201122449 六、發明說明： 【發明所屬之技術領域】 本揭不内容一般地係有關於具有移動軸及支撐該等軸 之軸承的總成’更特定言之，係有關於用以量測該等總成 之該等軸承中預付載及軸端隙狀況的系統及方法。 發明背景 有關於量測轉動總成之預付載及軸端隙的該等系統與 方法之實例係出現在以下的專利及公開案中： W007105655 ； W003071246 ； EP1717464 ； CA2016469 ； US6951146 ； US6460423 ； US6443624 ； US6505972 ； US6357922 ; US6286374 ; US5877433 ; US5263372 及 US3 665 75 8。該等參考資料之揭不内容於此係多用途地以全 文引用方式併入本案以為參考資料。 C發明内容3 發明概要 具有支撐軸承的轉動軸係為常見的機械總成，並且對 於自手錶之飛輪到動力產生渦輪軸的所有元件而言係為固 有的。於該等總成中一轴承表面典型地支撐一軸並容許該 軸以一定量之摩擦而轉動。該等軸承限制該軸在一軸方向 或一橫方向上或是，於一些例子中’在該二方向上的移動。 轴承可包含滾輪、錐形滚輪、套筒或是滾珠滾動元件。 複數轴及軸承轉動總成提供調整特性控制該正向力， 該力與和該滾珠或滾輪接觸的表面相對作用對著該滾動元 201122449 件本身。使用軸承的應用中通常規定在該滾動元件上施加 一正向力或預負載。具高轉速之應用規定作用在該軸承上 的一相對低預負載。具低轉速以及高施力的應用’諸如銑 床可具有高預負載力。 對該等滾動元件施以過大力量的狀況下，於作業期間 會產生過多熱量及摩擦，減少軸承壽命並增加維修成本。 施加在該等滾動元件的力量太小會使該軸之側向與軸向移 動超過規格。於複數之應用中，測定實際上施加至該等滾 動元件的該預負載力量係為必要的。 一裡川π你问研作性裂造應用中測試預只科 係對-轴及軸承施加遞增的軸輯，並量測由於該施加力 量所產生的位移。接著將料位移數值與源自於具有一不 同預負載設定的該相同心軸的—標準或參考組之位移數值 比較在固疋把力下介於該測試樣本與該標準之間的位 移差異’測定在料轴承上該尺寸預負載的差異。 當該標準數值組係根據—已知的預負載或軸端隙量 時’此夠由遠差異導出該測試心軸預負載。就組件材料、 十|配方^精確而言，利用此方法，該標準總成必 品與S亥測試樣本或試樣相同。 =測試設計相同但—單元不相同的心_，無法將總 的來源係為_承環、:=二上_^^ 組件的材料彈性上的差異=衫以及該總成之其他 異以及總成組件之製造尺寸上的變 珠與轉#承之料轴承環之間的接觸角之差 201122449 異會單獨地成為顯著變化的一來源，且整體而言會改變該 總成之視剛性或彈性。 總成之間的變化可於力-位移曲線中為顯而易見的，該 等曲線中該總成中的位移係對照施加至該總成之力描繪而 成。一典型的力-位移曲線在該曲線上的反曲點的外側具有 正區域及負區域。該等曲線之正側與負側表示所施加之力 的正與負值，或是在該軸向上推或拉。該等反曲點與用以 讓一組之雙重軸承組移開位置的足夠大小之作用力相符 合。介於該等反曲點之間的該區域係與作用力相對應，該 等作用力低於讓任一軸承移開位置所需的力量。 於該等移開位置區域中該曲線於任何點處的斜率係與 該試樣的彈性模數有關。就除了在軸承上預負載不同之外 為相同的二試樣而言，該曲線之該等移開位置區域將為平 行的以及偏位或是彼此相隔一段固定距離。不同預負載之 力-位移曲線間該偏位可用以量測該預負載。 該主曲線係為一假定的曲線表示零轴端隙及零預負 載。藉由針對一相同軸承選擇一主曲線，由該主曲線至該 預負載總成之該曲線的該偏位之數值將提供該預負載。 一測試試樣與一參考或主曲線試樣間材料、總成及尺 寸上的差異導致該等總成之視彈性或剛性上的一差異。於 此例子中，測試試樣及主力-位移曲線的斜率可不平行或等 同。該視彈性上的差異對於測定該等軸承上該預負載而言 會是一顯著的錯誤來源。可使用一修正係數測定一更為精 確的預負載大小，用以抵銷該彈性上的差異。 5 201122449 —將揭示用於測定軸承預負載的方法。儘管於此揭示内 容已說明特定的構形及機械以及方法，但該等實例係針對 說明之目的且不應視為具關性。複數之不同的變化及不 同的具體實施例可認為用以執行於此揭示的該等特徵之觀 點’其將視為等效的並涵蓋在此揭示内容之範嘴内。 一轉動總成可與機械工具中所使用的一心軸 一力-位移曲線的-彈性區域衫由聚集力及位移數據所 導出的-雜常數可_祕但與揚氏模數或是針對一材 料或總成的一勁度係數相似。 儘管於此可說明一轉動總成作為—實例，但_示的 該等方法及系統可同樣地剌在任何的麻系統。例如， 於此說明的該料法及系統可應用在—線性平移軸承系統 或是一帶螺紋轉動及平移軸承系統，諸如一滾珠螺釘。 圖式簡單說明 第1圖係為-轉動總成的-橫截面，包括_外殼、一轴 及二軸承，其巾料軸权料_承環舰裝韻轴以 及該等外軸承環係配裝在該外殼中。 第2圖係為-軸承的一橫截面，顯示_内轴承環、—外 軸承環錢-料蚊在料麻環之間，其+位在該等 軸承環上《珠之料接觸點定義㈣軸承的一㈣ 角0 包括一負載系統具 、一軸驅動器以及 第3圖係為一測試系統的一透視圖， 有一试樣底座、一負荷元件、一轉換器 一電腦包括一處理器及記憶體。 201122449 第4圖係為一力-位移圖 供轉動總成位移。 顯示軸承位移及組件位移提 第圖係為針對具有零預負載及零轴端隙的一心轴之 力^移®顯不由正向或推外加負載及負向或拉外加負 載所產生的位移。 第6圖係為-圖顯示針對一組輛承的力_位移曲線。 第圖係為係為一圖圖示具有該轴承之該接觸角中小 變化的該勁度比之變化。 第8圖係為具有一主曲線及一測試曲線的一力—位移 圖’圖示祕測定—轉動總成中之預負載的-方法。 第9圖係為第8圖之該圖的一細節，圖示使用-修正主 曲線用以測定該預負載尺寸的一方法。 第10圖係為包括一主曲線、一分段主曲線及一修正主 曲線的一力-位移圖，圖示使用一修正係素的一方法。 第11圖係為包括-主曲線、一修正主曲線其針對位在 該主曲線上的一點以及位在該修正主曲線上的—點之切線 的一力-位移圖，圖示微分學方法。 第12圖係為用於一線性平移總成的一軸承的一橫截 面。 第13圖係為一流程圖，顯示用於測定軸承預負載的一 方法。 第14圖係為一流程圖，顯示用於測定軸承預負載的一 方法。 I：實施方式3 7 201122449 較佳實施例之詳細說明 軸承對於任何類型的轉動式機械而 的’並具有複數之㈣具切料的轉動或可缺少 :。-些最為常見的軸承係為滾輪轴 ：之構 常地經配置作為具有該等滾珠或滾輪_在=經 的-總成，接受-轉動轴或是平移_:承環中 承環其_定至-外殼。具有相對輯 ^:夕卜輪 支撐位在一外殼中的一綠&± 止的藉由軸承 於 壯m絲、轉動軸或是其他組件的-總成， 此可視為一轉動總成。 成2可第 心軸或是轉動總成2的'橫截面。編 ㈣構4其料以並支軸加的組件。 =外:一軸承6具有一第-組之滾動元件《 _ 承環1〇八以及一内軸承環10B。-第二軸承Γ 5 ^也匕括帛—組之滾珠14、一外軸承環16Α以及一内奉 碎衣6外車由承環10Α可藉由一扣環固持在外殼4十， 乂及外，7|U衣16Α可藉由螺合入夕卜殼4的一具螺紋軸環· 持在外忒4中。一轴環22可接觸内軸承環1〇B及16B。軸驾 22亦可將第一軸承6與第二軸承12分開。内軸承環l〇B石 16B及軸環22可接受並固定至軸24並可為一單一單元一走 地轉動。 轉動總成2係經構形用以容許軸24相對於外殼4轉動， 具有最小的摩擦力以及軸24之最小的撗向與軸向平移，如 圖中虛線軸24’所示。對滚珠8及14施以一正向力或預負載 可利用一外加負載F使軸24之橫向與軸向平移減至最小。 201122449 第2圖係為第—轴承6之-詳細的橫截面。於此及之後 的圖式中可以使用相似的元件符號標示相似的元件。再次 地’軸承6包括滾動元件或滾珠8 ’為了清晰起見於此 顯示為一單—滾珠’外軸承環10A及内軸承環1()B。滾珠8 叮於 上—相對點30A及30B處與軸承環i〇A及10B接 觸，通H點的—線可為_接觸線32其與該等轴承環之 該平祕成-接觸_。具有—陡山肖接㈣的—軸承通常 係、、二選疋用於較南轴向負載的應用。具有—淺或是小接觸 角的-軸承係可經選定用於具有低轴向負載的—徑向負載 應用°即_用相同的裝配方法，軸承間接觸角34大體上 仍可加以良化。就滾珠8上預負載之變化而言，接觸角34可 為一重要的因素。 儘管於該等實例及圖式中可使用滾珠轴承，但該等方 法及實例_地可應用在滾輪軸承顧上^滾珠軸承係僅 使用作為一實例並且不應視為具限制性。返回第1圖，於此 實例中’ 6亥具螺紋軸環20之該位置可測定第一及第二軸承6 及12之3亥預負載或軸端隙。假若軸環20係經旋入外殼4中且 未與外轴承環16A接觸，則當滾珠8及14未與二相配的軸承 環接觸時’軸24可隨意地橫向或軸向地移動一段特定距 離。此係為具有零預負載的一軸端隙狀況。當具螺紋軸環 20進一步地旋入外殼4中並與外軸承環16A接觸時，軸承環 16A可相對於外殼4移動直至其接觸滾珠14並且滾珠14接觸 内軸承環16B為止。 當軸環20進一步地旋入時’可將第二軸承12推動靠著 9 201122449 軸= 22’其可推動頂著軸承6之内轴承環1⑽。内轴承環聰 接著接觸滾珠8而滾珠8接麟轴承環，其停止而靠著扣 U。當所有組件係如所說明地接觸時，將具螺紋轴環加 進一步地旋人外殼4靠著軸承環16A，增加包括滾珠MM 的組件間該正向力或賴力。接觸力增加會造成—些組件 相互靠著移動其之接觸位置，直至其抵達藉由組件間某程 度之正向力加以固定的一位置為止。施加至軸24的軸向負 載或力F會造成接觸表面之額外的移動或是組件材料之彈 性變形。當藉由將具螺紋軸環20進一步地旋入外殼4而施加 更大力里時，該力係經儲存作為總成組件之彈性變形。 作用在軸承6及12上的力量係為一預負載。此力之大小 可表示為一力量或是當參考如以下所說明的一力位移圖 時作為一尺寸。於此揭示内容中，於實例中為了清處起見 可使用預負載力，但能夠以一相似方式測定一預負載大小。 滚珠8及14可由鋼或陶竞或是任何固態材料構成。滚珠 及軸承環表面可為堅硬的並抗磨損。軸承溝道可為一表面 硬化材料，具有一軟質内部材料以及一硬質表面。、 第3圖係為用於量测一轉動總成或是測試試樣41上之 預負載的一測試系統4〇的一透視圖。測試系統4〇可包括一 負載系統42。負載系統42可包括一負載系統外殼44、一試 樣底座46其具有試樣底座支樓件46A及46B以及一試樣連 接軸環48、一負荷元件％、一轉換器系統52其具有轉換器 52A及目標盤52B、一負載設定構件54其具有—負載設定軸 54A及一負載設定把手54B。負裁系統42可包括一軸驅動器 201122449 56。軸驅動器56可包含一馬達56A，一驅動系統56、一驅動 轴56C及及轴驅動器外殼56D其之組件係以虛線標示為隱 藏及/或位於轴驅動器外殼56D内部。轴驅動器外殼56D可為 軟質藉由一軟質底座56E安裝至負載系統外殼44，用以容許201122449 VI. Description of the Invention: [Technical Field of the Invention] The present disclosure generally relates to an assembly having a moving shaft and a bearing supporting the shafts, more specifically, for measuring such A system and method for preloading and shaft end-gap conditions in such bearings. BACKGROUND OF THE INVENTION Examples of such systems and methods for measuring preload and shaft end play of a rotating assembly are found in the following patents and publications: W007105655; W003071246; EP1717464; CA2016469; US6951146; US6460423; US6443624; US6505972 US6357922; US6286374; US5877433; US5263372 and US366575. The disclosure of such references is hereby incorporated by reference in its entirety by reference in its entirety herein. C SUMMARY OF THE INVENTION 3 SUMMARY OF THE INVENTION A rotating shaft having a support bearing is a common mechanical assembly and is inherent to all components from the flywheel of the watch to the power generating turbine shaft. A bearing surface in the assembly typically supports a shaft and allows the shaft to rotate with a certain amount of friction. The bearings limit the movement of the shaft in either the axial direction or a transverse direction or, in some instances, in the two directions. The bearings can include rollers, tapered rollers, sleeves or ball rolling elements. The plurality of shaft and bearing rotation assemblies provide adjustment characteristics to control the positive force that opposes the surface of the rolling element 201122449 itself as opposed to the surface in contact with the ball or roller. The use of bearings typically provides for the application of a positive or preload on the rolling elements. Applications with high speeds specify a relatively low preload on the bearing. Applications with low speeds and high force applications such as milling machines can have high preload forces. In the event that excessive force is applied to the rolling elements, excessive heat and friction are generated during operation, reducing bearing life and increasing maintenance costs. Too small a force applied to the rolling elements causes the shaft to move laterally and axially beyond the gauge. In the plural application, it is necessary to determine the preload force actually applied to the rolling elements. Irikawa π You asked the pre-cursive application to apply an incremental axis to the -axis and bearing and measure the displacement due to the applied force. The material displacement value is then compared to the displacement value of the standard or reference group derived from the same mandrel having a different preload setting. The difference in displacement between the test sample and the standard under the solid force. The difference in preload of this size on the material bearing was determined. When the standard value set is based on the known preload or shaft end stop amount, this test spindle preload is derived from the far difference. In terms of component materials, ten|formulations^, with this method, the standard assembly must be the same as the S-hai test sample or sample. = test design is the same but - the unit is not the same heart _, the total source can not be _ ring, : = two _ ^ ^ The difference in material elasticity of the component = shirt and other components of the assembly and assembly The difference in contact angle between the variable bead on the manufacturing dimensions of the component and the bearing ring of the transfer bearing 201122449 will individually become a source of significant variation and will generally change the apparent stiffness or elasticity of the assembly. Variations between assemblies can be seen in the force-displacement curve in which the displacement in the assembly is plotted against the force applied to the assembly. A typical force-displacement curve has a positive region and a negative region on the outside of the inflection point on the curve. The positive and negative sides of the curves represent the positive and negative values of the applied force, or are pushed or pulled in the axial direction. These inflection points are compatible with a sufficient amount of force to move the set of double bearing sets away. The region between the inflection points corresponds to the force that is lower than the force required to move any of the bearings away. The slope of the curve at any point in the region of the removed position is related to the modulus of elasticity of the sample. In the case of the same two samples, except for the preload on the bearing, the removed position regions of the curve will be parallel and offset or at a fixed distance from each other. This offset can be used to measure the preload between the force-displacement curves of different preloads. The main curve is a hypothetical curve representing the zero-axis end gap and zero preload. By selecting a master curve for an identical bearing, the value of the offset from the master curve to the curve of the preload assembly will provide the preload. The difference in material, assembly and size between a test sample and a reference or main curve sample results in a difference in apparent elasticity or rigidity of the assemblies. In this example, the slopes of the test specimen and the main force-displacement curve may not be parallel or the same. This difference in apparent elasticity can be a significant source of error for determining the preload on the bearings. A correction factor can be used to determine a more accurate preload size to offset this difference in elasticity. 