P., and Schneider, L. W. (1999) “Human Subject Testing in Support of ASPECT,” SAE T echnical Paper 1999-01-0960.Schneider, L. W., Reed, M. P., Roe, R. W., Manary, and M. A., Flannagan, C. A. C. (1999) “ASPECT: The Next-Generation H-Point Machine and Related Vehicle and Seat Design and Measurement T ools,”SAE Technical Paper 1999-01-0962.Reed, M. P., Roe, R. W., and Schneider, L. W. (1999) “Design and Development of the ASPECT Manikin,”SAE Technical Paper 1999-01-0963.Reid Bush, T., Gregg, S., and Hubbard, R. (1999) “Measuring and Modeling Support Forces of People to Assist in the Development of the ASPECT Manikin Weighting,” SAE Technical Paper 1999-01-0961.2.See SAE J1100 for additional information on reference points, terms or dimensions used in this document.Roe, R. W., Reed, M. P ., and Schneider, L. W. (1999) “ASPECT Manikin Applications and Measurementsfor Design, Audit, and Benchmarking,” SAE Technical Paper 1999-01-0965.Reed, M. P ., Roe, R. W., Manary, M. A., Flannagan, C. A. C., and Schneider, L. W. (1999) “New Conceptsin Vehicle Design Using ASPECT,” SAE Technical Paper 1999-01-0967.3.Revision Differences—The tools and procedures described in this practice represent a major revision of theformer tools and practice. The changes made have resulted in improved repeatability, greater ease of use,clearer and more complete procedures for use, and additional features and measurement capabilities. All efforts were made to achieve these improvements, while minimizing their impact on the location of reference points and measurements. Discussed below are several of the fundamental changes.3.1Separate Components—For the new HPM, the legs (upper and lower), shoe, cushion pan and back pan are all separate pieces. This greatly improves the ease of installation.3.2‘Legless’ Manikin—The new tools allow the H-Point location to be defined without having to attach the legs. 3.3Shoe Tool—Several improvements were made to the shoe tool and how it is positioned in the vehicle,including:changing the location of the ball of foot,eliminating the use of the theta equation (from SAE J1516),creating an alpha equation which can be used in pedal design,establishing a new pedal reference point (PRP), anddefining a more complete procedure for positioning the shoe.As a result of these changes, the accelerator heel point (AHP) may be further rearward, and the ankle angle may be larger for carry-over pedal packages.3.4Cushion Angle—The cushion angle can now be measured independently of thigh angle, and at the same timethe other measurements are made. Previously, cushion angle was measured off the thigh line, and required a separate installation of the HPM.3.5Lumbar Support—The articulation of the back pan assembly allows the HPM to be better seated in contoured seats. It also allows for the measurement of the lumbar support prominence (LSP). This measurement is defined as:(Eq. 1)whereX is the distance between the lumbar-pelvic pivot to the back line, measured normal to the back line.In a neutral posture – when LSP equals zero – the distance between the lumbar-pelvic pivot and the back line is 57 mm. The contour of the back pan assembly is most similar to the previous H-Point machine when the HPM is in this neutral position.As LSP increases, the lumbar segment of the back pan assembly is pushed forward, the pelvic and thoracic segments are tipped, and the lumbar-pelvic pivot moves closer to the back line (see Figure 3).LSP 57mm X–=FIGURE 3—LUMBAR SUPPORT PROMINENCE (LSP)3.6Back Angle—Back angles for seats with an adjustable recliner are specified as 22 degrees for drivers and25 degrees for rear passenger seats. If a rear passenger seat cannot be set to 25 degrees, it is set to the value closest to 25 degrees. For example, a passenger seat with a maximum back angle of 23 degrees would be set to 23 degrees. Back angles for seats without an adjustable recliner are as specified by the manufacturer.4.Overview of H-Point Devices (HPM and HPD)—This section