ASSIGNMENT 2 SEM327- T2 2019

Note: Please answer the following questions with both filling the tables and demonstrating all the details and calculations, in a report not more than 10 pages. Each question is worth 7.5 marks. The answers file should be individual and includes the students’ ID and name, and be uploaded on the assignment folders by the deadline. The report should not be necessarily all typed though preferred, but there is some marks for well-written and structured answers which are concise and easy to understand with appropriate flow used and shown in derivations and calculations.

1- A compound epicyclic gear train (including three arms ????, ????, and ????) is shown in the figure where power enters from input shaft and transmits to the output shaft on the right. The arms ???? and ???? are fixed on output shafts while the arm ???? is rotating on the input shaft. Gears ???? and ???? are also fixed to the input shaft. The Gears ???? and ???? are planetary, carried by arms ???? and ????. Also, gear ???? rotates gear ???? which is fixed. Knowing the input shaft is rotating at ???????????? ???????????? at ???? ???????? anticlockwise and the number of teeth on the gears are as follows:

???? = ????, ???? = ????????, ???? = ????????, ???? = ????????, ???? = ???????????? and ???? = ????????.

Determine:

(a) Speed and direction of rotation of the gear ???? (????????)

(b) Speed and direction of rotation of the output shaft ????????????????????????????.

(c) Transmission torques of the input and output shafts if the efficiency of the train is ????????%

(???????????? and ????????????????).

Note: n is an individual value for each student that should be found from two right digits of student’s ID (e.g. Student ID: 215189534????? = ???????? . There might be one exception for a student ID which ends to 00? ???? = ????????????).

???????? (????????????) ???????????????????????????? (????????????) ????????????(????????) ???????????????? (????????)

Four masses ???? = ???? (????????), ???? = ???????????? (????????), ???? = ???????????? (????????), and ???? = ???????????? (????????) are revolving on a shaft. The radii and longitudinal distances of masses are shown in the figure and followings as:

???????? = ???????? (????????), ???????? = ???????? (????????), ???????? = ???????? (????????), ???????? = ???????? (????????)

The angles between the masses are measured counterclockwise ???????? = ????????°, ???????? = ????????°, ???????? = ????????????°. Design two masses with radii of ???????????? (????????) in planes ???? and ???? to balance the system both statically and dynamically. Determine magnitudes (???????? and ????????) and angular positions (???????? and ????????) of two balancing masses from horizontal line as shown in the figure.

Note: n is an individual value for each student that should be found from two right digits of student’s ID (e.g. Student ID: 215189534????? = ???????? (????????). There might be one exception for a student ID which ends to 00? ???? = ???????????? (????????)).

???????? (????????) ???????? (????????) ???????? (????????????) ???????? (????????????)

A mass of ???? (????????) is hung from a spring of stiffness ???? = ????. ???? × ???????????? (????) and

???? damper ???? = ???????????? ????. ????/????, which is attached to two aluminum beams with ???? = ???????? × ????????????(????????), moment of inertia ???? = ????. ???? × ????????-???? (????????), and length of ???????????? (????????). The beam is supported at its free end. Determine:

(a) Equivalent stiffness and equation of motion of the system.

(b) Damped natural frequency of the system (????????) in (????????).

(c) Free vibration response of the system in time domain, ????(????), when ????(????) = ???? and ?????(????) = ????.

(d) Simulation and plot of the response of system in MatLab/Simulink.

Note: n is an individual value for each student that should be found from two right digits of student’s ID (e.g. Student ID: 215189534????? = ???????? (????????). There might be one exception for a student ID which ends to 00? ???? = ???????????? (????????)).

???????????? (????/????) Equation of motion ???????? (????????) ????(????)

A uniform cylinder with mass, ????, and radius, ????, is attached to a spring and can oscillate without slip from point ????, the valley of the curvature with radius of ????, to ????. Knowing the following parameters as:

????

???? = ???? (????????), ???? = ???????? (????????), ???? = ???????????? (????????) ???? = ????????

????

Determine:

(a) Equivalent stiffness and equation of motion of the cylinder (Assuming that the force of spring is related to displacement of center of cylinder approximately as

????? (????-????)????.

(b) Natural frequency of system (????????) in (????????).

(c) Free vibration response of the system in time domain when ????(????) = ???? and

?????(????) = ????.

(d) Simulation and plot of the response of system in MatLab/Simulink.

Note: n is an individual value for each student that should be found from two right digits of student’s ID (e.g. Student ID: 215189534????? = ???????? (????????). There might be one exception for a student ID which ends to 00? ???? = ???????????? (????????)).

???????????? (????/????) Equation of motion ???????? (????????) ????(????)

