%%%%%% Q Brand - Engine Isolation Calculation % % Estimate if adding Engine Isolators will help reduce the vibration % inside of the airplane. % % In this example I calculate the ASP s52a with Jett exhaust on small % rubber engine mounts. % % In principle the eigenfrequencies calculated should be lower than the % engine's first engine order at Idle. For a 1 cyl. 2-stroke in % this example: 2000rpm/60 = 33Hz % %%%%%% %%%% Engine properties EngMass = 0.65; % [kg] Ixx = 2/5*0.8*(0.0772)^2; % Rough estimate with massive sphere with 2x radius. r = (2*) (0.65/(2700*4/3*pi))^(1/3) Iyy = Ixx*2; % Some more compared to the x-axis Izz = Ixx*2; %%%% Engine Mount properties % % - Distance from Engine's COG to center of Engine mount center plane % - Assume 4 equal rubber bushings. Distances from Engine Mount to bushings % - Bushing properties from internet % - Timoshenko coefficient 0.8291 for circular bushing cross section % - See https://en.wikipedia.org/wiki/Timoshenko_beam_theory % %%%% EngCOG2MountX = 0.04; % [m] EngCOG2MountY = 0.012; % [m] EngCOG2MountZ = 0.019; % [m] DistY = 0.02; % [m] DistZ = 0.02; % [m] Erubber = 3e6 ; % 2.5 tot 4 MPa according to paper Poisson = 0.5 ; % [-] Grubber = Erubber*Poisson; BushingDia = 0.006 ; % Diameter of Bushing [m] BushingHeight = 0.0065 ; % Bushing Height [m] %% Rubber Stiffness Elements KbushingAxial = Erubber * (pi/4 * BushingDia^2) / BushingHeight ; KbushingTangent = 3 * Erubber * (pi * (BushingDia/2)^4/4) / BushingHeight^3 + ... 0.8291*pi/4*BushingDia^2*Grubber/BushingHeight ; %% Displacement of Moment of Inertia from Engine COG to Bulkhead Ixx = Ixx + EngMass * (sqrt(EngCOG2MountY^2 + EngCOG2MountZ^2))^2 ; Iyy = Iyy + EngMass * (sqrt(EngCOG2MountX^2 + EngCOG2MountZ^2))^2 ; Izz = Izz + EngMass * (sqrt(EngCOG2MountX^2 + EngCOG2MountY^2))^2 ; %% Mass and Stiffness Matrix M = blkdiag(EngMass, EngMass, EngMass, Ixx, Iyy, Izz); K = blkdiag(4*KbushingAxial, 4*KbushingTangent, 4*KbushingTangent, ... 4*KbushingTangent*sqrt(DistY^2+DistZ^2), ... 4*KbushingAxial*DistZ, ... 4*KbushingAxial*DistY); %% EigenFrequencies [V,D] = eig(K,M); Freqs = diag(sqrt(D)/2/pi) V %%%%%%%%%%%%%%%%%% RESULTS %%%%%%%%% % % - Frequencies ranging from about 30Hz too 100Hz -> Isolation starts after % 6000rpm. % - Order of modes: Y,Z,X, YY, ZZ, XX % -> Will not help reducing the vibrations. %