5 201122449 - A method for determining the bearing preload will be disclosed. Although specific configurations and machinery and methods have been described herein, the examples are for illustrative purposes and should not be considered as being critical. Variations of the plural and various specific embodiments are considered to be considered to be equivalent to the features disclosed herein and are to be considered as being within the scope of the disclosure. A rotating assembly can be used with a mandrel used in a machine tool. The force-displacement curve-elastic region of the shirt is derived from the gathering force and displacement data. The heterogeneous constant can be used with the Young's modulus or for a material. Or the stiffness coefficient of the assembly is similar. Although a rotating assembly can be illustrated as an example, the methods and systems shown can be equally applied to any hemp system. For example, the method and system described herein can be applied to a linear translation bearing system or a threaded rotating and translational bearing system, such as a ball screw. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a cross-section of a rotating assembly, including a _ outer casing, a shaft and a two-bearing bearing, a material for the lining of the lining, a bearing shaft, and an outer bearing ring fitting. In the outer casing. Figure 2 is a cross-section of the bearing, showing _ inner bearing ring, - outer bearing ring money - material mosquito between the material ring, its + position on the bearing ring "bead material contact point definition (4) One (four) angle 0 of the bearing includes a load system, a shaft drive, and FIG. 3 is a perspective view of a test system having a sample base, a load component, a converter, a computer including a processor and a memory. 201122449 Figure 4 is a force-displacement diagram for the rotation assembly displacement. The bearing displacement and component displacement diagrams are shown for the displacement of a mandrel with zero preload and zero-axis end play, which is not caused by the forward or thrust applied load and the negative or pull applied load. Figure 6 is a graph showing the force_displacement curve for a group of bearings. The figure is a diagram illustrating the change in the stiffness ratio with a small change in the contact angle of the bearing. Figure 8 is a force-displacement diagram with a master curve and a test curve illustrating the method of determining the preload in the rotating assembly. Figure 9 is a detail of the figure of Figure 8, illustrating a method of using the -corrected master curve to determine the preload size. Figure 10 is a force-displacement diagram including a master curve, a segmented master curve, and a modified master curve, illustrating a method of using a modified velocide. Figure 11 is a force-displacement diagram including a -master curve, a modified master curve for a point on the master curve, and a tangent to the point on the modified master curve, illustrating a differential learning method. Figure 12 is a cross section of a bearing for a linear translation assembly. Figure 13 is a flow chart showing a method for determining the bearing preload. Figure 14 is a flow chart showing a method for determining the bearing preload. I: Embodiment 3 7 201122449 DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT Bearings of any type of rotary machine have a plurality of (four) cut rotations or may be absent:. - Some of the most common bearing systems are roller axles: the configuration is often configured to have such balls or rollers _ in the = warp-assembly, accept-rotate shaft or translate _: retaining ring in the ring To the outer casing. Having a relative series ^: The support of a green & ± stop in a housing by bearing a strong wire, rotating shaft or other components - the assembly, which can be regarded as a rotating assembly. The 2 can be the first axis or the 'cross section of the rotating assembly 2. (4) Structure 4 components that are added to the shaft. = Outer: A bearing 6 has a first set of rolling elements "_ ring 1-8 and an inner bearing ring 10B. -Second bearing Γ 5 ^ 匕 帛 帛 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 组 14 组 组7|U garment 16" can be held in the outer casing 4 by screwing into a threaded collar of the outer casing 4. A collar 22 can contact the inner bearing rings 1B and 16B. The axle drive 22 can also separate the first bearing 6 from the second bearing 12. The inner bearing ring 10B and the collar 22 are receivable and fixed to the shaft 24 and are rotatable for a single unit. The rotating assembly 2 is configured to permit rotation of the shaft 24 relative to the outer casing 4 with minimal friction and minimal axial and axial translation of the shaft 24, as indicated by the dashed axis 24'. Applying a positive or preload to the balls 8 and 14 minimizes the lateral and axial translation of the shaft 24 with an applied load F. 201122449 Fig. 2 is a detailed cross section of the first bearing 6 . Similar elements may be used to designate similar elements in the drawings and the following figures. Again, the bearing 6 includes rolling elements or balls 8' which are shown here as a single-ball' outer bearing ring 10A and inner bearing ring 1()B for clarity. The balls 8 are on the upper side - the contact points iA and 10B are in contact with the points 30A and 30B, and the line through the H point can be the contact line 32 which is in contact with the bearing ring. The bearing with the steep mountain splicing (four) is usually used for the application of the south axial load. A bearing system having a shallow or small contact angle can be selected for use with a low axial load - radial load application. That is, with the same assembly method, the inter-bearing contact angle 34 can still be substantially improved. The contact angle 34 can be an important factor in terms of variations in the preload on the ball 8. Although ball bearings can be used in these examples and figures, such methods and examples can be applied to roller bearings. Ball bearings are used only as an example and should not be considered limiting. Returning to Fig. 1, in this example, the position of the "6-coil threaded collar 20 can determine the 3 MPa preload or shaft end gap of the first and second bearings 6 and 12. If the collar 20 is screwed into the outer casing 4 and is not in contact with the outer bearing ring 16A, the shaft 24 can be freely moved laterally or axially by a certain distance when the balls 8 and 14 are not in contact with the two mating bearing rings. . This is a one-axis end-gap condition with zero preload. When the threaded collar 20 is further threaded into the outer casing 4 and brought into contact with the outer bearing ring 16A, the bearing ring 16A is movable relative to the outer casing 4 until it contacts the ball 14 and the ball 14 contacts the inner bearing ring 16B. When the collar 20 is further screwed in, the second bearing 12 can be pushed against the 9 201122449 shaft = 22' which can push against the inner bearing ring 1 (10) of the bearing 6. The inner bearing ring Cong then contacts the ball 8 and the ball 8 is connected to the bearing ring, which stops and leans against the buckle U. When all of the components are in contact as illustrated, the threaded collar is further rotated against the bearing ring 16A to increase the positive or repulsive force between the components including the balls MM. An increase in contact force causes the components to move their contact positions against each other until they reach a position that is fixed by a certain positive force between the components. The axial load or force F applied to the shaft 24 can cause additional movement of the contact surface or elastic deformation of the component material. When a greater force is applied by further screwing the threaded collar 20 into the outer casing 4, the force is stored as an elastic deformation of the assembly assembly. The forces acting on the bearings 6 and 12 are a preload. The magnitude of this force can be expressed as a force or as a dimension when referring to a force displacement map as explained below. In this disclosure, the preload force can be used in the examples for clarity, but a preload size can be determined in a similar manner. Balls 8 and 14 may be constructed of steel or ceramic or any solid material. The balls and bearing ring surfaces can be hard and resistant to wear. The bearing channel can be a hardened material with a soft inner material and a hard surface. Figure 3 is a perspective view of a test system 4 for measuring a pre-load on a rotating assembly or test coupon 41. The test system 4A can include a load system 42. The load system 42 can include a load system housing 44, a sample base 46 having sample base fulcrum members 46A and 46B, and a sample connection collar 48, a load component %, a converter system 52 having a converter 52A and target disk 52B, a load setting member 54 has a load setting shaft 54A and a load setting handle 54B. The negative cutting system 42 can include a shaft drive 201122449 56. The shaft drive 56 can include a motor 56A, a drive system 56, a drive shaft 56C, and a shaft drive housing 56D, the components of which are shown hidden by dashed lines and/or located inside the shaft drive housing 56D. The shaft drive housing 56D can be soft mounted to the load system housing 44 by a soft base 56E for
