Cross-spring pivots, formed by crossing two identical flexural beams at their midpoint, have been broadly used in precision engineering and aerospace fields. Many researches have been conducted on modeling and analysi...Cross-spring pivots, formed by crossing two identical flexural beams at their midpoint, have been broadly used in precision engineering and aerospace fields. Many researches have been conducted on modeling and analysis of cross-spring pivots. However the influence of application position and magnitude of the external loads on the load-rotation and parasitic motion characteristics has not yet been discussed. In order to reveal the effect of the external loads, this paper develops the accurate load-rotation and center shift models of cross-spring pivots, with generalized planar loads applied including bending moment, horizontal and vertical forces. Firstly, by using the energy method, the load-displacement models of the pivot are derived with the assumption of small rotational angles. Based on the models, the influence of generalized planar loads on the load-rotation relationship is discussed, which shows that both application position and magnitude of the vertical and horizontal forces influence the load-rotation behaviors. Then the accurate center shift expressions of the pivot with generalized planar loads are developed, which shows that the rotational angle is the dominant term for both components of the center shift while the vertical and horizontal forces are small. Finally, the accuracy of the proposed model is validated by finite element analysis（FEA）. Comparing the model data with the results obtained from FEA, the relative error of the load-rotation is less than 6% even if the rotational angle reaches 20°; the relative errors of the two components of center shift are less than 5% and 10% respectively when the rotational angle reaches 10°. The proposed model and analytical conclusions can be used to analyze and preliminarily design the compliant mechanisms containing cross-spring pivots.展开更多
Agricultural irrigation is a primary user for freshwater withdrawal. Irrigation plays an important role in crop production, as it provides the benefit of reducing the effects of prolonged dryness and erratic precipita...Agricultural irrigation is a primary user for freshwater withdrawal. Irrigation plays an important role in crop production, as it provides the benefit of reducing the effects of prolonged dryness and erratic precipitation. Center pivot irrigation system is the most common irrigation system in agriculture. As the center pivot irrigation system ages, the system could develop a leaking joint, clogged sprinklers, and physical damage. This can cause areas of non-uniformity that can lead to under- or over-irrigated in some areas of the land, resulting in excess energy use and cost, wasting resources, and environmental impacts. Thus, it is important to evaluate the performance of a center pivot irrigation system regularly to maximize return on investments and minimize wasting resources. This study focuses on evaluating the impacts and benefits of improved center pivot irrigation distribution uniformity by performing distribution uniformity evaluations pre- and post-retrofit. This study also focused on demonstrating an unmanned aerial vehicle (UAV) to assess the performance of the center pivot irrigation system in two irrigated farmlands. The Coefficient of Uniformity (CU), Distribution Uniformity (DU), and Scheduling Coefficient (SC) were calculated based on the catch can test data. The values were utilized to evaluate water and energy savings from the improved coefficients. The team has found that replacing sprinkler packages increased the CU from 78 to 89 and the DU from 77 to 82, and reduced the SC from 1.3 to 1.2 in Field A. In Field B, replacing sprinkler packages increased the CU from 73 to 91 and the DU from 62 to 84 and reduced the SC from 1.6 to 1.2. The estimated water savings in Field A due to the reduced scheduling coefficient was approximately 151,000 liters/hectare/year, with consideration of the corn and soybean rotation field in Michigan. The estimated water savings in Field B was 608,000 liters/hectare/year. The data from this demonstration study showed the value of distribution uniformity evaluation and retrofit of irrigation systems. This information will encourage farmers and agricultural industries to consider performing more distribution uniformity evaluations, ultimately improving irrigation water use efficiency and supporting sustainable water management in agriculture.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos. 50975007, 51105014)PhD Programs Foundation of Ministry of Education of China(Grant No. 20091102110023)China Postdoctoral Science Foundation(Grant No. 20100480179)
文摘Cross-spring pivots, formed by crossing two identical flexural beams at their midpoint, have been broadly used in precision engineering and aerospace fields. Many researches have been conducted on modeling and analysis of cross-spring pivots. However the influence of application position and magnitude of the external loads on the load-rotation and parasitic motion characteristics has not yet been discussed. In order to reveal the effect of the external loads, this paper develops the accurate load-rotation and center shift models of cross-spring pivots, with generalized planar loads applied including bending moment, horizontal and vertical forces. Firstly, by using the energy method, the load-displacement models of the pivot are derived with the assumption of small rotational angles. Based on the models, the influence of generalized planar loads on the load-rotation relationship is discussed, which shows that both application position and magnitude of the vertical and horizontal forces influence the load-rotation behaviors. Then the accurate center shift expressions of the pivot with generalized planar loads are developed, which shows that the rotational angle is the dominant term for both components of the center shift while the vertical and horizontal forces are small. Finally, the accuracy of the proposed model is validated by finite element analysis（FEA）. Comparing the model data with the results obtained from FEA, the relative error of the load-rotation is less than 6% even if the rotational angle reaches 20°; the relative errors of the two components of center shift are less than 5% and 10% respectively when the rotational angle reaches 10°. The proposed model and analytical conclusions can be used to analyze and preliminarily design the compliant mechanisms containing cross-spring pivots.
文摘Agricultural irrigation is a primary user for freshwater withdrawal. Irrigation plays an important role in crop production, as it provides the benefit of reducing the effects of prolonged dryness and erratic precipitation. Center pivot irrigation system is the most common irrigation system in agriculture. As the center pivot irrigation system ages, the system could develop a leaking joint, clogged sprinklers, and physical damage. This can cause areas of non-uniformity that can lead to under- or over-irrigated in some areas of the land, resulting in excess energy use and cost, wasting resources, and environmental impacts. Thus, it is important to evaluate the performance of a center pivot irrigation system regularly to maximize return on investments and minimize wasting resources. This study focuses on evaluating the impacts and benefits of improved center pivot irrigation distribution uniformity by performing distribution uniformity evaluations pre- and post-retrofit. This study also focused on demonstrating an unmanned aerial vehicle (UAV) to assess the performance of the center pivot irrigation system in two irrigated farmlands. The Coefficient of Uniformity (CU), Distribution Uniformity (DU), and Scheduling Coefficient (SC) were calculated based on the catch can test data. The values were utilized to evaluate water and energy savings from the improved coefficients. The team has found that replacing sprinkler packages increased the CU from 78 to 89 and the DU from 77 to 82, and reduced the SC from 1.3 to 1.2 in Field A. In Field B, replacing sprinkler packages increased the CU from 73 to 91 and the DU from 62 to 84 and reduced the SC from 1.6 to 1.2. The estimated water savings in Field A due to the reduced scheduling coefficient was approximately 151,000 liters/hectare/year, with consideration of the corn and soybean rotation field in Michigan. The estimated water savings in Field B was 608,000 liters/hectare/year. The data from this demonstration study showed the value of distribution uniformity evaluation and retrofit of irrigation systems. This information will encourage farmers and agricultural industries to consider performing more distribution uniformity evaluations, ultimately improving irrigation water use efficiency and supporting sustainable water management in agriculture.