provides descriptions of the parts and capabilities common to both tools and some basic dimensions. Complete dimensional information can be found in Section 16.4.1Major Common Components—(See Figure 4.)a.Back Pan—Consists of three segments: thoracic, lumbar, and pelvic.b.Cushion Panc.Thigh and Lower Leg Segments – The length of the leg segments can be adjusted. However, forestablishing SgRP and taking measurements defined in SAE J1100, the SgRP leg length values mustbe used. (See Table 1.)d.Shoe—The ball of foot (BOF), heel of shoe (HOS), and bottom of shoe are found on the shoe tool, andare key reference points or surfaces for using either H-Point device. The bare foot flesh line is used tocalculate ankle angle. This line is provided on the HPD only. However, the direct read-out scales on theHPM takes into consideration the bare foot flesh line in determining ankle angle. (See T able 2.)TABLE 1—LEG SEGMENT LENGTHSSgRPMid-Size Male Thigh Segment(knee pivot to H-Point)456 mm 432 mm Lower Leg Segment(knee pivot to ankle pivot)459 mm 417.5 mmFIGURE 4—COMMON MAJOR COMPONENTS4.2Pivot Locations—Both the HPM and the HPD can be articulated about six pivot locations: ankle pivot, kneepivot, H-Point (where cushion and back pan are joined), lumbar-pelvic pivot, thoracic-lumbar pivot, and sliding thoracic pivot. (See Figure 5.) The pivot locations are identical in both tools. In the HPD, the pivot point centers are provided as data points. In the HPM, the pivot point centers lie within the pivot mechanism.TABLE 2—SHOE TOOL DIMENSIONSDimensionValueOverall length of shoe306 mm BOF to HOS distance200 mm Ankle pivot107 mm above HOS 81 mm forward of HOS Bare foot flesh lineRelative to BOFRelative to HOS 6.5 degrees above the bottom of shoe.Originates 286.9 mm forward of HOS.99 mm above 32.76 mm aboveFIGURE 5—PIVOT POINTS4.3Measurement Capabilities—Both the HPM and the HPD can be used to make measurements. Several keymeasurements are summarized in Table 3. The methods for taking the measurements refer to reference lines, divots, and lands. These are discussed in later sections. See also SAE J1100 for more information.TABLE 3—KEY MEASUREMENTSSAE J1100Code Measurement HPD Method HPM MethodA40Back Angle Use the back line. The angle of the back line fromvertical.Define the back line using divots, or place inclinometer on back angle land on the back pan assembly, or the back angle land on the head room fixture with the fixture mounted flush to the back pan assembly.A27Cushion Angle Use the cushion line. The angle of the cushion linefrom horizontal.Define the cushion line using divots, or place inclinometer on the cushion angle land on the cushion pan assembly.A57Thigh Angle Use the thigh line (lower line on the thighsegment). The angle of the thigh line fromhorizontal.Define the thigh line using divot points, or place inclinometer on the thigh angle land.A42Hip Angle Use the thigh line and back line. The anglebetween the back and thigh lines.Measure the thigh angle and back angle. Hip angle = 90 degrees + back angle – thigh angle.A44Knee Angle Use the thigh line and lower leg line. The anglebetween the thigh and lower leg lines.A direct read-out scale is provided, or define the thigh and lower leg lines using divots.A46Ankle Angle Use the lower leg and bare foot flesh referencelines. The angle between the lower leg and barefoot flesh lines.A direct read-out scale is provided.A47, A48Pedal Plane Angle orFloor Plane Angle.Use the bottom of the shoe. The angle fromhorizontal of the bottom of the shoe.Define the bottom of the shoe using divots, orplace an inclinometer on the pedal plane and onthe shoe.L81Lumbar SupportProminence (LSP)Use the back line reference line and the lumbar-pelvic pivot point. See 3.5.A direct read-out scale is provided.4.4Locations of Key Reference Points and Lines—All reference points, lines, and pivot point centers arecontained within the HPD file (See Figures 6A and 6B). However, for the HPM, the points and reference lines