利用任何外加負载F讓軸驅動器56浮動。軸驅動器外殼56D 可替代地安裝至負荷元件50並可將力F經由驅動軸56C傳遞 至軸24。 於另一實例中，軸24可藉由與負載系統42及測試系統 40分開的一系統驅動，諸如測試試樣41内—分離的驅動系 統或是一驅動器。 負載系統42附加地包括一負載系統電腦或是負載系統 電子元件58,具有一處理器58A'記憶體或記憶體儲存系統 58B及一數據擷取卡58C係藉由虛線顯示為隱藏及/或位在 負載電子元件58内部。測試系統4〇可進一步包括一數據收 集系統60其具有-電腦61包含一處理器62、—記憶體或記 憶體儲存祕64錢-數據擷取卡6 6係藉由虛線顯示為隱 藏及/或位在電腦61内部。電腦61可為任一形式的計算系 統，包括一個人數據助理、一桌上型電腦、一膝上型電腦 或是一伺服器系統。 負載系統42可經構形用以對測試試樣41施加軸向負載 或力F。就此貫例而言，第丨圖之轉動總成2於此視為測試試 樣41的一特定實例，但試樣之其他型式或構形可經測試， 諸如以下說明的-線性平移總成。底座46可將轉動總成2之 外殼4固持在與負載系統4 2相#的一固定位置處。試樣連接 201122449 軸環48亦可提供軸24與負載系統42之間的一連接，口 對轉動總成2施加正向及負向負載F。負荷元件5咏== 加至軸24的負載F之大小。轉換器系統52在回應外加力F後 可量測測試試樣41之位移。軸驅動器56可附加地轉動轴 24,同時對轉動總成2施以軸向負載f。 於測試期間測試試樣41可藉由試樣底座46固持於適當 位置。試樣底座46可經構形用以在回應外加力F後將外^ 之移動減至最小。試樣底座46可為任—構形，於測試期間 適當地牢_試樣。底座46可經構形^與試樣連接 軸環48合作’將由負載設定練辦產生的正向及負向外 加負載F傳送至轴24。驅動軸56C可藉由試樣連接轴環料與 軸24連接。驅動馬達56A可經由驅動系統使驅動軸56c 才疋轉。當力F施加至軸24時，驅動軸56c可經由連接軸環48 使軸24旋轉。 負何疋件50可經配置與負載設定構件54與軸24成一直 線。負何疋件5〇可為任一類型的系統，量測一負載或外加 。負荷元件50可包含應變計及一結構橫樑在負載下撓 曲負荷疋件50可包含一液壓系統。 轉換益系統52可為任何類型之系統或組件，用於量測 線11平移或位移。轉換器系統52可包括轉換器52A其包含一 線性變懕55 r- a 益、—壓電組件、一感應性組件、一電容組件或 是雷射。轉換器系統52可進一步包括目標盤52B。目標盤 或旋轉驅動軸56C或是其他適當的轉動組件 目標盤52B可經構形用以搭配轉換器52A使用作為一 12 201122449 目‘ ’罝測«52Β之位移。轉換器系統52可量測外殼峭 軸24相關的軸向位移。 負載設定構件54可為一手動系統，諸如如圖所示的一 手動轉動螺釘或是-液壓或手動千斤頂。負載設定構仙 可為由-處理器，諸如處理器62所控制的一自動系統。負 載系統電子元件58可控制負載應用系統Μ，並自負荷元件 50及轉換器52收集數據。 數據收集系統60可包括用於收集數據的構件，諸如數 據擷取卡66。數據操取卡的可在操作上與處理器Μ及記憶 體64連接，並可進-步地在操作上與負載系統42連接。可 附加地傳达才曰令至負載系統42用以控制作業。數據操取卡 66可自負載系統42收集數據。卡％可自轉換器μ收集位移 數據^以及由負荷元件5〇收集外加負載數值並將該數據儲 存在記憶體64中。數據操取卡的可收集附加的數據。數據 。卡66可在操作上與負載系統電子元件Μ連接並可與負 載系統電子元件58相配合地操作。數_取卡 ^ 如6可與處理器Μ或是卡電子元件上的其他者之 功此性加以整合。 負載系統42可不具有負載系統電子元件％以及數據收 …'統60可直接由負載系統42收集數據。可任擇地，負載 系統42可具有負載系統電子元件％以及測 夫 括數據收集系統60。 了未包 負載系統42可藉由對軸24施以遞增的正向及負向轴向 而作動，並在每—遞增負載下量測轉動總成外殼4相 13 201122449 1::24之:移。數據收集系統60可在每-遞增負載下記 、’乂、於負何7C件5G的負載數據以及源自於轉換器52的位 移數據。錄24轉動或是使㈣靜止可產生數值。每-數 據點可經記錄作為-第一及第二分量諸如一力分量以及一 位移分量。 於此遞增負載應為意指—組負載大小數值，其可使用 負荷元件50及貞妓定構件54叫何順序施加至該試樣。 X 4、·且負載數值係，為足夠的數目用以描繪測試試樣 41的特性，並被約束在會致使轉動總成2中任何組件之塑性 變形的外限值。該遞增負載可連續地斜線上升以及為藉由 所收集的位移數據定義之增量。 產生力-位移曲線以及其與轉動總成搭配使用係為熟 知此技藝之人士所廣為熟知並廣泛地使用。在複數的教科 書中可取得該等概念的綜合性說明，於此不再贅述。力-位 移曲線係與材料科學之應力-應變曲線相似，並可反映機械 性質特性。 於作業中，測試系統4〇可用以測定針對測試試樣41的 -預負載狀況。可導出針對職試樣41的—力位移曲線並 與零負載及軸㈣之-假定參考曲線或主曲線比較，用以 通過圖表測定該預負載大小。 在一特定負載下，心軸位移可為轴承之位移及其他轴 承心軸組件之位移的結合。第4圖包括軸承位移曲線bd， 組件位移曲線CD及心軸絲曲線SD。在—設定負載下心 軸位移係為所有組件之位移的總和。於此，心轴位移的大 201122449 小係由線Ds圖示。心軸位移Ds係為該組件位移Dc及軸承位 移Db之總和。對於大部分測試軸承而言，於一力_位移曲線 中，軸承位移Db將提供最大部分之位移。 可由一數學模型產生一力-位移曲線。可構成包含每一 組件之該荨材料特性之轉動總成2的一數學模型，用以說明 轉動總成2之該位移或是轉動總成2之組件的位移。該數學 模型可在回應施力後說明組件之位移。該數學模型可使用 有限元素技術。 第5圖顯示一轉動總成或心軸的一假定主曲線，其包括 在二軸方向上心軸的特性。主曲線1^(：：係為針對具零軸端隙 及零預負載的一總成之一特定類型之力_位移曲線。主曲線 MC可包含一正部分或是推側p+以及一負部分或是拉側 P-。一轉動總成之一二列軸承構形中，主曲線MC之推側p+ 係與一第一列之軸承的位移相對應。於該二列軸承構形 中，拉側P-係與一第二列之軸承的位移相對應。 主曲線MC可為與由測試系統4〇所收集之數據點相配 合的一曲線。曲線MC可具有與該擬合曲線相關聯的數值， 其係與該等數據點不同。主曲線MC可用於測定相同設計之 轉動總成的該預負載力量。主曲線MC可藉由一方程式加 以說明並可包含一組數值。 根據一組針對一轉動總成的力-位移數值設定至一軸 端隙之狀況可產生該主曲線。針對該主曲線之該等數值可 藉由將該軸端隙作用自該等力-位移數值之每一位移分量 中扣除而加以定義。該等合成力_位移數值將與具零軸端隙 15 201122449 及零預負載的一轉動總成相對應。 可依轴承型式、軸承系列及軸承族將軸承特定化气群 組化。該軸承型式反映該軸承之構造及設計。—些軸承型 式包括滾輪軸承、錐形滾輪軸承、球形軸承、角接觸旁珠 軸承、單一列滾珠軸承及雙列滾珠軸承。 該軸承系列反映該等軸承之堅固性。該系列由最拳一 到最重’係為：8極薄斷面；9非常薄斷面；〇極釦· " ’ 1極輕 摧力；2輕；3中等以及4重。該等系列之每一者亦在該軸承 之s玄孔徑尺寸、外徑及厚度之間建立一關係。 ^ 一軸承族可包括大體上為相同軸承的一群組，其中 等輛承係以一或更多參數使之有所差異。例如，—軸表μ 除了接觸角之外係為相同的。另一族除了所使用的衰7朱、 尺寸不同外係為相同的。使軸承族的該等輛承有戶、之 其他參數包括轉動元件之數目、軸承之直徑或是與差異的 接觸的-轴承環之曲率半徑。可針對_特=/衰珠 承族，諸如機^軸或高速馬達。 計該轴 軸承族。 共同系列 可藉由共同使用一共同系列的命名而定義 可藉由一共同軸承型式定義一軸承族。 』错由 °名以及—共同軸承型式而定義一軸承族。 圖係為一力-位移 ，•农I野 線’該轴承族中之轴承除了接觸角3 _ —組主曲 %車由承族包括1G度、12度及13輯觸角^•相同的。此示 對10、12、11及13度軸承之力-位移曲綠以:6圖包括針The shaft drive 56 is floated with any applied load F. The shaft drive housing 56D can alternatively be mounted to the load element 50 and can transmit force F to the shaft 24 via the drive shaft 56C. In another example, the shaft 24 can be driven by a system separate from the load system 42 and the test system 40, such as a test drive 41 - a separate drive system or a drive. The load system 42 additionally includes a load system computer or load system electronics 58 having a processor 58A' memory or memory storage system 58B and a data capture card 58C shown as hidden and/or bit by dashed lines. Inside the load electronics 58. The test system 4 can further include a data collection system 60 having a computer 61 including a processor 62, a memory or a memory storage secret 64-data capture card 66 displayed by a dotted line as hidden and/or It is located inside the computer 61. Computer 61 can be any form of computing system, including a personal data assistant, a desktop computer, a laptop computer, or a server system. Load system 42 can be configured to apply an axial load or force F to test specimen 41. For this example, the rotation assembly 2 of the second diagram is considered to be a specific example of the test sample 41, but other versions or configurations of the sample may be tested, such as the linear translation assembly described below. The base 46 holds the outer casing 4 of the rotating assembly 2 at a fixed position with the load system 42. Sample Connection 201122449 The collar 48 can also provide a connection between the shaft 24 and the load system 42 that applies a positive and negative load F to the rotary assembly 2. The load element 5 咏 == the magnitude of the load F applied to the shaft 24 . The transducer system 52 can measure the displacement of the test specimen 41 after responding to the applied force F. The shaft drive 56 can additionally rotate the shaft 24 while applying an axial load f to the rotating assembly 2. The test specimen 41 can be held in place by the sample base 46 during the test. The sample base 46 can be configured to minimize movement of the outer surface after responding to the applied force F. The sample base 46 can be in any configuration and suitably secured to the sample during testing. The base 46 can be configured to cooperate with the sample connection collar 48 to deliver the positive and negative outward loads F generated by the load setting process to the shaft 24. The drive shaft 56C can be coupled to the shaft 24 by a sample connection collar. The drive motor 56A can cause the drive shaft 56c to be rotated via the drive system. When the force F is applied to the shaft 24, the drive shaft 56c can rotate the shaft 24 via the connecting collar 48. The negative member 50 can be configured to be in line with the load setting member 54 and the shaft 24. The negative load 5 can be used for any type of system to measure a load or add. The load element 50 can include a strain gauge and a structural beam that can flex under load. The load member 50 can include a hydraulic system. The conversion benefit system 52 can be any type of system or component for measuring line 11 translation or displacement. Converter system 52 can include converter 52A that includes a linear transformer 55 r-a, a piezoelectric component, an inductive component, a capacitive component, or a laser. Converter system 52 can further include target disk 52B. The target disk or rotary drive shaft 56C or other suitable rotating assembly target disk 52B can be configured to be used with the transducer 52A as a displacement of the 12 。 。 。 。 。 