壓縮與碰撞之修正理論應用於蔬果堅實度之量測

Modifications of Compression and Impact Theories on Firmness Measurement of Vegetables and Fruits

程安邦(An-Pan Cherng) ； 吳柏青(Po-Ching Wu) ； 林連雄(Lian-Hsiung Lin)

《農業機械學刊》 9卷1期 (2000/03) Pp. 19-32

https://doi.org/10.30062/JAM.200003.0002

摘要

本文針對傳統壓縮與碰撞理論及其應用在蔬果堅實度的量測進行系統化之分析。傳統上以Hertz接觸理論為主體的方法中，壓縮力與壓縮量之關係為非線性之3/2階多項式，而在蔬果碰撞實驗中，又多參考該模式而以最大碰撞力除以碰撞時間或其平方為堅實度指標。然而本研究對數種常見之水果進行壓縮試驗後發現該階數介於0.9至1.4之間，視水果種類而定，因此相關的壓縮與碰撞理論司加以修正。這樣的結果說明影響材料壓縮變形特性的參數除了彈性係數以外，尚有該多項式階數，因此如果引用這兩個參數對蔬果堅實度進行量化，或可提昇堅實度指標之準確性與一致性。本文除推導以多項式階數為可變參數之一的表示式，並提出階數、初速、邊界條件等對堅實度預測之影響，以期能提供實驗設計之基礎。

關鍵字

堅實度 ； 非破壞性檢測 ； 碰撞

並列摘要

This article presents a systematic analysis on the measurement of firmness for vegetables and fruits. The conventional Hertz's contact theory states that the relation between compression force and deformation is a polynomial of order 3/2. Based on this theory, the firmness index for agricultural products has been proposed in the literature as the ratio of maximum compression force to the duration of contact or its square. However, after some preliminary tests on several fruits in this study, it was found that the order of the polynomial was between 0.9 and 1.4, depending on fruit cultivars. It is therefore believed that the popular compression theory may need some modifications. The above experimental results also demonstrate that the parameters dominating the deformation of fruit under compression should include not only coefficient of elasticity but also the order of the polynomial. As a result, the estimation of firmness could be improved both in accuracy and in consistency, if the two parameters were involved in the analysis. To this end, a series of detailed derivations regarding fruit responses to compression and impact forces are provided. The influences of polynomial order, initial velocity, and boundary conditions, etc., on the estimation of firmness are also addressed, associated with some numerical examples.

並列關鍵字

Firmness ； Non-Destructive Tests ； Impact