Integrally Formed Designs for the Rotational Balancing of Disk Cams and Their Optimization and Experimental Verification

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Project title

Code/計畫編號

MOST107-2221-E019-031

Translated Name/計畫中文名

盤形凸輪之一體成型式轉動平衡設計及其最佳化與實驗驗證

Project Coordinator/計畫主持人

Wen-Tung Chang

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Mechanical and Mechatronic Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=12676707

Year

2018

Start date/計畫起

01-08-2018

Expected Completion/計畫迄

01-07-2019

Bugetid/研究經費

587千元

ResearchField/研究領域

機械工程

凸輪為各種機器裝置與自動化設備中常用的機械傳動元件，其透過直接接觸使從動件產生預定的不規則拘束運動，藉以達成所需的運動控制。若需在機器中進行高速且單調的往復式運動控制時，凸輪機構仍是極具可靠度的選擇。凸輪在做為機器中的局部運動控制單元時，有時必須以較高的轉速進行旋轉運動，以達到預設的功能需求。由於盤形凸輪本身具有非圓形且不規則的幾何特徵，在其未具有轉動平衡之設計且進行高速旋轉的情況下，勢必會形成機器中主要的振動來源之一。當旋轉的物體無法達到轉動平衡時，該旋轉物體的重力、慣性力與離心力之變化會對其機架造成一定程度的搖撼力與搖撼力矩，在此週期性的力與力矩之作用下並經長時間的累積之後，便有可能造成機件材料的過度磨損甚至疲勞破壞。為避免此情況，通常必須對旋轉物體施加配重，以使配重後的旋轉物體在理論上同時達到靜平衡與動平衡的完全轉動平衡狀態。若能使盤形凸輪本身達到完全轉動平衡，再另行設法降低從動件本身所造成的搖撼力與搖撼力矩，則對於高速凸輪機構的性能與附加價值之提升而言應具有相當大的助益。至今為止，盤形凸輪的轉動平衡設計問題較少被探討，但其在學術研究上與實務應用上均仍具有值得鑽研之處。　　本計畫的目的在於提出創新且具通用性的配重設計以應用於各種盤形凸輪在高轉速下的完全轉動平衡。針對此目的，本計畫預定以一年的時間完成研究工作。首先，會基於盤形凸輪輪廓的向量參數方程式以進行凸輪輪廓相關之幾何性質的推導工作。然後，會針對單片式凸輪與共軛式凸輪分別提出創新的一體成型式轉動平衡設計概念與對應的理論計算方法，並建立其最佳化數學模型，再透過設計實例的演示以驗證所提出之轉動平衡設計方法的正確性與最佳化數學模型的合理性。接著，會針對轉動平衡設計參數進行其公差敏感度分析，以評估製造誤差對於轉動平衡的影響性。最後，會針對單片式凸輪與共軛式凸輪分別設計與製作兩組驗證用機構的實體模型，以藉由實際的實驗驗證本計畫所提出之一體成型式轉動平衡設計的性能與功效。希望藉由本計畫的執行，能協助國內凸輪專業製造廠提升其對盤形凸輪產品的進階設計能力，並能協助國內機器裝置與自動化設備製造廠提升其裝置設備產品中之盤形凸輪機構的運轉性能與附加價值。 Cams are mechanical transmission components frequently used in various machine devices and automation equipment, which make their followers to produce prescribed constraint motions through direct contact in order to achieve motion control. When high speed and monotonous reciprocating motion control is required in machinery, cam mechanisms are still quite reliable choice. As a partial motion control unit in machinery, cams must sometimes rotate at a higher speed to achieve prescribe functions and requirements. Because disk cams are with non-circular and irregular geometries, when they rotate at a higher speed without possessing a rotational balancing design, vibrations will be produced in machinery. As a rotating object cannot achieve rotational balancing, variations of gravity, inertia force and centrifugal force of the rotating object will cause considerable shaking force and shaking moment applied to the frame; when undergoing such periodical force and moment for a long duration, excessive wear and even fatigue fracture of the material of mechanical components may occur. In order to avoid such a situation, counterweights must be added to the rotating object in order to theoretically achieve static balancing and dynamic balancing at the same time as a full rotational balancing state. If the disk cam can achieve a full rotational balancing, and the shaking force and shaking moment cause by the follower can be reduced by other ways, then the performance and additional value of high speed cam mechanisms should be considerably improved. Until now, the rotational balancing design of disk cams is less discussed, but it is still worth to be studied for both academic research and practical application aspects. The purpose of this project is to propose innovative and universal designs of counterweights that can be applied to the full rotational balancing of disk cams rotating at high speed. The term of the project is one year. First, based on parametric vector equations of disk cam profiles, theoretical derivation of geometric properties related to the cam profile will be carried out. Then, innovative concepts for integrally formed designs for the rotational balancing of single-disk cams and of conjugate-disk cams will be proposed and their corresponding theoretical calculation methods and optimization models will be established, and design case studies will be demonstrated to verify the correctness of the proposed design methods and the reasonability of the proposed optimization models. Further, tolerance sensitivity analysis for the design parameters of the counterweights will be performed to evaluate the influence of manufacturing errors on the rotational balancing. Finally, two sets of practical hardware models for the single-disk and conjugate-disk cam mechanisms will be designed and constructed to perform experiments for verifying the performance and effectiveness of the proposed integrally formed rotational balancing designs of disk cams. The execution of this project will help domestic manufacturers of cams in upgrading their advanced design abilities, and will also help domestic manufacturers of machine devices and automation equipment in upgrading the operating performance and additional values of cam mechanisms in their machinery products.

Keyword(s)

盤形凸輪
共軛凸輪
轉動平衡
一體成型式配重
最佳化
實驗驗證
Disk cams
Conjugate cams
Rotational balancing
Integrally formed counterweights
Optimization
Experimental verification

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Integrally Formed Designs for the Rotational Balancing of Disk Cams and Their Optimization and Experimental Verification

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