。. The converter system 52 measures the axial displacement associated with the housing shaft 24. The load setting member 54 can be a manual system such as a manually turned screw or a hydraulic or manual jack as shown. The load setting can be an automated system controlled by a processor, such as processor 62. The load system electronics 58 can control the load application system and collect data from the load component 50 and the converter 52. Data collection system 60 may include components for collecting data, such as data capture card 66. The data manipulation card can be operatively coupled to the processor and memory 64 and can be operatively coupled to the load system 42. Additional commands can be communicated to the load system 42 for controlling the job. Data manipulation card 66 can collect data from load system 42. The card % can collect the displacement data from the converter μ and collect the applied load value from the load element 5 并将 and store the data in the memory 64. The data manipulation card collects additional data. Data. Card 66 can be operatively coupled to load system electronics 并可 and can operate in conjunction with load system electronics 58. Number_Acquisition ^ If 6 can be integrated with the processor or other components on the card electronics. The load system 42 may have no load system electronics % and the data collection system 60 may collect data directly from the load system 42. Optionally, load system 42 can have load system electronics % and meter data collection system 60. The unpacked load system 42 can be actuated by applying incremental forward and negative axial directions to the shaft 24 and measuring the rotating assembly housing 4 phase 13 under each incremental load. 201122449 1::24: shift . Data collection system 60 can record, under each incremental load, load data for 5G of load and 5G of load data derived from converter 52. Recording 24 rotation or (4) stationary produces a value. Each data point can be recorded as - first and second components such as a force component and a displacement component. The incremental load herein should mean a set of load magnitude values that can be applied to the sample using the load element 50 and the set member 54 in any order. The X 4, and the load values are sufficient numbers to characterize the test specimen 41 and are constrained to the outer limits that would cause plastic deformation of any of the components of the rotating assembly 2. The incremental load can be ramped continuously and as an increment defined by the collected displacement data. The generation of force-displacement curves and their use in conjunction with a rotating assembly are well known and widely used by those skilled in the art. A comprehensive description of these concepts is available in a number of textbooks and will not be repeated here. The force-displacement curve is similar to the stress-strain curve of materials science and can reflect mechanical properties. In operation, the test system 4 can be used to determine the preload condition for the test sample 41. The force displacement curve for the active sample 41 can be derived and compared to the zero load and the axis (four) - assumed reference curve or master curve to determine the preload size by chart. At a particular load, the mandrel displacement can be a combination of displacement of the bearing and displacement of other bearing mandrel assemblies. Figure 4 includes the bearing displacement curve bd, the component displacement curve CD and the mandrel wire curve SD. The mandrel displacement is the sum of the displacements of all components under the set load. Here, the large displacement of the mandrel 201122449 is indicated by the line Ds. The mandrel displacement Ds is the sum of the component displacement Dc and the bearing displacement Db. For most test bearings, the bearing displacement Db will provide the largest part of the displacement in a force-displacement curve. A force-displacement curve can be generated from a mathematical model. A mathematical model of the rotational assembly 2 containing the characteristics of the material of each component can be constructed to account for the displacement of the rotating assembly 2 or the displacement of the assembly of the rotating assembly 2. This mathematical model can account for the displacement of the component after responding to the force applied. This mathematical model can use finite element techniques. Figure 5 shows an assumed master curve for a rotating assembly or mandrel that includes the characteristics of the mandrel in the two-axis direction. The main curve 1^(:: is a specific type of force_displacement curve for one of the assemblies with zero-axis end gap and zero preload. The main curve MC may include a positive portion or a push side p+ and a negative portion. Or pulling the side P-. In one of the two-row bearing configurations of the rotating assembly, the push-side p+ of the main curve MC corresponds to the displacement of the bearing of the first row. In the two-row bearing configuration, the pull The side P-system corresponds to the displacement of the bearings of a second row. The main curve MC can be a curve that matches the data points collected by the test system 4A. The curve MC can have a correlation with the fit curve. The value is different from the data points. The main curve MC can be used to determine the preload force of the rotating assembly of the same design. The main curve MC can be illustrated by a program and can contain a set of values. The main curve can be generated by setting the force-displacement value of a rotating assembly to a one-axis end-gap. The values for the main curve can be obtained by applying the end-gap from each of the force-displacement values. The component is deducted and defined. The resultant force _ displacement value Corresponds to a rotating assembly with zero-shaft end-gap 15 201122449 and zero preload. The bearing specific gas can be grouped according to the bearing type, bearing series and bearing family. The bearing type reflects the construction and design of the bearing. Some bearing types include roller bearings, tapered roller bearings, spherical bearings, angular contact ball bearings, single row ball bearings and double row ball bearings. This bearing series reflects the robustness of these bearings. The heaviest 'system is: 8 very thin section; 9 very thin section; bungee buckle · " '1 pole lightly damaging; 2 light; 3 medium and 4 weights. Each of these series is also in A relationship is established between the bearing's sinusoidal aperture size, outer diameter and thickness. ^ A bearing family may comprise a group of substantially identical bearings, wherein the ones are differentiated by one or more parameters. For example, the axis table μ is identical except for the contact angle. The other group is the same except for the fading and the different sizes used. The other parameters of the bearing family of the bearing family include rotation. The number of components, the straightness of the bearing Diameter or contact with the difference - the radius of curvature of the bearing ring. It can be used for _ special = / fading bead bearing, such as machine shaft or high speed motor. The shaft bearing family. The common series can be used together by a common series The naming is defined by defining a bearing family by a common bearing type. ” The fault is defined by the ° name and the common bearing type. The figure is a force-displacement, • agricultural I field 'in the bearing family In addition to the contact angle of the bearing 3 _ - group main song % car by the family including 1G degrees, 12 degrees and 13 series of antenna ^ ^ the same. This shows the force of 10, 12, 11 and 13 degrees bearing - displacement green :6 figure includes needle
Tl相切之數值MC(x)，與其之切線Τ2相士及與其之切線 刀之數值FC(X)、與 201122449 切線T2垂直的正切法向線TN及數值MC(n)。儘管為了清晰 起見僅顯示該圖之第一象限，但所有的技術及概念同樣地 應用至第二象限之該婁欠據。可由_ 1 1度試樣之一限定測試 里導出針對一11度接觸角軸承的主曲線MC，如一虛線所 示針對该11度轴承在該圖上諸如160的一固定力值下已知 該數值MC(x)以及通過MC(x)之該曲線或切線T丨之斜率，使 用針對其他軸承族曲線之主曲線以及在一固定力值下該等 斜率比的一修正係數可導出一完整的主曲線]^(：。 於一軸承族中，每一曲線之對應值處該斜率比大體上 為固定不變的。同樣地，在該等曲線之對應值下，二總成 之間勁度之比大體上為相等的。該10度軸承於每一點處之 X劫度係為已知，因此根據在每一對應值下該勁度比大體 上為固定不變可測定在每一對應值下針對該丨丨度軸承的斜 率。 可藉由一相等力（isoforce)或水平線之該曲線交切定義 忒等曲線之對應點。例如，仍參考第6圖，一相等力線諸如 圖表中所提及的160,可定義對應的數值^^^)及FC(x)。可 替代地藉由一相等位移或垂直線（未顯示）之該曲線交切定 義該等曲線之對應點。亦可藉由該已知力位移曲線之每一 ，值處該切線之-法向線的曲線交切定義該等曲線之對應 點。例如，該士刀線T2之一法向線TN可定義對應數值⑽⑻ WC(X)。可任擇地’可使用任何其他方法用以識別對應 點，於定義修正係數CF當中保持的一適當精確度。 假若藉由一多項式之形式描述針對1〇度軸承之該曲 17 201122449 線， y = k*x3+j*x + l (1) 則針對11度軸承之該曲線可具有相同的形式，除了該 等係數之數值之外。針對該軸承之主曲線MC可藉由選定係 數導出，以致該曲線通過該原點並通過點MC(x)具有與該線 T1相等斜率。可使用修正係數CF測定該等係數，其中： CF =斜率T1/斜率 T2 = KT1/KT2 (2) 即使在製造期間具嚴格的尺寸公差，但軸承單元間接 觸角34之該變化可加或減1度。因此，指定為一 15度軸承的 一軸承可具有14度或16度的一接觸角，並仍涵蓋於製造規 格内。第7圖係為一圖表圖示在一軸承之該視勁度方面接觸 角34的作用。該圖表之該15度軸承係任意地設定為1之一比 值。一14度之軸承將具有0.87的一比值，以及一 16度之軸 承將具有1.13的一比值。此係為一顯著的變化。使用針對 一 15度軸承的一主曲線其中該軸承實際上具有14度或是16 度的一接觸角，對於該測定的預負載將具有一顯著的影響。 第8圖係為一力-位移圖表，包括一測試曲線TC其在一 預負載下與轉動總成2相對應以及主曲線MC。測試曲線TC 包括第一反曲點IP 1及第二反曲點ΙΡ2。反曲點ΙΡ1及ΙΡ2之該 等力分量可與用以將一二列式轉動總成中一組軸承移開位 置所需的力量相對應。 反曲點IP1及IP2之定位作業可包括將主曲線MC之一 部分自該圖表之該正區域平移，用以覆蓋測試曲線TC超越 反曲點IP1的該部分。圖中以虛線顯示位移主曲線MC+。在 18 201122449 位移主曲線MC+與該X軸交切的該點處，繪製一垂直線匕2 與該測試曲線TC交切。此交切定義該反曲點IP2。使用一相 似方法定義位移主曲線MC-，利用一垂直線L1定位反曲點 IP1。曲線MC+及MC-之y-截距可定義該預負載力標示為正 預負載F(p+)及負預負載F(p-)。 介於線L1與L2之間的該段距離可定義尺寸.預負載 D(p)。尺寸預負載D(p)可由一正部分D(p+)及一負部分 所組成。位移主曲線MC+可平移一段距離D(p+)用以覆蓋測 試曲線TC之超越反曲點IP1該部分。位移主曲線MC-可平移 一段距離D(p-)用以覆蓋測試曲線tc之超越反曲點IP2該部 分。 測試曲線TC可為與使用測試系統40所取得的數據點 Ap相似的一組數據點配合的曲線。測試曲線TC可藉由一方 程式加以描述並可包含一組數值。 在零位移值處介於零負載與一移動主曲線MC之間的 該段垂直距離’係為測試試樣41之該等軸承的一預負載力 F(pl)。於第8圖中該移動主曲線MC係以虛線顯示。其係自 該MC移動D(p+)或D(p-)。正預負載力F(p+)、負預負載力 F(p-)及預負載力F(pl)可視為相同的預負載力並可為相等 的，但可由不同的圖解或是數學方法導出。F(pl)= F(p+)= F(p-) 於超越反曲點IP1及IP2的該區域中，在一固定力值下 介於測試曲線T C與主曲線M C之間的該段水平距離，係與一 預負載尺寸D(pl)相對應。尺寸預負載D(pl)係為D(p+)與D(p-) 19 201122449 之總和。尺寸預負載D(pl)、D(p+)與D(p-)可藉由不同的圖 表或數學方法導出。 第9圖係為第8圖中超越反曲點ip 1所配置的一虛線框c 標示之該第8圖之力-位移曲線的一細節。再次地，第9圖包 括測試曲線TC及主曲線MC。測試曲線TC之測試曲線斜率 K(tc)係顯示為測試曲線TC之二點間該力上升對位移前進 的比值，與測試試樣41之該勁度或彈性相對應。