Note: Please answer the following questions with both filling the tables and demonstrating all the details and calculations, in a report not more than 10 pages. Each question is worth 7.5 marks. The answers file should be individual and includes the students’ ID and name, and be uploaded on the assignment folders by the deadline. The report should not be necessarily all typed though preferred, but there is some marks for well-written and structured answers which are concise and easy to understand with appropriate flow used and shown in derivations and calculations.

1- A compound epicyclic gear train (including three arms ????, ????, and ????) is shown in the figure where power enters from input shaft and transmits to the output shaft on the right. The arms ???? and ???? are fixed on output shafts while the arm ???? is rotating on the input shaft. Gears ???? and ???? are also fixed to the input shaft. The Gears ???? and ???? are planetary, carried by arms ???? and ????. Also, gear ???? rotates gear ???? which is fixed. Knowing the input shaft is rotating at ???????????? ???????????? at ???? ???????? anticlockwise and the number of teeth on the gears are as follows:

???? = ????, ???? = ????????, ???? = ????????, ???? = ????????, ???? = ???????????? and ???? = ????????.

Determine:

(a) Speed and direction of rotation of the gear ???? (????????)

(b) Speed and direction of rotation of the output shaft ????????????????????????????.

(c) Transmission torques of the input and output shafts if the efficiency of the train is ????????%

(???????????? and ????????????????).

Note: n is an individual value for each student that should be found from two right digits of student’s ID (e.g. Student ID: 215189534????? = ???????? . There might be one exception for a student ID which ends to 00? ???? = ????????????).

???????? (????????????) ???????????????????????????? (????????????) ????????????(????????) ???????????????? (????????)

Four masses ???? = ???? (????????), ???? = ???????????? (????????), ???? = ???????????? (????????), and ???? = ???????????? (????????) are revolving on a shaft. The radii and longitudinal distances of masses are shown in the figure and followings as:

???????? = ???????? (????????), ???????? = ???????? (????????), ???????? = ???????? (????????), ???????? = ???????? (????????)

The angles between the masses are measured counterclockwise ???????? = ????????°, ???????? = ????????°, ???????? = ????????????°. Design two masses with radii of ???????????? (????????) in planes ???? and ???? to balance the system both statically and dynamically. Determine magnitudes (???????? and ????????) and angular positions (???????? and ????????) of two balancing masses from horizontal line as shown in the figure.

Note: n is an individual value for each student that should be found from two right digits of student’s ID (e.g. Student ID: 215189534????? = ???????? (????????). There might be one exception for a student ID which ends to 00? ???? = ???????????? (????????)).

???????? (????????) ???????? (????????) ???????? (????????????) ???????? (????????????)

A mass of ???? (????????) is hung from a spring of stiffness ???? = ????. ???? × ???????????? (????) and

???? damper ???? = ???????????? ????. ????/????, which is attached to two aluminum beams with ???? = ???????? × ????????????(????????), moment of inertia ???? = ????. ???? × ????????-???? (????????), and length of ???????????? (????????). The beam is supported at its free end. Determine:

(a) Equivalent stiffness and equation of motion of the system.

(b) Damped natural frequency of the system (????????) in (????????).

(c) Free vibration response of the system in time domain, ????(????), when ????(????) = ???? and ?????(????) = ????.

(d) Simulation and plot of the response of system in MatLab/Simulink.

Note: n is an individual value for each student that should be found from two right digits of student’s ID (e.g. Student ID: 215189534????? = ???????? (????????). There might be one exception for a student ID which ends to 00? ???? = ???????????? (????????)).

???????????? (????/????) Equation of motion ???????? (????????) ????(????)

A uniform cylinder with mass, ????, and radius, ????, is attached to a spring and can oscillate without slip from point ????, the valley of the curvature with radius of ????, to ????. Knowing the following parameters as:

????

???? = ???? (????????), ???? = ???????? (????????), ???? = ???????????? (????????) ???? = ????????

????

Determine:

(a) Equivalent stiffness and equation of motion of the cylinder (Assuming that the force of spring is related to displacement of center of cylinder approximately as

????? (????-????)????.

(b) Natural frequency of system (????????) in (????????).

(c) Free vibration response of the system in time domain when ????(????) = ???? and

?????(????) = ????.

(d) Simulation and plot of the response of system in MatLab/Simulink.

Note: n is an individual value for each student that should be found from two right digits of student’s ID (e.g. Student ID: 215189534????? = ???????? (????????). There might be one exception for a student ID which ends to 00? ???? = ???????????? (????????)).

???????????? (????/????) Equation of motion ???????? (????????) ????(????)

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