need to be calculated using divot points. Table 4 and T able 5 summarize the HPM locations. Divot points are described in greater detail in 4.5, and 16.7.4.5Divot Points—Fourteen divot points are provided on the HPM for use with CMM equipment (see Figure 7).The primary purpose of the divot points is to allow for the calculation of key reference points. (See Table 6.) For example, the coordinates of H1L and H1R are required to calculate the H-Point location. The coordinates of S1, S2, and S3 are required to calculate the location of the accelerator heel point (or floor reference point).Divot points can also be used to calculate with additional precision anything that can be measured directly from the HPM (e.g., back angle, cushion angle, knee angle, lumbar support prominence, etc.).On the HPM, divot points are located in the center of the small gold colored disks on the mechanism. For the HPD, divot points are represented as data points. These data points have been provided in the HPD file to allow for a mapping of the HPM location and attitude. Specific locations for the divot points can be found in Section 16.FIGURE 6A—REFERENCE POINTS AND LINESFIGURE 6B—POSTURE ANGLE MEASUREMENTSFIGURE 7—DIVOT POINTS ON THE HPMTABLE 4—KEY REFERENCE POINTSReference Point Description and HPD Location HPM LocationH-Point Located at the three-way intersection of the lateralcenterline, cushion line and back line.The intersection of the cushion line and back line corresponds to the pivot center of the cushion pan and back pan. This point is within the mechanism, and must be calculated using the divot points H1L and H1R. For additional accuracy, the divot points B1, B2, and C1 can be used to define the lateral centerline of the HPM.D-Point Located on the bottom of the cushion pan, at thelateral centerline, 25.5 mm (15 degrees) rearward ofthe H-Point (when cushion angle equals 0).Located by a divot on the surface of the cushion pan. However, when the HPM is installed, this point cannot be reached, but must be calculated relative to the H-Point.Heel of Shoe The heel point is found at the bottom of the back ofthe shoe, at the lateral centerline. It is used to definethe accelerator heel point (AHP) for the driver, andthe floor reference point (FRP) for passengers.The heel point can not be reached when the HPM is installed. The location must be calculated using S1, S2, and S3 divot points. (See 12.3.2.)Ball of Foot (BOF)The ball of foot (BOF) is located on the bottom of theshoe, at the lateral centerline, 200 mm from the heelpoint. It is used to define the pedal reference point(PRP) for the driver.A notch is provided along the lateral offset opening on the shoe. A more precise location can be calculated using S1, S2, and S3 divot points.4.6Support Points—There are nine support points; 5 are located on the outer surface of the cushion pan and 4on the back pan assembly (see Figure 8). The support points are provided to facilitate seat design. Additional information can be found in Section 16.TABLE 5—KEY REFERENCE LINESReference PointDescription and HPD Location HPM Location Back Line A line from the H-Point through the sliding thoracic pivot, located at the lateral centerline. The angle of this line fromvertical defines back angle.This line is established using the B1 and H1 divot points.Cushion Line A line from the H-point through the C1 divot point, located at the lateral centerline. The line runs along the top of thecushion pan. The angle of this line from horizontal definescushion angle.This line is established using the C1 and H1 divot points.Thigh LineA line from the H-Point through the knee pivot (along thebottom of the thigh segment). The angle of this line fromhorizontal defines thigh angle.This line can be established using the K1 and H1 divot points.Leg Line A line from the knee pivot through the ankle pivot (along the back side of the lower leg segment). The angle formedby the intersection of the thigh line and the leg line defineknee