主曲線Mc 之主曲線斜率K(mc)係顯示為主曲線MC之二點間該力上升 對位移前進的比值。於此，位在每一曲線上的量測點係以 測試曲線TC的測試值TC(pt)以及主曲線MC上的MC(pt 1)標 示0 就相同設計 '接觸角及材料的一測試試樣及一主曲線 試樣而言，斜率K(mc)及K(tc)將為相等的。實際上，個別試 樣間接觸角34方面的變化以及材料與尺寸上的變化導致斜 率K(mc)及K(tc)為不相等。假若主曲線mc之斜率K(mc)等 於K(tc)，則可僅偏置主曲線MC之該外區域並與主曲線MC 之該外區域等距離。 K(mc)及K(tc)不相等處該量測預負載力D(pl)並不精 確。修正係數CF應用至主曲線MC或測試曲線tc可產生一 修正曲線，可造成較尺寸預負載D(pl)更為精確的一數值。 就一實例而言’於測試系統40中用以產生測試曲線tc 的該測試試樣能夠於第6圖之曲線族中加以確認為具有i j 度之一接觸角。在針對具有一10度接觸角的一軸承比較測 試曲線TC與主曲線MC當中，顯而易見的是在對應的數值下 20 201122449 斜率K(mc)及K(tc)並不相等。測試試樣4丨可具有一丨丨度接觸 角，對於測試試樣41而言其係涵蓋余容限内。使用針對1〇 度軸承之主曲線MC並未提供一精確的預負載值。使用針對 10度軸承之修正係數CF主曲線MC,可經修正用以反映於此 11度例子中，在測試下針對測試試樣41之接觸角34的一零 負載主曲線。因而能夠測定預負載力F(corr)。 在一固定不變力狀況下進行針對距離D(p+)的量測，於 此顯示一相等力線或是水平線為3 · 9。距離D (p+)係為主曲線 MC之點MC(ptl)與該測試曲線TC之點TC(pt)之間該水平距 離。該修正距離D(c〇rr)係為測試曲線sTC(pt)與該修正主 曲線點MC(pt2)之間該段距離。 介於修正距離D(corr)與未修正距離D(p+)之間該差異 係標示為D(cf)並且 D(cf) = D(p+) - D(corr) (3A) 其中D(p+)係為在測試曲線Tc&主曲線MC上與量測數 據點相對應—值的尺寸分量上差異。修正距離D(corr)可 針對誤差來源加以補償及修正，並產生較尺寸預負載D(pi) 顯著地更為精確的數值。 再次參考第8圖，可藉由複數之方法形成修正主曲線 MC(corr^其中一方法可包括確認測試曲線Tc之斜率。修 正主曲線MC(corr)可包含自主曲線MC之一反曲點延伸具 有斜率K(tc)的一線。 另一用以形成修正主曲線MC(corr)的方法可包括以一 相似方式對於勁度比定義修正係數CF為主曲線斜率 21 201122449 與測試曲線斜率K(tc)之間的一關係或 CF = K(tc) / K(mc) (4) 修正係數CF可應用在主曲線MC之一或更多數值，用以 界定一或更多修正數據值’用以導出修正預負載力F(c〇rr)。 修正係數CF可應用在主曲線MC之一值用以測定該預 負載力F(pl)之大小。修正係數CF可簡單地應用在主曲線值 MC(ptl)產生一修正主曲線值 MC(pt2) = CF * MC(ptl) (5) 第10圖圖示用以形成修正主曲線MC(corr)的另一方 法。可藉由採用構成主曲線MC的一支組之數值並擬合連續 數據點或數值之間的線段而定義一分段主曲線MC(seg)。 MC(seg)之數值可包括Pl(seg)、P2(seg)及ip(seg)，可定義為 MC(seg)之一反曲點。圖中以虛線顯示主曲線MC，並為清 晰起見稍微偏移MC(seg)。 可使用修正係數CF形成修正主曲線MC(corr)。於 MC(seg)之點（0,0)開始，以一點對點或是反覆方式將修正係 數CF應用在每一分段之該斜率。例如，介於p 1 (seg)與 P2(seg)之間的該線段可具有一公式 P2(seg)(y)-Pl(seg)(y)=m(P2(seg)(x)-Pl(seg)(x))，其巾該m 係為介於該等點之間的該線之斜率，以及 P2(seg)(y)-Pl(seg)(y)係為連續點Pl(seg)與p2(seg)之該等垂 直分量之差。p2(seg)(x)-Pl(seg)(x)係為連續點P1(seg)與 P2(seg)之該等水平分量之差。 再者，定義修正主曲線MC(corr)之數值P2(c〇rr)。於之 22 201122449 前重述中以及藉由定義P2(corr)與P2(seg)之x分量係 為相等而測定Pl(c〇rr)。在尋求pi(corr)與P2(corr)之 間該線段當中，使用一相似公式其中 P2(corr)(y)-P 1 (corr)(y)=m(corr)*(P2(corr)(x)_p 1 (c〇rr)(x))。 於此，該斜率m(corr)將等於介於pi(seg)與P2(seg)之間該線 的斜率m乘上CF或 m(corr) = m * CF (6) 反覆涵蓋所有選定點及其之片段產生具有一修正反曲 點IP(corr)的一修正主曲線MC(corr)。 此特定演算法係為對於產生一修正主曲線之片段的一 貫例。可使用其他相似的演算法並且仍涵蓋於此揭示内容 之該範疇内。 於產生一修正主曲線MC(corr)的另一方法中，可使用 曲線擬合及微積分學方法。第n圖圖示產生一修正曲線的 一微積分學方法，並包括主曲線MC及修正主曲線 MC(c〇rr)。主曲線MC可為一曲線並可藉由對測試一組轉動 總成2所需之一組數據點應用最佳擬合技術而產生。可與主 曲線MC之數值相對應的一支組之數據點係以橢圓形虛線 標示為點Ap。針對此圖，位移分量及力分量可以乂及^符號 表示。 可藉與構成該曲線的一組主數據值相對應的—方程式 說明主曲線MC。在主曲線MC上的任一點（Xl，yi)可具有一對 應的切線或斜率Tangh^y!)。主曲線!^^可具有一反曲點 IP(mc)。修正主曲線MC(corr)亦可具有一反曲點ip(c〇吶以 23 201122449 及在修正主曲線MC(corr)上的任一點（x2,y2)可具有一斜率 Tang(x2，y2)。 曲線擬合技術係為熟知此技藝之人士廣為熟知的。主 曲線MC與數據點Ap擬合可藉由具有任何數目之項的一方 程式加以說明，一般地並可表示為 Y = Σ a * xn (7) 以及針對此曲線在任何點處的斜率可表示為方程式7 之導數： y’ = Σ η * a * xn_1 (8) 針對一擬合曲線具有二項的一方程式之--般的實例 可為該多項式： y = a*x2 + b*x (9) 其中a及b及c係為常數並且該曲線通過該原點。此或具 有更多或較少項的一相似方程式可說明主曲線M C。位於此 多項式或位在主曲線MC上的每一點處該斜率因而可藉由 方程式9之一階導數加以說明： y’ = 2*a*x + b (10) 其可與該斜率或是切線Tang(xi，yi)相對應。 產生修正主曲線MC(corr)可包括將修正係數CF應用在 主曲線MC之該斜率。於一實例中，修正主曲線MC(corr)之 該斜率或切線可藉由以下方程式加以說明： y(corr)5 = (2*a*x + b) * CF = 2*a*x*CF + b*CF (11) 此可與修正主曲線MC(corr)之斜率或切線Tang(x2,y2)相對 應。 24 201122449 使用微積分學之該等技術，修正主曲線MC(c〇rr)可藉 由方程式11之積分加以定義或： MC(corr) = a*CF*x2 + b*CF*x + d (12) 於此d係為一常數其可藉由評估由方程式12表示的修 正主曲線MC(corr)而加以測定，其中該χ之數值係等於零以 及MC(corr)係等於零。 主曲線MC可藉由一擬合曲線而近似，其中每一曲線使 與不同支組之數據點Ap近似。例如，介於零與該反曲點 IP(mc)之間該段可藉由諸如方程式9的一多項式加以說 明，以及超越反曲點IP(mc)的該區域可藉由針對一不同曲 線或是一直線的一方程式加以說明。針對不同段的該等方 程式在對於該等對應支組之數據點AP的該等邊界處大體上 可為連續的。如於第9圖中所說明的相似方法可使用此修正 主曲線MC用以測定預負載。 .儘管已於方程式9中使用一二次多項式，但此僅係針對 說明之目的。一較高階或較低階之方程式可用以說明—曲 線與數據點Ap擬合。由測試複數主總成以及將收集數據平 均化之數據數值可取得與主曲線M C對應的數據點A p。 於另一實例中，一轉動總成2可用以形成主曲線1^(：及 測試曲線TC。與主曲線MC相對應的數據點Ap可由對測試 試樣41進行測試而取得。測試試樣41首先可經裝配以致該 軸係處於一軸端隙狀況。測試試樣41可安裝於測試系統4〇 中。使用測s式系統40取得的數據點Ap可使用第5圖中所示方 法用以定義曲線A及主曲線MC。測試試樣41因而可自測試 25 201122449 系統40去除，以一設定預負載重新裝配並再次安裝在測試 系統40中。在重新裝配及預負載的測試試樣41上使用測試 系統40取得的另一組數據點，可於擬合測試曲線Tc當中使 用。與以上所述相似的技術因而可由測試曲線Tc與主曲線 MC之間的差異用以測定預負載力F(c〇rr)或預負載尺寸 D(c〇rr)，其中該測試曲線TC及主曲線⑽二者係在不同的 預負載狀況下自相同總成導出。 修正係數C F可應用在測試曲線數值用以導出一修正測 試曲線而非將修正係數CF應用在主曲線數值，用以導出％ 正主曲線MC(corr)。如以上所述的相似方法可用以自一修 正測試曲線測定一修正預負載數值。於此僅使用修正主曲 線MC(corr)作為一實例。如以上所述以一相似方式使用該 等曲線之該負部分同樣地能夠導出該預負載力。該正部分 係僅使用作為實例。 為測定一預負載值F(pl)，可藉由測試系統4〇對軸或橫 樑110遞增地施以一力F。量測的力-位移值可用以定義至少 一部分之測試曲線TC。於以上針對轉動總成2的相似方法 中’能夠藉由測試曲線T C與主曲線M C之間該段距離測定— 預負載F(pl)。 第12圖係為一平移軸承100，包括第一軸承1〇2以及第 二軸承104。平移轴承1 〇〇亦包含一頂部外殼1 〇6及底部外殼 108其支撐第一及第二軸承102及104。軸承1〇2及104支撐軸 或橫樑110。橫樑110可在軸承102與104之間移動或是平 移，如圖中虛線所示之橫樑110’。外殼106及108可施以一 26 201122449 力頂著軸承102及104作為一預負載。 第13圖係為一流程圖圖示用於一測試心軸之一組軸承 上測定一預負載的一方法200,該測試心軸具有一測試心軸 外殼及一測試心軸。於步驟202，針對具有一外殼及一軸的 一參考心軸定義一第一組之參考值。每一參考值可包括與 施加至該參考心軸的一參考力相對應的一力分量，以及與 該參考心軸的該位移相對應的一位移分量。該參考值及參 考心轴可取自於相同設計的任一心軸單元。於步驟204，由 該第一組之參考值測定一參考彈性常數。 於步驟206中，測定針對該測試心軸的一第二組之測試 值。每一值可包括與施加至該測試心軸的一力相對應的一 測試力分量，以及與該測試心軸在回應該外加測試力後相 對於該測試心軸外殼的該位移相對應的一位移分量。於步 驟208中，由該第二組之測試值測定一測試彈性常數。於步 驟210中，定義一修正係數。該修正值可定義為該參考彈性 常數及該測試彈性常數的一函數。於步驟212中，藉由對自 一數值群組中選定的一組數值中之至少一數值施以該修正 係數，定義一第三組之修正值。該數值群組可由該第一組 之參考值及第二組之測試值所組成。 於步驟214中，使用源自於該第三組之修正值的至少一 數值以及在定義該第三組之數值當中未自該數值群組選定 的該組值中的至少一數值，用以測定該測試心軸之該組軸 承上的預負載。因此，假若該等修正值係使用源自於該等 參考值的至少一值定義，則該預負載係使用源自於該修正 27 201122449 值的至少一值以及該第二組之測試值加以測定。假若該等 修正值係使用該第二組之測試值加以定義，則使用源自於 該等修正值的至少一值以及源自於該第一組之參考數值中 至少一數值測定該預負載。 第14圖係為一流程圖，圖示藉由產生一組補償主曲線 值，每一值包括一位移分量及一力分量，測定該預負載的 一方法300。方法300包含之步驟包括步驟302利用相同設計 針對一主曲線選擇一組參考數值，每一值包含一力分量及 一位移分量，以及步驟304係針對參考值之該主曲線測定一 第一彈性常數。於步驟306中，針對一測試心軸在一對應的 數值下測定一第二彈性常數。於步驟308中，由該主曲線彈 性常數與該測試心轴彈性常數之比產生一修正係數。於步 驟310中，將該修正係數應用在該等主曲線參考值上。步驟 312導出該組之修正主曲線值用以測定測試心軸之該預負 載。 每一值之該第一分量可為一尺寸分量。藉由該等尺寸 分量間之差用以測定一預負載力而測定該預負載。 該等經說明的系統及總成係為實例並不具限制性。其 他執行相同功能的測試系統之構形仍涵蓋於此揭示内容之 範疇。執行相同功能的類似方法亦涵蓋於此揭示内容之範 疇。 儘管已特別地顯示並說明一測試系統及其使用方法之 具體實施例，但於此仍可作複數之變化。此揭示内容可包 括針對特性、功能、元件及/或性質之不同結合的一或更多 28 201122449 獨立或互助的發明，其中一或更多者可於以下該等申請專 利範圍中疋義。之後於此或是一相關的申請案中可主張特 性、功能、7C件及/或性質之其他的結合及次結合。該等變 化’無論就料而言是不同的、較為廣泛的、較為狹p益的 或疋等同的，亦係視為包括於本揭示内容之主題内。應察 知的是目前未域的巾請專㈣圍的有效性或重要性可能 目前未被實現。因此，該f前述的具體實施例係為說明的， ^無單i性或元件或是其之結合料此或是—以後的申 請案中可主張的所有可能結合係為不可缺的。每-申請專 利範圍定義於該先前揭示内容中所揭示的—發明，但任— 申請專利範圍並非必要地包含所有能夠主張的特性或結 合。其中該等申請專利範圍詳述“一，，或“一第_，，元件或是 其之等效物，該等中請專利範圍包括—或更多該等元件， 既不需要亦非不包括二或更多該等林。再者針對識別 疋件，順序性指標，諸如第―、第二或是第三，除非特別 提及否則偏以區別該等元件而非⑹料元件的一 部分或是限制之數目。 【圖式簡單說明】 第1圖係為-轉動總成的一橫截面，包括一外殼、—轴 及Γ轴承，其中該等軸承之該等内轴承環係配裝至該軸以 及δ亥等外軸承環係配裝在該外殼中。 第2圖係為-軸承的一橫截面，顯示—内轴承環、一外 軸承環以及-滾珠固定在該等軸承環之間，其中位在 轴承環上職珠之該等接觸.較義㈣帅承的一_ 29 201122449 角0 第3圖係為一測試系統的一透視圖，包括一負載系統具 有一試樣底座、一負荷元件、一轉換器、一軸驅動器以及 一電腦包括一處理器及記憶體。 第4圖係為一力-位移圖，顯示軸承位移及組件位移提 供轉動總成位移。 第5圖係為針對具有零預負载及零軸端隙的—心軸之 -力-位移圖’顯示由正向或推外加負載及負向或拉外加負 載所產生的位移。 第6圖係為一圖顯示針對一組軸承的力_位移曲線。 第7圖係為係為一圖圖示具有該軸承之該接觸角中小 變化的該勁度比之變化。 第8圖係為具有一主曲線及一測試曲線的一力—位移 圖，圖示用於測定一轉動總成中之預負載的一方法。 第9圖係為第8圖之該圖的一細節，圖示使用一修正主 曲線用以測定該預負載尺寸的一方法。 第1〇圖係為包括一主曲線、一分段主曲線及一修正主 曲線的一力-位移圖，圖示使用一修正係素的一方法。 第11圖係為包括一主曲線、一修正主曲線其針對位在 該主曲線上的-點以及位在該修正主曲線上的—點之切線 的一力-位移圖，圖示微分學方法。 第12圖係為用於-線性平移總成的-軸承的-橫截 面。 第13圖係為_流程圖，顯示用於測定軸承預負載的一 30 201122449 方法。 第14圖係為一流程圖，顯示用於測定軸承預負載的一 方法。 【主要元件符號說明】The value of T1 tangent is MC(x), the tangent to the tangent Τ2 and the value of the tangent knife FC(X), the tangent normal line TN perpendicular to the tangent line T2 of 201122449, and the value MC(n). Although only the first quadrant of the figure is shown for clarity, all of the techniques and concepts apply equally to the second quadrant. The main curve MC for an 11 degree contact angle bearing can be derived from a test defined by one of the _1 degree samples, as indicated by a dashed line, for which the value is known for a fixed force value such as 160 on the 11 degree bearing. MC(x) and the slope of the curve or tangent T丨 through MC(x), using a master curve for other bearing family curves and a correction factor for the slope ratios at a fixed force value to derive a complete master Curve]^(:. In a bearing family, the slope ratio is substantially constant at the corresponding value of each curve. Similarly, under the corresponding values of the curves, the stiffness between the two assemblies The ratio is substantially equal. The X-degree of the 10 degree bearing at each point is known, so the stiffness ratio can be determined at each corresponding value according to each of the corresponding values. For the slope of the temperature bearing, the corresponding point of the curve can be defined by the curve of an equal force or horizontal line. For example, still refer to Figure 6, an equal force line such as that mentioned in the chart And 160, you can define the corresponding values ^^^) and FC(x). The corresponding points of the curves can alternatively be defined by the intersection of an equal displacement or a vertical line (not shown). The corresponding points of the curves can also be defined by the intersection of the curve of the tangent to the normal line of the known force displacement curve. For example, one of the normal lines TN of the knife line T2 can define a corresponding value (10) (8) WC (X). Optionally, any other method can be used to identify the corresponding point to define an appropriate precision maintained in the correction factor CF. If the curve 17 201122449 for a 1 degree bearing is described by a polynomial form, y = k*x3+j*x + l (1), the curve for the 11 degree bearing may have the same form, except Beyond the value of the coefficient. The main curve MC for the bearing can be derived by selecting the coefficient such that the curve passes through the origin and has a slope equal to the line T1 through the point MC(x). These coefficients can be determined using