在一般運動元件接觸界面間，磨屑的產生是不可避免的情況，在如此三體接觸之情況下，外力是由兩個運動表面粗度波峰接觸處，及表面與顆粒接觸處共同承擔，因此摩擦與磨損亦在這些分離的接觸點上發生，而過去許多研究只探討表面波峰對表面波峰(surface-to-surface)接觸之特性，較少將磨屑考慮其中，且許多分析研究常常將摩擦係數設為一個固定值，這對摩擦特性分析會造成很大的誤差。這些存在兩表面之間的顆粒會影響其真實接觸面積、摩擦與接觸溫度，本論文將根據三體微接觸理論與接觸摩擦理論，建構出摩擦係數隨著操作參數而改變之三體微接觸溫度模式。
研究結果顯示，在界面存在有磨屑或外來顆粒的接觸情況下，隨著負荷增加，界面負載先由顆粒完全承擔的二體接觸顆粒對表面(particle-to-surface)的接觸特徵，直到負荷上升至特定臨界負荷(critical load)後，才進入真正三體接觸情況，此臨界負荷隨著xa / σ的增加而增加。在一般工程表面粗糙度下(σ = 50 nm ~ 400 nm)，三體接觸之總摩擦係數在任一負荷與表面粗糙度下，xa / σ愈大其摩擦係數愈小，顯示表面對表面接觸之摩擦係數大於有圓形磨屑顆粒的摩擦係數值。在相同表面粗糙度與xa / σ下，負荷增加，摩擦係數增加或減少並不一定，而是由xa / σ決定之，此臨界xa / σ在表面粗糙度愈小時，其值愈大。在混合摩擦的接觸條件下，顆粒溫升參數值隨著xa/σ的增加幾乎成線性增加，而表面溫升參數值在xa/σ小於1.0時幾乎保持不變，當xa/σ大於1.0後，表面溫升參數值隨著xa/σ的增加而減少。由於較高的接觸點溫升參數值對於材料疲勞、磨損與失效機制伴演著重要的角色。故在三體接觸時，所產生熱量平衡分配給顆粒與表面是理想運轉條件，因為當顆粒較小時，表面接觸溫度過高，而顆粒較大時，顆粒接觸溫度過高，因此，若能夠有效的過濾在運轉過程中所產生的磨屑顆粒大小在特定範圍內，是避免接觸溫度過高造成表面損傷(wear, scuffing)的重要對策。例如，在滾珠軸承或滾珠螺桿的接觸面間，當表面粗糙度400 nm時，將顆粒密度控制在1011 /m2與顆粒大小300 ~ 400 nm以下，其接觸點溫度可控制在理想的範圍。本文創新的分析方法與結果有助於更深入了解運動元件之接觸性質與避免元件發生損傷，更可作為元件設計與製作的重要參考。

The wear debris generation is unavoidable between the contact interfaces of moving components. In three-body contact instances, the external load are borne by contact point of two surface roughness, and contact point of the particles and surface, and friction and wear therefore occur at these separate contact points. Many studies in the past have less consideration on the contact properties of the third particle between the two surfaces, and many analyses often set the friction coefficient to a constant, which created a large disparity in the analysis of the friction characteristics. These particles affect the real contact area, friction and contact temperature between two rough surfaces. Based on three-body microcontact model and contact friction model, this thesis establishes a new three-body microcontact temperature model in which the friction coefficient changes with the operating parameters.
The results show that for the wear debris or foreign particles present in the interface of contact, as external load initially increases, the external load is fully borne by the contact characteristics of two-body contact particle-to- surface. Until the external load rises to particular critical external load, it enters the real three-body situation, and the critical external load thus increases with an increase in the ratio of particle size-to-surface roughness. In the range of engineering surface roughness (σ =50 nm ~ 400 nm), at each external load and surface roughness, the total friction coefficient decreases with increasing the ratio of particle size-to-surface roughness under three-body contact, and this indicates the friction coefficient of surface-to-surface contact larger than that of sphere wear debris between contact interface. At the same surface roughness, as the external load increases, the friction coefficient is up or down not necessarily. For the fixed ratio of particle size-to-surface roughness and external load, the friction coefficient increases with decreasing surface roughness. Under hybrid friction contact conditions, the temperature rise of particle increases almost linearly with increasing the ratio of particle size-to-roughness. The temperature rise of surface remains almost unchanged for particle size-to-roughness ratios smaller than 1.0 and decreases with increasing particle size-to-roughness ratios greater than 1.0. The high contact point temperatures are believed to play an important role in fatigue, wear, and failure mechanisms. The resulting heat balance is assigned to the particles and the surface in the three-body contact situation, which is the ideal operating condition; this is because the surface contact temperature is too high at the smaller particles, and the particle contact temperature is too high at the larger particles. If the wear debris size can be effectively filtered within a specific range in the course of operation, it will be the important countermeasures of avoiding the contact temperature so high as to cause the surface damage. For example, between the contact surfaces of the ball bearing or the ball screw when the surface roughness σ = 400 nm, the area density of particle is controlled about below 1011 / m2 and the particle size below 300 ~ 400 nm, and then the contact point temperature rise can be controlled in the ideal range. The innovative methods and results of this study not only can provide deeper understand the contact properties of the moving components and avoid the damage of the components, but also can be used as an important reference for the design and production of components.

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