February 2010 Archives

Major contributing factors for selecting ballscrews are:

	1.	Mass of the work and the table (m) (moving objects)
	2.	Feed speed
	3.	Time constant

The 2. and 3. above determine the acceleration (α). Therefore, it can be understood that the moving mass (m) and acceleration (α) are related to selecting ballscrews. This means that it is important to select proper ballscrews in relation to the linear force (F) generated according to Newton's Second Law: F=mα Furthermore, inertial moments (equivalent to mass (m) of rotary motion, see tutorial #111) will affect the driven object during an interval of staring and stopping motions.

Maximum reduction of driven mass (m) and acceleration (α), which will give the most flexibility in ballscrew selection, is where the LCA designer's abilities are measured.

Explanation on technical terms for ballscrew selection

Explanation on technical terms for ballscrew selection

Allowable rotational speed: DN Value

Determined by a product of multiplying ball diameter D (mm) and shaft rotational speed N (rpm). Typical DN value ≦50000〜70000.

Critical speed

When the shaft's angular velocity corresponds with its resonant frequency, an oscillation begins and the shaft will rotate with increased wobble. This causes the shaft to distort. The speed which this occurs is called the Critical Speed.

(Feed screw's) Rigidity

The rigidity can be expressed and understood as same as spring constant. When the whole mechanism is considered as a spring system, the load (P) and the deformation (Λ) are in a proportional relationship, and the inverse of this proportional constant is called the Rigidity. When the mechanism is defined as a spring, this is called Hook's Law and its proportional constant is an elastic coefficient.

Time constant

This is a value indicating the time it takes for the system to reach a targeted control condition (defined as the motor's slew speed in MISUMI catalog), in other words the Rise Time. Small time constant will mean a control that can reach the targeted speed in a short time, which in the control terms requires a higher acceleration.

In motion mechanism designs, moment of inertia, angular acceleration, and friction torque may need to be evaluated in order to select actuator's outputs and sizes. Here, we shall get acquainted with some terms that appear in technical discussions of rotating machine elements such as ballscrews and cams.

(1) Moment of inertia

It can be understood that Moment of Inertia (I) is an equivalent of the mass in linear motion.
This can be interpreted as a physical quantity of how difficult it would be to rotate an object or stop a rotating object. An object with large moment of inertia will require a motor with large stating torque as well as large rated torque in order to rotate.

(2) Another way to express the moment of inertia

The moment of inertia (I) is sometimes expressed in mass units（GD²）. In this case the moment of inertia (I) and GD² can be expressed in a formula as below.

Three fundamental elements of LCA, the Mechanism, the Actuator, and the Controller are explained in this section. Firstly, definitions of the three elements are discussed.

Definitions of the fundamental LCA elements

Mechanism

Construction elements that generate added value such as process/assemble by taking inputs from actuator and controller/sensor.

Actuator

Construction elements that extract mechanical energy as outputs from non-mechanical energy inputs.

Controller

Construction elements that generate non-mechanical energy as outputs from input signals.

Sensor

Construction elements that generate signal outputs from physical phenomena inputs.

Regarding LCA construction elements

Environmental changes such as shorter product life cycles and globalization in the manufacturing sector have forced the manufacturing styles to change for smaller lot size production in order to avoid risks of dead-stock conditions. As the result, product change-over occurs more frequently, and the associated indirect costs such as parts sourcing, work operation management, and production line equipment, etc. have increased noticeably.
With this background, large scale production facility investments have been suppressed for more efficient investment turnover, and cellular manufacturing concept that enables "small lot / wide variety" is vigorously being considered.

Typical examples of the cellular manufacturing scheme are "U-shaped production line" (see [Fig.1]) and "One-person production" method. These can be characterized by the nature where the operators' capabilities and the hardware capabilities are effectively combined to provide more flexible manufacturing. In order to realize this concept, abilities to quickly self-devise highly efficient production tools (LCA, etc.) to increase the production line efficiency based on the actual field expertise.

Furthermore, IT based improvement (KAIZEN) efforts are quickly circulated via the internet. This can connect everyone involved anytime and anywhere, even if the work floors are far distance apart.
The hardware needs for such cellular manufacturing schemes are shown below.

Additionally, part-time work force is utilized more and more to effectively adjust and reduce labor cost wastes associated with varying production lot sizes. With the "One-person production" method, a part time worker reports to work at a time convenient for an individual and works, and is paid for the amount of the production result. These production schemes match the life styles of this country, and is with a merit of clarifying the individual's responsibility for the production quality and efficiency.

For the previous three sessions, we've discussed the flow of LCA along with the changes in the manufacturing environment. All of the LCA discussed are composed of the fundamental elements shown in the [Fig.2] below.

LCA = Mechanism (mechanical elements) + Actuator (drive element) + Controller (control element)