angle.This line can be established using K1 and S1 divot points.Bottom of Shoe A line from the heel of shoe through the BOF , at the lateralcenterline. The angle of this line from horizontal definesthe pedal plane angle (driver) or floor plane angle(passengers).The sole of the shoe is 3 mm thick, so the bottom of shoe lies 3 mm below the sole. It can also be calculated using the S2 and S3 divots (defines a line parallel to the bottom of shoe) or S1 and S3 divots (defines a perpendicularline).Bare Foot Flesh Line A line originating from a point 286.9 mm from the heel ofshoe, on the bottom of shoe line, at a 6.5 degree angle.The angle formed by the intersection of this line and theleg line define ankle (or foot) angle.Not provided.TABLE 6—DIVOT POINT OVERVIEWDivot Type Summary of UseBack Pan Divot Points (B1, B2) and Cushion Pan Divot Points (C1, H1R, H1L)The B1 point can be used with the H1 points to define the back angle. This can then be compared to B2 for a measure of lumbar support. The C1 point can be used with the H1 points to define thecushion angle. Additionally, B1 and B2 can be used together with C1 to define the centerline of the HPM.H-Point Divot Points(H1R & H1L)The H1 points are used to define the H-Point location. The actual H-Point is located at the intersection of centerline of the HPM, the back line and the cushion line. The H1 locations areaveraged to define the x, y, z coordinates of the H-Point. (Alternatively, B1, B2, and C1 can beused to define the H-Point y coordinate.)Shoe Divot Points (S1R, S1L, S2R, S2L, S3R and S3L)Shoe divot points are used to define the AHP (accelerator heel point). They can also be used todefine the PRP (pedal reference point), the pedal plane angle, and the floor plane angle.K Divot Points(K1L, K1R, and K2)K divot points can be used to locate the knee pivot point center. By using this in combination with the S1 and H1 points, knee angle can be determined.FIGURE 8—SUPPORT POINTS5.H-Point Design Tool (HPD)5.1File Format—The HPD is available from SAE, 400 Commonwealth Drive, Warrendale, PA, 15096-0001.Currently, it is only available in the IGES format. The IGES file can be used as a template for creating native geometry within the resident CAD system. (This is recommended.) Tolerances are provided in Section 16.5.2Datum Lines—In addition to the reference lines discussed in Section 3, other datum lines are provided toassist the user. (See Figure 2.)Lateral centerline of shoeLateral centerline of manikin (through back pan and cushion pan)Effective Head Room LineSection curves cut through support pointsAdditional section curves cut through the cushion and back pansThe additional section curves are provided to convey the size and shape of complex torso geometry. This is a quality assurance measure, and provides an effective way of validating geometry across CAD systems.6.H-Point Machine (HPM)—The HPM is available from SAE, 400 Commonwealth Drive, Warrendale, PA,15096-0001.6.1HPM-Specific Parts—In addition to the parts listed in Section 4, the HPM also contains the parts andcapabilities described as follows.6.1.1S HOE F IXTURE—The shoe fixture is unique to the HPM. It is used to hold the shoe tool in place on theaccelerator. (See Figure 9.)2 leveling screwsBubble levelFork (for attaching shoe tool)FIGURE 9—SHOE AND SHOE FIXTURE6.1.2S PRING L OADED P ROBE—The probe is used to deliver 89 N (20 lb) of force at the appropriate applicationsites.6.1.3F ORCE A PPLICATION S ITES—There are two sites for applying force using the spring loaded probe; one on theback pan and one on the cushion pan.6.1.4I NCLINOMETER (E LECTRONIC L EVEL)—An inclinometer is provided for determining various posture angleswhen using the HPM, including back angle, thigh angle, cushion angle, and pedal plane angle. Specific sites for placing the inclinometer – referred to as lands – are provided on the appropriate components.6.1.5I NCLINOMETER L ANDS—There are six locations provided for positioning the inclinometer; lower