the correction factor CF, where: CF = slope T1/slope T2 = KT1/KT2 (2) Even with strict dimensional tolerances during manufacturing, this change in contact angle 34 between bearing units can be increased or decreased by one. degree. Therefore, a bearing designated as a 15 degree bearing can have a contact angle of 14 degrees or 16 degrees and still be covered by the manufacturing specifications. Figure 7 is a diagram illustrating the effect of the contact angle 34 in terms of the apparent stiffness of a bearing. The 15 degree bearing of the graph is arbitrarily set to a ratio of one. A 14 degree bearing will have a ratio of 0.87 and a 16 degree bearing will have a ratio of 1.13. This is a significant change. Using a master curve for a 15 degree bearing where the bearing actually has a contact angle of 14 degrees or 16 degrees will have a significant impact on the preload of the measurement. Figure 8 is a force-displacement diagram comprising a test curve TC corresponding to the rotating assembly 2 under a preload and the main curve MC. The test curve TC includes a first inflection point IP 1 and a second inflection point ΙΡ2. The equal force components of the inflection points ΙΡ1 and ΙΡ2 may correspond to the forces required to move a set of bearings in a two-column rotating assembly. The positioning of the inflection points IP1 and IP2 may include translating a portion of the main curve MC from the positive region of the graph to cover the portion of the test curve TC that exceeds the inflection point IP1. The displacement master curve MC+ is shown by a broken line in the figure. At the point where the displacement master curve MC+ intersects the X-axis at 18 201122449, a vertical line 匕2 is drawn to intersect the test curve TC. This intersection defines the inflection point IP2. A similar method is used to define the displacement master curve MC-, and a vertical line L1 is used to locate the inflection point IP1. The y-intercepts of the curves MC+ and MC- define the preload force as positive preload F(p+) and negative preload F(p-). The distance between the lines L1 and L2 can be defined as the size. Preload D(p). The size preload D(p) may consist of a positive portion D(p+) and a negative portion. The displacement master curve MC+ can be translated by a distance D(p+) to cover the portion of the test curve TC that exceeds the inflection point IP1. The displacement master curve MC- can be translated by a distance D(p-) to cover the portion of the test curve tc beyond the inflection point IP2. The test curve TC can be a set of data point fits similar to the data point Ap taken using the test system 40. The test curve TC can be described by a program and can contain a set of values. The vertical distance ' between the zero load and a moving main curve MC at the zero displacement value is a preload force F(pl) of the bearings of the test specimen 41. The moving main curve MC is shown in broken lines in Fig. 8. It moves D(p+) or D(p-) from the MC. The positive preload force F(p+), the negative preload force F(p-), and the preload force F(pl) can be considered as the same preload force and can be equal, but can be derived by different graphical or mathematical methods. F(pl)= F(p+)= F(p-) is the horizontal distance between the test curve TC and the main curve MC at a fixed force value in this region beyond the inflection points IP1 and IP2. , corresponding to a preload size D(pl). The size preload D(pl) is the sum of D(p+) and D(p-) 19 201122449. The size preloads D(pl), D(p+) and D(p-) can be derived by different graphs or mathematical methods. Figure 9 is a detail of the force-displacement curve of the Figure 8 indicated by a dashed box c disposed in the dashed line ip 1 in Figure 8. Again, Figure 9 includes the test curve TC and the main curve MC. The test curve slope K(tc) of the test curve TC is shown as the ratio of the force rise to the displacement advancement between the two points of the test curve TC, corresponding to the stiffness or elasticity of the test specimen 41. The main curve slope K(mc) of the main curve Mc shows the ratio of the force rise to the displacement advance between the two points of the main curve MC. Here, the measurement points on each curve are marked with the test value TC(pt) of the test curve TC and the MC (pt 1) mark on the main curve MC. The same design 'contact angle and material test For the sample and a master curve sample, the slopes K(mc) and K(tc) will be equal. In fact, changes in the contact angle 34 between individual samples and changes in material and size result in unequal slopes K(mc) and K(tc). If the slope K(mc) of the main curve mc is equal to K(tc), then only the outer region of the main curve MC can be offset and equidistant from the outer region of the main curve MC. The measured preload force D(pl) is not accurate where K(mc) and K(tc) are not equal. Applying the correction factor CF to the main curve MC or the test curve tc produces a correction curve which results in a more accurate value for the larger preload D(pl). For an example, the test sample used to generate the test curve tc in the test system 40 can be confirmed in the family of curves in Fig. 6 as having a contact angle of i j degrees. In comparing the test curve TC with the main curve MC for a bearing having a contact angle of 10 degrees, it is apparent that the slopes K(mc) and K(tc) are not equal under the corresponding values 20 201122449. The test sample 4丨 may have a twist contact angle, which is within the tolerance for the test sample 41. The use of a master curve MC for a 1 degree bearing does not provide an accurate preload value. Using the correction factor CF master curve MC for the 10 degree bearing, it can be modified to reflect the zero load main curve for the contact angle 34 of the test specimen 41 under this test in the 11 degree example. Therefore, the preload force F(corr) can be measured. The measurement for the distance D(p+) is performed under a constant force condition, and an equal force line or a horizontal line of 3·9 is displayed. The distance D (p+) is the horizontal distance between the point MC (ptl) of the main curve MC and the point TC (pt) of the test curve TC. The correction distance D(c〇rr) is the distance between the test curve sTC(pt) and the corrected main curve point MC(pt2). Between the correction distance D(corr) and the uncorrected distance D(p+), the difference is indicated as D(cf) and D(cf) = D(p+) - D(corr) (3A) where D(p+) It is the difference in the size component corresponding to the measured data point on the test curve Tc & main curve MC. The correction distance D(corr) compensates and corrects for the source of the error and produces a significantly more accurate value for the pre-load D(pi). Referring again to FIG. 8, a modified main curve MC can be formed by a complex method (corr^), which may include confirming the slope of the test curve Tc. The modified main curve MC(corr) may include an inflection point extension of the autonomous curve MC. A line having a slope K(tc). Another method for forming a modified master curve MC(corr) may include defining a correction factor CF for a stiffness ratio in a similar manner as a main curve slope 21 201122449 and a test curve slope K(tc a relationship between them or CF = K(tc) / K(mc) (4) The correction factor CF can be applied to one or more values of the main curve MC to define one or more corrected data values 'for The corrected preload force F(c〇rr) is derived. The correction factor CF can be applied to one of the main curves MC to determine the magnitude of the preload force F(pl). The correction factor CF can be simply applied to the main curve value MC. (ptl) produces a corrected main curve value MC(pt2) = CF * MC(ptl) (5) Fig. 10 illustrates another method for forming a modified main curve MC(corr). Define a segmented master curve MC(seg) by the value of a group of MCs and fitting a line segment between consecutive data points or values The value of MC(seg) may include Pl(seg), P2(seg), and ip(seg), which may be defined as one of the inflection points of MC(seg). The main curve MC is shown by a broken line in the figure, and for the sake of clarity Slightly offset MC(seg). Correction master curve MC(corr) can be formed using correction factor CF. Starting at point (0,0) of MC(seg), correction coefficient CF is applied to each point in a point-to-point or over-repeated manner. The slope of a segment. For example, the line segment between p 1 (seg) and P2 (seg) may have a formula P2(seg)(y)-Pl(seg)(y)=m(P2( Seg)(x)-Pl(seg)(x)), the towel m is the slope of the line between the points, and P2(seg)(y)-Pl(seg)(y) It is the difference between the vertical components of the continuous points P1(seg) and p2(seg). p2(seg)(x)-Pl(seg)(x) is the continuous point P1(seg) and P2(seg) The difference between the horizontal components. Further, define the value P2(c〇rr) of the modified main curve MC(corr). In the restatement before 22 201122449 and by defining P2(corr) and P2(seg) The component is equal and P1(c〇rr) is determined. In the line between seeking pi(corr) and P2(corr), a similarity formula is used where P2(corr)(y)-P 