leg, thigh,head room fixture, shoe tool, back pan, and cushion pan.6.1.6W EIGHTS—The HPM comes with 3 types of weights: pelvic, thigh, and back. The total number of weights is24. T wo of the pelvic weights have beveled edges. See Section 16 for a full specification.6.1.7H EAD R OOM F IXTURE—A separate fixture is provided for measuring effective head room (see Figure 10 andSAE J1100, dimension code H61). The fixture consists of:Fork (for attaching to the HPM)An adjusting screw for setting the angle of the fixtureA land for measuring the angle of the fixtureA sliding tube with probeEffective head room scaleFIGURE 10—HEAD ROOM FIXTURE 6.1.8S HOE T OOL—(See Figure 9)—Unique parts include:Locking screwAnkle angle scaleBOF lateral offset scalePedal plane angle inclinometer land6.1.9L OWER L EG S EGMENT—(See Figure 11)—Unique parts include:Knee pivot slotLeg length scaleLeg length locking pinLeg length locking screwsKnee angle scaleLeg angle inclinometer land6.1.10T HIGH S EGMENT—(See Figure 12)—Unique parts include:Locking bushing (for attaching lower leg)Knee pivot rodThigh length scalesThigh length locking pinsThigh length locking screwsFork (for attaching to H-Point rod)Lateral leg position scaleThigh angle inclinometer landFIGURE 11—LOWER LEG SEGMENTFIGURE 12—THIGH SEGMENT6.1.11C USHION P AN—(See Figure 13)—Unique parts include:HandleH-Point saddle (with locations for pelvic weights)H-Point rodsLocking bushings (for attaching back pan)Locking bushings (for attaching thigh segment)Load application point (receptacle for spring loaded probe)Lateral levelThigh weight platform and locating pinsFIGURE 13—CUSHION PAN 6.1.12B ACK P AN A SSEMBLY—(See Figure 14)—Unique parts include:HandleTorso articulation locking leverH-Point shaft (sits on H-Point saddle)Load application point (receptacle for spring loaded probe)Back angle inclinometer landUpper weight rackLower weight rackFIGURE 14—BACK PAN7.Overview of Design Procedures—The HPD is used during design to establish key reference points within thevehicle, including the SgRP (seating reference point) for each occupant position, and heel points (accelerator heel point for the driver and floor reference points for passengers). These points are then used to configure and measure many aspects of the interior compartment.The SgRP is a specific and unique H-Point for a given designated seating position. (Although adjustable seats will have many H-Points within their H-Point travel path, only one H-Point is defined as the SgRP for any occupant position.) The SgRP is established early in the vehicle design process. The most critical SgRP is the one defined for the driver (SgRP-Front). It is used in positioning other design tools, defining a number of key vehicle dimensions (e.g., legroom, shoulder room, etc.), and is referenced by several national and international standards and regulations.8.Driver Designated Seating Position Design Procedures—This procedure is used to position the HPD in thecorrect location for the driver’s position, and establishes the SgRP-Front, pedal reference point (PRP), and accelerator heel point (AHP).8.1Determine the Initial Target Values—Determine the initial target values for the dimensions listed in Table 7(see SAE J1100 for definitions). Some of these values may be modified during the procedure, resulting indifferent final values.8.2Define Shoe Tool Location and Attitude—The shoe tool is positioned on the undepressed accelerator pedal.The flat area of the tool, from ball of foot (BOF) to the heel of shoe, lays on the pedal plane, with the BOF contacting the centerline of the accelerator, and the heel of shoe contacting the depressed floor covering. The pedal reference point (PRP) is the point on the accelerator centerline that is contacted by the BOF , while the accelerator heel point (AHP) is the point on the depressed floor covering that is contacted by the heel of shoe.