1 (corr)(y )=m(corr)*(P2(corr) ) (x)_p 1 (c〇rr)(x)). Here, the slope m(corr) will be equal to the slope m of the line between pi(seg) and P2(seg) multiplied by CF or m(corr) = m * CF (6), which covers all selected points and The segment thereof produces a modified master curve MC(corr) having a modified inflection point IP(corr). This particular algorithm is a consistent example of generating a segment of a modified master curve. Other similar algorithms can be used and still fall within this scope of the disclosure. In another method of generating a modified master curve MC(corr), curve fitting and calculus methods can be used. The nth diagram illustrates a calculus method that produces a correction curve and includes a main curve MC and a modified main curve MC(c〇rr). The main curve MC can be a curve and can be generated by applying a best fit technique to a set of data points required to test a set of rotation assemblies 2. The data points of a group which can correspond to the value of the main curve MC are indicated by the elliptical dotted line as the point Ap. For this figure, the displacement component and the force component can be represented by the ^ symbol. The main curve MC can be explained by an equation corresponding to a set of main data values constituting the curve. Any point (Xl, yi) on the main curve MC may have a corresponding tangent or slope Tangh^y!). The main curve !^^ can have an inflection point IP(mc). The modified main curve MC(corr) may also have an inflection point ip (c〇呐 with 23 201122449 and any point (x2, y2) on the modified main curve MC(corr) may have a slope Tang(x2, y2) Curve fitting techniques are well known to those skilled in the art. The fitting of the main curve MC to the data point Ap can be illustrated by a program having any number of terms, generally and can be expressed as Y = Σ a * xn (7) and the slope at any point for this curve can be expressed as the derivative of Equation 7: y' = Σ η * a * xn_1 (8) For a fitting curve with a binomial program - An example of this can be the polynomial: y = a*x2 + b*x (9) where a and b and c are constants and the curve passes through the origin. This or a similar equation with more or less terms can Describe the main curve MC. This slope at each point of the polynomial or bit on the main curve MC can thus be explained by the first derivative of Equation 9: y' = 2*a*x + b (10) The slope corresponds to the tangent Tang(xi, yi). Producing the corrected master curve MC(corr) may include applying the correction coefficient CF to the main curve MC The slope. In one example, the slope or tangent of the modified main curve MC(corr) can be illustrated by the following equation: y(corr)5 = (2*a*x + b) * CF = 2*a* x*CF + b*CF (11) This corresponds to the slope or tangent Tang(x2, y2) of the modified main curve MC(corr). 24 201122449 Using the techniques of calculus, the main curve MC is corrected (c〇 Rr) can be defined by the integral of equation 11 or: MC(corr) = a*CF*x2 + b*CF*x + d (12) where d is a constant which can be represented by equation 12 The corrected main curve MC(corr) is determined, wherein the value of the χ is equal to zero and the MC(corr) system is equal to zero. The main curve MC can be approximated by a fitting curve, wherein each curve makes a different branch The data point Ap is approximated. For example, between zero and the inflection point IP(mc), the segment can be illustrated by a polynomial such as Equation 9, and the region beyond the inflection point IP(mc) can be used by Describe a program for a different curve or a straight line. The equations for the different segments are generally at the boundaries of the data points AP for the corresponding branches. It may be continuous. This modified master curve MC can be used to determine the preload as in the similar method illustrated in Figure 9. Although a quadratic polynomial has been used in Equation 9, this is for illustrative purposes only. A higher order or lower order equation can be used to illustrate - the curve is fitted to the data point Ap. The data point Ap corresponding to the main curve M C can be obtained by testing the complex main assembly and the data values that will be averaged over the collected data. In another example, a rotation assembly 2 can be used to form a main curve 1 (: and a test curve TC. A data point Ap corresponding to the main curve MC can be obtained by testing the test sample 41. The test sample 41 First, the shafting can be assembled so that the shaft is in a one-axis end-gap condition. The test specimen 41 can be installed in the test system 4. The data point Ap obtained using the s-type system 40 can be defined using the method shown in FIG. Curve A and main curve MC. Test sample 41 can thus be removed from test 25 201122449 system 40, reassembled with a set preload and reinstalled in test system 40. Used on reassembled and preloaded test specimen 41 Another set of data points taken by the test system 40 can be used in the fitted test curve Tc. Techniques similar to those described above can thus be used to determine the preload force F(c) from the difference between the test curve Tc and the main curve MC. 〇rr) or preload size D(c〇rr), wherein the test curve TC and the main curve (10) are derived from the same assembly under different preload conditions. The correction factor CF can be applied to the test curve value for Export a fix Instead of applying the correction factor CF to the main curve value, the test curve is used to derive the % positive master curve MC(corr). A similar method as described above can be used to determine a modified preload value from a modified test curve. The modified master curve MC(corr) is used as an example. The use of the negative portion of the curves in a similar manner as described above is equally capable of deriving the preload force. The positive portion is only used as an example. The load value F(pl) can be incrementally applied to the shaft or beam 110 by the test system 4〇. The measured force-displacement value can be used to define at least a portion of the test curve TC. In a similar method of 2, 'the distance between the test curve TC and the main curve MC can be determined as the preload F(pl). Fig. 12 is a translation bearing 100 including the first bearing 1〇2 and the second The bearing 104. The translation bearing 1 〇〇 also includes a top housing 1 〇 6 and a bottom housing 108 that supports the first and second bearings 102 and 104. The bearings 1 〇 2 and 104 support the shaft or beam 110. The beam 110 can be in the bearing 102 Move between 104 and Move, as shown by the dashed line in the figure, the beam 110'. The outer casings 106 and 108 can be applied with a 26 201122449 force against the bearings 102 and 104 as a preload. Fig. 13 is a flow chart for a test heart A method 200 for determining a preload on a set of bearings, the test mandrel having a test mandrel housing and a test mandrel. In step 202, a first reference axis is defined for a housing and an axis. Reference value of the set. Each reference value may include a force component corresponding to a reference force applied to the reference mandrel, and a displacement component corresponding to the displacement of the reference mandrel. The reference value and the reference mandrel can be taken from any of the mandrel units of the same design. In step 204, a reference elastic constant is determined from the reference values of the first set. In step 206, a second set of test values for the test mandrel is determined. Each value may include a test force component corresponding to a force applied to the test mandrel, and a corresponding to the test mandrel corresponding to the displacement of the test mandrel shell after the test force is applied Displacement component. In step 208, a test elastic constant is determined from the test values of the second set. In step 210, a correction factor is defined. The correction value can be defined as a function of the reference elastic constant and the test elastic constant. In step 212, a third set of correction values is defined by applying the correction factor to at least one of a selected set of values from a group of values. The group of values may consist of a reference value of the first group and a test value of the second group. In step 214, at least one value derived from the correction value of the third group and at least one value of the set of values not selected from the group of values among the values defining the third group are used to determine The preload on the set of bearings of the test mandrel. Therefore, if the correction values are defined using at least one value derived from the reference values, the preload is determined using at least one value derived from the value of the correction 27 201122449 and the test value of the second group. . If the correction values are defined using the test values of the second set, the preload is determined using at least one value derived from the correction values and at least one of the reference values derived from the first set. Figure 14 is a flow diagram illustrating a method 300 for determining the preload by generating a set of compensated master curve values, each value including a displacement component and a force component. The method 300 includes the steps of: step 302: selecting a set of reference values for a master curve using the same design, each value comprising a force component and a displacement component, and step 304 determining a first elastic constant for the master curve of the reference value . In step 306, a second elastic constant is determined for a test mandrel at a corresponding value. In step 308, a correction factor is generated from the ratio of the elastic constant of the main curve to the elastic constant of the test mandrel. In step 310, the correction factor is applied to the master curve reference values. Step 312 derives the modified master curve value for the set to determine the preload of the test spindle. The first component of each value can be a size component. The preload is determined by measuring the difference between the components of the dimensions to determine a preload force. The illustrated systems and assemblies are examples and are not limiting. The configuration of other test systems that perform the same function still covers the scope of this disclosure. Similar methods of performing the same functions also cover the scope of this disclosure. Although a specific embodiment of a test system and method of use thereof has been specifically shown and described, it is to be varied herein. This disclosure may include one or more of the various combinations of features, functions, components and/or properties. The invention may be delineated by one or more of the following patent applications. Other combinations and sub-combinations of features, functions, 7C pieces and/or properties may be claimed herein or in a related application. Such variations are considered to be encompassed within the subject matter of the present disclosure, whether they are different, broader, narrower, or equivalent. It should be noted that the validity or importance of the current (4) circumference of the non-domain towel may not be realized. Thus, the foregoing specific embodiments are illustrative, and that no single element or element or combination thereof may be indispensable for all possible combinations that may be claimed in subsequent applications. The scope of each application patent is defined by the invention disclosed in the foregoing disclosure, but the scope of the patent application does not necessarily include all features or combinations that can be claimed. Wherein, the scope of such patent application is described as "one," or "a", an element or equivalent thereof, and the scope of the patent includes - or more of such elements, neither required nor included Two or more of these forests. Further, for the identification of the components, the sequential indicators, such as the first, second or third, are not to be distinguished unless they are specifically mentioned, rather than distinguishing the components rather than the number of components or the number of restrictions. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a cross section of a rotating assembly including a casing, a shaft and a Γ bearing, wherein the inner bearing rings of the bearings are fitted to the shaft and δ hai, etc. An outer bearing ring is fitted in the outer casing. Figure 2 is a cross-section of the bearing, showing that the inner bearing ring, an outer bearing ring and the - ball are fixed between the bearing rings, wherein the contact on the bearing ring is the same. (4) A _ 29 201122449 角 0 Figure 3 is a perspective view of a test system, including a load system having a sample base, a load component, a converter, a shaft drive, and a computer including a processor and Memory. Figure 4 is a force-displacement diagram showing bearing displacement and component displacement providing rotational assembly displacement. Figure 5 shows the displacement of the mandrel with a zero preload and a zero-axis end-gap - force-displacement diagram showing the displacement caused by the forward or thrust applied load and the negative or pull applied load. Figure 6 is a graph showing the force-displacement curve for a set of bearings. Fig. 7 is a diagram showing the change in the stiffness ratio with a small change in the contact angle of the bearing. Figure 8 is a force-displacement diagram with a master curve and a test curve illustrating a method for determining the preload in a rotating assembly. Figure 9 is a detail of the figure of Figure 8, illustrating a method for determining the preload size using a modified master curve. The first diagram is a force-displacement diagram comprising a master curve, a segmented master curve, and a modified master curve, illustrating a method of using a modified velocide. Figure 11 is a force-displacement diagram including a main curve, a modified main curve for a - point on the main curve, and a tangent to the point on the modified main curve, illustrating a differential learning method . Figure 12 is a cross-section of the bearing for the linear translation assembly. Figure 13 is a flow chart showing a 30 201122449 method for determining bearing preload. Figure 14 is a flow chart showing a method for determining the bearing preload. [Main component symbol description]
Ap···數據點 IP2...第二反曲點 BD...軸承位移曲線 IP(corr)...修正反曲點 CD...組件位移曲線 IP(mc)···反曲點 CF...修正係數 IP(seg).··反曲點 C...虛線框 K(tc)...測試曲線斜率 D(corr). ·.修正距離 K(mc) ··•主曲線斜率 Ds·.·心軸位移 L1，L2_"垂直線 Dc...組件位移 m，m(corr)…斜率 Db...轴承位移 MC...主曲線 D(cf)·..差異 MC(corr)...修正主曲線 D(p)...尺寸預負載 MC(ptl)...主要值 D(pl)...尺寸預負載 MC(pt2)...修正主曲線點 D(p+)...正部分/未修正距離 MC(seg).··分段主曲線 D(p-)...負部分 MC+,MC-...位移主曲線 F...外加負載 P1 (corr)，P2(corr)…數值 F(corr)…修正預負載力 P1 (seg),P2(seg) ·..反曲點 F(p+)...正預負載 P+...正部分或是推側 F(p-)...負預負載 P-...負部分或是拉側 F(pl).·.預負載力 SD...心軸位移曲線 IP1···第一反曲點 T1,T2...切線 31 201122449Ap···Data point IP2...Second inflection point BD...Bearing displacement curve IP(corr)...Correct inflection point CD...Component displacement curve IP(mc)···Recurve point CF...correction factor IP(seg).··recursion point C...dashed box K(tc)...test curve slope D(corr). ·correction distance K(mc) ··•master curve Slope Ds··· mandrel displacement L1, L2_" vertical line Dc... component displacement m, m(corr)...slope Db...bearing displacement MC...main curve D(cf)·..differential MC( Corr)...corrected main curve D(p)...size preload MC(ptl)...main value D(pl)...size preload MC(pt2)...correct main curve point D ( p+)...positive part/uncorrected distance MC(seg).·Segment main curve D(p-)...negative part MC+,MC-...displacement main curve F...added load P1 ( Corr), P2(corr)...value F(corr)...correct preload force P1 (seg), P2(seg) ·..recurve point F(p+)...positive preload P+...positive part or Is the push side F (p-)... negative preload P-... negative part or pull side F (pl). Preload force SD... mandrel displacement curve IP1··· first anti Curve point T1, T2... tangent 31 201122449
Tang(x! ,y i) ·..切線或斜率 Tang(x2,y2)...切線或斜率 TC...測試曲線 TC(pt)...測試值 TN...正切法向線 2.. .心轴或是轉動總成 4.. .外殼或結構 6.. .第一軸承 8.. .滚動元件或滚珠 IOA. ..外軸承環 IOB. ..内軸承環 12.. .第二軸承 14.. .滚珠 16A...外轴承環 16B...内轴承環 18.. .扣環 20.. .具螺紋軸環 22.. .軸環 24··.軸 24’...虛線軸 30A,30B...相對點 32.. .接觸線 34.. .接觸角 40.. .測試系統 41.. .轉動總成或是測試試樣 42.. .負載系統 44.. .負載系統外殼 46.. .試樣底座 46A,46B...試樣底座支撐件 48.. .試樣連接軸環 50.. .負荷元件 52.. .轉換器系統 52A...轉換器 52B...目標盤 54.. .負載設定構件 54A...負載設定軸 54B...負載設定把手 56.. .軸驅動器 56A··.馬達 56B...驅動系統 56C...驅動軸 56D...軸驅動器外殼 56E...軟質底座 58.. .電子元件 58A.··處理器 58B...記憶體或記憶體儲存系統 58C...負載電子元件 60.. .數據收集系統 32 201122449 61...電腦 200...方法 62...處理器 202...步驟 64…記憶體或記憶體儲存系統 204··.步驟 66...數據擷取卡 206...步驟 100...平移軸承 208...步驟 102…第一軸承 210...步驟 104...第二軸承 300...方法 106...頂部外殼 302...步驟 108...底部外殼 304··.步驟 110,110’...軸或橫樑 306...步驟 33Tang(x!, yi) ·.. tangent or slope Tang(x2, y2)...tangent or slope TC...test curve TC(pt)...test value TN...tangential normal line 2. .. Mandrel or Rotating Assembly 4... Shell or Structure 6.. First Bearing 8. Rolling Element or Ball IOA.. Outer Bearing Ring IOB..... Inner Bearing Ring 12.. The second bearing 14: ball 16A... outer bearing ring 16B... inner bearing ring 18.. buckle 20.. with threaded collar 22.. collar 24 · · shaft 24'. .. dotted axis 30A, 30B... relative point 32.. contact line 34.. contact angle 40.. test system 41.. rotation assembly or test sample 42.. load system 44. . Load system housing 46.. Sample base 46A, 46B... Sample base support 48.. Sample connection collar 50.. Load element 52.. Converter system 52A...Conversion 52B...target disk 54.. load setting member 54A...load setting axis 54B...load setting handle 56.. shaft drive 56A··.motor 56B...drive system 56C...driver Shaft 56D... Shaft Driver Housing 56E... Soft Base 58.. Electronic Component 58A.. Processor 58B... Memory or Memory Storage System 58C... Loaded Electronic Component 60.. According to the collection system 32 201122449 61...computer 200...method 62...processor 202...step 64...memory or memory storage system 204··.step 66...data capture card 206. Step 100... translation bearing 208... step 102... first bearing 210... step 104... second bearing 300... method 106... top housing 302... step 108.. .Bottom casing 304··. Step 110, 110'...shaft or beam 306...Step 33