(See Figure 15.)FIGURE 15—SHOE REFERENCE POINTSThe pedal plane angle defines the attitude of the shoe tool. When viewed from the side, the segment from BOF to the heel of the shoe is held at the pedal plane angle. Lateral splay is not permitted. In other words, the segment from BOF to the heel of the shoe is kept vertical and square to the grid when viewed from the rear.TABLE 7—VALUES FOR INITIAL POSITIONING OF THE HPD FOR DRIVERDimensionCode Final Values Seat HeightH30 –1(T arget)The final value of H30 will be defined during this procedure.Occupant Centerline W20 –1(T arget)If the seat track has an outboard/inboard angle, then the final value of W20may be different than the target value (depending on the fore-aft location ofSgRP).Back Angle A40 –1 = 22 degrees 22 degrees.A40 is a seat characteristic. It is neither calculated nor modified by thisprocedure. Rather, it is used to define the orientation of the back panassembly.Lumbar Support Prominence (LSP)L81 –1L81 is a seat characteristic. It is neither calculated nor modified by thisprocedure. Rather, it is used to posture the back pan articulation, specifyingthe distance (X) of the lumbar-pelvic pivot (L/P pivot) to the back line,measured normal to the back line (See Figure 3).LSP=57-X mmCushion Angle A27 –1A27 is a seat characteristic. It is neither calculated nor modified by thisprocedure. It is used to position the attitude of the cushion pan assembly.。
《机械工程测试技术基础》(第三版,熊诗波等主编)课后答案机械工程测试技术基础第三版课后题答案1.1求周期方波(图1-4)的傅立叶级数(复指数函数形式)。
画出频谱图|Cn|―ω ;φn―ω 图并与表1-1对比。
解:傅立叶级数的复指数形式表达式:x(t)nCenjn 0t;n 0, 1, 2, 3,式中:T0T00 11 jn t jn t jn 0t0022 Cn x(t)edt ( A)edt AedtTT0 0T0 20T0 2T021 A jn 0t 1 A jn 0t ee T jn T jn T0 00 0 0 02jAjA1 jn Ajn1 cosn e e jn n 2n2A j;n 1, 3, 5,n n 2, 4, 6, 0;所以:2A jn 0tx(t) ;n 1, 3, 5, 7, j en n幅值频谱:2A22Cn nR CnI ;n 1, 3, 5,n相位频谱:2A;n 1,3,5, CnI 2 n arctg arctgCnR0 ;n 1, 3, 5, 2傅立叶级数的复指数形式的幅值频谱图和相位频谱都是双边频谱图。
1.2求正弦信号x(t)=x0sinωt的绝对均值μ|x |和均方根值x rms解:T 1T02x2x limx(t)dt x0sin tdt 0;式中:T0T 0 T001T021T0x02x x(t)dt xsin dtdt rms0 T00T0021.3求指数函数x ( Ae t; ( 0 ; t 0 ) 的频谱。
t) 解:j2 ft t j2 ftX(f) x(t)edtAe eAdtj2 f1.4求符号函数(题图1-1a)和单位阶跃函数(题图1-1b)的频谱. 解:1) 符号函数的频谱:令:x1(t) limetx(t);X1(f) x1(t)e j2 ftdt0 t tj2 ft lim e( 1)edt ee j2 ftdt 0 01 j f2)单位阶跃函数的频谱:2x(t) limetx(t)j2 ft;t1 j2 ft dt lim eedt 0 0 j2 f22-------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------- 1.5求被截断的余弦函数cosω0t(题图1-2)的傅立叶变换。
机械工程测试第四章课后答案1. 分析复习题1.1 试述破坏性试验与非破坏性试验的区别。
破坏性试验和非破坏性试验是机械工程中常用的两种试验方法。
破坏性试验是通过对材料进行加载,直到其失效为止,以获得材料性能的试验方法。
这种试验方法通常使用大于或接近于材料的极限负荷,以快速且彻底地确定材料的强度或硬度。
破坏性试验的优点是能够提供准确的材料性能参数,但缺点是试样被破坏,因此只能进行有限次数的试验。
非破坏性试验是对材料进行负载,并在不破坏试样的情况下测量其性能参数的试验方法。
这种试验方法可以用来评估材料的强度、硬度、韧性等性能参数,而无需破坏试样。
非破坏性试验的优点是可以对同一试样进行多次测试,以获取更多的数据,缺点是无法提供与破坏性试验相同的准确性。
1.2 试述弹性变形和塑性变形的区别。
弹性变形和塑性变形是物体在受到外力作用后发生的两种不同的变形状态。
弹性变形指的是在外力作用下,物体发生变形后,当外力消失时,物体能够完全恢复到原始形态的能力。
即物体受力后,其变形是可逆的。
弹性变形的特点是应变和应力之间呈线性关系,符合胡克定律。
弹性变形的过程中,能量的耗散是很小的。
塑性变形是指在外力作用下,物体会发生形状和结构上的永久性改变。
当外力消失后,物体不能完全恢复到原始形态。
塑性变形的特点是应变和应力之间不再呈线性关系,变形过程中会有能量的耗散。
1.3 试述调质钢和淬火钢的区别。
调质钢和淬火钢是两种常见的钢材处理方法。
调质钢是指将马氏体钢经过过贾格淬火和稍微低于临界淬火温度回火处理得到的一种组织。
调质钢具有较高的强度、韧性和不同程度的硬度。
其耐磨性和耐热性相对较好,广泛应用于制造高负荷、高速度工作的机械零部件,如汽车曲轴、齿轮等。
淬火钢是指钢材在淬火过程中产生的马氏体组织比较多,达到较高的硬度的一类材料。
淬火钢具有优异的硬度和耐磨性,但其韧性较差。
淬火钢广泛应用于制造需要高硬度和耐磨性的工具或零部件,如刀具、轴承等。
第二章习题一、选择题1.测试装置传递函数H (s )的分母与( )有关。
A.输入量x (t )B.输入点的位置C.装置的结构2.非线形度是表示定度曲线( )的程度。
A.接近真值B.偏离其拟合直线C.正反行程的不重合3.测试装置的频响函数H (j ω)是装置动态特性在( )中的描述。
A .幅值域 B.时域 C.频率域 D.复数域4.用常系数微分方程描述的系统称为( )系统。
A.相似B.物理C.力学D.线形5.下列微分方程中( )是线形系统的数学模型。
A.225d y dy dx t y x dt dt dt ++=+ B. 22d y dx y dt dt += C.22105d y dy y x dt dt-=+ 6.线形系统的叠加原理表明( )。
A.加于线形系统的各个输入量所产生的响应过程互不影响B.系统的输出响应频率等于输入激励的频率C.一定倍数的原信号作用于系统所产生的响应,等于原信号的响应乘以该倍数7.测试装置能检测输入信号的最小变化能力,称为( )。
A.精度B.灵敏度C.精密度D.分辨率8.一般来说,测试系统的灵敏度越高,其测量范围( )。
A.越宽B. 越窄C.不变9.测试过程中,量值随时间而变化的量称为( )。
A.准静态量B.随机变量C.动态量10.线形装置的灵敏度是( )。
A.随机变量B.常数C.时间的线形函数11.若测试系统由两个环节串联而成,且环节的传递函数分别为12(),()H s H s ,则该系统总的传递函数为( )。
若两个环节并联时,则总的传递函数为( )。
A. 12()()H s H s +B.12()()H s H s ⋅C.12()()H s H s -D.12()/()H s H s12.输出信号与输入信号的相位差随频率变化的关系就是( )。
A.幅频特性B.相频特性C.传递函数D.频率响应函数13.时间常数为τ的一阶装置,输入频率为 1ωτ=的正弦信号,则其输出与输入间的相位差是( )。